675

C      ALGORITHM 675, COLLECTED ALGORITHMS FROM ACM.
C      THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C      VOL. 15, NO. 3, PP. 243-256.
C
C     This is the driver for SUBROUTINE SRCF.
C     The routine is in TOMS.FOR and uses the file SRCF.IN as
C     input file from which N, P, A, B, C, R and Q are read.
C     Output is sent to file SRCF.OUT .
C
      INTEGER I, ISTEP, J, N, M, P, LDS, LDA, LDB, LDQ, LDC, LDR, LDK,
     *        LDW
      DOUBLE PRECISION A(10,10), B(10,5), C(7,10), R(7,7), Q(5,5),
     *                 WRK(22,22), S(10,10), K(10,7),
     *                 SSP(10,10)
      DOUBLE PRECISION DDOT, TOL
      LOGICAL MULTBQ, WITHK
C
      WITHK = .TRUE.
      MULTBQ = .TRUE.
      LDS = 10
      LDA = 10
      LDB = 10
      LDQ = 5
      LDC = 7
      LDR = 7
      LDK = 10
      LDW = 22
      TOL = 1.D-15
C
C     READ N, P, A, B, C, Q and R from the file SRCF.IN
C     The matrices A, B, C, Q and R are to be read columnwise.
C     The input dimension M is specified by the loop index.
C
C
      REWIND 1
      DO 750 M = 2, 3
         READ (1,51) N, P
  51  FORMAT(2I5)
  53  FORMAT(1H ,'*** N =', I3, ' M =', I3,' P = ', I3)
         IF (M .EQ. 2) THEN
            WRITE(2,940)
         ELSE
            WRITE(2,941)
         END IF
         DO 50 J = 1, N
            DO 50 I = 1, N
               READ(1,52) A(I,J)
  50     CONTINUE
  52  FORMAT(D25.15)
         DO 60 J = 1, M
            DO 60 I = 1, N
               READ(1,52) B(I,J)
  60     CONTINUE
         DO 68 J = 1, N
            DO 68 I = 1, P
               READ(1,52) C(I,J)
  68     CONTINUE
         DO 76 J = 1, P
            DO 76 I = 1, P
               READ(1,52) R(I,J)
  76     CONTINUE
         DO 84 J = 1, M
            DO 84 I = 1, M
               READ(1,52) Q(I,J)
  84     CONTINUE
C
C     Initialize the S matrix to be the null matrix.
C
         DO 350 J = 1, N
            DO 350 I = 1, N
               S(I,J) = 0.0D0
  350    CONTINUE
         WRITE(2,950)
         WRITE(2,53) N, M, P
         CALL PRMT(A,LDA,N,N,'A matrix',2,4)
         CALL PRMT(B,LDB,N,M,'B matrix',2,4)
         CALL PRMT(S,LDS,N,N,'S matrix',2,4)
         CALL PRMT(C,LDC,P,N,'C matrix',2,4)
         CALL PRMT(R,LDR,P,P,'R matrix',2,4)
         CALL PRMT(Q,LDQ,M,M,'Q matrix',2,4)
C
C     Now perform three steps of the Kalman filter recursion
C    (in square root covariance form) with MULTBQ = .TRUE.
C
         WRITE(2,951)
         DO 500 ISTEP = 1, 3
            WRITE(2,935)ISTEP
            CALL SRCF(S, LDS, A, LDA, B, LDB, Q, LDQ, C, LDC, R, LDR,
     *                N, M, P, K, LDK, WRK, LDW, MULTBQ, WITHK, TOL)
            CALL PRMT(S,LDS,N,N,'S matrix',2,4)
            CALL PRMT(K,LDK,N,P,'K matrix',2,4)
            DO 450 J = 1, N
               DO 450 I = 1, N
                  SSP(I,J) = DDOT(N, S(I,1), LDS, S(J,1), LDS)
  450       CONTINUE
            CALL PRMT(SSP,LDS,N,N,'SS'' m. ',2,4)
  500    CONTINUE
         WRITE(2,952)
C
C     Initialize the S matrix to be the null matrix.
C
         DO 550 J = 1, N
            DO 550 I = 1, N
               S(I,J) = 0.0D0
  550    CONTINUE
C
C     Now perform three steps of the Kalman filter recursion
C    (in square root covariance form) with MULTBQ = .FALSE.
C
         MULTBQ = .FALSE.
         DO 700 ISTEP = 1, 3
            WRITE(2,935)ISTEP
            CALL SRCF(S, LDS, A, LDA, B, LDB, Q, LDQ, C, LDC, R, LDR,
     *                N, M, P, K, LDK, WRK, LDW, MULTBQ, WITHK, TOL)
            CALL PRMT(S,LDS,N,N,'S matrix',2,4)
            CALL PRMT(K,LDK,N,P,'K matrix',2,4)
            DO 650 J = 1, N
               DO 650 I = 1, N
                  SSP(I,J) = DDOT(N, S(I,1), LDS, S(J,1), LDS)
  650       CONTINUE
            CALL PRMT(SSP,LDS,N,N,'SS'' m. ',2,4)
  700    CONTINUE
         IF (M .EQ. 2) THEN
            WRITE(2,945)
         ELSE
            WRITE(2,946)
         END IF
  750 CONTINUE
  935 FORMAT(' *** ISTEP =', I3)
  940 FORMAT(
     * ' *** First example : Square root covariance filter with dense'/
     * ' *** A, B, C and lower triangular Q, R.')
  941 FORMAT(
     * '1*** Second example : Square root covariance filter with dense'/
     * ' *** A, B, C and lower triangular Q, R.')
  945 FORMAT(
     * '1*** In both these tests we start with S=0 and perform three'/
     * ' *** iterations of the filter.'/
     * ' *** The ranks of S in these three steps must be equal to '/
     * ' *** M(=2), 2M(=4) and 3M(=6).'/
     * ' *** K must be 0 in the first step and nonzero afterwards.'/
     * ' *** The results for MULTBQ = .TRUE. and .FALSE. must be equal'/
     * ' *** since we chose Q=I.'/
     * ' *** The SS'' matrices are meant for comparison with SRCFOB.')
  946 FORMAT(
     * '1*** In both these tests we start with S=0 and perform three'/
     * ' *** iterations of the filter.'/
     * ' *** The ranks of S in these three steps must be equal to '/
     * ' *** M(=3), 2M(=6) and min(N,3M)(=6).'/
     * ' *** K must be 0 in the first step and nonzero afterwards.'/
     * ' *** The results for MULTBQ = .TRUE. and .FALSE. must be equal'/
     * ' *** since we chose Q=I.'/
     * ' *** The SS'' matrices are meant for comparison with SRCFOB.')
  950 FORMAT(// ' *** Input SRCF' //)
  951 FORMAT(// ' *** Output SRCF for MULTBQ=.TRUE.' //)
  952 FORMAT(// ' *** Output SRCF for MULTBQ=.FALSE.' //)
C
C *** Last line of SRCF/MAIN ******************************************
C
      END
C
C     This is the driver for SUBROUTINE SRIF.
C     The routine is in TOMS.FOR and uses the file SRIF.IN as
C     input file from which N, M, Ainv, C, AinvB, Qinv, Rinv, Z, X
C     and Y are read. Output is sent to file SRIF.OUT .
C
      INTEGER I, ISTEP, J, N, M, P, LDS, LDA, LDB, LDQ, LDC, LDR, LDW,
     *        NMP
      DOUBLE PRECISION AINV(10,10), C(5,10), RINV(5,5), QINV(7,7)
      DOUBLE PRECISION WRK(22,22), SINV(10,10), Y(5)
      DOUBLE PRECISION SPS(10,10), Z(7), X(10)
      DOUBLE PRECISION AINVB(10,7), RINVY(5)
      DOUBLE PRECISION DDOT, TOL
      LOGICAL MULTAB, MULTRC, WITHX
C
      WITHX = .TRUE.
      MULTAB = .TRUE.
      MULTRC = .FALSE.
      LDS = 10
      LDA = 10
      LDB = 10
      LDQ = 7
      LDC = 5
      LDR = 5
      LDW = 22
      TOL = 1.D-15
C
C     READ N, M, Ainv, C, AinvB, Qinv, Rinv, Z, X and Y from the file
C     SRIF.IN. The matrices Ainv, C, AinvB, Qinv and Rinv are to be
C     read columnwise.
C     The input dimension P is specified by the loop index.
C
      REWIND 1
      DO 750 P = 2, 3
         READ (1,51) N, M
         NMP = N + M + P
         IF (LDW .LT. NMP) WRITE(6,901)
  51  FORMAT(2I5)
  53  FORMAT(1H ,'*** N =', I3,' M =', I3,' P = ', I3)
         IF (P .EQ. 2) THEN
            WRITE(2,940)
         ELSE
            WRITE(2,941)
         END IF
         DO 50 J = 1, N
            DO 50 I = 1, N
               READ(1,52) AINV(J,I)
  50     CONTINUE
  52  FORMAT(D25.15)
         DO 60 J = 1, P
            DO 60 I = 1, N
               READ(1,52) C(J,I)
  60     CONTINUE
         DO 68 I = 1, M
            DO 68 J = 1, N
               READ(1,52) AINVB(J,I)
  68     CONTINUE
         DO 76 J = 1, M
            DO 76 I = 1, M
               READ(1,52) QINV(J,I)
  76     CONTINUE
         DO 81 J = 1, P
            DO 81 I = 1, P
               READ(1,52) RINV(J,I)
  81     CONTINUE
         DO 86 J = 1, M
            READ(1,52) Z(J)
  86     CONTINUE
         DO 88 J = 1, N
            READ(1,52) X(J)
  88     CONTINUE
         DO 90 J = 1, P
            READ(1,52) Y(J)
  90     CONTINUE
C
C     Initialize the SINV matrix to be the unit matrix.
C
         DO 100 J = 1, N
            DO 100 I = 1, N
               SINV(I,J) = 0.0D0
  100    CONTINUE
         DO 110 I = 1, N
            SINV(I,I) = 1.0D0
  110    CONTINUE
         WRITE(2,950)
         WRITE(2,53) N, M, P
         CALL PRMT(AINV,LDA,N,N,'Ainv    ',2,4)
         CALL PRMT(AINVB,LDA,N,M,'AinvB   ',2,4)
         CALL PRMT(C,LDC,P,N,'C matrix',2,4)
         CALL PRMT(SINV,LDS,N,N,'Sinv    ',2,4)
         CALL PRMT(QINV,LDQ,M,M,'Qinv    ',2,4)
         CALL PRMT(RINV,LDR,P,P,'Rinv    ',2,4)
         CALL PRMT(Z,LDQ,M,1,'Z vector',2,4)
         CALL PRMT(X,LDA,N,1,'X vector',2,4)
         CALL PRMT(Y,LDC,P,1,'Y vector',2,4)
C
C     Calculation of RINV x Y.
C
         DO 260 I = 1, P
            RINVY(I) = DDOT(P, RINV(I,1), LDR, Y, 1)
  260    CONTINUE
C
C     Now perform four steps of the Kalman filter recursion
C     (in square root covariance form).
C
         WRITE(2,951)
         DO 500 ISTEP = 1, 4
            WRITE(2,935)ISTEP
            CALL SRIF(SINV, LDS, AINV, LDA, AINVB, LDB, RINV, LDR, C,
     *                LDC, QINV, LDQ, X, RINVY, Z, N, M, P, WRK, LDW,
     *                MULTAB, MULTRC, WITHX, TOL)
            CALL PRMT(SINV,LDS,N,N,'Sinv    ',2,4)
            CALL PRMT(X,LDA,N,1,'X vector',2,4)
            DO 450 J = 1, N
               DO 450 I = 1, N
                  SPS(I,J) = DDOT(N, SINV(1,I), 1, SINV(1,J), 1)
  450       CONTINUE
            CALL PRMT(SPS,LDS,N,N,'Sin''Sin',2,4)
  500    CONTINUE
         IF (P .EQ. 2) THEN
            WRITE(2,945)
         ELSE
            WRITE(2,946)
         END IF
  750 CONTINUE
C
  900 FORMAT(' ', 8(D12.6,1X), D12.6)
  901 FORMAT(' *********** Dimensions of WRK are less than N+M+P ')
  935 FORMAT(' *** ISTEP =', I3)
  940 FORMAT(
     * '1*** First example : Square root information filter with'/
     * ' *** dense A, B, C and upper triangular Q, R. ***')
  941 FORMAT(
     * '1*** Second example : Square root information filter with'/
     * ' *** dense A, B, C and upper triangular Q, R. ***')
  945 FORMAT(
     * '1*** In both these tests we start with Sinv=I and perform'/
     * ' *** four iterations of the filter.'/
     * ' *** The Sinv''Sinv matrices and X vectors are meant for '/
     * ' *** comparison with SRIFCO.')
  946 FORMAT(
     * '1*** In both these tests we start with Sinv=I and perform'/
     * ' *** four iterations of the filter.'/
     * ' *** The Sinv''Sinv matrices and X vectors are meant for '/
     * ' *** comparison with SRIFCO.')
  950 FORMAT(// ' *** Input SRIF' //)
  951 FORMAT(// ' *** Output SRIF' //)
C
C *** Last line of the program SRIF ***********************************
C
      END
C
C This is the driver for SUBROUTINE OBHESS.
C The routine is in TOMS.FOR and uses the file OBHESS.IN as
C input file from which N, UPPER, TOL, A and B are read.
C Output is sent to file OBHESS.OUT .
C
C     .. Local Scalars ..
      DOUBLE PRECISION SCALE,SUMSQ,TOL
      INTEGER I,J,LDA,LDB,LDU,M,N
      LOGICAL UPPER,WITHU
C     ..
C     .. Local Arrays ..
      DOUBLE PRECISION A(10,10),A0(10,10),B(5,10),B0(5,10),U(10,10),
     *                 WORK(10)
C     ..
C     .. External Subroutines ..
      EXTERNAL DCOPY,DGEMV,OBHESS,F06FBF,F06FJF
C     ..
C     .. Intrinsic Functions ..
      INTRINSIC DSQRT
C     ..
      WITHU = .TRUE.
      LDA = 10
      LDB = 5
      LDU = 10
C
C READ N, UPPER, TOL, A and B from file OBHESS.IN
C The matrices A and B are to be read column by column.
C The input dimension M is specified by the loop index.
C
      REWIND 1
      READ (1,FMT='()')
      DO 700 M = 2,3
          READ (1,FMT=15) N,UPPER,TOL
 
   15     FORMAT (I5,L5,D11.1)
   17     FORMAT (1H ,'*** N =',I3,' M =',I3,' UPPER = ',L3,' TOL =',
     *           D8.1)
 
          IF (M.EQ.2) THEN
              WRITE (2,FMT=940)
 
          ELSE
              WRITE (2,FMT=941)
          END IF
C
C The matrices A and B are read, and also stored in A0 and B0 for
C later use.
C
          READ (1,FMT=52) ((A(I,J),I=1, N),J=1, N)
          DO 51 J = 1,N
              CALL DCOPY(N,A(1,J),1,A0(1,J),1)
   51     CONTINUE
 
   52     FORMAT (D25.15)
 
          READ (1,FMT=52) ((B(I,J),I=1, M),J=1, N)
          DO 61 J = 1,N
              CALL DCOPY(M,B(1,J),1,B0(1,J),1)
   61     CONTINUE
C
C The matrix U is initialized as the identity matrix.
C
          DO 100 J = 1,N
              DO 90 I = 1,N
                  U(I,J) = 0.D0
   90         CONTINUE
              U(J,J) = 1.D0
  100     CONTINUE
          WRITE (2,FMT=950)
          WRITE (2,FMT=17) N,M,UPPER,TOL
          CALL PRMT(A0,LDA,N,N,'A0 matr. ',2,4)
          CALL PRMT(B0,LDB,M,N,'B0 matr. ',2,4)
C
C Calling the controller Hessenberg form routine.
C
          CALL OBHESS(A,LDA,N,B,LDB,M,U,LDU,WITHU,UPPER)
C
C The transformed matrices A and B, and the transformation matrix U
C are output.
C
          WRITE (2,FMT=951)
          CALL PRMT(A,LDA,N,N,'A matrix',2,4)
          CALL PRMT(B,LDB,M,N,'B matrix',2,4)
          CALL PRMT(U,LDU,N,N,'U matrix',2,4)
C
C Checking the Frobenius norm of (UxA0-AxU),(UxB0-B) and (UxU'-I)
C without altering A,B,U,A0,B0.
C
          SCALE = 1.D0
          SUMSQ = 0.D0
          DO 400 I = 1,N
              CALL DGEMV('N',N,N,1.D0,A,LDA,U(1,I),1,0.D0,WORK,1)
              CALL DGEMV('N',N,N,1.D0,U,LDU,A0(1,I),1,-1.D0,WORK,1)
              CALL F06FJF(N,WORK,1,SCALE,SUMSQ)
  400     CONTINUE
          SUMSQ = SCALE*DSQRT(SUMSQ)
          WRITE (2,FMT=980) SUMSQ
          SCALE = 1.D0
          SUMSQ = 0.D0
          DO 500 I = 1,M
              CALL DCOPY(N,B0(I,1),LDB,WORK,1)
              CALL DGEMV('T',N,N,1.D0,U,LDU,B(I,1),LDB,-1.D0,WORK,1)
              CALL F06FJF(N,WORK,1,SCALE,SUMSQ)
  500     CONTINUE
          SUMSQ = SCALE*DSQRT(SUMSQ)
          WRITE (2,FMT=981) SUMSQ
          SCALE = 1.D0
          SUMSQ = 0.D0
          DO 600 I = 1,N
              CALL F06FBF(N,0.D0,WORK,1)
              WORK(I) = 1.D0
              CALL DGEMV('T',N,N,1.D0,U,LDU,U(1,I),1,-1.D0,WORK,1)
              CALL F06FJF(N,WORK,1,SCALE,SUMSQ)
  600     CONTINUE
          SUMSQ = SCALE*DSQRT(SUMSQ)
          WRITE (2,FMT=982) SUMSQ
          IF (M.EQ.2) THEN
              WRITE (2,FMT=945)
 
          ELSE
              WRITE (2,FMT=946)
          END IF
 
  700 CONTINUE
 
  940 FORMAT (/ ' *** First example : upper Hessenberg form' /)
  941 FORMAT (/ '1*** Second example : lower Hessenberg form' /)
  945 FORMAT (
     * '1*** This first example is a well-conditioned one.'/
     * ' *** The above norm tests should be close to the machine '/
     * ' *** precision and A, B, U should be close to those obtained'/
     * ' *** on any other machine.')
  946 FORMAT (
     * '1*** This second example is an ill-conditioned one.'/
     * ' *** Therefore A, B and U can differ a lot from those obtained'/
     * ' *** on another machine, but the above norm tests should yet'/
     * ' *** be close to the machine precision (because of backward'/
     * ' *** stability).')
  950 FORMAT (// ' *** Input Data *************' //)
  951 FORMAT (// ' *** Output Data ************' //)
  980 FORMAT (
     * ' *** Testing norm U*A0-A*U =',D12.6,/
     * ' *** which should be of the order of the machine precision'/
     * ' *** norm(A)')
  981 FORMAT (
     * ' *** Testing norm U*B0-B =',D12.6,/
     * ' *** which should be of the order of the machine precision'/
     * ' *** norm(B)')
  982 FORMAT (
     * ' *** Testing norm U*UP-I =',D12.6,/
     * ' *** which should be of the order of the machine precision')
C
C *** Last line of the program OBHESS *********************************
C
      END
C
C This is the driver for SUBROUTINE COHESS.
C The routine is in TOMS.FOR and uses the file COHESS.IN as
C input file from which N, UPPER, TOL, A and B are read.
C Output is sent to file COHESS.OUT .
C
C     .. Local Scalars ..
      DOUBLE PRECISION SCALE,SUMSQ,TOL
      INTEGER I,J,LDA,LDB,LDU,M,N
      LOGICAL UPPER,WITHU
C     ..
C     .. Local Arrays ..
      DOUBLE PRECISION A(10,10),A0(10,10),B(10,5),B0(10,5),U(10,10),
     *                 WORK(10)
C     ..
C     .. External Subroutines ..
      EXTERNAL COHESS,DCOPY,DGEMV,F06FBF,F06FJF
C     ..
C     .. Intrinsic Functions ..
      INTRINSIC DSQRT
C     ..
      WITHU = .TRUE.
      LDA = 10
      LDB = 10
      LDU = 10
C
C READ N, UPPER, TOL, A and B from file COHESS.IN
C The matrices A and B are to be read column by column.
C The input dimension M is specified by the loop index.
C
      REWIND 1
      READ (1,FMT='()')
      DO 700 M = 2,3
          READ (1,FMT=15) N,UPPER,TOL
 
   15     FORMAT (I5,L5,D11.1)
   17     FORMAT (1H ,'*** N =',I3,' M =',I3,' UPPER = ',L3,' TOL =',
     *           D8.1)
 
          IF (M.EQ.2) THEN
              WRITE (2,FMT=940)
 
          ELSE
              WRITE (2,FMT=941)
          END IF
C
C The matrices A and B are read, and also stored in A0 and B0 for
C later use.
C
          READ (1,FMT=52) ((A(I,J),I=1, N),J=1, N)
          DO 51 J = 1,N
              CALL DCOPY(N,A(1,J),1,A0(1,J),1)
   51     CONTINUE
 
   52     FORMAT (D25.15)
 
          READ (1,FMT=52) ((B(I,J),I=1, N),J=1, M)
          DO 61 J = 1,M
              CALL DCOPY(N,B(1,J),1,B0(1,J),1)
   61     CONTINUE
C
C The matrix U is initialized as the identity matrix.
C
          DO 100 J = 1,N
              DO 90 I = 1,N
                  U(I,J) = 0.D0
   90         CONTINUE
              U(J,J) = 1.D0
  100     CONTINUE
          WRITE (2,FMT=950)
          WRITE (2,FMT=17) N,M,UPPER,TOL
          CALL PRMT(A0,LDA,N,N,'A0 matr. ',2,4)
          CALL PRMT(B0,LDB,N,M,'B0 matr. ',2,4)
C
C Calling the controller Hessenberg form routine.
C
          CALL COHESS(A,LDA,N,B,LDB,M,U,LDU,WITHU,UPPER)
C
C The transformed matrices A and B, and the transformation matrix U
C are output.
C
          WRITE (2,FMT=951)
          CALL PRMT(A,LDA,N,N,'A matrix',2,4)
          CALL PRMT(B,LDB,N,M,'B matrix',2,4)
          CALL PRMT(U,LDU,N,N,'U matrix',2,4)
C
C Checking the Frobenius norm of (UxA0-AxU),(UxB0-B) and (UxU'-I)
C without altering A,B,U,A0,B0.
C
          SCALE = 1.D0
          SUMSQ = 0.D0
          DO 400 I = 1,N
              CALL DGEMV('N',N,N,1.D0,A,LDA,U(1,I),1,0.D0,WORK,1)
              CALL DGEMV('N',N,N,1.D0,U,LDU,A0(1,I),1,-1.D0,WORK,1)
              CALL F06FJF(N,WORK,1,SCALE,SUMSQ)
  400     CONTINUE
          SUMSQ = SCALE*DSQRT(SUMSQ)
          WRITE (2,FMT=980) SUMSQ
          SCALE = 1.D0
          SUMSQ = 0.D0
          DO 500 I = 1,M
              CALL DCOPY(N,B(1,I),1,WORK,1)
              CALL DGEMV('N',N,N,1.D0,U,LDU,B0(1,I),1,-1.D0,WORK,1)
              CALL F06FJF(N,WORK,1,SCALE,SUMSQ)
  500     CONTINUE
          SUMSQ = SCALE*DSQRT(SUMSQ)
          WRITE (2,FMT=981) SUMSQ
          SCALE = 1.D0
          SUMSQ = 0.D0
          DO 600 I = 1,N
              CALL F06FBF(N,0.D0,WORK,1)
              WORK(I) = 1.D0
              CALL DGEMV('T',N,N,1.D0,U,LDU,U(1,I),1,-1.D0,WORK,1)
              CALL F06FJF(N,WORK,1,SCALE,SUMSQ)
  600     CONTINUE
          SUMSQ = SCALE*DSQRT(SUMSQ)
          WRITE (2,FMT=982) SUMSQ
          IF (M.EQ.2) THEN
              WRITE (2,FMT=945)
 
          ELSE
              WRITE (2,FMT=946)
          END IF
 
  700 CONTINUE
 
  940 FORMAT (' *** First example : upper Hessenberg form')
  941 FORMAT ('1*** Second example : lower Hessenberg form')
  945 FORMAT (
     * '1*** This first example is a well-conditioned one.'/
     * ' *** The above norm tests should be close to the machine'/
     * ' *** precision and A, B, U should be close to those obtained'/
     * ' *** on any other machine.')
  946 FORMAT (
     * '1*** This second example is an ill-conditioned one.'/
     * ' *** Therefore A, B and U can differ a lot from those obtained'/
     * ' *** on another machine, but the above norm tests should yet'/
     * ' *** be close to the machine precision (because of backward'/
     * ' *** stability).')
  950 FORMAT (// ' *** Input Data *************' //)
  951 FORMAT (// ' *** Output Data ************' //)
  980 FORMAT (
     * ' *** Testing norm U*A0-A*U =',D12.6,/
     * ' *** which should be of the order of the machine precision'/
     * ' *** norm(A)')
  981 FORMAT (
     * ' *** Testing norm U*B0-B =',D12.6,/
     * ' *** which should be of the order of the machine precision'/
     * ' *** norm(B)')
  982 FORMAT (
     * ' *** Testing norm U*UP-I =',D12.6,/
     * ' *** which should be of the order of the machine precision')
C
C *** Last line of the program COHESS *********************************
 
      END
C
C     This is the driver for SUBROUTINE SRCFOB.
C     The routine is in TOMS.FOR and uses the file SRCFOB.IN as
C     input file from which N, P, A, B, C, R and Q are read.
C     Output is sent to file SRCFOB.OUT .
C
      INTEGER I, ISTEP, J, N, M, P, LDS, LDA, LDB, LDQ, LDC, LDR, LDK,
     *        LDW, LDU
      DOUBLE PRECISION A(10,10), B(10,5), C(7,10), Q(5,5), R(7,7),
     *                 WRK(22,22), S(10,10), UB(10,5),
     *                 K(10,7), U(10,10), SSP(10,10),
     *                 UPSSP(10,10), UPSSPU(10,10)
      DOUBLE PRECISION DDOT, TOL
      LOGICAL WITHU, UPPER, MULTBQ, WITHK
C
      WITHK = .TRUE.
      UPPER = .FALSE.
      WITHU = .TRUE.
      MULTBQ = .TRUE.
      LDS = 10
      LDA = 10
      LDB = 10
      LDC = 7
      LDQ = 5
      LDR = 7
      LDK = 10
      LDW = 22
      LDU = 10
      TOL = 1.D-15
C
C     READ N, P, A, B, C, Q and R from the file SRCFOB.IN .
C     The matrices A, B, C, Q and R are to be read columnwise.
C     The input dimension M is specified by the loop index.
C
C
      REWIND 1
      DO 750 M = 2, 3
         READ (1,51) N, P
  51  FORMAT(2I5)
  53  FORMAT(1H ,'*** N =', I3,' M =', I3,' P = ', I3)
         IF (M .EQ. 2) THEN
            WRITE(2,940)
         ELSE
            WRITE(2,941)
         END IF
         DO 50 J = 1, N
            DO 50 I = 1, N
               READ(1,52) A(I,J)
  50     CONTINUE
  52  FORMAT(D25.15)
         DO 60 J = 1, M
            DO 60 I = 1, N
               READ(1,52) B(I,J)
  60     CONTINUE
         DO 68 J = 1, N
            DO 68 I = 1, P
               READ(1,52) C(I,J)
  68     CONTINUE
         DO 76 J = 1, P
            DO 76 I = 1, P
               READ(1,52) R(I,J)
  76     CONTINUE
         DO 84 J = 1, M
            DO 84 I = 1, M
               READ(1,52) Q(I,J)
  84     CONTINUE
         DO 90 J = 1, N
            DO 90 I = 1, N
               U(I,J) = 0.0D0
   90    CONTINUE
         DO 100 I = 1, N
            U(I,I) = 1.0D0
  100    CONTINUE
         WRITE(2,950)
         WRITE(2,947)
         WRITE(2,53) N, M, P
         WRITE(2,944)
         CALL PRMT(A,LDA,N,N,'A matrix',2,4)
         CALL PRMT(B,LDB,N,M,'B matrix',2,4)
         CALL PRMT(C,LDC,P,N,'C matrix',2,4)
C
C     Transform (A,B,C) to lower observer Hessenberg form.
C
         CALL OBHESS(A, LDA, N, C, LDC, P, U, LDU, WITHU, UPPER)
         DO 140 J = 1, M
            DO 140 I = 1, N
               UB(I,J) = DDOT(N, U(I,1), LDU, B(1,J), 1)
  140    CONTINUE
         WRITE(2,948)
         CALL PRMT(A,LDA,N,N,'Au matr.',2,4)
         CALL PRMT(B,LDB,N,M,'Bu matr.',2,4)
         CALL PRMT(C,LDC,P,N,'Cu matr.',2,4)
         CALL PRMT(U,LDU,N,N,'U matr. ',2,4)
         WRITE(2,949)
         CALL PRMT(R,LDR,P,P,'R matr. ',2,4)
         CALL PRMT(Q,LDQ,M,M,'Q matr. ',2,4)
C
C     Now perform three steps of the Kalman filter recursion
C     (in square root covariance form) with MULTBQ = .TRUE.
C
         WRITE(2,951)
C
C     Initialize the S matrix to be the null matrix.
C
         DO 350 J = 1, N
            DO 350 I = 1, N
               S(I,J) = 0.0D0
  350    CONTINUE
         DO 500 ISTEP = 1, 3
            WRITE(2,935)ISTEP
            CALL SRCFOB(S, LDS, A, LDA, UB, LDU, Q, LDQ, C, LDC, R,
     *                  LDR, N, M, P, K, LDK, WRK, LDW, MULTBQ,
     *                  WITHK, TOL)
            CALL PRMT(S,LDS,N,N,'Su matr.',2,4)
            CALL PRMT(K,LDK,N,P,'Ku matr.',2,4)
            DO 450 J = 1, N
               DO 450 I = 1, N
                  SSP(I,J) = DDOT(N, S(I,1), LDS, S(J,1), LDS)
  450       CONTINUE
            DO 460 J = 1, N
               DO 460 I = 1, N
                  UPSSP(I,J) = DDOT(N, U(1,I), 1, SSP(1,J), 1)
  460       CONTINUE
            DO 470 J = 1, N
               DO 470 I = 1, N
                  UPSSPU(I,J) = DDOT(N, UPSSP(I,1), LDU, U(1,J), 1)
  470       CONTINUE
            CALL PRMT(UPSSPU,LDU,N,N,'U''SuSu''U',2,4)
  500    CONTINUE
         WRITE(2,952)
C
C     Initialize the S matrix to be the null matrix.
C
         DO 550 J = 1, N
            DO 550 I = 1, N
               S(I,J) = 0.0D0
  550    CONTINUE
C
C     Now perform three steps of the Kalman filter recursion
C     (in square root covariance form) with MULTBQ = .FALSE.
C
         MULTBQ = .FALSE.
         DO 700 ISTEP = 1, 3
            WRITE(2,935)ISTEP
            CALL SRCFOB(S, LDS, A, LDA, UB, LDU, Q, LDQ, C, LDC, R,
     *                  LDR, N, M, P, K, LDK, WRK, LDW, MULTBQ,
     *                  WITHK, TOL)
            CALL PRMT(S,LDS,N,N,'Su matr.',2,4)
            CALL PRMT(K,LDK,N,P,'Ku matr.',2,4)
            DO 650 J = 1, N
               DO 650 I = 1, N
                  SSP(I,J) = DDOT(N, S(I,1), LDS, S(J,1), LDS)
  650       CONTINUE
            DO 660 J = 1, N
               DO 660 I = 1, N
                  UPSSP(I,J) = DDOT(N, U(1,I), 1, SSP(1,J), 1)
  660       CONTINUE
            DO 670 J = 1, N
               DO 670 I = 1, N
                  UPSSPU(I,J) = DDOT(N, UPSSP(I,1), LDU, U(1,J), 1)
  670       CONTINUE
            CALL PRMT(UPSSPU,LDU,N,N,'U''SuSu''U',2,4)
  700    CONTINUE
         IF (M .EQ. 2) THEN
            WRITE(2,945)
         ELSE
            WRITE(2,946)
         END IF
  750 CONTINUE
  935 FORMAT(' *** ISTEP =', I3)
  940 FORMAT(
     * '1*** First example : Square root covariance filter with '/
     * ' *** A, B, C in (lower) observer Hessenberg form and'/
     * ' *** lower triangular Q, R.')
  941 FORMAT(
     * '1*** Second example : Square root covariance filter with'/
     * ' *** A, B, C in (lower) observer Hessenberg form and'/
     * ' *** lower triangular Q, R.')
  944 FORMAT(// ' *** UPPER = .FALSE.' //)
  945 FORMAT(
     * '1*** In both these tests we start with Su=0 and perform three'/
     * ' *** iterations of the filter.'/
     * ' *** The ranks of Su in these three steps must be equal to '/
     * ' *** M(=2), 2M(=4) and 3M(=6).'/
     * ' *** K must be 0 in the first step and nonzero afterwards.'/
     * ' *** The results for MULTBQ = .TRUE. and .FALSE. must be equal'/
     * ' *** since we chose Q=I.'/
     * ' *** The U''SuSu''U matrices are meant for comparison with '/
     * ' *** SRCF.')
  946 FORMAT(
     * '1*** In both these tests we start with Su=0 and perform three'/
     * ' *** iterations of the filter.'/
     * ' *** The ranks of Su in these three steps must be equal to '/
     * ' *** M(=3), 2M(=6) and min(N,3M)(=6).'/
     * ' *** K must be 0 in the first step and nonzero afterwards.'/
     * ' *** The results for MULTBQ = .TRUE. and .FALSE. must be equal'/
     * ' *** since we chose Q=I.'/
     * ' *** The U''SuSu''U matrices are meant for comparison with '/
     * ' *** SRCF.')
  947 FORMAT(// ' *** Input OBHESS' //)
  948 FORMAT(// ' *** Output OBHESS' //)
  949 FORMAT(// ' *** Additional input to SRCFOB' //)
  950 FORMAT(// ' *** Input SRCFOB' //)
  951 FORMAT(// ' *** Output SRCFOB for MULTBQ=.TRUE.' //)
  952 FORMAT(// ' *** Output SRCFOB for MULTBQ=.FALSE.' //)
C
C *** Last line of the program SRCFOB *********************************
C
      END
C
C     This is the driver for SUBROUTINE SRIFCO.
C     The routine is in TOMS.FOR and uses the file SRIFCO.IN as
C     input file from which N, M, Ainv, C, AinvB, Qinv, Rinv, Z, X,
C     and Y are read. Output is sent to file SRIFCO.OUT .
C
      INTEGER I, ISTEP, J, N, M, P, LDS, LDA, LDB, LDC, LDR, LDQ, LDW,
     *        LDU, NMP
      DOUBLE PRECISION AINV(10,10), AINVB(10,7), C(5,10), RINV(5,5),
     *                 AINVU(10,10), AINVBU(10,7), CU(5,10),
     *                 WRK(22,22), SINV(10,10), QINV(7,7), Y(5),
     *                 SPS(10,10), Z(7), X(10), XU(10),
     *                 RINVY(5), U(10,10),
     *                 SINVU(10,10)
      DOUBLE PRECISION DDOT, TOL
      LOGICAL MULTRC, WITHU, UPPER, WITHX
C
      WITHX = .TRUE.
      UPPER = .TRUE.
      MULTRC = .FALSE.
      WITHU = .TRUE.
      LDS = 10
      LDA = 10
      LDB = 10
      LDQ = 7
      LDC = 5
      LDR = 5
      LDW = 22
      LDU = 10
      TOL = 1.D-15
C
C     READ N, M, Ainv, C, AinvB, Qinv, Rinv, Z, X, and Y from the file
C     SRIFCO.IN.
C     The matrices Ainv, C, AinvB, Qinv and Rinv are to be read column-
C     wise.
C     The input dimension P is specified by the loop index.
C
C
      REWIND 1
      DO 750 P = 2, 3
         READ (1,51) N, M
         NMP = N + M + P
         IF (LDW .LT. NMP) WRITE(6,901)
  51  FORMAT(2I5)
  53  FORMAT(1H , '*** N =', I3, ' M =', I3, ' P = ', I3)
         IF (P .EQ. 2) THEN
            WRITE(2,940)
         ELSE
            WRITE(2,941)
         END IF
         DO 50 J = 1, N
            DO 50 I =1, N
               READ(1,52) AINV(J,I)
  50     CONTINUE
  52  FORMAT(D25.15)
         DO 60 J = 1, P
            DO 60 I = 1, N
               READ(1,52) C(J,I)
  60     CONTINUE
         DO 68 I = 1, M
            DO 68 J = 1, N
               READ(1,52) AINVB(J,I)
  68     CONTINUE
         DO 76 J = 1, M
            DO 76 I = 1, M
               READ(1,52) QINV(J,I)
  76     CONTINUE
         DO 81 J = 1, P
            DO 81 I = 1, P
               READ(1,52) RINV(J,I)
  81     CONTINUE
         DO 86 J = 1, M
            READ(1,52) Z(J)
  86     CONTINUE
         DO 88 J = 1, N
            READ(1,52) X(J)
  88     CONTINUE
         DO 90 J = 1, P
            READ(1,52) Y(J)
  90     CONTINUE
C
C     Initialize the U matrix to be the unity matrix.
C
         DO 100 J = 1, N
            DO 100 I = 1, N
               U(I,J) = 0.0D0
  100    CONTINUE
         DO 110 I = 1, N
            U(I,I) = 1.0D0
  110    CONTINUE
C
         WRITE(2,950)
         WRITE(2,947)
         WRITE(2,53) N, M, P
         WRITE(2,944)
         CALL PRMT(AINV,LDA,N,N,'Ainv    ',2,4)
         CALL PRMT(AINVB,LDA,N,M,'AinvB   ',2,4)
         CALL PRMT(C,LDC,P,N,'C matrix',2,4)
C
C     Transform (A,B,C) to upper Hessenberg form.
C
         CALL COHESS(AINV, LDA, N, AINVB, LDB, M, U, LDU, WITHU, UPPER)
         DO 150 I = 1, P
            CALL DGEMV('N', N, N, 1.0D0, U, LDU, C(I,1), LDC, 0.0D0,
     *                 CU(I,1), LDC)
  150    CONTINUE
         WRITE(2,948)
         CALL PRMT(AINV,LDA,N,N,'Ainvu   ',2,4)
         CALL PRMT(AINVB,LDA,N,M,'AinvBu   ',2,4)
         CALL PRMT(CU,LDC,P,N,'Cu matr.',2,4)
C
C     Initialize the SINVu matrix to be the unity matrix.
C
         DO 200 J = 1, N
            DO 190 I = 1, N
               SINVU(I,J) = 0.0D0
  190       CONTINUE
            SINVU(J,J) = 1.0D0
  200    CONTINUE
C
         CALL PRMT(SINVU,LDS,N,N,'Sinvu   ',2,4)
         WRITE(2,949)
         CALL PRMT(QINV,LDQ,M,M,'QINV    ',2,4)
         CALL PRMT(RINV,LDR,P,P,'RINV    ',2,4)
         CALL PRMT(Z,LDQ,M,1,'Z vector',2,4)
         CALL DGEMV('N', N, N, 1.0D0, U, LDU, X, 1, 0.0D0, XU, 1)
         CALL PRMT(XU,LDA,N,1,'XU vect.',2,4)
         CALL PRMT(Y,LDC,P,1,'Y vector',2,4)
C
C     Calculation of RINV x Y.
C
         DO 270 I = 1, P
            RINVY(I) = DDOT(P, RINV(I,1), LDR, Y, 1)
  270    CONTINUE
C
C     Now perform four steps of the Kalman filter recursion
C     (in square root covariance form).
C
         WRITE(2,951)
         DO 500 ISTEP = 1, 4
            WRITE(2,935)ISTEP
            CALL SRIFCO(SINVU, LDS, AINV, LDA, AINVB, LDB, RINV, LDR,
     *                  CU, LDC, QINV, LDQ, XU, RINVY, Z, N, M, P,
     *                  WRK, LDW, MULTRC, WITHX, TOL)
            CALL PRMT(SINVU,LDS,N,N,'Sinvu   ',2,4)
            DO 440 I = 1, N
               CALL DGEMV('N', N, N, 1.0D0, SINVU, LDS, U(1,I), 1,
     *                    0.0D0, SINV(1,I), 1)
  440       CONTINUE
            DO 460 J = 1, N
               DO 450 I = 1, N
                  SPS(I,J) = DDOT(N, SINV(1,I), 1, SINV(1,J), 1)
  450          CONTINUE
  460       CONTINUE
            CALL DGEMV('T', N, N, 1.0D0, U, LDU, XU, 1, 0.0D0, X, 1)
            CALL PRMT(X,LDA,N,1,'X vector',2,4)
            CALL PRMT(SPS,LDS,N,N,'Sin''Sin',2,4)
  500    CONTINUE
         IF (P .EQ. 2) THEN
            WRITE(2,945)
         ELSE
            WRITE(2,946)
         END IF
  750 CONTINUE
  900 FORMAT(' ', 8(D12.6,1X), D12.6)
  901 FORMAT(' *********** Dimensions of WRK are less than N+M+P ')
  935 FORMAT(' *** ISTEP =', I3)
  940 FORMAT(
     * '1*** First example : Square root information filter with'/
     * ' *** A, B, C in (upper) controller Hessenberg form'/
     * ' *** and upper triangular Q, R.')
  941 FORMAT(
     * '1*** Second example : Square root information filter with'/
     * ' *** A, B, C in (upper) controller Hessenberg form'/
     * ' *** and upper triangular Q, R.')
  944 FORMAT(// ' *** UPPER = .TRUE.'  //)
  945 FORMAT(
     * '1*** In both these tests we start with Sinvu=I and perform'/
     * ' *** four iterations of the filter.'/
     * ' *** The Sinv''Sinv matrices and X vectors are meant for '/
     * ' *** comparison with SRIF.')
  946 FORMAT(
     * '1*** In both these tests we start with Sinvu=I and perform'/
     * ' *** four iterations of the filter.'/
     * ' *** The Sinv''Sinv matrices and X vectors are meant for '/
     * ' *** comparison with SRIF.')
  947 FORMAT(// ' *** Input COHESS'  //)
  948 FORMAT(// ' *** Output COHESS'  //)
  949 FORMAT(// ' *** Additional input to SRIFCO'  //)
  950 FORMAT(// ' *** Input SRIFCO'  //)
  951 FORMAT(// ' *** Output SRIFCO MULTRC=.TRUE.'  //)
  952 FORMAT(// ' *** Output SRIFCO MULTRC=.FALSE.'  //)
C
C *** Last line of the program SRIFCO *********************************
C
      END
      SUBROUTINE SRCF(S, LDS, A, LDA, B, LDB, Q, LDQ, C, LDC, R, LDR,
     *                N, M, P, K, LDK, WRK, LDW, MULTBQ, WITHK, TOL)
C
C     PURPOSE:
C
C     The algorithm calculates a combined measurement and time update
C     of one iteration of the Kalman filter. This update is given for
C     the square root covariance filter, using dense matrices.
C
C     CONTRIBUTORS:
C
C     M. Vanbegin, P. Van Dooren (PRLB)
C     M. Verhaegen (NASA Ames)
C
C     REVISIONS:
C
C     1988, Sept. 9.
C
C     Specification of parameters.
C
C     .. Scalar Arguments ..
C
      INTEGER LDS, LDA, LDB, LDQ, LDC, LDR, N, M, P, LDK, LDW
      DOUBLE PRECISION TOL
      LOGICAL MULTBQ, WITHK
C
C     .. Array Arguments ..
C
      DOUBLE PRECISION S(LDS,*), A(LDA,*), B(LDB,*), Q(LDQ,*), C(LDC,*),
     *                 R(LDR,*), K(LDK,*), WRK(LDW,*)
C
C     EXTERNAL SUBROUTINES:
C
C     DTRCO from LINPACK
C     DGEMV, DTRSV from EXTENDED-BLAS,
C     F06FBF, F06FUF, F06FSF from NAG-BLAS.
C     DCOPY from BLAS.
C
C     Local variables.
C
      INTEGER I, I1, J, P1, PN, PNM, PI, PI1, PJ
      DOUBLE PRECISION DZ1, RCOND
C
C     Construction of the pre-array WRK.
C
      P1 = P + 1
      PN = P + N
      PNM = PN + M
      DO 20 J = 1, PNM
         CALL F06FBF(PN, 0.0D+0, WRK(1,J), 1)
   20 CONTINUE
C
C     First part -  Storing lower triangular factor R in the (1,1) block
C                   of WRK.
C
      DO 40 I = 1, P
         CALL DCOPY(P-I+1, R(I,I), 1, WRK(I,I), 1)
   40 CONTINUE
C
C     Second part -  Storing B x Q in the (2,3) block of WRK.
C
      IF (MULTBQ) THEN
         DO 60 I = 1, M
            CALL DCOPY(N, B(1,I), 1, WRK(P1,P+N+I), 1)
   60    CONTINUE
      ELSE
         DO 80 I = 1, M
            CALL DGEMV('N', N, M-I+1, 1.D0, B(1,I), LDB, Q(I,I), 1,
     *                 0.0D0, WRK(P1,P+N+I), 1)
   80    CONTINUE
      END IF
C
C     Third part -  Storing C x S in the (1,2) block of WRK.
C
      DO 100 I = 1, N
         CALL DGEMV('N', P, N-I+1, 1.D0, C(1,I), LDC, S(I,I), 1, 0.D0,
     *              WRK(1,P+I), 1)
  100 CONTINUE
C
C     Fourth part  -  Storing A x S in the (2,2) block of WRK.
C
      DO 120 I = 1, N
         CALL DGEMV('N', N, N-I+1, 1.D0, A(1,I), LDA, S(I,I), 1, 0.D0,
     *              WRK(P1,P+I), 1)
  120 CONTINUE
C
C     Triangularization (2 steps).
C
C     Step 1: eliminate the (1,2) block of WRK.
C
      DO 160 I = 1, P
         CALL F06FSF(N, WRK(I,I), WRK(I,P1), LDW, TOL, DZ1)
         I1 = I + 1
         DO 140 J = I1, PN
            CALL F06FUF(N, WRK(I,P1), LDW, DZ1, WRK(J,I), WRK(J,P1),
     *                  LDW)
  140    CONTINUE
         CALL DTRCO(WRK, LDW, P, RCOND, WRK(1,PNM), 0)
         IF (RCOND .LT. TOL) WITHK = .FALSE.
  160 CONTINUE
C
C     Step 2: triangularize the remaining (2,2) and (2,3) blocks of WRK.
C
      DO 200 I = 1, N
         PI = P + I
         PI1 = PI + 1
         CALL F06FSF(N+M-I, WRK(PI,PI), WRK(PI,PI1), LDW, TOL, DZ1)
         IF (PI1 .LE. PN) THEN
            DO 180 J = PI1, PN
               CALL F06FUF(N+M-I, WRK(PI,PI1), LDW, DZ1, WRK(J,PI),
     *                     WRK(J,PI1), LDW)
  180       CONTINUE
         END IF
  200 CONTINUE
C
C     Output K and S.
C
      IF (WITHK) THEN
         DO 220 J = 1, N
            CALL DCOPY(P, WRK(P+J,1), LDW, K(J,1), LDK)
            CALL DTRSV('L', 'T', 'N', P, WRK, LDW, K(J,1), LDK)
  220    CONTINUE
      END IF
      DO 240 J = 1, N
         PJ = P + J
         CALL DCOPY(N-J+1, WRK(PJ,PJ), 1, S(J,J), 1)
  240 CONTINUE
      RETURN
C
C *** Last line of the SRCF subroutine ********************************
C
      END
      SUBROUTINE SRIF(T, LDT, AINV, LDA, B, LDB, RINV, LDR, C, LDC,
     *                QINV, LDQ, X, RINVY, W, N, M, P, WRK, LDW,
     *                MULTAB, MULTRC, WITHX, TOL)
C
C     PURPOSE:
C
C     The algorithm calculates a combined measurement and time update
C     of one iteration of the Kalman filter. This update is given for
C     the square root information filter, using dense matrices.
C
C     CONTRIBUTORS:
C
C     M. Vanbegin, P. Van Dooren (PRLB)
C     M. Verhaegen (NASA Ames)
C
C     REVISIONS:
C
C     1988, Sept. 9.
C
C     Specification of parameters.
C
C     .. Scalar Arguments ..
C
      INTEGER LDT, LDA, LDB, LDR, LDC, LDQ, N, M, P, LDW
      DOUBLE PRECISION TOL
      LOGICAL MULTAB, MULTRC, WITHX
C
C     .. Array Arguments ..
C
      DOUBLE PRECISION T(LDT,*), AINV(LDA,*), B(LDB,*), RINV(LDR,*),
     *                 C(LDC,*), QINV(LDQ,*), X(*), RINVY(*), W(*),
     *                 WRK(LDW,*)
C
C     EXTERNAL SUBROUTINES:
C
C     DTRCO from LINPACK
C     DGEMV, DTRMV, DTRSV from Extended-BLAS,
C     F06FBF, F06FSF, F06FUF from NAG-BLAS,
C     DCOPY from BLAS
C
C     Local variables.
C
      INTEGER I, I1, J, J1, MN1, MNP
      DOUBLE PRECISION DZ1, RCOND
C
C     Construction of the pre-array WRK.
C
      MN1 = M + N + 1
      MNP = M + N + P
      DO 20 J = 1, MN1
         CALL F06FBF(MNP, 0.0D+0, WRK(1,J), 1)
   20 CONTINUE
C
C     First part - Storing QINV in the (1,1) block of WRK.
C
C
      DO 40 J = 1, M
         CALL DCOPY(J, QINV(1,J), 1, WRK(1,J), 1)
   40 CONTINUE
C
C     Second part - Storing the process noise mean value in the (1,3)
C                   block of WRK.
C
      CALL DCOPY(M, W, 1, WRK(1,M+N+1), 1)
      CALL DTRMV('U', 'N', 'N', M, QINV, LDQ, WRK(1,M+N+1), 1)
C
C     Third part - Storing T x AINV and T x AINV x B in the
C                  (2,1) and (2,2) blocks of WRK.
C
      DO 80 I = 1, N
         CALL DCOPY(N, AINV(1,I), 1, WRK(M+1,M+I), 1)
         CALL DTRMV('U', 'N', 'N', N, T, LDT, WRK(M+1,M+I), 1)
   80 CONTINUE
      IF (MULTAB) THEN
         DO 100 I = 1, M
            CALL DCOPY(N, B(1,I), 1, WRK(M+1,I), 1)
            CALL DTRMV('U', 'N', 'N', N, T, LDT, WRK(M+1,I), 1)
  100    CONTINUE
      ELSE
         DO 120 I = 1, M
            CALL DGEMV('N', N, N, 1.0D0, WRK(M+1,M+1), LDW, B(1,I), 1,
     *                 0.0D0, WRK(M+1,I), 1)
  120    CONTINUE
      END IF
C
C     Fourth part - Storing T x X in the (2,3) block of WRK.
C
      CALL DCOPY(N, X, 1, WRK(M+1,M+N+1), 1)
      CALL DTRMV('U', 'N', 'N', N, T, LDT, WRK(M+1,M+N+1), 1)
C
C     Fifth part - Storing RINV x C in the (3,2) block of WRK.
C
      IF (MULTRC) THEN
         DO 160 J = 1, N
            CALL DCOPY(P, C(1,J), 1, WRK(M+N+1,M+J), 1)
  160    CONTINUE
      ELSE
         DO 180 I = 1, N
            CALL DCOPY(P, C(1,I), 1, WRK(M+N+1,M+I), 1)
            CALL DTRMV('U', 'N', 'N', P, RINV, LDR, WRK(M+N+1,M+I), 1)
  180    CONTINUE
      END IF
C
C     Sixth part - Storing the measurement in the (3,3) block of WRK.
C
      CALL DCOPY(P, RINVY, 1, WRK(M+N+1,M+N+1), 1)
C
C     Triangularization (2 steps).
C
C     Step 1: eliminate the (2,1) block of WRK.
C
      DO 220 I = 1, M
         I1 = I + 1
         CALL F06FSF(N, WRK(I,I), WRK(M+1,I), 1, TOL, DZ1)
         DO 200 J = I1, MN1
            CALL F06FUF(N, WRK(M+1,I), 1, DZ1, WRK(I,J), WRK(M+1,J), 1)
  200    CONTINUE
  220 CONTINUE
C
C     Step 2: triangularize the remaining (2,2) and (3,2) blocks of WRK.
C
      DO 260 I = 1, N
         CALL F06FSF(N+P-I, WRK(M+I,M+I), WRK(M+I+1,M+I), 1, TOL, DZ1)
         J1 = N - I + 1
         DO 240 J = 1, J1
            CALL F06FUF(N+P-I, WRK(M+I+1,M+I), 1, DZ1, WRK(M+I,M+I+J),
     *                  WRK(M+I+1,M+I+J), 1)
  240    CONTINUE
         CALL DTRCO(WRK(M+1,M+1), LDW, N, RCOND, WRK(M+1,1), 1)
         IF (RCOND .LT. TOL) WITHX = .FALSE.
  260 CONTINUE
C
C     Output T and X.
C
      DO 280 J = 1, N
         CALL DCOPY(J, WRK(M+1,M+J), 1, T(1,J), 1)
  280 CONTINUE
C
      IF (WITHX) THEN
         CALL DCOPY(N, WRK(M+1,M+N+1), 1, X, 1)
         CALL DTRSV('U', 'N', 'N', N, T, LDT, X, 1)
      END IF
C
      RETURN
C
C *** Last line of the SRIF subroutine ********************************
C
      END
      SUBROUTINE OBHESS(A, LDA, N, C, LDC, P, U, LDU, WITHU, UPPER)
C
C     PURPOSE:
C
C     OBHESS computes a unitary state space transformation U reducing
C     the pair (A,C) to upper or lower observer Hessenberg form.
C
C     CONTRIBUTORS:
C
C     M. Vanbegin, P. Van Dooren (PRLB)
C     M. Verhaegen (NASA Ames)
C
C     REVISIONS:
C
C     1988, Sept. 9.
C
C     Specification of parameters.
C
C     .. Scalar Arguments ..
C
      INTEGER LDA, N, LDC, P, LDU
      LOGICAL WITHU, UPPER
C
C     .. Array Arguments ..
C
      DOUBLE PRECISION A(LDA,*), C(LDC,*), U(LDU,*)
C
C     EXTERNAL SUBROUTINES:
C
C     F06FSF, F06FUF from NAG-BLAS,
C
C     Local variables.
C
      INTEGER P1, N1, NJ, JJ, II, J, PAR1, PAR2, PAR3,
     *        PAR4, PAR5, PAR6
      DOUBLE PRECISION TL, DZ
C
      TL = 0.0D0
      P1 = P + 1
      N1 = N - 1
C
C     Perform transformations involving both C and A.
C
      DO 120 J = 1, MIN(P,N1)
         NJ = N - J
         IF (UPPER) THEN
            PAR1 = P - J + 1
            PAR2 = NJ + 1
            PAR3 = 1
            PAR4 = P - J
            PAR5 = NJ
         ELSE
            PAR1 = J
            PAR2 = J
            PAR3 = J + 1
            PAR4 = P
            PAR5 = N
         END IF
         CALL F06FSF(NJ, C(PAR1,PAR2), C(PAR1,PAR3), LDC, TL, DZ)
C
C        Update A.
C
         DO 20 JJ = 1, N
            CALL F06FUF(NJ, C(PAR1,PAR3), LDC, DZ, A(PAR2,JJ),
     *                  A(PAR3,JJ), 1)
   20    CONTINUE
         DO 40 II = 1, N
            CALL F06FUF(NJ, C(PAR1,PAR3), LDC,DZ, A(II,PAR2),
     *                  A(II,PAR3), LDA)
   40    CONTINUE
C
         IF (WITHU) THEN
C
C           Update U.
C
            DO 60 JJ = 1, N
               CALL F06FUF(NJ, C(PAR1,PAR3), LDC, DZ, U(PAR2, JJ),
     *                     U(PAR3,JJ), 1)
   60       CONTINUE
         END IF
         IF (J .NE. P) THEN
C
C           Update C.
C
            DO 80 JJ = PAR3, PAR4
               CALL F06FUF(NJ, C(PAR1,PAR3), LDC, DZ, C(JJ,PAR2),
     *                     C(JJ,PAR3), LDC)
   80       CONTINUE
         END IF
         DO 100 II = PAR3, PAR5
            C(PAR1,II) = 0.0D0
  100    CONTINUE
  120 CONTINUE
      IF (P1 .LE. N1) THEN
         DO 240 J = P1, N1
C
C           Perform next transformations only involving A.
C
            NJ = N - J
            IF (UPPER) THEN
               PAR1 = N + P1 - J
               PAR2 = NJ + 1
               PAR3 = 1
               PAR4 = NJ
               PAR5 = 1
               PAR6 = N + P - J
            ELSE
               PAR1 = J - P
               PAR2 = J
               PAR3 = J + 1
               PAR4 = N
               PAR5 = J - P + 1
               PAR6 = N
            END IF
            IF (NJ .GT. 0) THEN
               CALL F06FSF(NJ, A(PAR1,PAR2), A(PAR1,PAR3), LDA, TL, DZ)
C
C              Update A.
C
               DO 160 JJ = 1, N
                  CALL F06FUF(NJ, A(PAR1,PAR3), LDA, DZ, A(PAR2,JJ),
     *                        A(PAR3,JJ), 1)
  160          CONTINUE
               DO 180 II = PAR5, PAR6
                  CALL F06FUF(NJ, A(PAR1,PAR3), LDA, DZ, A(II,PAR2),
     *                        A(II,PAR3), LDA)
  180          CONTINUE
C
               IF (WITHU) THEN
C
C                 Update U.
C
                  DO 200 JJ = 1, N
                     CALL F06FUF(NJ, A(PAR1,PAR3), LDA, DZ, U(PAR2,JJ),
     *                           U(PAR3,JJ), 1)
  200             CONTINUE
               END IF
               DO 220 II = PAR3, PAR4
                  A(PAR1,II) = 0.0D0
  220          CONTINUE
            END IF
  240    CONTINUE
      END IF
      RETURN
C
C *** Last line of the OBHESS subroutine ******************************
C
      END
      SUBROUTINE COHESS(A, LDA, N, B, LDB, M, U, LDU, WITHU, UPPER)
C
C     PURPOSE:
C
C     COHESS computes a unitary state space transformation U reducing
C     the pair (A,B) to upper or lower controller Hessenberg form.
C
C     CONTRIBUTORS:
C
C     M. Vanbegin, P. Van Dooren (PRLB)
C     M. Verhaegen (NASA Ames)
C
C     REVISIONS:
C
C     1988, Sept. 9.
C
C     Specification of parameters.
C
C     .. Scalar Arguments ..
C
      INTEGER LDA, N, LDB, M, LDU
      LOGICAL WITHU, UPPER
C
C     .. Array Arguments ..
C
      DOUBLE PRECISION A(LDA,*), B(LDB,*), U(LDU,*)
C
C     EXTERNAL ROUTINES:
C
C     F06FSF, F06FUF from NAG-BLAS,
C
C     Local variables.
C
      INTEGER M1, N1, NJ, JJ, II, J, PAR1, PAR2, PAR3, PAR4,
     *        PAR5, PAR6
      DOUBLE PRECISION TL, DZ
C
      TL = 0.0D0
      M1 = M + 1
      N1 = N - 1
C
C     Perform transformations involving both B and A.
C
      DO 120 J = 1, MIN(M,N1)
         NJ = N - J
         IF (UPPER) THEN
            PAR1 = J
            PAR2 = J
            PAR3 = J + 1
            PAR4 = M
            PAR5 = N
         ELSE
            PAR1 = M - J + 1
            PAR2 = NJ + 1
            PAR3 = 1
            PAR4 = M - J
            PAR5 = NJ
         END IF
         CALL F06FSF(NJ, B(PAR2,PAR1), B(PAR3,PAR1), 1, TL, DZ)
C
C        Update A
C
         DO 20 JJ = 1, N
            CALL F06FUF(NJ, B(PAR3,PAR1), 1, DZ, A(PAR2,JJ),
     *                  A(PAR3,JJ), 1)
   20    CONTINUE
         DO 40 II = 1, N
            CALL F06FUF(NJ, B(PAR3,PAR1), 1, DZ, A(II,PAR2),
     *                  A(II,PAR3), LDA)
   40    CONTINUE
         IF (WITHU) THEN
C
C           Update U
C
            DO 60 JJ = 1, N
               CALL F06FUF(NJ, B(PAR3,PAR1), 1, DZ, U(PAR2,JJ),
     *                  U(PAR3,JJ), 1)
   60       CONTINUE
         END IF
         IF (J .NE. M) THEN
C
C           Update B
C
            DO 80 JJ = PAR3, PAR4
               CALL F06FUF(NJ, B(PAR3,PAR1), 1, DZ, B(PAR2,JJ),
     *                     B(PAR3,JJ), 1)
   80       CONTINUE
         END IF
         DO 100 II = PAR3, PAR5
            B(II,PAR1) = 0.0D0
  100    CONTINUE
  120 CONTINUE
      IF (M1 .LE. N1) THEN
         DO 240 J = M1, N1
C
C           Perform next transformations only involving A.
C
            NJ = N - J
            IF (UPPER) THEN
               PAR1 = J - M
               PAR2 = J
               PAR3 = J + 1
               PAR4 = N
               PAR5 = J - M + 1
               PAR6 = N
            ELSE
               PAR1 = N + M1 - J
               PAR2 = NJ + 1
               PAR3 = 1
               PAR4 = NJ
               PAR5 = 1
               PAR6 = N + M - J
            END IF
            CALL F06FSF(NJ, A(PAR2,PAR1), A(PAR3,PAR1), 1, TL, DZ)
C
C           Update A
C
            DO 160 JJ = PAR5, PAR6
               CALL F06FUF(NJ, A(PAR3,PAR1), 1, DZ, A(PAR2,JJ),
     *                     A(PAR3,JJ), 1)
  160       CONTINUE
            DO 180 II = 1, N
               CALL F06FUF(NJ, A(PAR3,PAR1), 1, DZ, A(II,PAR2),
     *                     A(II,PAR3), LDA)
  180       CONTINUE
            IF (WITHU) THEN
C
C              Update U
C
               DO 200 JJ = 1, N
                  CALL F06FUF(NJ, A(PAR3,PAR1), 1, DZ, U(PAR2,JJ),
     *                        U(PAR3,JJ), 1)
  200          CONTINUE
            END IF
            DO 220 II = PAR3, PAR4
               A(II,PAR1) = 0.0D0
  220       CONTINUE
  240    CONTINUE
      END IF
      RETURN
C
C *** Last line of the COHESS subroutine ******************************
C
      END
      SUBROUTINE SRCFOB(S, LDS, A, LDA, B, LDB, Q, LDQ, C, LDC, R, LDR,
     *                 N, M, P, K, LDK, WRK, LDW, MULTBQ, WITHK, TOL)
C
C     PURPOSE:
C
C     The algorithm calculates a combined measurement and time update
C     of one iteration of the time-invariant Kalman filter. This update
C     is given for the square root covariance filter, using the
C     condensed observer-Hessenberg form.
C
C     CONTRIBUTORS:
C
C     M. Vanbegin, P. Van Dooren (PRLB)
C     M. Verhaegen (NASA Ames)
C
C     REVISIONS:
C
C     1988, Sept. 9.
C
C     Specification of parameters.
C
C     .. Scalar arguments ..
C
      INTEGER LDS, LDA, LDB, LDQ, LDC, LDR, N, M, P, LDK, LDW
      DOUBLE PRECISION TOL
      LOGICAL MULTBQ, WITHK
C
C     .. Array Arguments ..
C
      DOUBLE PRECISION S(LDS,*), A(LDA,*), B(LDB,*), Q(LDQ,*), C(LDC,*),
     *                 R(LDR,*), K(LDK,*), WRK(LDW,*)
C
C     EXTERNAL SUBROUTINES:
C
C     DTRCO from LINPACK
C     DGEMV, DTRSV from Extended-BLAS,
C     F06FBF, F06FSF, F06FUF from NAG-BLAS,
C     DAXPY, DCOPY from BLAS.
C
C     Local variables.
C
      INTEGER I, I1, IN, IND, IPM, J, MINPN, MINMP, P1, PM1, PNM, PN,
     *        PI, PI1, PJ, NAXPY
      DOUBLE PRECISION DZ1, RCOND
C
C     Construction of the pre-array WRK.
C
      MINPN = MIN(P,N)
      P1 = P + 1
      PM1 = P1 + M
      PN = P + N
      PNM = PN + M
      DO 20 J = 1, PNM
         CALL F06FBF(PN, 0.0D+0, WRK(1,J), 1)
   20 CONTINUE
C
C     First part -  Storing lower triangular factor R in the (1,1) block
C                   of WRK.
C
      DO 40 I = 1, P
         CALL DCOPY(P-I+1, R(I,I), 1, WRK(I,I), 1)
   40 CONTINUE
C
C     Second part - Storing B x Q in the (2,2) block of WRK.
C
      IF (MULTBQ) THEN
         DO 60 I = 1, M
            CALL DCOPY(N, B(1,I), 1, WRK(P1,P+I), 1)
   60    CONTINUE
      ELSE
         DO 80 I = 1, M
            CALL DGEMV('N', N, M-I+1, 1.0D0, B(1,I), LDB, Q(I,I), 1,
     *                 0.0D0, WRK(P1,P+I), 1)
   80    CONTINUE
      END IF
C
C     Third part -  Storing C x S in the (1,3) block of WRK.
C
      DO 120 I = 1, MINPN
         IPM = I + P + M
         NAXPY = P - I + 1
         DO 100 J = I, MINPN
            CALL DAXPY(NAXPY, S(J,I), C(J,J), 1, WRK(J,IPM), 1)
            NAXPY = NAXPY - 1
  100    CONTINUE
  120 CONTINUE
C
C     Fourth part  -  Storing A x S in the (2,3) block of WRK.
C
      DO 160 I = 1, N
         IPM = I + P + M
         NAXPY = N
         IND = 1
         DO 140 J = I, N
            IF (J .GT. P1) THEN
               IND = IND + 1
               NAXPY = NAXPY - 1
            END IF
            CALL DAXPY(NAXPY, S(J,I), A(IND,J), 1, WRK(IND+P,IPM), 1)
  140    CONTINUE
  160 CONTINUE
C
C     Triangularization (2 steps).
C
C     Step 1: eliminate the (1,3) block WRK.
C
      DO 200 I = 1, P
         IN = MIN(I,N)
         CALL F06FSF(IN, WRK(I,I), WRK(I,PM1), LDW, TOL, DZ1)
         I1 = I + 1
         DO 180 J = I1, PN
            CALL F06FUF(IN, WRK(I,PM1), LDW, DZ1, WRK(J,I), WRK(J,PM1),
     *                  LDW)
  180    CONTINUE
         CALL DTRCO(WRK, LDW, P, RCOND, WRK(1,PNM), 0)
         IF (RCOND .LT. TOL) WITHK = .FALSE.
  200 CONTINUE
C
C     Step 2: triangularize the remaining (2,2) and (2,3) blocks of WRK.
C
      DO 240 I = 1, N
         MINMP = MIN(M+P,M+N-I)
         PI = P + I
         PI1 = PI + 1
         CALL F06FSF(MINMP, WRK(PI,PI), WRK(PI,PI1), LDW, TOL, DZ1)
         IF (PI1 .LE. PN) THEN
            DO 220 J = PI1, PN
               CALL F06FUF(MINMP, WRK(PI,PI1), LDW, DZ1, WRK(J,PI),
     *                     WRK(J,PI1), LDW)
  220       CONTINUE
         END IF
  240 CONTINUE
C
C     Output K and S.
C
      IF (WITHK) THEN
         DO 260 J = 1, N
            CALL DCOPY(P, WRK(P+J,1), LDW, K(J,1), LDK)
            CALL DTRSV('L', 'T', 'N', P, WRK, LDW, K(J,1), LDK)
  260    CONTINUE
      END IF
      DO 280 J = 1, N
         PJ = P + J
         CALL DCOPY(N-J+1, WRK(PJ,PJ), 1, S(J,J), 1)
  280 CONTINUE
      RETURN
C
C *** Last line of the SRCFOB subroutine ******************************
C
      END
      SUBROUTINE SRIFCO(T, LDT, AINV, LDA, AINVB, LDB, RINV, LDR, C,
     *                  LDC, QINV, LDQ, X, RINVY, W, N, M, P, WRK,
     *                  LDW, MULTRC, WITHX, TOL)
C
C     PURPOSE:
C
C     The algorithm calculates a combined measurement and time update
C     of one iteration of the time-invariant Kalman filter. This update
C     is given for the square root information filter, using the
C     condensed controller-Hessenberg form.
C
C     CONTRIBUTORS:
C
C     M. Vanbegin, P. Van Dooren (PRLB)
C     M. Verhaegen (NASA Ames)
C
C     REVISIONS:
C
C     1988, Sept. 9.
C
C     Specification of parameters.
C
C     .. Scalar Arguments ..
C
      INTEGER LDT, LDA, LDB, LDR, LDC, LDQ, N, M, P, LDW
      DOUBLE PRECISION TOL
      LOGICAL MULTRC,WITHX
C
C     .. Array Arguments ..
C
      DOUBLE PRECISION T(LDT,*), AINV(LDA,*), AINVB(LDB,*),
     *                 RINV(LDR,*), C(LDC,*), QINV(LDQ,*), X(*),
     *                 RINVY(*), W(*), WRK(LDW,*)
C
C     EXTERNAL SUBROUTINES:
C
C     DTRCO from LINPACK
C     DTRMV, DTRSV from Extended-BLAS,
C     F06FBF, F06FSF, F06FUF from NAG-BLAS,
C     DAXPY, DCOPY from BLAS.
C
C     Local variables.
C
      INTEGER I, I1, IN, J, MI, MI1, MINMP, MN1, MP1, MNP
      DOUBLE PRECISION DZ1, RCOND
C
C     Construction of the pre-array WRK.
C
      MN1 = M + N + 1
      MP1 = M + P + 1
      MNP = M + N + P
      DO 20 J = 1, MN1
         CALL F06FBF(MNP, 0.0D+0, WRK(1,J), 1)
   20 CONTINUE
C
C     First part - Storing QINV in the (1,1) block of WRK.
C
      DO 40 J = 1, M
         CALL DCOPY(J, QINV(1,J), 1, WRK(1,J), 1)
   40 CONTINUE
C
C     Second part - Storing the process noise mean value
C                   in the (1,3) block of WRK.
C
      CALL DCOPY(M, W, 1, WRK(1,M+N+1), 1)
      CALL DTRMV('U', 'N', 'N', M, QINV, LDQ, WRK(1,M+N+1), 1)
C
C     Third part - Storing RINV x C in the (2,2) block of WRK.
C
      IF (MULTRC) THEN
         DO 80 J = 1, N
            CALL DCOPY(P, C(1,J), 1, WRK(M+1,M+J), 1)
   80    CONTINUE
      ELSE
         DO 100 I = 1, N
            CALL DCOPY(P, C(1,I), 1, WRK(M+1,M+I), 1)
            CALL DTRMV('U', 'N', 'N', P, RINV, LDR, WRK(M+1,M+I), 1)
  100    CONTINUE
      END IF
C
C     Fourth part - Storing the measurement in the (2,3) block of WRK.
C
      CALL DCOPY(P, RINVY, 1, WRK(M+1,M+N+1), 1)
C
C     Fifth part - Storing T x A and T x A x B in the (3,1) and
C                  (3,2) blocks of WRK.
*
      DO 140 I = 1, M
         DO 120 J = 1, MIN(I,N)
            CALL DAXPY(J, AINVB(J,I), T(1,J), 1, WRK(MP1,I), 1)
  120    CONTINUE
  140 CONTINUE
      DO 180 I = 1, N
         DO 160 J = 1, MIN(M+I,N)
            CALL DAXPY(J, AINV(J,I), T(1,J), 1, WRK(MP1,M+I), 1)
  160    CONTINUE
  180 CONTINUE
C
C     Sixth part - Storing T x X in the (3,3) block of WRK.
C
      CALL DCOPY(N, X, 1, WRK(MP1,M+N+1), 1)
      CALL DTRMV('U', 'N', 'N', N, T, LDT, WRK(MP1,M+N+1), 1)
C
C     Triangularization (2 steps).
C
C     Step 1: eliminate the (3,1) block  of WRK.
C
      DO 240 I = 1, M
         I1 = I + 1
         IN = MIN(I,N)
         CALL F06FSF(IN, WRK(I,I), WRK(MP1,I), 1, TOL, DZ1)
         DO 220 J = I1, MN1
            CALL F06FUF(IN, WRK(MP1,I), 1, DZ1, WRK(I,J), WRK(MP1,J), 1)
  220    CONTINUE
  240 CONTINUE
C
C     Step 2: triangularize the remaining (2,2) and (3,2) blocks of WRK.
C
      DO 280 I = 1, N
         MINMP = MIN(M+P,P+N-I)
         MI = M + I
         MI1 = MI + 1
         CALL F06FSF(MINMP, WRK(MI,MI), WRK(MI1,MI), 1, TOL, DZ1)
         DO 260 J = MI1, MN1
            CALL F06FUF(MINMP, WRK(MI1,MI), 1, DZ1, WRK(MI,J),
     *                WRK(MI1,J), 1)
  260    CONTINUE
         CALL DTRCO(WRK(M+1,M+1), LDW, N, RCOND, WRK(M+1,1), 1)
         IF (RCOND .LT. TOL) WITHX = .FALSE.
  280 CONTINUE
C
C     Output T and X.
C
      DO 300 J = 1, N
         CALL DCOPY(J, WRK(M+1,M+J), 1, T(1,J), 1)
  300 CONTINUE
C
      IF (WITHX) THEN
         CALL DCOPY(N, WRK(M+1,M+N+1), 1, X, 1)
         CALL DTRSV('U', 'N', 'N', N, T, LDT, X, 1)
      END IF
C
      RETURN
C
C *** Last line of the SRIFCO subroutine ******************************
C
      END
************************************************************************
*
      SUBROUTINE F06PAF( TRANS, M, N, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Entry Points ..
      ENTRY      DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, BETA
      INTEGER            INCX, INCY, LDA, M, N
      CHARACTER*1        TRANS
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  F06PAF performs one of the matrix-vector operations
*
*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,
*
*  where alpha and beta are scalars, x and y are vectors and A is an
*  m by n matrix.
*
*  Parameters
*  ==========
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
*
*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
*
*              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y
*.
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry, the leading m by n part of the array A must
*           contain the matrix of coefficients.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the leading dimension of A as
*           declared in the calling (sub) program. LDA must be at least
*           m.
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X.
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*           Before entry with BETA non-zero, the incremented array Y
*           must contain the vector y. On exit, Y is overwritten by the
*           updated vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y.
*           Unchanged on exit.
*
*
*  Note that TRANS, M, N and LDA must be such that the value of the
*  LOGICAL variable OK in the following statement is true.
*
*     OK = ( ( TRANS.EQ.'N' ).OR.( TRANS.EQ.'n' ).OR.
*    $       ( TRANS.EQ.'T' ).OR.( TRANS.EQ.'t' ).OR.
*    $       ( TRANS.EQ.'C' ).OR.( TRANS.EQ.'c' )     )
*    $     .AND.
*    $     ( M.GE.0 )
*    $     .AND.
*    $     ( N.GE.0 )
*    $     .AND.
*    $     ( LDA.GE.M )
*
*
*
*  Level 2 Blas routine.
*
*  -- Written on 30-August-1985.
*     Sven Hammarling, Nag Central Office.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   TEMP
      INTEGER            I, IX, IY, J, JX, JY, KX, KY, LENX, LENY
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.
     $    ( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set LENX and LENY, the lengths of the vectors x and y.
*
      IF( ( TRANS.EQ.'N' ).OR.( TRANS.EQ.'n' ) )THEN
         LENX = N
         LENY = M
      ELSE
         LENX = M
         LENY = N
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
*     First form  y := beta*y  and set up the start points in X and Y if
*     the increments are not both unity.
*
      IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
         IF( BETA.NE.ONE )THEN
            IF( BETA.EQ.ZERO )THEN
               DO 10, I = 1, LENY
                  Y( I ) = ZERO
   10          CONTINUE
            ELSE
               DO 20, I = 1, LENY
                  Y( I ) = BETA*Y( I )
   20          CONTINUE
            END IF
         END IF
      ELSE
         IF( INCX.GT.0 )THEN
            KX = 1
         ELSE
            KX = 1 - ( LENX - 1 )*INCX
         END IF
         IF( INCY.GT.0 )THEN
            KY = 1
         ELSE
            KY = 1 - ( LENY - 1 )*INCY
         END IF
         IF( BETA.NE.ONE )THEN
            IY = KY
            IF( BETA.EQ.ZERO )THEN
               DO 30, I = 1, LENY
                  Y( IY ) = ZERO
                  IY      = IY   + INCY
   30          CONTINUE
            ELSE
               DO 40, I = 1, LENY
                  Y( IY ) = BETA*Y( IY )
                  IY      = IY           + INCY
   40          CONTINUE
            END IF
         END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      IF( ( TRANS.EQ.'N' ).OR.( TRANS.EQ.'n' ) )THEN
*
*        Form  y := alpha*A*x + y.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 60, J = 1, N
               IF( X( J ).NE.ZERO )THEN
                  TEMP = ALPHA*X( J )
                  DO 50, I = 1, M
                     Y( I ) = Y( I ) + TEMP*A( I, J )
   50             CONTINUE
               END IF
   60       CONTINUE
         ELSE
            JX = KX
            DO 80, J = 1, N
               IF( X( JX ).NE.ZERO )THEN
                  TEMP = ALPHA*X( JX )
                  IY   = KY
                  DO 70, I = 1, M
                     Y( IY ) = Y( IY ) + TEMP*A( I, J )
                     IY      = IY      + INCY
   70             CONTINUE
               END IF
               JX = JX + INCX
   80       CONTINUE
         END IF
      ELSE
*
*        Form  y := alpha*A'*x + y.
*
         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
            DO 100, J = 1, N
               TEMP = ZERO
               DO 90, I = 1, M
                  TEMP = TEMP + A( I, J )*X( I )
   90          CONTINUE
               Y( J ) = Y( J ) + ALPHA*TEMP
  100       CONTINUE
         ELSE
            JY = KY
            DO 120, J = 1, N
               TEMP = ZERO
               IX   = KX
               DO 110, I = 1, M
                  TEMP = TEMP + A( I, J )*X( IX )
                  IX   = IX   + INCX
  110          CONTINUE
               Y( JY ) = Y( JY ) + ALPHA*TEMP
               JY      = JY      + INCY
  120       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of F06PAF. ( DGEMV )
*
      END
*
************************************************************************
*
      SUBROUTINE F06PFF( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*     .. Entry Points ..
      ENTRY      DTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  F06PFF performs one of the matrix-vector operations
*
*     x := A*x,   or   x := A'*x,
*
*  where x is n element vector and A is an n by n unit, or non-unit,
*  upper or lower triangular matrix.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   x := A*x.
*
*              TRANS = 'T' or 't'   x := A'*x.
*
*              TRANS = 'C' or 'c'   x := A'*x.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular matrix and the strictly lower triangular part of
*           A is not referenced.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular matrix and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
*           A are not referenced either, but are assumed to be unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least n.
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x. On exit, X is overwritten with the
*           tranformed vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X.
*           Unchanged on exit.
*
*
*  Note that UPLO, TRANS, DIAG, N and LDA must be such that the value of
*  the LOGICAL variable OK in the following statement is true.
*
*     OK = ( ( UPLO.EQ.'U' ).OR.( UPLO.EQ.'u' ).OR.
*    $       ( UPLO.EQ.'L' ).OR.( UPLO.EQ.'l' )     )
*    $     .AND.
*    $     ( ( TRANS.EQ.'N' ).OR.( TRANS.EQ.'n' ).OR.
*    $       ( TRANS.EQ.'T' ).OR.( TRANS.EQ.'t' ).OR.
*    $       ( TRANS.EQ.'C' ).OR.( TRANS.EQ.'c' )     )
*    $     .AND.
*    $     ( ( DIAG.EQ.'U' ).OR.( DIAG.EQ.'u' ).OR.
*    $       ( DIAG.EQ.'N' ).OR.( DIAG.EQ.'n' )     )
*    $     .AND.
*    $     ( N.GE.0 )
*    $     .AND.
*    $     ( LDA.GE.N )
*
*
*
*  Level 2 Blas routine.
*
*  -- Written on 30-September-1985.
*     Sven Hammarling, Nag Central Office.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER        ( ZERO = 0.0D+0 )
*     .. Local Scalars ..
      INTEGER            I, IX, J, JX, KX
      LOGICAL            NOUNIT
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
      NOUNIT = ( DIAG.EQ.'N' ).OR.( DIAG.EQ.'n' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
      IF( ( TRANS.EQ.'N' ).OR.( TRANS.EQ.'n' ) )THEN
*
*        Form  x := A*x.
*
         IF( ( UPLO.EQ.'U' ).OR.( UPLO.EQ.'u' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 20, J = 1, N
                  IF( X( J ).NE.ZERO )THEN
                     DO 10, I = 1, J - 1
                        X( I ) = X( I ) + X( J )*A( I, J )
   10                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*A( J, J )
                  END IF
   20          CONTINUE
            ELSE
               JX = KX
               DO 40, J = 1, N
                  IF( X( JX ).NE.ZERO )THEN
                     IX = KX
                     DO 30, I = 1, J - 1
                        X( IX ) = X( IX ) + X( JX )*A( I, J )
                        IX      = IX      + INCX
   30                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*A( J, J )
                  END IF
                  JX = JX + INCX
   40          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 60, J = N, 1, -1
                  IF( X( J ).NE.ZERO )THEN
                     DO 50, I = N, J + 1, -1
                        X( I ) = X( I ) + X( J )*A( I, J )
   50                CONTINUE
                     IF( NOUNIT )
     $                  X( J ) = X( J )*A( J, J )
                  END IF
   60          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 80, J = N, 1, -1
                  IF( X( JX ).NE.ZERO )THEN
                     IX  = KX
                     DO 70, I = N, J + 1, -1
                        X( IX ) = X( IX ) + X( JX )*A( I, J )
                        IX      = IX      - INCX
   70                CONTINUE
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )*A( J, J )
                  END IF
                  JX = JX - INCX
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := A'*x.
*
         IF( ( UPLO.EQ.'U' ).OR.( UPLO.EQ.'u' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 100, J = N, 1, -1
                  IF( NOUNIT )
     $               X( J ) = X( J )*A( J, J )
                  DO 90, I = J - 1, 1, -1
                     X( J ) = X( J ) + A( I, J )*X( I )
   90             CONTINUE
  100          CONTINUE
            ELSE
               JX = KX + ( N - 1 )*INCX
               DO 120, J = N, 1, -1
                  IX = JX
                  IF( NOUNIT )
     $               X( JX ) = X( JX )*A( J, J )
                  DO 110, I = J - 1, 1, -1
                     IX      = IX      - INCX
                     X( JX ) = X( JX ) + A( I, J )*X( IX )
  110             CONTINUE
                  JX = JX - INCX
  120          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 140, J = 1, N
                  IF( NOUNIT )
     $               X( J ) = X( J )*A( J, J )
                  DO 130, I = J + 1, N
                     X( J ) = X( J ) + A( I, J )*X( I )
  130             CONTINUE
  140          CONTINUE
            ELSE
               JX = KX
               DO 160, J = 1, N
                  IX = JX
                  IF( NOUNIT )
     $               X( JX ) = X( JX )*A( J, J )
                  DO 150, I = J + 1, N
                     IX      = IX      + INCX
                     X( JX ) = X( JX ) + A( I, J )*X( IX )
  150             CONTINUE
                  JX = JX + INCX
  160          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of F06PFF. ( DTRMV )
*
      END
*
************************************************************************
*
      SUBROUTINE F06PJF( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*     .. Entry Points ..
      ENTRY      DTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*     .. Scalar Arguments ..
      INTEGER            INCX, LDA, N
      CHARACTER*1        DIAG, TRANS, UPLO
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * )
*     ..
*
*  Purpose
*  =======
*
*  F06PJF solves one of the systems of equations
*
*     A*x = b,   or   A'*x = b,
*
*  where b and x are n element vectors and A is an n by n unit, or
*  non-unit, upper or lower triangular matrix.
*
*  No test for singularity or near-singularity is included in this
*  routine. Such tests must be performed before calling this routine.
*
*  Parameters
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the matrix is an upper or
*           lower triangular matrix as follows:
*
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
*
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
*
*           Unchanged on exit.
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the equations to be solved as
*           follows:
*
*              TRANS = 'N' or 'n'   A*x = b.
*
*              TRANS = 'T' or 't'   A'*x = b.
*
*              TRANS = 'C' or 'c'   A'*x = b.
*
*           Unchanged on exit.
*
*  DIAG   - CHARACTER*1.
*           On entry, DIAG specifies whether or not A is unit
*           triangular as follows:
*
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
*
*              DIAG = 'N' or 'n'   A is not assumed to be unit
*                                  triangular.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
*           upper triangular part of the array A must contain the upper
*           triangular matrix and the strictly lower triangular part of
*           A is not referenced.
*           Before entry with UPLO = 'L' or 'l', the leading n by n
*           lower triangular part of the array A must contain the lower
*           triangular matrix and the strictly upper triangular part of
*           A is not referenced.
*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
*           A are not referenced either, but are assumed to be unity.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least n.
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element right-hand side vector b. On exit, X is overwritten
*           with the solution vector x.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X.
*           Unchanged on exit.
*
*
*  Note that UPLO, TRANS, DIAG, N and LDA must be such that the value of
*  the LOGICAL variable OK in the following statement is true.
*
*     OK = ( ( UPLO.EQ.'U' ).OR.( UPLO.EQ.'u' ).OR.
*    $       ( UPLO.EQ.'L' ).OR.( UPLO.EQ.'l' )     )
*    $     .AND.
*    $     ( ( TRANS.EQ.'N' ).OR.( TRANS.EQ.'n' ).OR.
*    $       ( TRANS.EQ.'T' ).OR.( TRANS.EQ.'t' ).OR.
*    $       ( TRANS.EQ.'C' ).OR.( TRANS.EQ.'c' )     )
*    $     .AND.
*    $     ( ( DIAG.EQ.'U' ).OR.( DIAG.EQ.'u' ).OR.
*    $       ( DIAG.EQ.'N' ).OR.( DIAG.EQ.'n' )     )
*    $     .AND.
*    $     ( N.GE.0 )
*    $     .AND.
*    $     ( LDA.GE.N )
*
*
*
*  Level 2 Blas routine.
*
*  -- Written on 30-September-1985.
*     Sven Hammarling, Nag Central Office.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER        ( ZERO = 0.0D+0 )
*     .. Local Scalars ..
      INTEGER            I, IX, J, JX, KX
      LOGICAL            NOUNIT
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible.
*
      IF( N.EQ.0 )
     $   RETURN
      NOUNIT = ( DIAG.EQ.'N' ).OR.( DIAG.EQ.'n' )
*
*     Set up the start point in X if the increment is not unity. This
*     will be  ( N - 1 )*INCX  too small for descending loops.
*
      IF( INCX.LE.0 )THEN
         KX = 1 - ( N - 1 )*INCX
      ELSE IF( INCX.NE.1 )THEN
         KX = 1
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
      IF( ( TRANS.EQ.'N' ).OR.( TRANS.EQ.'n' ) )THEN
*
*        Form  x := inv( A )*x.
*
         IF( ( UPLO.EQ.'U' ).OR.( UPLO.EQ.'u' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 20, J = N, 1, -1
                  IF( X( J ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( J, J )
                     DO 10, I = J - 1, 1, -1
                        X( I ) = X( I ) - X( J )*A( I, J )
   10                CONTINUE
                  END IF
   20          CONTINUE
            ELSE
               JX = KX + ( N - 1 )*INCX
               DO 40, J = N, 1, -1
                  IF( X( JX ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( J, J )
                     IX = JX
                     DO 30, I = J - 1, 1, -1
                        IX      = IX      - INCX
                        X( IX ) = X( IX ) - X( JX )*A( I, J )
   30                CONTINUE
                  END IF
                  JX = JX - INCX
   40          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 60, J = 1, N
                  IF( X( J ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( J ) = X( J )/A( J, J )
                     DO 50, I = J + 1, N
                        X( I ) = X( I ) - X( J )*A( I, J )
   50                CONTINUE
                  END IF
   60          CONTINUE
            ELSE
               JX = KX
               DO 80, J = 1, N
                  IF( X( JX ).NE.ZERO )THEN
                     IF( NOUNIT )
     $                  X( JX ) = X( JX )/A( J, J )
                     IX = JX
                     DO 70, I = J + 1, N
                        IX      = IX      + INCX
                        X( IX ) = X( IX ) - X( JX )*A( I, J )
   70                CONTINUE
                  END IF
                  JX = JX + INCX
   80          CONTINUE
            END IF
         END IF
      ELSE
*
*        Form  x := inv( A' )*x.
*
         IF( ( UPLO.EQ.'U' ).OR.( UPLO.EQ.'u' ) )THEN
            IF( INCX.EQ.1 )THEN
               DO 100, J = 1, N
                  DO 90, I = 1, J - 1
                     X( J ) = X( J ) - A( I, J )*X( I )
   90             CONTINUE
                  IF( NOUNIT )
     $               X( J ) = X( J )/A( J, J )
  100          CONTINUE
            ELSE
               JX = KX
               DO 120, J = 1, N
                  IX = KX
                  DO 110, I = 1, J - 1
                     X( JX ) = X( JX ) - A( I, J )*X( IX )
                     IX      = IX      + INCX
  110             CONTINUE
                  IF( NOUNIT )
     $               X( JX ) = X( JX )/A( J, J )
                  JX = JX + INCX
  120          CONTINUE
            END IF
         ELSE
            IF( INCX.EQ.1 )THEN
               DO 140, J = N, 1, -1
                  DO 130, I = N, J + 1, -1
                     X( J ) = X( J ) - A( I, J )*X( I )
  130             CONTINUE
                  IF( NOUNIT )
     $               X( J ) = X( J )/A( J, J )
  140          CONTINUE
            ELSE
               KX = KX + ( N - 1 )*INCX
               JX = KX
               DO 160, J = N, 1, -1
                  IX = KX
                  DO 150, I = N, J + 1, -1
                     X( JX ) = X( JX ) - A( I, J )*X( IX )
                     IX      = IX      - INCX
  150             CONTINUE
                  IF( NOUNIT )
     $               X( JX ) = X( JX )/A( J, J )
                  JX = JX - INCX
  160          CONTINUE
            END IF
         END IF
      END IF
*
      RETURN
*
*     End of F06PJF. ( DTRSV )
*
      END
*
************************************************************************
*
      SUBROUTINE F06FBF( N, CONST, X, INCX )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   CONST
      INTEGER            INCX, N
*     .. Array Arguments ..
      DOUBLE PRECISION   X( * )
*     ..
*
*  F06FBF performs the operation
*
*     x = const*e,   e' = ( 1  1 ... 1 ).
*
*
*  Nag Fortran 77 O( n ) basic linear algebra routine.
*
*  -- Written on 22-September-1983.
*     Sven Hammarling, Nag Central Office.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER        ( ZERO = 0.0D+0 )
*     .. Local Scalars ..
      INTEGER            IX
*     ..
*     .. Executable Statements ..
      IF( N.GT.0 )THEN
         IF( CONST.NE.ZERO )THEN
            DO 10, IX = 1, 1 + ( N - 1 )*INCX, INCX
               X( IX ) = CONST
   10       CONTINUE
         ELSE
            DO 20, IX = 1, 1 + ( N - 1 )*INCX, INCX
               X( IX ) = ZERO
   20       CONTINUE
         END IF
      END IF
*
      RETURN
*
*     End of F06FBF. ( SLOAD )
*
      END
*
************************************************************************
*
      SUBROUTINE F06FUF( N, Z, INCZ, Z1, ALPHA, X, INCX )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, Z1
      INTEGER            INCX, INCZ, N
*     .. Array Arguments ..
      DOUBLE PRECISION   X( * ), Z( * )
*     ..
*
*  F06FUF performs a Householder reflection given by
*
*     ( alpha ) = P*( alpha ) ,
*     (   x   )     (   x   )
*
*  where the orthogonal matrix p is given in the form
*
*     P = I - ( 1/z( 1 ) )*z*z'.
*
*  z( 1 ) must be supplied in Z1 and the remaining n elements in Z.
*  If Z1 is zero then P is assumed to be the unit matrix and the
*  transformation is skipped, otherwise Z1 must be in the range
*  ( 1.0, 2.0 ). Z1 and Z will usually be supplied by routine F06FSF.
*
*
*  Nag Fortran 77 O( n ) basic linear algebra routine.
*
*  -- Written on 2-November-1982.
*     Sven Hammarling, Nag Central Office.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER        ( ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   BETA
*     .. External Functions ..
      DOUBLE PRECISION   DDOT
      EXTERNAL           DDOT
*     .. External Subroutines ..
      EXTERNAL           DAXPY
*     ..
*     .. Executable Statements ..
      IF( Z1.NE.ZERO )THEN
         BETA  = ALPHA*Z1 + DDOT( N, Z, INCZ, X, INCX )
         ALPHA = ALPHA    - BETA
         CALL DAXPY( N, -BETA/Z1, Z, INCZ, X, INCX )
      END IF
*
      RETURN
*
*     End of F06FUF. ( SREF )
*
      END
*
************************************************************************
*
      SUBROUTINE F06FSF( N, ALPHA, X, INCX, TOL, Z1 )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, TOL, Z1
      INTEGER            INCX, N
*     .. Array Arguments ..
      DOUBLE PRECISION   X( * )
*     ..
*
*  F06FSF generates details of a Householder reflection, P, such that
*
*     P*( alpha ) = ( beta ),   P'*P = I.
*       (   X   )   (   0  )
*
*  P is given in the form
*
*     P = I - ( 1/z( 1 ) )*z*z',
*
*  where z is an ( n + 1 ) element vector.
*
*  z( 1 ) is returned in Z1. If the elements of x are all zero, or if
*  the elements of x are all less than tol*abs( alpha ) in absolute
*  value, then Z1 is returned as zero and P can be taken to be the
*  unit matrix. Otherwise Z1 always lies in the range ( 1.0, 2.0 ).
*
*  If TOL is not in the range ( 0.0, 1.0 ) then the value 0.0 is used in
*  place of TOL.
*
*  The remaining elements of z are overwritten on X and beta is
*  overwritten on ALPHA.
*
*
*  Nag Fortran 77 O( n ) basic linear algebra routine.
*
*  -- Written on 2-November-1982.
*     Sven Hammarling, Nag Central Office.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   BETA, SCALE, SSQ, TL
*     .. Local Arrays ..
      DOUBLE PRECISION   WORK( 1 )
*     .. External Functions ..
      DOUBLE PRECISION   F06BMF
      EXTERNAL           F06BMF
*     .. External Subroutines ..
      EXTERNAL           F06FJF, DSCAL
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, SIGN
*     ..
*     .. Executable Statements ..
      IF( N.LT.1 )THEN
         Z1 = ZERO
      ELSE
         IF( ( TOL.LE.ZERO ).OR.( TOL.GT.ONE ) )THEN
            TL = ZERO
         ELSE
            TL = ABS( ALPHA )*TOL
         END IF
         SSQ   = ONE
         SCALE = ZERO
         CALL F06FJF( N, X, INCX, SCALE, SSQ )
         IF( ( SCALE.EQ.ZERO ).OR.( SCALE.LT.TL ) )THEN
            Z1 = ZERO
         ELSE
            IF( ALPHA.NE.ZERO )THEN
               WORK( 1 ) = ALPHA
               CALL F06FJF( 1, WORK( 1 ), 1, SCALE, SSQ )
               BETA = -SIGN( F06BMF( SCALE, SSQ ), ALPHA )
               Z1   =  ( BETA - ALPHA )/BETA
            ELSE
               BETA = -F06BMF( SCALE, SSQ )
               Z1   =  ONE
            END IF
            CALL DSCAL( N, -ONE/BETA, X, INCX )
            ALPHA = BETA
         END IF
      END IF
*
      RETURN
*
*     End of F06FSF. ( SREFG )
*
      END
*
************************************************************************
*
      SUBROUTINE F06FJF( N, X, INCX, SCALE, SUMSQ )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   SCALE, SUMSQ
      INTEGER            INCX, N
*     .. Array Arguments ..
      DOUBLE PRECISION   X( * )
*     ..
*
*  F06FJF returns the values scl and smsq such that
*
*     ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
*
*  where y( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is assumed
*  to be at least unity and the value of smsq will then satisfy
*
*     1.0 .le. smsq .le. ( sumsq + n ) .
*
*  scale is assumed to be non-negative and scl returns the value
*
*     scl = max( scale, abs( x( i ) ) ) .
*
*  scale and sumsq must be supplied in SCALE and SUMSQ respectively.
*  scl and smsq are overwritten on SCALE and SUMSQ respectively.
*
*  The routine makes only one pass through the vector X.
*
*
*  Nag Fortran 77 O( n ) basic linear algebra routine.
*
*  -- Written on 22-October-1982.
*     Sven Hammarling, Nag Central Office.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO
      PARAMETER        ( ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   ABSXI
      INTEGER            IX
*     .. Intrinsic Functions ..
      INTRINSIC          ABS
*     ..
*     .. Executable Statements ..
      IF( N.GT.0 )THEN
         DO 10, IX = 1, 1 + ( N - 1 )*INCX, INCX
            IF( X( IX ).NE.ZERO )THEN
               ABSXI = ABS( X( IX ) )
               IF( SCALE.LT.ABSXI )THEN
                  SUMSQ = 1     + SUMSQ*( SCALE/ABSXI )**2
                  SCALE = ABSXI
               ELSE
                  SUMSQ = SUMSQ +       ( ABSXI/SCALE )**2
               END IF
            END IF
   10    CONTINUE
      END IF
      RETURN
*
*     End of F06FJF. ( SSSQ )
*
      END
*
************************************************************************
*
      DOUBLE PRECISION FUNCTION F06BMF( SCALE, SSQ )
*     .. Scalar Arguments ..
      DOUBLE PRECISION                  SCALE, SSQ
*     ..
*
*  F06BMF returns the value norm given by
*
*     norm = scale*sqrt( ssq )
*
*  via the function name.
*
*
*  Nag Fortran 77 O( 1 ) basic linear algebra routine.
*
*  -- Written on 22-October-1982.
*     Sven Hammarling, Nag Central Office.
*     Modified by M. Vanbegin and P. Van Dooren, PRLB
*
*     .. Intrinsic Functions ..
      INTRINSIC             SQRT
*     ..
*     .. Executable Statements ..
*
      F06BMF = SCALE*SQRT( SSQ )
      RETURN
*
*     End of F06BMF. ( SNORM )
*
      END
*
************************************************************************
      SUBROUTINE PRMT(A, LDA, M, N, TEXT, KW, L)
C
C     LIBRARY INDEX:
C
C     1.4. General input/output routines.
C
C     PURPOSE:
C
C     This routine prints out the M by N matrix A row by row.
C     The elements of A are printed out with FORMAT(D15.7).
C     The routine first prints the contents of TEXT as a title
C     and next the elements of the matrix A in the following way.
C     - if N <= L, the M x L block is printed.
C     - if N = k L + p, k > 0, then k  M x L blocks of
C       consecutive columns of A are printed one after the other
C       followed by the M x p block of the p last columns of A.
C     Row numbers are printed on the left of each row and a column
C     number on top of each column.
C     If M <= 0 or N <= 0 or L <= 0 then the subroutine call is
C     an empty statement.
C     The routine uses 2 + (k + 1) x (m + 1) lines and 5 + c x 15
C     positions on each line where c is the actual number of columns,
C     (i.e., c = L or c = p).
C
C     CONTRIBUTOR:
C
C     H. Willemsen, Eindhoven University of Technology.
C
C     REVISIONS:
C
C     1987, November 23.
C
C     .. Scalar arguments ..
C
      INTEGER KW, L, M, LDA, N
      CHARACTER*8 TEXT
C
C     .. Array arguments ..
C
      DOUBLE PRECISION A(LDA,N)
C
C     Local variables:
C
      INTEGER I, J, J1, J2, JJ, N1
*
      WRITE (KW, FMT=999) TEXT, M, N
      IF (M.LE.0 .OR. N.LE.0 .OR. L.LE.0) RETURN
      IF (L.GE.9) L = 8
      N1 = (N - 1)/L
      J1 = 1
      J2 = L
      DO 20 J = 1, N1
         WRITE (KW, FMT=996) (JJ, JJ=J1,J2)
         DO 10 I = 1, M
            WRITE (KW, FMT=998) I, (A(I,JJ), JJ=J1,J2)
   10    CONTINUE
         WRITE (KW, FMT=997)
         J1 = J1 + L
         J2 = J2 + L
   20 CONTINUE
      WRITE (KW, FMT=996) (J, J=J1,N)
      DO 30 I = 1, M
         WRITE (KW, FMT=998) I, (A(I,JJ), JJ=J1,N)
   30 CONTINUE
      WRITE (KW, FMT=997)
*
  996 FORMAT (5X, 8(6X, I2, 7X))
  997 FORMAT (1H )
  998 FORMAT (X, I2, 2X, 8D15.7)
  999 FORMAT (1X, A8, 2H (, I2, 1HX, I2, 1H), /)
*
      RETURN
C *** Last line of PRMT *****************************************
      END
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OBHESS EXAMPLE PROGRAM DATA
    8T        1.0D-15
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COHESS EXAMPLE PROGRAM DATA
    8T        1.0D-15
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    7.227253080345690D-01
    0.100000000000000D+01
    0.000000000000000D+00
    0.000000000000000D+00
    0.000000000000000D+00
    0.100000000000000D+01
    0.000000000000000D+00
    0.000000000000000D+00
    0.000000000000000D+00
    0.100000000000000D+01
    6    2
    2.113248654641211D-01
    7.560438541695476D-01
    2.211346291005611D-04
    3.303270917385817D-01
    6.653811042197049D-01
    6.283917883411050D-01
    8.497452358715236D-01
    6.857310198247433D-01
    8.782164813019335D-01
    6.837403681129217D-02
    5.608486062847078D-01
    6.623569373041391D-01
    7.263506767340004D-01
    1.985143842175603D-01
    5.442573162727058D-01
    2.320747897028923D-01
    2.312237196601927D-01
    2.164632631465793D-01
    8.833887814544141D-01
    6.525134947150946D-01
    3.076090742833912D-01
    9.329616213217378D-01
    2.146007861010730D-01
    3.126419968903065D-01
    3.616361008025706D-01
    2.922266637906432D-01
    5.664248815737665D-01
    4.826471973210573D-01
    3.321718913502991D-01
    5.935094701126218D-01
    5.015341597609222D-01
    4.368587583303452D-01
    2.693124809302390D-01
    6.325744865462184D-01
    4.051954015158117D-01
    9.184707831591368D-01
    4.373343335464597D-02
    4.818508932366967D-01
    2.639556000940502D-01
    4.148103706538677D-01
    2.806498021818697D-01
    1.280058464035392D-01
    7.783128595910966D-01
    2.119030449539423D-01
    1.121354666538537D-01
    6.856895955279469D-01
    1.531216683797538D-01
    6.970850601792336D-01
   -8.805478919554635D-01
   -6.075186830105965D-01
    1.325720297292248D+00
    1.038692635378422D+00
    2.103992672620125D+00
   -8.531300887844145D-01
    5.207520803914895D-01
    1.168888377692620D+00
   -1.693905277102395D-01
   -2.305788643040025D-01
   -1.115920973086452D+00
    6.597088570821635D-01
    8.813347620889544D-02
    4.498763345181942D-01
    0.000000000000000D+00
    7.227253080345690D-01
    0.100000000000000D+01
    0.000000000000000D+00
    0.000000000000000D+00
    0.100000000000000D+01
    1.964506227523088D-03
    5.075221331790090D-01
    4.076042952947319D-01
    8.408046141266823D-01
    5.017265700735152D-01
    9.128780765458941D-01
    2.129064607433975D-01
    5.591450631618500D-01
    4.304965981282294D-01
    2.280548494309187D-02
    6    2
    2.113248654641211D-01
    7.560438541695476D-01
    2.211346291005611D-04
    3.303270917385817D-01
    6.653811042197049D-01
    6.283917883411050D-01
    8.497452358715236D-01
    6.857310198247433D-01
    8.782164813019335D-01
    6.837403681129217D-02
    5.608486062847078D-01
    6.623569373041391D-01
    7.263506767340004D-01
    1.985143842175603D-01
    5.442573162727058D-01
    2.320747897028923D-01
    2.312237196601927D-01
    2.164632631465793D-01
    8.833887814544141D-01
    6.525134947150946D-01
    3.076090742833912D-01
    9.329616213217378D-01
    2.146007861010730D-01
    3.126419968903065D-01
    3.616361008025706D-01
    2.922266637906432D-01
    5.664248815737665D-01
    4.826471973210573D-01
    3.321718913502991D-01
    5.935094701126218D-01
    5.015341597609222D-01
    4.368587583303452D-01
    2.693124809302390D-01
    6.325744865462184D-01
    4.051954015158117D-01
    9.184707831591368D-01
    4.373343335464597D-02
    4.818508932366967D-01
    2.639556000940502D-01
    4.148103706538677D-01
    2.806498021818697D-01
    1.280058464035392D-01
    7.783128595910966D-01
    2.119030449539423D-01
    1.121354666538537D-01
    6.856895955279469D-01
    1.531216683797538D-01
    6.970850601792336D-01
    8.415518426336355D-01
    4.062024755403405D-01
    4.094825475476685D-01
    8.784125801175835D-01
    1.138359685428445D-01
    1.998337740078575D-01
   -8.805478919554635D-01
   -6.075186830105965D-01
    1.325720297292248D+00
    1.038692635378422D+00
    2.103992672620125D+00
   -8.531300887844145D-01
    5.207520803914895D-01
    1.168888377692620D+00
   -1.693905277102395D-01
   -2.305788643040025D-01
   -1.115920973086452D+00
    6.597088570821635D-01
    8.813347620889544D-02
    4.498763345181942D-01
    0.000000000000000D+00
    7.227253080345690D-01
    0.100000000000000D+01
    0.000000000000000D+00
    0.000000000000000D+00
    0.000000000000000D+00
    0.100000000000000D+01
    0.000000000000000D+00
    0.000000000000000D+00
    0.000000000000000D+00
    0.100000000000000D+01
    1.964506227523088D-03
    5.075221331790090D-01
    2.129064607433975D-01
    4.076042952947319D-01
    8.408046141266823D-01
    5.017265700735152D-01
    9.128780765458941D-01
    2.129064607433975D-01
    5.591450631618500D-01
    4.304965981282294D-01
    2.280548494309187D-02
 *** First example : Square root covariance filter with dense
 *** A, B, C and lower triangular Q, R.
 
 
 *** Input SRCF
 
 
 *** N =  6 M =  2 P =   2
 A matrix ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.8497452D+00  0.7263507D+00  0.8833888D+00
  2    0.7560439D+00  0.6857310D+00  0.1985144D+00  0.6525135D+00
  3    0.2211346D-03  0.8782165D+00  0.5442573D+00  0.3076091D+00
  4    0.3303271D+00  0.6837404D-01  0.2320748D+00  0.9329616D+00
  5    0.6653811D+00  0.5608486D+00  0.2312237D+00  0.2146008D+00
  6    0.6283918D+00  0.6623569D+00  0.2164633D+00  0.3126420D+00
 
            5              6
  1    0.3616361D+00  0.5015342D+00
  2    0.2922267D+00  0.4368588D+00
  3    0.5664249D+00  0.2693125D+00
  4    0.4826472D+00  0.6325745D+00
  5    0.3321719D+00  0.4051954D+00
  6    0.5935095D+00  0.9184708D+00
 
 B matrix ( 6X 2)
 
            1              2
  1    0.4373343D-01  0.7783129D+00
  2    0.4818509D+00  0.2119030D+00
  3    0.2639556D+00  0.1121355D+00
  4    0.4148104D+00  0.6856896D+00
  5    0.2806498D+00  0.1531217D+00
  6    0.1280058D+00  0.6970851D+00
 
 S matrix ( 6X 6)
 
            1              2              3              4
  1    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 C matrix ( 2X 6)
 
            1              2              3              4
  1    0.5618661D+00  0.6853980D+00  0.5042213D+00  0.3873779D+00
  2    0.5896177D+00  0.8906225D+00  0.3493615D+00  0.9222899D+00
 
            5              6
  1    0.9488184D+00  0.3760119D+00
  2    0.3435337D+00  0.7340941D+00
 
 R matrix ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.0000000D+00
  2    0.4498763D+00  0.7227253D+00
 
 Q matrix ( 2X 2)
 
            1              2
  1    0.1000000D+01  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01
 
 
 
 *** Output SRCF for MULTBQ=.TRUE.
 
 
 *** ISTEP =  1
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.7795406D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.2386019D+00 -0.4692039D+00  0.0000000D+00  0.0000000D+00
  3   -0.1267672D+00 -0.2572489D+00 -0.7208110D-17  0.0000000D+00
  4   -0.7078812D+00 -0.3756888D+00 -0.6210064D-17 -0.3548608D-17
  5   -0.1686254D+00 -0.2716174D+00 -0.1347688D-16 -0.3339866D-17
  6   -0.7031685D+00 -0.8869670D-01 -0.5456637D-17  0.1299417D-16
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.5383138D-34  0.0000000D+00
  6    0.3014557D-33 -0.6029114D-33
 
 K matrix ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.6076835D+00  0.1859999D+00  0.9882016D-01  0.5518221D+00
  2    0.1859999D+00  0.2770832D+00  0.1509491D+00  0.3451765D+00
  3    0.9882016D-01  0.1509491D+00  0.8224692D-01  0.1863816D+00
  4    0.5518221D+00  0.3451765D+00  0.1863816D+00  0.6422379D+00
  5    0.1314503D+00  0.1676783D+00  0.9124946D-01  0.2214104D+00
  6    0.5481484D+00  0.2093942D+00  0.1119558D+00  0.5310821D+00
 
            5              6
  1    0.1314503D+00  0.5481484D+00
  2    0.1676783D+00  0.2093942D+00
  3    0.9124946D-01  0.1119558D+00
  4    0.2214104D+00  0.5310821D+00
  5    0.1022106D+00  0.1426636D+00
  6    0.1426636D+00  0.5023131D+00
 
 *** ISTEP =  2
 S matrix ( 6X 6)
 
            1              2              3              4
  1    0.7868764D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.2273402D+00 -0.5459259D+00  0.0000000D+00  0.0000000D+00
  3    0.1514945D+00 -0.9733132D-01 -0.3517791D+00  0.0000000D+00
  4    0.6892584D+00 -0.4908556D+00  0.1062363D+00  0.4678404D-01
  5    0.1596434D+00 -0.3431025D+00  0.4431593D-01 -0.1047820D-01
  6    0.6853944D+00 -0.2465013D+00  0.2493496D+00 -0.8488101D-03
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.3841753D-17  0.0000000D+00
  6   -0.4091042D-17  0.4623528D-17
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1219251D+01 -0.7073020D-01
  2    0.1020628D+01  0.3334420D-01
  3    0.8427590D+00 -0.1177335D+00
  4    0.9118190D+00  0.4698194D-01
  5    0.7423412D+00  0.2789512D-01
  6    0.1028336D+01  0.4279473D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.6191745D+00  0.1788886D+00  0.1192075D+00  0.5423612D+00
  2    0.1788886D+00  0.3497187D+00  0.8757649D-01  0.4246670D+00
  3    0.1192075D+00  0.8757649D-01  0.1561725D+00  0.1148228D+00
  4    0.5423612D+00  0.4246670D+00  0.1148228D+00  0.7294913D+00
  5    0.1256196D+00  0.2236019D+00  0.4199030D-01  0.2826671D+00
  6    0.5393206D+00  0.2903891D+00  0.4010983D-01  0.6198606D+00
 
            5              6
  1    0.1256196D+00  0.5393206D+00
  2    0.2236019D+00  0.2903891D+00
  3    0.4199030D-01  0.4010983D-01
  4    0.2826671D+00  0.6198606D+00
  5    0.1452790D+00  0.2050529D+00
  6    0.2050529D+00  0.5927042D+00
 
 *** ISTEP =  3
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.7875798D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.2282566D+00 -0.5463528D+00  0.0000000D+00  0.0000000D+00
  3   -0.1531191D+00 -0.9665556D-01  0.3602623D+00  0.0000000D+00
  4   -0.6918649D+00 -0.4911218D+00 -0.9211386D-01  0.8945543D-01
  5   -0.1588470D+00 -0.3430107D+00 -0.5139605D-01 -0.3067111D-01
  6   -0.6874011D+00 -0.2457059D+00 -0.2271285D+00  0.1066565D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1631460D-01  0.0000000D+00
  6   -0.4378999D-02 -0.7058028D-01
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1213994D+01 -0.6668582D-01
  2    0.1015168D+01  0.3575130D-01
  3    0.8426375D+00 -0.1085532D+00
  4    0.9028467D+00  0.5821063D-01
  5    0.7414864D+00  0.2391058D-01
  6    0.1024749D+01  0.5428391D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.6202819D+00  0.1797702D+00  0.1205935D+00  0.5448988D+00
  2    0.1797702D+00  0.3506024D+00  0.8775846D-01  0.4262485D+00
  3    0.1205935D+00  0.8775846D-01  0.1625767D+00  0.1202222D+00
  4    0.5448988D+00  0.4262485D+00  0.1202222D+00  0.7363649D+00
  5    0.1251047D+00  0.2236627D+00  0.3896033D-01  0.2803513D+00
  6    0.5413832D+00  0.2911459D+00  0.4717723D-01  0.6267229D+00
 
            5              6
  1    0.1251047D+00  0.5413832D+00
  2    0.2236627D+00  0.2911459D+00
  3    0.3896033D-01  0.4717723D-01
  4    0.2803513D+00  0.6267229D+00
  5    0.1467371D+00  0.2018021D+00
  6    0.2018021D+00  0.6008554D+00
 
 
 
 *** Output SRCF for MULTBQ=.FALSE.
 
 
 *** ISTEP =  1
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.7795406D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.2386019D+00 -0.4692039D+00  0.0000000D+00  0.0000000D+00
  3   -0.1267672D+00 -0.2572489D+00 -0.7208110D-17  0.0000000D+00
  4   -0.7078812D+00 -0.3756888D+00 -0.6210064D-17 -0.3548608D-17
  5   -0.1686254D+00 -0.2716174D+00 -0.1347688D-16 -0.3339866D-17
  6   -0.7031685D+00 -0.8869670D-01 -0.5456637D-17  0.1299417D-16
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.5383138D-34  0.0000000D+00
  6    0.3014557D-33 -0.6029114D-33
 
 K matrix ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.6076835D+00  0.1859999D+00  0.9882016D-01  0.5518221D+00
  2    0.1859999D+00  0.2770832D+00  0.1509491D+00  0.3451765D+00
  3    0.9882016D-01  0.1509491D+00  0.8224692D-01  0.1863816D+00
  4    0.5518221D+00  0.3451765D+00  0.1863816D+00  0.6422379D+00
  5    0.1314503D+00  0.1676783D+00  0.9124946D-01  0.2214104D+00
  6    0.5481484D+00  0.2093942D+00  0.1119558D+00  0.5310821D+00
 
            5              6
  1    0.1314503D+00  0.5481484D+00
  2    0.1676783D+00  0.2093942D+00
  3    0.9124946D-01  0.1119558D+00
  4    0.2214104D+00  0.5310821D+00
  5    0.1022106D+00  0.1426636D+00
  6    0.1426636D+00  0.5023131D+00
 
 *** ISTEP =  2
 S matrix ( 6X 6)
 
            1              2              3              4
  1    0.7868764D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.2273402D+00 -0.5459259D+00  0.0000000D+00  0.0000000D+00
  3    0.1514945D+00 -0.9733132D-01 -0.3517791D+00  0.0000000D+00
  4    0.6892584D+00 -0.4908556D+00  0.1062363D+00  0.4678404D-01
  5    0.1596434D+00 -0.3431025D+00  0.4431593D-01 -0.1047820D-01
  6    0.6853944D+00 -0.2465013D+00  0.2493496D+00 -0.8488101D-03
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.3841753D-17  0.0000000D+00
  6   -0.4091042D-17  0.4623528D-17
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1219251D+01 -0.7073020D-01
  2    0.1020628D+01  0.3334420D-01
  3    0.8427590D+00 -0.1177335D+00
  4    0.9118190D+00  0.4698194D-01
  5    0.7423412D+00  0.2789512D-01
  6    0.1028336D+01  0.4279473D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.6191745D+00  0.1788886D+00  0.1192075D+00  0.5423612D+00
  2    0.1788886D+00  0.3497187D+00  0.8757649D-01  0.4246670D+00
  3    0.1192075D+00  0.8757649D-01  0.1561725D+00  0.1148228D+00
  4    0.5423612D+00  0.4246670D+00  0.1148228D+00  0.7294913D+00
  5    0.1256196D+00  0.2236019D+00  0.4199030D-01  0.2826671D+00
  6    0.5393206D+00  0.2903891D+00  0.4010983D-01  0.6198606D+00
 
            5              6
  1    0.1256196D+00  0.5393206D+00
  2    0.2236019D+00  0.2903891D+00
  3    0.4199030D-01  0.4010983D-01
  4    0.2826671D+00  0.6198606D+00
  5    0.1452790D+00  0.2050529D+00
  6    0.2050529D+00  0.5927042D+00
 
 *** ISTEP =  3
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.7875798D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.2282566D+00 -0.5463528D+00  0.0000000D+00  0.0000000D+00
  3   -0.1531191D+00 -0.9665556D-01  0.3602623D+00  0.0000000D+00
  4   -0.6918649D+00 -0.4911218D+00 -0.9211386D-01  0.8945543D-01
  5   -0.1588470D+00 -0.3430107D+00 -0.5139605D-01 -0.3067111D-01
  6   -0.6874011D+00 -0.2457059D+00 -0.2271285D+00  0.1066565D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1631460D-01  0.0000000D+00
  6   -0.4378999D-02 -0.7058028D-01
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1213994D+01 -0.6668582D-01
  2    0.1015168D+01  0.3575130D-01
  3    0.8426375D+00 -0.1085532D+00
  4    0.9028467D+00  0.5821063D-01
  5    0.7414864D+00  0.2391058D-01
  6    0.1024749D+01  0.5428391D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.6202819D+00  0.1797702D+00  0.1205935D+00  0.5448988D+00
  2    0.1797702D+00  0.3506024D+00  0.8775846D-01  0.4262485D+00
  3    0.1205935D+00  0.8775846D-01  0.1625767D+00  0.1202222D+00
  4    0.5448988D+00  0.4262485D+00  0.1202222D+00  0.7363649D+00
  5    0.1251047D+00  0.2236627D+00  0.3896033D-01  0.2803513D+00
  6    0.5413832D+00  0.2911459D+00  0.4717723D-01  0.6267229D+00
 
            5              6
  1    0.1251047D+00  0.5413832D+00
  2    0.2236627D+00  0.2911459D+00
  3    0.3896033D-01  0.4717723D-01
  4    0.2803513D+00  0.6267229D+00
  5    0.1467371D+00  0.2018021D+00
  6    0.2018021D+00  0.6008554D+00
 
1*** In both these tests we start with S=0 and perform three
 *** iterations of the filter.
 *** The ranks of S in these three steps must be equal to
 *** M(=2), 2M(=4) and 3M(=6).
 *** K must be 0 in the first step and nonzero afterwards.
 *** The results for MULTBQ = .TRUE. and .FALSE. must be equal
 *** since we chose Q=I.
 *** The SS' matrices are meant for comparison with SRCFOB.
1*** Second example : Square root covariance filter with dense
 *** A, B, C and lower triangular Q, R.
 
 
 *** Input SRCF
 
 
 *** N =  6 M =  3 P =   2
 A matrix ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.8497452D+00  0.7263507D+00  0.8833888D+00
  2    0.7560439D+00  0.6857310D+00  0.1985144D+00  0.6525135D+00
  3    0.2211346D-03  0.8782165D+00  0.5442573D+00  0.3076091D+00
  4    0.3303271D+00  0.6837404D-01  0.2320748D+00  0.9329616D+00
  5    0.6653811D+00  0.5608486D+00  0.2312237D+00  0.2146008D+00
  6    0.6283918D+00  0.6623569D+00  0.2164633D+00  0.3126420D+00
 
            5              6
  1    0.3616361D+00  0.5015342D+00
  2    0.2922267D+00  0.4368588D+00
  3    0.5664249D+00  0.2693125D+00
  4    0.4826472D+00  0.6325745D+00
  5    0.3321719D+00  0.4051954D+00
  6    0.5935095D+00  0.9184708D+00
 
 B matrix ( 6X 3)
 
            1              2              3
  1    0.4373343D-01  0.7783129D+00  0.8415518D+00
  2    0.4818509D+00  0.2119030D+00  0.4062025D+00
  3    0.2639556D+00  0.1121355D+00  0.4094825D+00
  4    0.4148104D+00  0.6856896D+00  0.8784126D+00
  5    0.2806498D+00  0.1531217D+00  0.1138360D+00
  6    0.1280058D+00  0.6970851D+00  0.1998338D+00
 
 S matrix ( 6X 6)
 
            1              2              3              4
  1    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 C matrix ( 2X 6)
 
            1              2              3              4
  1    0.5618661D+00  0.6853980D+00  0.5042213D+00  0.3873779D+00
  2    0.5896177D+00  0.8906225D+00  0.3493615D+00  0.9222899D+00
 
            5              6
  1    0.9488184D+00  0.3760119D+00
  2    0.3435337D+00  0.7340941D+00
 
 R matrix ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.0000000D+00
  2    0.4498763D+00  0.7227253D+00
 
 Q matrix ( 3X 3)
 
            1              2              3
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01
 
 
 
 *** Output SRCF for MULTBQ=.TRUE.
 
 
 *** ISTEP =  1
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.1147124D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.4601424D+00 -0.4799506D+00  0.0000000D+00  0.0000000D+00
  3   -0.3865502D+00 -0.2904752D+00 -0.1269880D+00  0.0000000D+00
  4   -0.1125469D+01 -0.3836103D+00  0.3174747D-02 -0.2312022D-16
  5   -0.1981035D+00 -0.2557825D+00  0.1024672D+00 -0.1006863D-16
  6   -0.6244478D+00 -0.6734577D-02  0.3902131D+00 -0.2981111D-16
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.1506057D-16  0.0000000D+00
  6   -0.3856464D-16 -0.3227013D-17
 
 K matrix ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.1315893D+01  0.5278403D+00  0.4434210D+00  0.1291052D+01
  2    0.5278403D+00  0.4420836D+00  0.3172819D+00  0.7019898D+00
  3    0.4434210D+00  0.3172819D+00  0.2499229D+00  0.5460763D+00
  4    0.1291052D+01  0.7019898D+00  0.5460763D+00  0.1413847D+01
  5    0.2272492D+00  0.2139188D+00  0.1378633D+00  0.3214053D+00
  6    0.7163189D+00  0.2905672D+00  0.1937843D+00  0.7066186D+00
 
            5              6
  1    0.2272492D+00  0.7163189D+00
  2    0.2139188D+00  0.2905672D+00
  3    0.1378633D+00  0.1937843D+00
  4    0.3214053D+00  0.7066186D+00
  5    0.1151692D+00  0.1654119D+00
  6    0.1654119D+00  0.5422466D+00
 
 *** ISTEP =  2
 S matrix ( 6X 6)
 
            1              2              3              4
  1    0.1153393D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.4553510D+00 -0.5605252D+00  0.0000000D+00  0.0000000D+00
  3    0.4005667D+00 -0.1226901D+00  0.3865794D+00  0.0000000D+00
  4    0.1109665D+01 -0.4880872D+00 -0.7453123D-01  0.1641879D+00
  5    0.1931709D+00 -0.3282473D+00 -0.7733069D-01  0.9275831D-02
  6    0.6065784D+00 -0.1487211D+00 -0.3478213D+00  0.1728302D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.8810857D-01  0.0000000D+00
  6    0.3359240D+00 -0.7290827D-04
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1241933D+01 -0.7098306D-01
  2    0.1055207D+01  0.3295873D-01
  3    0.8288548D+00 -0.1175785D+00
  4    0.8985842D+00  0.4712947D-01
  5    0.7530441D+00  0.2777581D-01
  6    0.9674702D+00  0.4347324D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.1330316D+01  0.5251988D+00  0.4620110D+00  0.1279880D+01
  2    0.5251988D+00  0.5215331D+00  0.2511694D+00  0.7788723D+00
  3    0.4620110D+00  0.2511694D+00  0.3249502D+00  0.4755661D+00
  4    0.1279880D+01  0.7788723D+00  0.4755661D+00  0.1502098D+01
  5    0.2228020D+00  0.2719514D+00  0.8775607D-01  0.3818548D+00
  6    0.6996234D+00  0.3595680D+00  0.1267612D+00  0.7999878D+00
 
            5              6
  1    0.2228020D+00  0.6996234D+00
  2    0.2719514D+00  0.3595680D+00
  3    0.8775607D-01  0.1267612D+00
  4    0.3818548D+00  0.7999878D+00
  5    0.1588905D+00  0.2240887D+00
  6    0.2240887D+00  0.6537501D+00
 
 *** ISTEP =  3
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.1156046D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.4561407D+00 -0.5614451D+00  0.0000000D+00  0.0000000D+00
  3   -0.4005205D+00 -0.1199883D+00 -0.3971595D+00  0.0000000D+00
  4   -0.1115942D+01 -0.4848378D+00  0.5700188D-01 -0.1979035D+00
  5   -0.1928119D+00 -0.3292330D+00  0.8235161D-01  0.6542748D-03
  6   -0.6104152D+00 -0.1440359D+00  0.3138531D+00 -0.2417539D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.9185958D-01  0.0000000D+00
  6   -0.3114030D+00 -0.1568331D+00
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1226356D+01 -0.6043595D-01
  2    0.1048668D+01  0.3563242D-01
  3    0.8222839D+00 -0.1070870D+00
  4    0.8701889D+00  0.7072797D-01
  5    0.7546189D+00  0.2360331D-01
  6    0.9484350D+00  0.6437479D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.1336443D+01  0.5273198D+00  0.4630203D+00  0.1290080D+01
  2    0.5273198D+00  0.5232849D+00  0.2500605D+00  0.7812362D+00
  3    0.4630203D+00  0.2500605D+00  0.3325495D+00  0.4824935D+00
  4    0.1290080D+01  0.7812362D+00  0.4824935D+00  0.1522808D+01
  5    0.2228995D+00  0.2727956D+00  0.8402249D-01  0.3793561D+00
  6    0.7056683D+00  0.3593035D+00  0.1371167D+00  0.8167559D+00
 
            5              6
  1    0.2228995D+00  0.7056683D+00
  2    0.2727956D+00  0.3593035D+00
  3    0.8402249D-01  0.1371167D+00
  4    0.3793561D+00  0.8167559D+00
  5    0.1607912D+00  0.2194102D+00
  6    0.2194102D+00  0.6718702D+00
 
 
 
 *** Output SRCF for MULTBQ=.FALSE.
 
 
 *** ISTEP =  1
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.1147124D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.4601424D+00 -0.4799506D+00  0.0000000D+00  0.0000000D+00
  3   -0.3865502D+00 -0.2904752D+00 -0.1269880D+00  0.0000000D+00
  4   -0.1125469D+01 -0.3836103D+00  0.3174747D-02 -0.2312022D-16
  5   -0.1981035D+00 -0.2557825D+00  0.1024672D+00 -0.1006863D-16
  6   -0.6244478D+00 -0.6734577D-02  0.3902131D+00 -0.2981111D-16
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.1506057D-16  0.0000000D+00
  6   -0.3856464D-16 -0.3227013D-17
 
 K matrix ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.1315893D+01  0.5278403D+00  0.4434210D+00  0.1291052D+01
  2    0.5278403D+00  0.4420836D+00  0.3172819D+00  0.7019898D+00
  3    0.4434210D+00  0.3172819D+00  0.2499229D+00  0.5460763D+00
  4    0.1291052D+01  0.7019898D+00  0.5460763D+00  0.1413847D+01
  5    0.2272492D+00  0.2139188D+00  0.1378633D+00  0.3214053D+00
  6    0.7163189D+00  0.2905672D+00  0.1937843D+00  0.7066186D+00
 
            5              6
  1    0.2272492D+00  0.7163189D+00
  2    0.2139188D+00  0.2905672D+00
  3    0.1378633D+00  0.1937843D+00
  4    0.3214053D+00  0.7066186D+00
  5    0.1151692D+00  0.1654119D+00
  6    0.1654119D+00  0.5422466D+00
 
 *** ISTEP =  2
 S matrix ( 6X 6)
 
            1              2              3              4
  1    0.1153393D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.4553510D+00 -0.5605252D+00  0.0000000D+00  0.0000000D+00
  3    0.4005667D+00 -0.1226901D+00  0.3865794D+00  0.0000000D+00
  4    0.1109665D+01 -0.4880872D+00 -0.7453123D-01  0.1641879D+00
  5    0.1931709D+00 -0.3282473D+00 -0.7733069D-01  0.9275831D-02
  6    0.6065784D+00 -0.1487211D+00 -0.3478213D+00  0.1728302D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.8810857D-01  0.0000000D+00
  6    0.3359240D+00 -0.7290827D-04
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1241933D+01 -0.7098306D-01
  2    0.1055207D+01  0.3295873D-01
  3    0.8288548D+00 -0.1175785D+00
  4    0.8985842D+00  0.4712947D-01
  5    0.7530441D+00  0.2777581D-01
  6    0.9674702D+00  0.4347324D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.1330316D+01  0.5251988D+00  0.4620110D+00  0.1279880D+01
  2    0.5251988D+00  0.5215331D+00  0.2511694D+00  0.7788723D+00
  3    0.4620110D+00  0.2511694D+00  0.3249502D+00  0.4755661D+00
  4    0.1279880D+01  0.7788723D+00  0.4755661D+00  0.1502098D+01
  5    0.2228020D+00  0.2719514D+00  0.8775607D-01  0.3818548D+00
  6    0.6996234D+00  0.3595680D+00  0.1267612D+00  0.7999878D+00
 
            5              6
  1    0.2228020D+00  0.6996234D+00
  2    0.2719514D+00  0.3595680D+00
  3    0.8775607D-01  0.1267612D+00
  4    0.3818548D+00  0.7999878D+00
  5    0.1588905D+00  0.2240887D+00
  6    0.2240887D+00  0.6537501D+00
 
 *** ISTEP =  3
 S matrix ( 6X 6)
 
            1              2              3              4
  1   -0.1156046D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.4561407D+00 -0.5614451D+00  0.0000000D+00  0.0000000D+00
  3   -0.4005205D+00 -0.1199883D+00 -0.3971595D+00  0.0000000D+00
  4   -0.1115942D+01 -0.4848378D+00  0.5700188D-01 -0.1979035D+00
  5   -0.1928119D+00 -0.3292330D+00  0.8235161D-01  0.6542748D-03
  6   -0.6104152D+00 -0.1440359D+00  0.3138531D+00 -0.2417539D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.9185958D-01  0.0000000D+00
  6   -0.3114030D+00 -0.1568331D+00
 
 K matrix ( 6X 2)
 
            1              2
  1    0.1226356D+01 -0.6043595D-01
  2    0.1048668D+01  0.3563242D-01
  3    0.8222839D+00 -0.1070870D+00
  4    0.8701889D+00  0.7072797D-01
  5    0.7546189D+00  0.2360331D-01
  6    0.9484350D+00  0.6437479D-01
 
 SS' m.  ( 6X 6)
 
            1              2              3              4
  1    0.1336443D+01  0.5273198D+00  0.4630203D+00  0.1290080D+01
  2    0.5273198D+00  0.5232849D+00  0.2500605D+00  0.7812362D+00
  3    0.4630203D+00  0.2500605D+00  0.3325495D+00  0.4824935D+00
  4    0.1290080D+01  0.7812362D+00  0.4824935D+00  0.1522808D+01
  5    0.2228995D+00  0.2727956D+00  0.8402249D-01  0.3793561D+00
  6    0.7056683D+00  0.3593035D+00  0.1371167D+00  0.8167559D+00
 
            5              6
  1    0.2228995D+00  0.7056683D+00
  2    0.2727956D+00  0.3593035D+00
  3    0.8402249D-01  0.1371167D+00
  4    0.3793561D+00  0.8167559D+00
  5    0.1607912D+00  0.2194102D+00
  6    0.2194102D+00  0.6718702D+00
 
1*** In both these tests we start with S=0 and perform three
 *** iterations of the filter.
 *** The ranks of S in these three steps must be equal to
 *** M(=3), 2M(=6) and min(N,3M)(=6).
 *** K must be 0 in the first step and nonzero afterwards.
 *** The results for MULTBQ = .TRUE. and .FALSE. must be equal
 *** since we chose Q=I.
 *** The SS' matrices are meant for comparison with SRCFOB.
1*** First example : Square root information filter with
 *** dense A, B, C and upper triangular Q, R. ***
 
 
 *** Input SRIF
 
 
 *** N =  6 M =  2 P =   2
 Ainv     ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.7560439D+00  0.2211346D-03  0.3303271D+00
  2    0.8497452D+00  0.6857310D+00  0.8782165D+00  0.6837404D-01
  3    0.7263507D+00  0.1985144D+00  0.5442573D+00  0.2320748D+00
  4    0.8833888D+00  0.6525135D+00  0.3076091D+00  0.9329616D+00
  5    0.3616361D+00  0.2922267D+00  0.5664249D+00  0.4826472D+00
  6    0.5015342D+00  0.4368588D+00  0.2693125D+00  0.6325745D+00
 
            5              6
  1    0.6653811D+00  0.6283918D+00
  2    0.5608486D+00  0.6623569D+00
  3    0.2312237D+00  0.2164633D+00
  4    0.2146008D+00  0.3126420D+00
  5    0.3321719D+00  0.5935095D+00
  6    0.4051954D+00  0.9184708D+00
 
 AinvB    ( 6X 2)
 
            1              2
  1   -0.8805479D+00  0.5207521D+00
  2   -0.6075187D+00  0.1168888D+01
  3    0.1325720D+01 -0.1693905D+00
  4    0.1038693D+01 -0.2305789D+00
  5    0.2103993D+01 -0.1115921D+01
  6   -0.8531301D+00  0.6597089D+00
 
 C matrix ( 2X 6)
 
            1              2              3              4
  1    0.4373343D-01  0.4818509D+00  0.2639556D+00  0.4148104D+00
  2    0.7783129D+00  0.2119030D+00  0.1121355D+00  0.6856896D+00
 
            5              6
  1    0.2806498D+00  0.1280058D+00
  2    0.1531217D+00  0.6970851D+00
 
 Sinv     ( 6X 6)
 
            1              2              3              4
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.1000000D+01
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1000000D+01  0.0000000D+00
  6    0.0000000D+00  0.1000000D+01
 
 Qinv     ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.4498763D+00
  2    0.0000000D+00  0.7227253D+00
 
 Rinv     ( 2X 2)
 
            1              2
  1    0.1000000D+01  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01
 
 Z vector ( 2X 1)
 
            1
  1    0.1964506D-02
  2    0.5075221D+00
 
 X vector ( 6X 1)
 
            1
  1    0.4076043D+00
  2    0.8408046D+00
  3    0.5017266D+00
  4    0.9128781D+00
  5    0.2129065D+00
  6    0.5591451D+00
 
 Y vector ( 2X 1)
 
            1
  1    0.4304966D+00
  2    0.2280548D-01
 
 
 
 *** Output SRIF
 
 
 *** ISTEP =  1
 Sinv     ( 6X 6)
 
            1              2              3              4
  1   -0.1309385D+01 -0.9011780D+00 -0.5716204D+00 -0.1139520D+01
  2    0.0000000D+00  0.8355616D+00  0.2465342D+00  0.4338284D+00
  3    0.0000000D+00  0.0000000D+00 -0.5837402D+00  0.3857901D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.5323176D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.6398017D+00 -0.1203367D+01
  2    0.6177402D+00  0.4069786D+00
  3   -0.1602595D+00 -0.1570353D+00
  4    0.3096385D-01 -0.3501873D+00
  5   -0.2993971D+00 -0.5734618D+00
  6    0.0000000D+00  0.2538284D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.1274126D+00
  2    0.5536566D+00
  3    0.3481973D+00
  4    0.5286097D+00
  5   -0.9193801D-02
  6   -0.3619102D+00
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.1714490D+01  0.1179989D+01  0.7484713D+00  0.1492071D+01
  2    0.1179989D+01  0.1510285D+01  0.7211262D+00  0.1389401D+01
  3    0.7484713D+00  0.7211262D+00  0.7282816D+00  0.5331254D+00
  4    0.1492071D+01  0.1389401D+01  0.5331254D+00  0.1918910D+01
  5    0.8377470D+00  0.1092735D+01  0.6115677D+00  0.9187512D+00
  6    0.1575671D+01  0.1424504D+01  0.8798712D+00  0.1673648D+01
 
            5              6
  1    0.8377470D+00  0.1575671D+01
  2    0.1092735D+01  0.1424504D+01
  3    0.6115677D+00  0.8798712D+00
  4    0.9187512D+00  0.1673648D+01
  5    0.9072298D+00  0.1207340D+01
  6    0.1207340D+01  0.2154303D+01
 
 *** ISTEP =  2
 Sinv     ( 6X 6)
 
            1              2              3              4
  1    0.1675346D+01  0.1430175D+01  0.8236751D+00  0.1550070D+01
  2    0.0000000D+00  0.6869953D+00  0.3906490D+00  0.2478286D+00
  3    0.0000000D+00  0.0000000D+00  0.2136248D+00 -0.1422752D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.3763702D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.1055136D+01  0.1712885D+01
  2    0.4680036D+00  0.1384571D+00
  3    0.1390191D+00  0.2161770D+00
  4   -0.4779113D-01  0.1517750D+00
  5    0.1737174D+00  0.2538410D+00
  6    0.0000000D+00 -0.1248382D+00
 
 X vector ( 6X 1)
 
            1
  1    0.5520679D+00
  2   -0.1257842D+01
  3    0.1402490D+01
  4    0.1279330D+01
  5    0.1134170D+01
  6   -0.2059006D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2806785D+01  0.2396039D+01  0.1379941D+01  0.2596905D+01
  2    0.2396039D+01  0.2517363D+01  0.1446374D+01  0.2387129D+01
  3    0.1379941D+01  0.1446374D+01  0.8766829D+00  0.1343175D+01
  4    0.2596905D+01  0.2387129D+01  0.1343175D+01  0.2626034D+01
  5    0.1767717D+01  0.1830545D+01  0.1081612D+01  0.1713753D+01
  6    0.2869676D+01  0.2544845D+01  0.1511130D+01  0.2715773D+01
 
            5              6
  1    0.1767717D+01  0.2869676D+01
  2    0.1830545D+01  0.2544845D+01
  3    0.1081612D+01  0.1511130D+01
  4    0.1713753D+01  0.2715773D+01
  5    0.1384126D+01  0.1939020D+01
  6    0.1939020D+01  0.3102934D+01
 
 *** ISTEP =  3
 Sinv     ( 6X 6)
 
            1              2              3              4
  1   -0.1686827D+01 -0.1449843D+01 -0.8614954D+00 -0.1530604D+01
  2    0.0000000D+00  0.6800828D+00  0.4027329D+00  0.2562922D+00
  3    0.0000000D+00  0.0000000D+00 -0.1563938D+00  0.1791086D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.2884050D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.1100984D+01 -0.1761025D+01
  2    0.4727669D+00  0.1612967D+00
  3   -0.1239199D+00 -0.1431808D+00
  4    0.1919640D-01 -0.1044032D+00
  5   -0.9366813D-01 -0.2052520D+00
  6    0.0000000D+00  0.5028876D-01
 
 X vector ( 6X 1)
 
            1
  1    0.2315943D+01
  2   -0.6344640D+01
  3    0.3674095D+00
  4    0.3464291D+01
  5    0.9289437D+01
  6   -0.6222618D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2845387D+01  0.2445634D+01  0.1453194D+01  0.2581864D+01
  2    0.2445634D+01  0.2564556D+01  0.1522925D+01  0.2393434D+01
  3    0.1453194D+01  0.1522925D+01  0.9288272D+00  0.1393814D+01
  4    0.2581864D+01  0.2393434D+01  0.1393814D+01  0.2523690D+01
  5    0.1857170D+01  0.1917774D+01  0.1158272D+01  0.1778605D+01
  6    0.2970545D+01  0.2662904D+01  0.1604467D+01  0.2741235D+01
 
            5              6
  1    0.1857170D+01  0.2970545D+01
  2    0.1917774D+01  0.2662904D+01
  3    0.1158272D+01  0.1604467D+01
  4    0.1778605D+01  0.2741235D+01
  5    0.1460172D+01  0.2050080D+01
  6    0.2050080D+01  0.3203283D+01
 
 *** ISTEP =  4
 Sinv     ( 6X 6)
 
            1              2              3              4
  1    0.1677041D+01  0.1441873D+01  0.8634620D+00  0.1518237D+01
  2    0.0000000D+00  0.6777607D+00  0.4023206D+00  0.2557285D+00
  3    0.0000000D+00  0.0000000D+00  0.1426564D+00 -0.1525080D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.2695154D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.1103674D+01  0.1765745D+01
  2    0.4705363D+00  0.1575076D+00
  3    0.1189427D+00  0.1522564D+00
  4   -0.3686556D-01  0.5202285D-01
  5   -0.6626387D-01 -0.1388171D+00
  6    0.0000000D+00  0.3565161D-01
 
 X vector ( 6X 1)
 
            1
  1    0.4516508D+01
  2   -0.1027816D+02
  3   -0.5650702D+00
  4    0.5048174D+01
  5    0.1620299D+02
  6   -0.1035923D+02
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2812466D+01  0.2418079D+01  0.1448061D+01  0.2546146D+01
  2    0.2418079D+01  0.2538357D+01  0.1517679D+01  0.2362428D+01
  3    0.1448061D+01  0.1517679D+01  0.9277794D+00  0.1392069D+01
  4    0.2546146D+01  0.2362428D+01  0.1392069D+01  0.2466339D+01
  5    0.1850907D+01  0.1910269D+01  0.1159255D+01  0.1767893D+01
  6    0.2961227D+01  0.2652733D+01  0.1609743D+01  0.2711900D+01
 
            5              6
  1    0.1850907D+01  0.2961227D+01
  2    0.1910269D+01  0.2652733D+01
  3    0.1159255D+01  0.1609743D+01
  4    0.1767893D+01  0.2711900D+01
  5    0.1459398D+01  0.2048311D+01
  6    0.2048311D+01  0.3189095D+01
 
1*** In both these tests we start with Sinv=I and perform
 *** four iterations of the filter.
 *** The Sinv'Sinv matrices and X vectors are meant for
 *** comparison with SRIFCO.
1*** Second example : Square root information filter with
 *** dense A, B, C and upper triangular Q, R. ***
 
 
 *** Input SRIF
 
 
 *** N =  6 M =  2 P =   3
 Ainv     ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.7560439D+00  0.2211346D-03  0.3303271D+00
  2    0.8497452D+00  0.6857310D+00  0.8782165D+00  0.6837404D-01
  3    0.7263507D+00  0.1985144D+00  0.5442573D+00  0.2320748D+00
  4    0.8833888D+00  0.6525135D+00  0.3076091D+00  0.9329616D+00
  5    0.3616361D+00  0.2922267D+00  0.5664249D+00  0.4826472D+00
  6    0.5015342D+00  0.4368588D+00  0.2693125D+00  0.6325745D+00
 
            5              6
  1    0.6653811D+00  0.6283918D+00
  2    0.5608486D+00  0.6623569D+00
  3    0.2312237D+00  0.2164633D+00
  4    0.2146008D+00  0.3126420D+00
  5    0.3321719D+00  0.5935095D+00
  6    0.4051954D+00  0.9184708D+00
 
 AinvB    ( 6X 2)
 
            1              2
  1   -0.8805479D+00  0.5207521D+00
  2   -0.6075187D+00  0.1168888D+01
  3    0.1325720D+01 -0.1693905D+00
  4    0.1038693D+01 -0.2305789D+00
  5    0.2103993D+01 -0.1115921D+01
  6   -0.8531301D+00  0.6597089D+00
 
 C matrix ( 3X 6)
 
            1              2              3              4
  1    0.4373343D-01  0.4818509D+00  0.2639556D+00  0.4148104D+00
  2    0.7783129D+00  0.2119030D+00  0.1121355D+00  0.6856896D+00
  3    0.8415518D+00  0.4062025D+00  0.4094825D+00  0.8784126D+00
 
            5              6
  1    0.2806498D+00  0.1280058D+00
  2    0.1531217D+00  0.6970851D+00
  3    0.1138360D+00  0.1998338D+00
 
 Sinv     ( 6X 6)
 
            1              2              3              4
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.1000000D+01
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1000000D+01  0.0000000D+00
  6    0.0000000D+00  0.1000000D+01
 
 Qinv     ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.4498763D+00
  2    0.0000000D+00  0.7227253D+00
 
 Rinv     ( 3X 3)
 
            1              2              3
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01
 
 Z vector ( 2X 1)
 
            1
  1    0.1964506D-02
  2    0.5075221D+00
 
 X vector ( 6X 1)
 
            1
  1    0.2129065D+00
  2    0.4076043D+00
  3    0.8408046D+00
  4    0.5017266D+00
  5    0.9128781D+00
  6    0.2129065D+00
 
 Y vector ( 3X 1)
 
            1
  1    0.5591451D+00
  2    0.4304966D+00
  3    0.2280548D-01
 
 
 
 *** Output SRIF
 
 
 *** ISTEP =  1
 Sinv     ( 6X 6)
 
            1              2              3              4
  1   -0.1556502D+01 -0.9777240D+00 -0.7022618D+00 -0.1433535D+01
  2    0.0000000D+00  0.8481398D+00  0.2368015D+00  0.4063157D+00
  3    0.0000000D+00  0.0000000D+00 -0.5888216D+00  0.3568368D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.5857219D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.5997716D+00 -0.1120359D+01
  2    0.6515018D+00  0.4837346D+00
  3   -0.1404640D+00 -0.1025184D+00
  4   -0.9499430D-01  0.1419510D+00
  5   -0.3274962D+00 -0.7391188D+00
  6    0.0000000D+00 -0.3578763D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.2569291D+00
  2   -0.7735836D+00
  3    0.9761830D-01
  4    0.5768679D+00
  5    0.1493255D+01
  6   -0.1070294D+00
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2422699D+01  0.1521830D+01  0.1093072D+01  0.2231301D+01
  2    0.1521830D+01  0.1675285D+01  0.8874590D+00  0.1746214D+01
  3    0.1093072D+01  0.8874590D+00  0.8959575D+00  0.8928200D+00
  4    0.2231301D+01  0.1746214D+01  0.8928200D+00  0.2690518D+01
  5    0.9335458D+00  0.1138976D+01  0.6581816D+00  0.1018746D+01
  6    0.1743842D+01  0.1505677D+01  0.9616997D+00  0.1849185D+01
 
            5              6
  1    0.9335458D+00  0.1743842D+01
  2    0.1138976D+01  0.1505677D+01
  3    0.6581816D+00  0.9616997D+00
  4    0.1018746D+01  0.1849185D+01
  5    0.9201884D+00  0.1230088D+01
  6    0.1230088D+01  0.2194236D+01
 
 *** ISTEP =  2
 Sinv     ( 6X 6)
 
            1              2              3              4
  1    0.1892270D+01  0.1497028D+01  0.9019158D+00  0.1796936D+01
  2    0.0000000D+00  0.7605080D+00  0.3112295D+00  0.1927141D+00
  3    0.0000000D+00  0.0000000D+00 -0.3727009D+00 -0.1274571D-01
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.4404712D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.1007581D+01  0.1602841D+01
  2    0.5662957D+00  0.2886638D+00
  3   -0.8451214D-01 -0.1577847D+00
  4    0.1474118D+00  0.1163742D+00
  5    0.2461278D+00  0.6079888D+00
  6    0.0000000D+00 -0.2875915D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.1456113D+01
  2   -0.4309217D-01
  3    0.5894792D-01
  4    0.1416551D+01
  5   -0.8426659D+00
  6    0.7265106D+00
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.3580686D+01  0.2832780D+01  0.1706668D+01  0.3400289D+01
  2    0.2832780D+01  0.2819464D+01  0.1586885D+01  0.2836624D+01
  3    0.1706668D+01  0.1586885D+01  0.1049222D+01  0.1685414D+01
  4    0.3400289D+01  0.2836624D+01  0.1685414D+01  0.3460296D+01
  5    0.1906616D+01  0.1939049D+01  0.1116499D+01  0.1855839D+01
  6    0.3033008D+01  0.2619028D+01  0.1594275D+01  0.2886584D+01
 
            5              6
  1    0.1906616D+01  0.3033008D+01
  2    0.1939049D+01  0.2619028D+01
  3    0.1116499D+01  0.1594275D+01
  4    0.1855839D+01  0.2886584D+01
  5    0.1425362D+01  0.1958594D+01
  6    0.1958594D+01  0.3143224D+01
 
 *** ISTEP =  3
 Sinv     ( 6X 6)
 
            1              2              3              4
  1   -0.1892777D+01 -0.1498278D+01 -0.9391399D+00 -0.1770376D+01
  2    0.0000000D+00  0.7534233D+00  0.3363931D+00  0.1893335D+00
  3    0.0000000D+00  0.0000000D+00 -0.3573020D+00  0.1536839D-01
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.4089454D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.1040285D+01 -0.1647775D+01
  2    0.5753470D+00  0.3207106D+00
  3   -0.7365386D-01 -0.1219101D+00
  4   -0.1404414D+00 -0.1919790D+00
  5   -0.2108559D+00 -0.6019307D+00
  6    0.0000000D+00 -0.1576478D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.2360051D+01
  2    0.5336696D+01
  3   -0.2252791D+00
  4    0.4210842D+00
  5   -0.8901653D+01
  6    0.3138066D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.3582605D+01  0.2835907D+01  0.1777583D+01  0.3350927D+01
  2    0.2835907D+01  0.2812484D+01  0.1660539D+01  0.2795164D+01
  3    0.1777583D+01  0.1660539D+01  0.1122809D+01  0.1720830D+01
  4    0.3350927D+01  0.2795164D+01  0.1720830D+01  0.3337550D+01
  5    0.1969028D+01  0.1992116D+01  0.1196833D+01  0.1892063D+01
  6    0.3118870D+01  0.2710456D+01  0.1698934D+01  0.2897519D+01
 
            5              6
  1    0.1969028D+01  0.3118870D+01
  2    0.1992116D+01  0.2710456D+01
  3    0.1196833D+01  0.1698934D+01
  4    0.1892063D+01  0.2897519D+01
  5    0.1482826D+01  0.2061537D+01
  6    0.2061537D+01  0.3256908D+01
 
 *** ISTEP =  4
 Sinv     ( 6X 6)
 
            1              2              3              4
  1    0.1886329D+01  0.1493744D+01  0.9393694D+00  0.1765233D+01
  2    0.0000000D+00  0.7516328D+00  0.3332270D+00  0.1910338D+00
  3    0.0000000D+00  0.0000000D+00 -0.3555036D+00  0.2734832D-02
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.3898780D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.1041975D+01  0.1651591D+01
  2    0.5719306D+00  0.3161135D+00
  3   -0.7640232D-01 -0.1335814D+00
  4    0.1540774D+00  0.2383378D+00
  5    0.1990389D+00  0.5734484D+00
  6    0.0000000D+00 -0.1522297D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.2525420D+01
  2    0.9904315D+01
  3    0.1568047D+00
  4   -0.1263859D+01
  5   -0.1548146D+02
  6    0.4935227D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.3558236D+01  0.2817693D+01  0.1771960D+01  0.3329810D+01
  2    0.2817693D+01  0.2796224D+01  0.1653642D+01  0.2780394D+01
  3    0.1771960D+01  0.1653642D+01  0.1119838D+01  0.1720891D+01
  4    0.3329810D+01  0.2780394D+01  0.1720891D+01  0.3304554D+01
  5    0.1965507D+01  0.1986326D+01  0.1196543D+01  0.1888306D+01
  6    0.3115443D+01  0.2704655D+01  0.1704280D+01  0.2882543D+01
 
            5              6
  1    0.1965507D+01  0.3115443D+01
  2    0.1986326D+01  0.2704655D+01
  3    0.1196543D+01  0.1704280D+01
  4    0.1888306D+01  0.2882543D+01
  5    0.1482010D+01  0.2062778D+01
  6    0.2062778D+01  0.3254345D+01
 
1*** In both these tests we start with Sinv=I and perform
 *** four iterations of the filter.
 *** The Sinv'Sinv matrices and X vectors are meant for
 *** comparison with SRIFCO.
 
 *** First example : upper Hessenberg form
 
 
 
 *** Input Data *************
 
 
 *** N =  8 M =  2 UPPER =   T TOL = 0.1D-14
 A0 matr. ( 8X 8)
 
            1              2              3              4
  1    0.2113249D+00  0.7560439D+00  0.2211346D-03  0.3303271D+00
  2    0.8782165D+00  0.6837404D-01  0.5608486D+00  0.6623569D+00
  3    0.2312237D+00  0.2164633D+00  0.8833888D+00  0.6525135D+00
  4    0.3616361D+00  0.2922267D+00  0.5664249D+00  0.4826472D+00
  5    0.2693125D+00  0.6325745D+00  0.4051954D+00  0.9184708D+00
  6    0.2806498D+00  0.1280058D+00  0.7783129D+00  0.2119030D+00
  7    0.8415518D+00  0.4062025D+00  0.4094825D+00  0.8784126D+00
  8    0.6853980D+00  0.8906225D+00  0.5042213D+00  0.3493615D+00
 
            5              6              7              8
  1    0.6653811D+00  0.6283918D+00  0.8497452D+00  0.6857310D+00
  2    0.7263507D+00  0.1985144D+00  0.5442573D+00  0.2320748D+00
  3    0.3076091D+00  0.9329616D+00  0.2146008D+00  0.3126420D+00
  4    0.3321719D+00  0.5935095D+00  0.5015342D+00  0.4368588D+00
  5    0.4373343D-01  0.4818509D+00  0.2639556D+00  0.4148104D+00
  6    0.1121355D+00  0.6856896D+00  0.1531217D+00  0.6970851D+00
  7    0.1138360D+00  0.1998338D+00  0.5618661D+00  0.5896177D+00
  8    0.3873779D+00  0.9222899D+00  0.9488184D+00  0.3435337D+00
 
 B0 matr. ( 2X 8)
 
            1              2              3              4
  1    0.3760119D+00  0.7340941D+00  0.2615761D+00  0.4993494D+00
  2    0.2256303D+00  0.6274093D+00  0.7608433D+00  0.4855662D-01
 
            5              6              7              8
  1    0.2638578D+00  0.5253563D+00  0.5376230D+00  0.1199926D+00
  2    0.6723950D+00  0.2017173D+00  0.3911574D+00  0.8300317D+00
 
 
 
 *** Output Data ************
 
 
 A matrix ( 8X 8)
 
            1              2              3              4
  1   -0.1066326D+00  0.1316800D+00 -0.4225355D+00  0.2602046D+00
  2    0.4222147D-01  0.4075197D-01 -0.1300144D+00  0.3053751D+00
  3   -0.2665044D+00  0.3407614D+00 -0.4747604D+00 -0.1301455D+00
  4    0.0000000D+00  0.4550986D+00  0.2153786D+00  0.1687042D-01
  5    0.0000000D+00  0.0000000D+00 -0.1547913D+00 -0.2118666D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.6209869D+00
  7    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  8    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6              7              8
  1    0.5405883D-01  0.3829733D+00 -0.2657399D-01 -0.2721774D+00
  2   -0.2719752D+00  0.3012927D+00  0.1240728D-01 -0.1776388D+00
  3   -0.2152574D+00  0.5033204D-01 -0.6876272D-01 -0.1065149D+00
  4   -0.4249745D-01 -0.1202603D-01 -0.4990164D-01 -0.1514647D+00
  5    0.6450252D+00 -0.4609640D+00  0.6618764D+00  0.3834935D+00
  6   -0.5963368D+00  0.3255731D-01  0.3797258D+00  0.8405580D+00
  7    0.3785231D+00  0.7106583D+00  0.3614025D+00  0.1242073D+01
  8    0.0000000D+00  0.1079634D+01  0.1891566D+01  0.2765343D+01
 
 B matrix ( 2X 8)
 
            1              2              3              4
  1    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6              7              8
  1    0.0000000D+00  0.0000000D+00 -0.9280606D+00 -0.8864600D+00
  2    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.1536409D+01
 
 U matrix ( 8X 8)
 
            1              2              3              4
  1    0.3335950D+00  0.2658968D+00 -0.3390163D+00  0.6761545D-01
  2    0.6578012D+00 -0.1698221D-01  0.4123120D-01 -0.6620397D+00
  3    0.6097985D-03  0.2776749D+00  0.1776868D+00  0.2204007D+00
  4   -0.3343031D+00 -0.1174397D+00 -0.4726773D+00 -0.1590310D+00
  5   -0.3857639D+00  0.1508882D+00  0.5015998D+00 -0.2224189D+00
  6   -0.3220374D+00  0.6984517D+00 -0.3082140D+00 -0.4181673D+00
  7   -0.2648860D+00 -0.4009421D+00  0.1911584D+00 -0.5078696D+00
  8   -0.1468556D+00 -0.4083608D+00 -0.4952087D+00 -0.3160396D-01
 
            5              6              7              8
  1    0.6365555D-01  0.1801780D+00 -0.7639997D+00  0.2798173D+00
  2   -0.2710194D+00  0.1205978D+00  0.1872044D+00 -0.6302186D-01
  3   -0.7692868D+00 -0.3789945D+00  0.4056943D-02  0.3275541D+00
  4   -0.1991020D+00  0.4653542D+00  0.2963752D+00  0.5307544D+00
  5   -0.2599677D+00  0.5479370D+00 -0.3319697D+00 -0.2220910D+00
  6    0.1185801D+00 -0.2848421D+00  0.7354156D-01 -0.1949175D+00
  7    0.1337122D+00 -0.4406735D+00 -0.3361175D+00  0.3867309D+00
  8   -0.4376406D+00 -0.1312914D+00 -0.2545919D+00 -0.5402413D+00
 
 *** Testing norm U*A0-A*U =0.204484D-15
 *** which should be of the order of the machine precision
 *** norm(A)
 *** Testing norm U*B0-B =0.312732D-16
 *** which should be of the order of the machine precision
 *** norm(B)
 *** Testing norm U*UP-I =0.940255D-16
 *** which should be of the order of the machine precision
1*** This first example is a well-conditioned one.
 *** The above norm tests should be close to the machine
 *** precision and A, B, U should be close to those obtained
 *** on any other machine.
 
1*** Second example : lower Hessenberg form
 
 
 
 *** Input Data *************
 
 
 *** N =  8 M =  3 UPPER =   F TOL = 0.1D-14
 A0 matr. ( 8X 8)
 
            1              2              3              4
  1    0.3873477D+00  0.3918023D+00  0.8812843D+00  0.1060378D+00
  2    0.8473940D+00  0.4636857D+00  0.3559455D+00  0.3694990D+00
  3    0.7374331D+00  0.2647072D+00  0.4988408D+00  0.2652388D+00
  4    0.6409741D+00  0.7735630D+00  0.4649064D-01  0.6780052D+00
  5    0.4583488D+00  0.2002479D+00  0.8438306D+00  0.1104381D+00
  6    0.1038978D+01  0.6918569D+00  0.9853348D+00  0.6900804D-01
  7    0.5348427D-01  0.8177994D+00  0.9278763D+00  0.5622625D+00
  8    0.1524701D+00  0.7537430D+00  0.2635828D+00  0.5579221D+00
 
            5              6              7              8
  1    0.2266084D+00  0.5448077D+00  0.6020714D+00  0.7053985D+00
  2    0.9836764D+00  0.9097085D+00  0.3720863D+00  0.4218672D+00
  3    0.5206147D+00  0.5406439D+00  0.1177871D+00  0.2220884D+00
  4    0.1824547D+00  0.4034298D+00  0.8210721D+00  0.5734830D+00
  5    0.3204257D+00  0.8385232D+00  0.8656382D+00  0.5517682D+00
  6    0.6834312D+00  0.4518941D+00  0.5781638D+00  0.8057772D+00
  7    0.5864726D+00  0.8062577D+00  0.6401329D-01  0.5710292D+00
  8    0.9494382D+00  0.7644782D+00 -0.1447037D-01  0.5608479D+00
 
 B0 matr. ( 3X 8)
 
            1              2              3              4
  1   -0.5008794D+00 -0.3867745D+00 -0.4096848D+00 -0.4216298D+00
  2   -0.3262392D+00 -0.2503598D+00 -0.2308553D+00 -0.2886426D+00
  3   -0.7949956D-01 -0.7925883D-01 -0.4774682D+00  0.9378121D-01
 
            5              6              7              8
  1   -0.5412259D+00 -0.4651283D+00 -0.1880768D+00 -0.4747183D+00
  2   -0.3257056D+00 -0.2651356D+00 -0.1016262D+00 -0.3350921D+00
  3   -0.3932090D+00 -0.5072632D+00 -0.2690981D+00  0.2214139D+00
 
 
 
 *** Output Data ************
 
 
 A matrix ( 8X 8)
 
            1              2              3              4
  1    0.4034462D+01 -0.5496913D+00  0.1719497D+00 -0.8122496D+00
  2   -0.2977289D+00  0.4007473D+00 -0.2570347D-01  0.2044011D+00
  3    0.5083343D+00  0.2864055D+00  0.2294080D+00  0.5126002D-01
  4   -0.8287784D+00  0.1869646D+00  0.5808706D+00 -0.5533826D+00
  5    0.7146230D+00  0.1241547D-03  0.4931101D-01 -0.1721749D+00
  6    0.1171479D+00  0.1402102D+00 -0.1825322D+00  0.2086584D+00
  7    0.1029053D+00 -0.6033020D-01  0.2782224D+00 -0.5591695D+00
  8   -0.1477774D-01 -0.3893580D+00  0.9691826D-01  0.1154625D+00
 
            5              6              7              8
  1    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7314053D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  3    0.3585806D+00  0.4321407D+00  0.0000000D+00  0.0000000D+00
  4   -0.1406535D+00 -0.3410269D+00  0.4663396D+00  0.0000000D+00
  5    0.2241386D+00 -0.7456636D-02  0.5860687D-01  0.1257189D+00
  6   -0.6053474D-01 -0.3088876D+00  0.6906574D+00  0.1947131D+00
  7   -0.3465267D+00  0.4003948D-01 -0.2039871D+00  0.1220821D-01
  8    0.1743335D+00 -0.9037824D-01 -0.7293658D-01 -0.3974386D+00
 
 B matrix ( 3X 8)
 
            1              2              3              4
  1    0.1231295D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7750438D+00  0.6343140D-01  0.0000000D+00  0.0000000D+00
  3    0.5041883D+00 -0.7270036D+00  0.1179168D-14  0.0000000D+00
 
            5              6              7              8
  1    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
 U matrix ( 8X 8)
 
            1              2              3              4
  1   -0.4067906D+00 -0.3141200D+00 -0.3327266D+00 -0.3424278D+00
  2   -0.1727633D+00 -0.1088259D+00  0.4260107D+00 -0.3664759D+00
  3    0.9821569D-01  0.1747594D+00 -0.2611676D+00 -0.6035494D+00
  4    0.2484576D-01  0.3021913D+00  0.2121400D-01 -0.5276975D+00
  5    0.4833731D+00 -0.3586663D+00  0.6105964D+00 -0.2339988D+00
  6    0.8941257D-01 -0.6807586D+00 -0.3088866D+00 -0.1509972D+00
  7   -0.7396980D+00 -0.4293286D-01  0.4130181D+00 -0.1206687D-01
  8   -0.7492188D-01 -0.4167831D+00 -0.1806899D-01  0.1673345D+00
 
            5              6              7              8
  1   -0.4395582D+00 -0.3777553D+00 -0.1527471D+00 -0.3855438D+00
  2    0.2360220D+00  0.4357659D+00  0.2642143D+00 -0.5719375D+00
  3    0.3246967D+00  0.2223279D+00 -0.5887776D+00  0.1606727D+00
  4   -0.4380017D+00  0.7047588D-01  0.5201828D+00  0.4021765D+00
  5   -0.1824962D+00 -0.3224208D+00 -0.2551388D+00  0.8814617D-01
  6    0.4178200D+00 -0.5350911D-01  0.3917789D+00  0.2818414D+00
  7    0.1925442D+00 -0.1497564D+00 -0.1344767D+00  0.4502108D+00
  8   -0.4570089D+00  0.6955337D+00 -0.2300857D+00  0.2163046D+00
 
 *** Testing norm U*A0-A*U =0.181730D-15
 *** which should be of the order of the machine precision
 *** norm(A)
 *** Testing norm U*B0-B =0.399740D-16
 *** which should be of the order of the machine precision
 *** norm(B)
 *** Testing norm U*UP-I =0.115364D-15
 *** which should be of the order of the machine precision
1*** This second example is an ill-conditioned one.
 *** Therefore A, B and U can differ a lot from those obtained
 *** on another machine, but the above norm tests should yet
 *** be close to the machine precision (because of backward
 *** stability).
 *** First example : upper Hessenberg form
 
 
 *** Input Data *************
 
 
 *** N =  8 M =  2 UPPER =   T TOL = 0.1D-14
 A0 matr. ( 8X 8)
 
            1              2              3              4
  1    0.2113249D+00  0.8782165D+00  0.2312237D+00  0.3616361D+00
  2    0.7560439D+00  0.6837404D-01  0.2164633D+00  0.2922267D+00
  3    0.2211346D-03  0.5608486D+00  0.8833888D+00  0.5664249D+00
  4    0.3303271D+00  0.6623569D+00  0.6525135D+00  0.4826472D+00
  5    0.6653811D+00  0.7263507D+00  0.3076091D+00  0.3321719D+00
  6    0.6283918D+00  0.1985144D+00  0.9329616D+00  0.5935095D+00
  7    0.8497452D+00  0.5442573D+00  0.2146008D+00  0.5015342D+00
  8    0.6857310D+00  0.2320748D+00  0.3126420D+00  0.4368588D+00
 
            5              6              7              8
  1    0.2693125D+00  0.2806498D+00  0.8415518D+00  0.6853980D+00
  2    0.6325745D+00  0.1280058D+00  0.4062025D+00  0.8906225D+00
  3    0.4051954D+00  0.7783129D+00  0.4094825D+00  0.5042213D+00
  4    0.9184708D+00  0.2119030D+00  0.8784126D+00  0.3493615D+00
  5    0.4373343D-01  0.1121355D+00  0.1138360D+00  0.3873779D+00
  6    0.4818509D+00  0.6856896D+00  0.1998338D+00  0.9222899D+00
  7    0.2639556D+00  0.1531217D+00  0.5618661D+00  0.9488184D+00
  8    0.4148104D+00  0.6970851D+00  0.5896177D+00  0.3435337D+00
 
 B0 matr. ( 8X 2)
 
            1              2
  1    0.3760119D+00  0.2256303D+00
  2    0.7340941D+00  0.6274093D+00
  3    0.2615761D+00  0.7608433D+00
  4    0.4993494D+00  0.4855662D-01
  5    0.2638578D+00  0.6723950D+00
  6    0.5253563D+00  0.2017173D+00
  7    0.5376230D+00  0.3911574D+00
  8    0.1199926D+00  0.8300317D+00
 
 
 
 *** Output Data ************
 
 
 A matrix ( 8X 8)
 
            1              2              3              4
  1    0.3073461D+01  0.1597260D+01  0.9935550D+00  0.5449534D+00
  2    0.9477666D+00  0.5328502D-01  0.2994773D+00 -0.2491275D+00
  3    0.1289013D+01  0.2277233D+00 -0.1592217D+00 -0.2861971D+00
  4    0.0000000D+00 -0.3170384D+00 -0.4215699D+00  0.8368042D+00
  5    0.0000000D+00  0.0000000D+00 -0.6526426D+00 -0.8269145D-01
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.1472833D+00
  7    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  8    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6              7              8
  1   -0.1467351D+00 -0.1160526D+00  0.1077854D+00 -0.2103641D+00
  2   -0.7645254D-01 -0.2571071D-01  0.1318937D+00 -0.1822896D+00
  3   -0.2057470D-01  0.4516401D-02 -0.2256003D+00  0.3922944D+00
  4   -0.5005736D-01 -0.2187927D+00  0.3288077D+00 -0.3786623D-01
  5    0.1991062D-01 -0.1550908D+00 -0.2915320D+00  0.2469861D+00
  6    0.1904332D+00 -0.4778007D+00  0.1327942D+00 -0.4390592D+00
  7   -0.4718741D+00 -0.3248509D+00  0.3568817D-01 -0.1357299D+00
  8    0.0000000D+00 -0.2570300D+00 -0.4627137D-01 -0.1015688D+00
 
 B matrix ( 8X 2)
 
            1              2
  1   -0.1283397D+01 -0.1061219D+01
  2    0.0000000D+00 -0.1111021D+01
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
  7    0.0000000D+00  0.0000000D+00
  8    0.0000000D+00  0.0000000D+00
 
 U matrix ( 8X 8)
 
            1              2              3              4
  1   -0.2929817D+00 -0.5719930D+00 -0.2038155D+00 -0.3890841D+00
  2    0.7676492D-01 -0.1836104D-01 -0.4901352D+00  0.3279388D+00
  3   -0.3966096D+00  0.7145636D+00 -0.1946706D+00 -0.4558610D+00
  4   -0.3085818D+00 -0.8686278D-03  0.5556092D+00 -0.1285489D+00
  5   -0.3338481D+00 -0.1033058D+00 -0.4631284D+00 -0.1477288D+00
  6    0.1744592D-01  0.2832372D+00  0.2012673D+00  0.2281305D+00
  7   -0.6480461D+00  0.2453867D-01 -0.5085770D-01  0.6636951D+00
  8    0.3521709D+00  0.2653062D+00 -0.3377063D+00  0.4875664D-01
 
            5              6              7              8
  1   -0.2055933D+00 -0.4093483D+00 -0.4189062D+00 -0.9349605D-01
  2   -0.4088271D+00  0.2094388D+00  0.4805837D-01 -0.6577841D+00
  3    0.6067180D-01 -0.1619920D+00  0.1370878D-02 -0.2376330D+00
  4   -0.2792192D+00  0.5959267D+00 -0.3400152D+00 -0.1756353D+00
  5   -0.2375938D+00  0.4456759D+00  0.2962034D+00  0.5465778D+00
  6   -0.7582829D+00 -0.4019507D+00 -0.1087490D-01  0.3004074D+00
  7    0.2727204D+00 -0.1154239D+00 -0.2088603D+00  0.7095565D-01
  8    0.5592075D-01  0.1835355D+00 -0.7583656D+00  0.2779114D+00
 
 *** Testing norm U*A0-A*U =0.251624D-15
 *** which should be of the order of the machine precision
 *** norm(A)
 *** Testing norm U*B0-B =0.566962D-16
 *** which should be of the order of the machine precision
 *** norm(B)
 *** Testing norm U*UP-I =0.108573D-15
 *** which should be of the order of the machine precision
1*** This first example is a well-conditioned one.
 *** The above norm tests should be close to the machine
 *** precision and A, B, U should be close to those obtained
 *** on any other machine.
1*** Second example : lower Hessenberg form
 
 
 *** Input Data *************
 
 
 *** N =  8 M =  3 UPPER =   F TOL = 0.1D-14
 A0 matr. ( 8X 8)
 
            1              2              3              4
  1    0.3873477D+00  0.8473940D+00  0.7374331D+00  0.6409741D+00
  2    0.3918023D+00  0.4636857D+00  0.2647072D+00  0.7735630D+00
  3    0.8812843D+00  0.3559455D+00  0.4988408D+00  0.4649064D-01
  4    0.1060378D+00  0.3694990D+00  0.2652388D+00  0.6780052D+00
  5    0.2266084D+00  0.9836764D+00  0.5206147D+00  0.1824547D+00
  6    0.5448077D+00  0.9097085D+00  0.5406439D+00  0.4034298D+00
  7    0.6020714D+00  0.3720863D+00  0.1177871D+00  0.8210721D+00
  8    0.7053985D+00  0.4218672D+00  0.2220884D+00  0.5734830D+00
 
            5              6              7              8
  1    0.4583488D+00  0.1038978D+01  0.5348427D-01  0.1524701D+00
  2    0.2002479D+00  0.6918569D+00  0.8177994D+00  0.7537430D+00
  3    0.8438306D+00  0.9853348D+00  0.9278763D+00  0.2635828D+00
  4    0.1104381D+00  0.6900804D-01  0.5622625D+00  0.5579221D+00
  5    0.3204257D+00  0.6834312D+00  0.5864726D+00  0.9494382D+00
  6    0.8385232D+00  0.4518941D+00  0.8062577D+00  0.7644782D+00
  7    0.8656382D+00  0.5781638D+00  0.6401329D-01 -0.1447037D-01
  8    0.5517682D+00  0.8057772D+00  0.5710292D+00  0.5608479D+00
 
 B0 matr. ( 8X 3)
 
            1              2              3
  1   -0.5008794D+00 -0.3262392D+00 -0.7949956D-01
  2   -0.3867745D+00 -0.2503598D+00 -0.7925883D-01
  3   -0.4096848D+00 -0.2308553D+00 -0.4774682D+00
  4   -0.4216298D+00 -0.2886426D+00  0.9378121D-01
  5   -0.5412259D+00 -0.3257056D+00 -0.3932090D+00
  6   -0.4651283D+00 -0.2651356D+00 -0.5072632D+00
  7   -0.1880768D+00 -0.1016262D+00 -0.2690981D+00
  8   -0.4747183D+00 -0.3350921D+00  0.2214139D+00
 
 
 
 *** Output Data ************
 
 
 A matrix ( 8X 8)
 
            1              2              3              4
  1   -0.3878784D+00 -0.5913089D-01 -0.1924701D+00  0.1697809D+00
  2    0.2059667D-01 -0.4559455D-01  0.6316019D+00  0.1505255D+00
  3    0.1127074D+00 -0.9252113D-01 -0.4889181D+00 -0.2166241D+00
  4   -0.9210843D-02 -0.2794070D-01  0.2152139D+00  0.1533163D-01
  5   -0.2095089D+00 -0.5987008D+00  0.2860237D+00 -0.3431023D+00
  6   -0.1240162D-01 -0.2037373D+00  0.9907237D-01 -0.4453803D+00
  7    0.2494413D+00  0.4637544D-01  0.2310500D+00 -0.7920494D+00
  8    0.3054973D+00 -0.8968967D-01  0.1274212D+00  0.7108702D+00
 
            5              6              7              8
  1    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.2261718D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  3   -0.2876969D+00 -0.4964409D+00  0.0000000D+00  0.0000000D+00
  4   -0.3701628D+00  0.2270329D+00 -0.6736611D+00  0.0000000D+00
  5   -0.2960558D+00 -0.2426556D+00 -0.9720622D-01  0.8643250D+00
  6   -0.5791077D+00  0.1929659D+00 -0.1733950D+00  0.1622291D+00
  7    0.2089043D-01 -0.5959984D+00  0.2457527D+01 -0.1724138D+01
  8    0.1510422D+00  0.1608398D+00 -0.1976100D+01  0.1977683D+01
 
 B matrix ( 8X 3)
 
            1              2              3
  1    0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.1622871D-15  0.0000000D+00  0.0000000D+00
  7    0.1011789D+01  0.6730231D+00  0.0000000D+00
  8   -0.7016915D+00 -0.3895592D+00 -0.8847260D+00
 
 U matrix ( 8X 8)
 
            1              2              3              4
  1    0.5250820D-01  0.5335586D+00  0.4595955D-01 -0.2127771D+00
  2   -0.6850818D+00 -0.2543760D+00  0.3399596D+00  0.3472912D-01
  3    0.3080434D+00 -0.5491208D+00 -0.4315157D+00 -0.2360687D+00
  4   -0.3525289D+00  0.4719685D+00 -0.4204442D+00 -0.2274918D+00
  5    0.3357097D+00 -0.3000886D-01  0.4431278D+00 -0.5634715D+00
  6    0.2667688D-01 -0.1220868D+00  0.1754470D+00  0.5262863D+00
  7   -0.4327255D+00 -0.3201388D+00 -0.3063530D-01 -0.4902299D+00
  8    0.8985783D-01  0.8958573D-01  0.5396792D+00 -0.1060003D+00
 
            5              6              7              8
  1    0.4158960D+00 -0.6555736D+00  0.1189098D+00 -0.2197406D+00
  2    0.2862171D+00 -0.2141755D+00  0.5610616D-01  0.4671593D+00
  3    0.4292047D+00 -0.7918714D-01  0.3899397D+00  0.1382066D+00
  4   -0.1632578D+00  0.3050322D+00  0.4955571D+00  0.2432462D+00
  5   -0.4324927D+00 -0.1542155D+00  0.1550020D+00  0.3710500D+00
  6   -0.3134849D+00 -0.2620370D+00  0.6840440D+00 -0.2043815D+00
  7   -0.2266926D+00 -0.6207724D-01  0.2505416D-01 -0.6427481D+00
  8    0.4444415D+00  0.5733563D+00  0.3041598D+00 -0.2502627D+00
 
 *** Testing norm U*A0-A*U =0.303913D-15
 *** which should be of the order of the machine precision
 *** norm(A)
 *** Testing norm U*B0-B =0.104837D-15
 *** which should be of the order of the machine precision
 *** norm(B)
 *** Testing norm U*UP-I =0.210819D-15
 *** which should be of the order of the machine precision
1*** This second example is an ill-conditioned one.
 *** Therefore A, B and U can differ a lot from those obtained
 *** on another machine, but the above norm tests should yet
 *** be close to the machine precision (because of backward
 *** stability).
1*** First example : Square root covariance filter with
 *** A, B, C in (lower) observer Hessenberg form and
 *** lower triangular Q, R.
 
 
 *** Input SRCFOB
 
 
 
 
 *** Input OBHESS
 
 
 *** N =  6 M =  2 P =   2
 
 
 *** UPPER = .FALSE.
 
 
 A matrix ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.8497452D+00  0.7263507D+00  0.8833888D+00
  2    0.7560439D+00  0.6857310D+00  0.1985144D+00  0.6525135D+00
  3    0.2211346D-03  0.8782165D+00  0.5442573D+00  0.3076091D+00
  4    0.3303271D+00  0.6837404D-01  0.2320748D+00  0.9329616D+00
  5    0.6653811D+00  0.5608486D+00  0.2312237D+00  0.2146008D+00
  6    0.6283918D+00  0.6623569D+00  0.2164633D+00  0.3126420D+00
 
            5              6
  1    0.3616361D+00  0.5015342D+00
  2    0.2922267D+00  0.4368588D+00
  3    0.5664249D+00  0.2693125D+00
  4    0.4826472D+00  0.6325745D+00
  5    0.3321719D+00  0.4051954D+00
  6    0.5935095D+00  0.9184708D+00
 
 B matrix ( 6X 2)
 
            1              2
  1    0.4373343D-01  0.7783129D+00
  2    0.4818509D+00  0.2119030D+00
  3    0.2639556D+00  0.1121355D+00
  4    0.4148104D+00  0.6856896D+00
  5    0.2806498D+00  0.1531217D+00
  6    0.1280058D+00  0.6970851D+00
 
 C matrix ( 2X 6)
 
            1              2              3              4
  1    0.5618661D+00  0.6853980D+00  0.5042213D+00  0.3873779D+00
  2    0.5896177D+00  0.8906225D+00  0.3493615D+00  0.9222899D+00
 
            5              6
  1    0.9488184D+00  0.3760119D+00
  2    0.3435337D+00  0.7340941D+00
 
 
 
 *** Output OBHESS
 
 
 Au matr. ( 6X 6)
 
            1              2              3              4
  1    0.2555206D+01  0.1028752D+01  0.1692890D+00  0.0000000D+00
  2    0.8254461D+00  0.5689337D+00 -0.2275675D+00  0.5039626D+00
  3    0.5521221D+00  0.4692318D-01  0.1783014D+00 -0.4475458D+00
  4    0.3535732D+00 -0.5489957D-01  0.1106179D+00  0.2362827D+00
  5   -0.9226369D-01 -0.2917360D+00  0.1524245D+00 -0.1157029D-01
  6    0.1003704D+00 -0.8503523D-01 -0.2923006D+00 -0.7379939D-01
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.4314205D+00  0.0000000D+00
  4    0.2492206D+00 -0.2010546D+00
  5   -0.2519957D+00 -0.4671646D+00
  6    0.4474299D+00  0.3381892D+00
 
 Bu matr. ( 6X 2)
 
            1              2
  1    0.4373343D-01  0.7783129D+00
  2    0.4818509D+00  0.2119030D+00
  3    0.2639556D+00  0.1121355D+00
  4    0.4148104D+00  0.6856896D+00
  5    0.2806498D+00  0.1531217D+00
  6    0.1280058D+00  0.6970851D+00
 
 Cu matr. ( 2X 6)
 
            1              2              3              4
  1   -0.1493789D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.1390508D+01 -0.9148361D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
 
 U matr.  ( 6X 6)
 
            1              2              3              4
  1   -0.3761348D+00 -0.4588318D+00 -0.3375452D+00 -0.2593257D+00
  2   -0.7279893D-01 -0.2761292D+00  0.1311687D+00 -0.6139846D+00
  3   -0.3363314D+00 -0.8806412D-01 -0.4842760D+00  0.6014684D+00
  4   -0.4538942D-01  0.7750182D+00 -0.7832899D-01 -0.1614651D+00
  5    0.8587101D+00 -0.2248876D+00 -0.3086938D+00  0.7347054D-01
  6    0.2570883D-01  0.2329016D+00 -0.7300051D+00 -0.4031625D+00
 
            5              6
  1   -0.6351756D+00 -0.2517168D+00
  2    0.5899235D+00 -0.4198344D+00
  3    0.4091945D+00 -0.3397031D+00
  4   -0.1993882D+00 -0.5703723D+00
  5   -0.8402300D-01 -0.3229441D+00
  6    0.1851660D+00  0.4640712D+00
 
 
 
 *** Additional input to SRCFOB
 
 
 R matr.  ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.0000000D+00
  2    0.4498763D+00  0.7227253D+00
 
 Q matr.  ( 2X 2)
 
            1              2
  1    0.1000000D+01  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01
 
 
 
 *** Output SRCFOB for MULTBQ=.TRUE.
 
 
 *** ISTEP =  1
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1089571D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7281569D+00 -0.2311728D+00  0.0000000D+00  0.0000000D+00
  3   -0.2636141D-02 -0.1666184D+00  0.0000000D+00  0.0000000D+00
  4    0.2459465D+00 -0.3725796D+00  0.0000000D+00  0.0000000D+00
  5   -0.2107426D+00  0.3863074D+00  0.0000000D+00  0.0000000D+00
  6    0.2928585D-01  0.1462207D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.6076835D+00  0.1859999D+00  0.9882016D-01  0.5518221D+00
  2    0.1859999D+00  0.2770832D+00  0.1509491D+00  0.3451765D+00
  3    0.9882016D-01  0.1509491D+00  0.8224692D-01  0.1863816D+00
  4    0.5518221D+00  0.3451765D+00  0.1863816D+00  0.6422379D+00
  5    0.1314503D+00  0.1676783D+00  0.9124946D-01  0.2214104D+00
  6    0.5481484D+00  0.2093942D+00  0.1119558D+00  0.5310821D+00
 
            5              6
  1    0.1314503D+00  0.5481484D+00
  2    0.1676783D+00  0.2093942D+00
  3    0.9124946D-01  0.1119558D+00
  4    0.2214104D+00  0.5310821D+00
  5    0.1022106D+00  0.1426636D+00
  6    0.1426636D+00  0.5023131D+00
 
 *** ISTEP =  2
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1137694D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7765132D+00  0.2534073D+00  0.0000000D+00  0.0000000D+00
  3   -0.6769487D-01  0.4761430D-01 -0.3163097D+00  0.0000000D+00
  4    0.2449570D+00  0.3316677D+00 -0.1730311D+00 -0.2070183D-01
  5   -0.1761697D+00 -0.2962042D+00  0.2965832D+00  0.4669850D-02
  6   -0.4744392D-01 -0.2449730D+00 -0.2222014D+00  0.7303788D-01
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2178193D+01  0.1037101D-01
  2   -0.8136910D+00 -0.4985807D-01
  3   -0.4052180D+00  0.1030031D+00
  4   -0.2121238D+00  0.7178771D-03
  5    0.2298249D+00 -0.4460418D-01
  6   -0.9910064D-01  0.9797726D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.6191745D+00  0.1788886D+00  0.1192075D+00  0.5423612D+00
  2    0.1788886D+00  0.3497187D+00  0.8757649D-01  0.4246670D+00
  3    0.1192075D+00  0.8757649D-01  0.1561725D+00  0.1148228D+00
  4    0.5423612D+00  0.4246670D+00  0.1148228D+00  0.7294913D+00
  5    0.1256196D+00  0.2236019D+00  0.4199030D-01  0.2826671D+00
  6    0.5393206D+00  0.2903891D+00  0.4010983D-01  0.6198606D+00
 
            5              6
  1    0.1256196D+00  0.5393206D+00
  2    0.2236019D+00  0.2903891D+00
  3    0.4199030D-01  0.4010983D-01
  4    0.2826671D+00  0.6198606D+00
  5    0.1452790D+00  0.2050529D+00
  6    0.2050529D+00  0.5927042D+00
 
 *** ISTEP =  3
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1139678D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7809824D+00  0.2603205D+00  0.0000000D+00  0.0000000D+00
  3   -0.6587458D-01  0.5751174D-01 -0.3191852D+00  0.0000000D+00
  4    0.2470454D+00  0.3329142D+00 -0.1692704D+00  0.5785183D-01
  5   -0.1750882D+00 -0.2802188D+00  0.2810173D+00 -0.1184551D+00
  6   -0.4504221D-01 -0.2265318D+00 -0.2330436D+00 -0.1011985D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.7575174D-01  0.0000000D+00
  6   -0.1291215D-01 -0.3847776D-01
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2169897D+01  0.1373540D-02
  2   -0.8053058D+00 -0.6368138D-01
  3   -0.4074378D+00  0.9820538D-01
  4   -0.2124421D+00 -0.5890905D-02
  5    0.2271468D+00 -0.4705703D-01
  6   -0.9862450D-01  0.9200723D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.6202819D+00  0.1797702D+00  0.1205935D+00  0.5448988D+00
  2    0.1797702D+00  0.3506024D+00  0.8775846D-01  0.4262485D+00
  3    0.1205935D+00  0.8775846D-01  0.1625767D+00  0.1202222D+00
  4    0.5448988D+00  0.4262485D+00  0.1202222D+00  0.7363649D+00
  5    0.1251047D+00  0.2236627D+00  0.3896033D-01  0.2803513D+00
  6    0.5413832D+00  0.2911459D+00  0.4717723D-01  0.6267229D+00
 
            5              6
  1    0.1251047D+00  0.5413832D+00
  2    0.2236627D+00  0.2911459D+00
  3    0.3896033D-01  0.4717723D-01
  4    0.2803513D+00  0.6267229D+00
  5    0.1467371D+00  0.2018021D+00
  6    0.2018021D+00  0.6008554D+00
 
 
 
 *** Output SRCFOB for MULTBQ=.FALSE.
 
 
 *** ISTEP =  1
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1089571D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7281569D+00 -0.2311728D+00  0.0000000D+00  0.0000000D+00
  3   -0.2636141D-02 -0.1666184D+00  0.0000000D+00  0.0000000D+00
  4    0.2459465D+00 -0.3725796D+00  0.0000000D+00  0.0000000D+00
  5   -0.2107426D+00  0.3863074D+00  0.0000000D+00  0.0000000D+00
  6    0.2928585D-01  0.1462207D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.6076835D+00  0.1859999D+00  0.9882016D-01  0.5518221D+00
  2    0.1859999D+00  0.2770832D+00  0.1509491D+00  0.3451765D+00
  3    0.9882016D-01  0.1509491D+00  0.8224692D-01  0.1863816D+00
  4    0.5518221D+00  0.3451765D+00  0.1863816D+00  0.6422379D+00
  5    0.1314503D+00  0.1676783D+00  0.9124946D-01  0.2214104D+00
  6    0.5481484D+00  0.2093942D+00  0.1119558D+00  0.5310821D+00
 
            5              6
  1    0.1314503D+00  0.5481484D+00
  2    0.1676783D+00  0.2093942D+00
  3    0.9124946D-01  0.1119558D+00
  4    0.2214104D+00  0.5310821D+00
  5    0.1022106D+00  0.1426636D+00
  6    0.1426636D+00  0.5023131D+00
 
 *** ISTEP =  2
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1137694D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7765132D+00  0.2534073D+00  0.0000000D+00  0.0000000D+00
  3   -0.6769487D-01  0.4761430D-01 -0.3163097D+00  0.0000000D+00
  4    0.2449570D+00  0.3316677D+00 -0.1730311D+00 -0.2070183D-01
  5   -0.1761697D+00 -0.2962042D+00  0.2965832D+00  0.4669850D-02
  6   -0.4744392D-01 -0.2449730D+00 -0.2222014D+00  0.7303788D-01
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2178193D+01  0.1037101D-01
  2   -0.8136910D+00 -0.4985807D-01
  3   -0.4052180D+00  0.1030031D+00
  4   -0.2121238D+00  0.7178771D-03
  5    0.2298249D+00 -0.4460418D-01
  6   -0.9910064D-01  0.9797726D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.6191745D+00  0.1788886D+00  0.1192075D+00  0.5423612D+00
  2    0.1788886D+00  0.3497187D+00  0.8757649D-01  0.4246670D+00
  3    0.1192075D+00  0.8757649D-01  0.1561725D+00  0.1148228D+00
  4    0.5423612D+00  0.4246670D+00  0.1148228D+00  0.7294913D+00
  5    0.1256196D+00  0.2236019D+00  0.4199030D-01  0.2826671D+00
  6    0.5393206D+00  0.2903891D+00  0.4010983D-01  0.6198606D+00
 
            5              6
  1    0.1256196D+00  0.5393206D+00
  2    0.2236019D+00  0.2903891D+00
  3    0.4199030D-01  0.4010983D-01
  4    0.2826671D+00  0.6198606D+00
  5    0.1452790D+00  0.2050529D+00
  6    0.2050529D+00  0.5927042D+00
 
 *** ISTEP =  3
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1139678D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.7809824D+00  0.2603205D+00  0.0000000D+00  0.0000000D+00
  3   -0.6587458D-01  0.5751174D-01 -0.3191852D+00  0.0000000D+00
  4    0.2470454D+00  0.3329142D+00 -0.1692704D+00  0.5785183D-01
  5   -0.1750882D+00 -0.2802188D+00  0.2810173D+00 -0.1184551D+00
  6   -0.4504221D-01 -0.2265318D+00 -0.2330436D+00 -0.1011985D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.7575174D-01  0.0000000D+00
  6   -0.1291215D-01 -0.3847776D-01
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2169897D+01  0.1373540D-02
  2   -0.8053058D+00 -0.6368138D-01
  3   -0.4074378D+00  0.9820538D-01
  4   -0.2124421D+00 -0.5890905D-02
  5    0.2271468D+00 -0.4705703D-01
  6   -0.9862450D-01  0.9200723D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.6202819D+00  0.1797702D+00  0.1205935D+00  0.5448988D+00
  2    0.1797702D+00  0.3506024D+00  0.8775846D-01  0.4262485D+00
  3    0.1205935D+00  0.8775846D-01  0.1625767D+00  0.1202222D+00
  4    0.5448988D+00  0.4262485D+00  0.1202222D+00  0.7363649D+00
  5    0.1251047D+00  0.2236627D+00  0.3896033D-01  0.2803513D+00
  6    0.5413832D+00  0.2911459D+00  0.4717723D-01  0.6267229D+00
 
            5              6
  1    0.1251047D+00  0.5413832D+00
  2    0.2236627D+00  0.2911459D+00
  3    0.3896033D-01  0.4717723D-01
  4    0.2803513D+00  0.6267229D+00
  5    0.1467371D+00  0.2018021D+00
  6    0.2018021D+00  0.6008554D+00
 
1*** In both these tests we start with Su=0 and perform three
 *** iterations of the filter.
 *** The ranks of Su in these three steps must be equal to
 *** M(=2), 2M(=4) and 3M(=6).
 *** K must be 0 in the first step and nonzero afterwards.
 *** The results for MULTBQ = .TRUE. and .FALSE. must be equal
 *** since we chose Q=I.
 *** The U'SuSu'U matrices are meant for comparison with
 *** SRCF.
1*** Second example : Square root covariance filter with
 *** A, B, C in (lower) observer Hessenberg form and
 *** lower triangular Q, R.
 
 
 *** Input SRCFOB
 
 
 
 
 *** Input OBHESS
 
 
 *** N =  6 M =  3 P =   2
 
 
 *** UPPER = .FALSE.
 
 
 A matrix ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.8497452D+00  0.7263507D+00  0.8833888D+00
  2    0.7560439D+00  0.6857310D+00  0.1985144D+00  0.6525135D+00
  3    0.2211346D-03  0.8782165D+00  0.5442573D+00  0.3076091D+00
  4    0.3303271D+00  0.6837404D-01  0.2320748D+00  0.9329616D+00
  5    0.6653811D+00  0.5608486D+00  0.2312237D+00  0.2146008D+00
  6    0.6283918D+00  0.6623569D+00  0.2164633D+00  0.3126420D+00
 
            5              6
  1    0.3616361D+00  0.5015342D+00
  2    0.2922267D+00  0.4368588D+00
  3    0.5664249D+00  0.2693125D+00
  4    0.4826472D+00  0.6325745D+00
  5    0.3321719D+00  0.4051954D+00
  6    0.5935095D+00  0.9184708D+00
 
 B matrix ( 6X 3)
 
            1              2              3
  1    0.4373343D-01  0.7783129D+00  0.8415518D+00
  2    0.4818509D+00  0.2119030D+00  0.4062025D+00
  3    0.2639556D+00  0.1121355D+00  0.4094825D+00
  4    0.4148104D+00  0.6856896D+00  0.8784126D+00
  5    0.2806498D+00  0.1531217D+00  0.1138360D+00
  6    0.1280058D+00  0.6970851D+00  0.1998338D+00
 
 C matrix ( 2X 6)
 
            1              2              3              4
  1    0.5618661D+00  0.6853980D+00  0.5042213D+00  0.3873779D+00
  2    0.5896177D+00  0.8906225D+00  0.3493615D+00  0.9222899D+00
 
            5              6
  1    0.9488184D+00  0.3760119D+00
  2    0.3435337D+00  0.7340941D+00
 
 
 
 *** Output OBHESS
 
 
 Au matr. ( 6X 6)
 
            1              2              3              4
  1    0.2555206D+01  0.1028752D+01  0.1692890D+00  0.0000000D+00
  2    0.8254461D+00  0.5689337D+00 -0.2275675D+00  0.5039626D+00
  3    0.5521221D+00  0.4692318D-01  0.1783014D+00 -0.4475458D+00
  4    0.3535732D+00 -0.5489957D-01  0.1106179D+00  0.2362827D+00
  5   -0.9226369D-01 -0.2917360D+00  0.1524245D+00 -0.1157029D-01
  6    0.1003704D+00 -0.8503523D-01 -0.2923006D+00 -0.7379939D-01
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.4314205D+00  0.0000000D+00
  4    0.2492206D+00 -0.2010546D+00
  5   -0.2519957D+00 -0.4671646D+00
  6    0.4474299D+00  0.3381892D+00
 
 Bu matr. ( 6X 3)
 
            1              2              3
  1    0.4373343D-01  0.7783129D+00  0.8415518D+00
  2    0.4818509D+00  0.2119030D+00  0.4062025D+00
  3    0.2639556D+00  0.1121355D+00  0.4094825D+00
  4    0.4148104D+00  0.6856896D+00  0.8784126D+00
  5    0.2806498D+00  0.1531217D+00  0.1138360D+00
  6    0.1280058D+00  0.6970851D+00  0.1998338D+00
 
 Cu matr. ( 2X 6)
 
            1              2              3              4
  1   -0.1493789D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2   -0.1390508D+01 -0.9148361D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
 
 U matr.  ( 6X 6)
 
            1              2              3              4
  1   -0.3761348D+00 -0.4588318D+00 -0.3375452D+00 -0.2593257D+00
  2   -0.7279893D-01 -0.2761292D+00  0.1311687D+00 -0.6139846D+00
  3   -0.3363314D+00 -0.8806412D-01 -0.4842760D+00  0.6014684D+00
  4   -0.4538942D-01  0.7750182D+00 -0.7832899D-01 -0.1614651D+00
  5    0.8587101D+00 -0.2248876D+00 -0.3086938D+00  0.7347054D-01
  6    0.2570883D-01  0.2329016D+00 -0.7300051D+00 -0.4031625D+00
 
            5              6
  1   -0.6351756D+00 -0.2517168D+00
  2    0.5899235D+00 -0.4198344D+00
  3    0.4091945D+00 -0.3397031D+00
  4   -0.1993882D+00 -0.5703723D+00
  5   -0.8402300D-01 -0.3229441D+00
  6    0.1851660D+00  0.4640712D+00
 
 
 
 *** Additional input to SRCFOB
 
 
 R matr.  ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.0000000D+00
  2    0.4498763D+00  0.7227253D+00
 
 Q matr.  ( 3X 3)
 
            1              2              3
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01
 
 
 
 *** Output SRCFOB for MULTBQ=.TRUE.
 
 
 *** ISTEP =  1
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1473197D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.9933841D+00  0.2313773D+00  0.0000000D+00  0.0000000D+00
  3    0.4834992D-02  0.1668591D+00 -0.2217796D-02  0.0000000D+00
  4    0.2047631D+00  0.3663481D+00  0.1559494D+00  0.0000000D+00
  5   -0.4892480D+00 -0.3954030D+00  0.2080681D+00  0.0000000D+00
  6    0.3063678D+00 -0.1337691D+00 -0.2990338D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.1315893D+01  0.5278403D+00  0.4434210D+00  0.1291052D+01
  2    0.5278403D+00  0.4420836D+00  0.3172819D+00  0.7019898D+00
  3    0.4434210D+00  0.3172819D+00  0.2499229D+00  0.5460763D+00
  4    0.1291052D+01  0.7019898D+00  0.5460763D+00  0.1413847D+01
  5    0.2272492D+00  0.2139188D+00  0.1378633D+00  0.3214053D+00
  6    0.7163189D+00  0.2905672D+00  0.1937843D+00  0.7066186D+00
 
            5              6
  1    0.2272492D+00  0.7163189D+00
  2    0.2139188D+00  0.2905672D+00
  3    0.1378633D+00  0.1937843D+00
  4    0.3214053D+00  0.7066186D+00
  5    0.1151692D+00  0.1654119D+00
  6    0.1654119D+00  0.5422466D+00
 
 *** ISTEP =  2
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1509250D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.1028535D+01  0.2648476D+00  0.0000000D+00  0.0000000D+00
  3   -0.4479169D-01  0.5438558D-01  0.3209755D+00  0.0000000D+00
  4    0.2051662D+00  0.3611828D+00  0.1509357D+00 -0.1667655D+00
  5   -0.4592073D+00 -0.2608942D+00 -0.3265998D+00 -0.2396053D+00
  6    0.2422058D+00 -0.2359756D+00  0.2792051D+00  0.2933618D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1248865D+00  0.0000000D+00
  6    0.1325540D+00 -0.9864988D-04
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2185942D+01  0.1045739D-01
  2   -0.7867206D+00 -0.5015872D-01
  3   -0.3920627D+00  0.1028564D+00
  4   -0.1505459D+00  0.3143631D-04
  5    0.2636031D+00 -0.4498072D-01
  6   -0.1012425D+00  0.9800114D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.1330316D+01  0.5251988D+00  0.4620110D+00  0.1279880D+01
  2    0.5251988D+00  0.5215331D+00  0.2511694D+00  0.7788723D+00
  3    0.4620110D+00  0.2511694D+00  0.3249502D+00  0.4755661D+00
  4    0.1279880D+01  0.7788723D+00  0.4755661D+00  0.1502098D+01
  5    0.2228020D+00  0.2719514D+00  0.8775607D-01  0.3818548D+00
  6    0.6996234D+00  0.3595680D+00  0.1267612D+00  0.7999878D+00
 
            5              6
  1    0.2228020D+00  0.6996234D+00
  2    0.2719514D+00  0.3595680D+00
  3    0.8775607D-01  0.1267612D+00
  4    0.3818548D+00  0.7999878D+00
  5    0.1588905D+00  0.2240887D+00
  6    0.2240887D+00  0.6537501D+00
 
 *** ISTEP =  3
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1513045D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.1036342D+01  0.2789338D+00  0.0000000D+00  0.0000000D+00
  3   -0.4444386D-01  0.6319867D-01  0.3251781D+00  0.0000000D+00
  4    0.2097397D+00  0.3699629D+00  0.1503332D+00 -0.1731548D+00
  5   -0.4596034D+00 -0.2352881D+00 -0.3086596D+00 -0.1971504D+00
  6    0.2439566D+00 -0.2132917D+00  0.2854132D+00  0.3035185D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.2491755D+00  0.0000000D+00
  6   -0.6822330D-01 -0.1241220D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2163711D+01 -0.7008579D-02
  2   -0.7582881D+00 -0.7601443D-01
  3   -0.3930339D+00  0.9937889D-01
  4   -0.1392636D+00 -0.1409697D-01
  5    0.2576544D+00 -0.4442942D-01
  6   -0.9546321D-01  0.9064929D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.1336443D+01  0.5273198D+00  0.4630203D+00  0.1290080D+01
  2    0.5273198D+00  0.5232849D+00  0.2500605D+00  0.7812362D+00
  3    0.4630203D+00  0.2500605D+00  0.3325495D+00  0.4824935D+00
  4    0.1290080D+01  0.7812362D+00  0.4824935D+00  0.1522808D+01
  5    0.2228995D+00  0.2727956D+00  0.8402249D-01  0.3793561D+00
  6    0.7056683D+00  0.3593035D+00  0.1371167D+00  0.8167559D+00
 
            5              6
  1    0.2228995D+00  0.7056683D+00
  2    0.2727956D+00  0.3593035D+00
  3    0.8402249D-01  0.1371167D+00
  4    0.3793561D+00  0.8167559D+00
  5    0.1607912D+00  0.2194102D+00
  6    0.2194102D+00  0.6718702D+00
 
 
 
 *** Output SRCFOB for MULTBQ=.FALSE.
 
 
 *** ISTEP =  1
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1473197D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.9933841D+00  0.2313773D+00  0.0000000D+00  0.0000000D+00
  3    0.4834992D-02  0.1668591D+00 -0.2217796D-02  0.0000000D+00
  4    0.2047631D+00  0.3663481D+00  0.1559494D+00  0.0000000D+00
  5   -0.4892480D+00 -0.3954030D+00  0.2080681D+00  0.0000000D+00
  6    0.3063678D+00 -0.1337691D+00 -0.2990338D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.1315893D+01  0.5278403D+00  0.4434210D+00  0.1291052D+01
  2    0.5278403D+00  0.4420836D+00  0.3172819D+00  0.7019898D+00
  3    0.4434210D+00  0.3172819D+00  0.2499229D+00  0.5460763D+00
  4    0.1291052D+01  0.7019898D+00  0.5460763D+00  0.1413847D+01
  5    0.2272492D+00  0.2139188D+00  0.1378633D+00  0.3214053D+00
  6    0.7163189D+00  0.2905672D+00  0.1937843D+00  0.7066186D+00
 
            5              6
  1    0.2272492D+00  0.7163189D+00
  2    0.2139188D+00  0.2905672D+00
  3    0.1378633D+00  0.1937843D+00
  4    0.3214053D+00  0.7066186D+00
  5    0.1151692D+00  0.1654119D+00
  6    0.1654119D+00  0.5422466D+00
 
 *** ISTEP =  2
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1509250D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.1028535D+01  0.2648476D+00  0.0000000D+00  0.0000000D+00
  3   -0.4479169D-01  0.5438558D-01  0.3209755D+00  0.0000000D+00
  4    0.2051662D+00  0.3611828D+00  0.1509357D+00 -0.1667655D+00
  5   -0.4592073D+00 -0.2608942D+00 -0.3265998D+00 -0.2396053D+00
  6    0.2422058D+00 -0.2359756D+00  0.2792051D+00  0.2933618D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1248865D+00  0.0000000D+00
  6    0.1325540D+00 -0.9864988D-04
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2185942D+01  0.1045739D-01
  2   -0.7867206D+00 -0.5015872D-01
  3   -0.3920627D+00  0.1028564D+00
  4   -0.1505459D+00  0.3143631D-04
  5    0.2636031D+00 -0.4498072D-01
  6   -0.1012425D+00  0.9800114D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.1330316D+01  0.5251988D+00  0.4620110D+00  0.1279880D+01
  2    0.5251988D+00  0.5215331D+00  0.2511694D+00  0.7788723D+00
  3    0.4620110D+00  0.2511694D+00  0.3249502D+00  0.4755661D+00
  4    0.1279880D+01  0.7788723D+00  0.4755661D+00  0.1502098D+01
  5    0.2228020D+00  0.2719514D+00  0.8775607D-01  0.3818548D+00
  6    0.6996234D+00  0.3595680D+00  0.1267612D+00  0.7999878D+00
 
            5              6
  1    0.2228020D+00  0.6996234D+00
  2    0.2719514D+00  0.3595680D+00
  3    0.8775607D-01  0.1267612D+00
  4    0.3818548D+00  0.7999878D+00
  5    0.1588905D+00  0.2240887D+00
  6    0.2240887D+00  0.6537501D+00
 
 *** ISTEP =  3
 Su matr. ( 6X 6)
 
            1              2              3              4
  1    0.1513045D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.1036342D+01  0.2789338D+00  0.0000000D+00  0.0000000D+00
  3   -0.4444386D-01  0.6319867D-01  0.3251781D+00  0.0000000D+00
  4    0.2097397D+00  0.3699629D+00  0.1503332D+00 -0.1731548D+00
  5   -0.4596034D+00 -0.2352881D+00 -0.3086596D+00 -0.1971504D+00
  6    0.2439566D+00 -0.2132917D+00  0.2854132D+00  0.3035185D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5   -0.2491755D+00  0.0000000D+00
  6   -0.6822330D-01 -0.1241220D+00
 
 Ku matr. ( 6X 2)
 
            1              2
  1   -0.2163711D+01 -0.7008579D-02
  2   -0.7582881D+00 -0.7601443D-01
  3   -0.3930339D+00  0.9937889D-01
  4   -0.1392636D+00 -0.1409697D-01
  5    0.2576544D+00 -0.4442942D-01
  6   -0.9546321D-01  0.9064929D-01
 
 U'SuSu'U ( 6X 6)
 
            1              2              3              4
  1    0.1336443D+01  0.5273198D+00  0.4630203D+00  0.1290080D+01
  2    0.5273198D+00  0.5232849D+00  0.2500605D+00  0.7812362D+00
  3    0.4630203D+00  0.2500605D+00  0.3325495D+00  0.4824935D+00
  4    0.1290080D+01  0.7812362D+00  0.4824935D+00  0.1522808D+01
  5    0.2228995D+00  0.2727956D+00  0.8402249D-01  0.3793561D+00
  6    0.7056683D+00  0.3593035D+00  0.1371167D+00  0.8167559D+00
 
            5              6
  1    0.2228995D+00  0.7056683D+00
  2    0.2727956D+00  0.3593035D+00
  3    0.8402249D-01  0.1371167D+00
  4    0.3793561D+00  0.8167559D+00
  5    0.1607912D+00  0.2194102D+00
  6    0.2194102D+00  0.6718702D+00
 
1*** In both these tests we start with Su=0 and perform three
 *** iterations of the filter.
 *** The ranks of Su in these three steps must be equal to
 *** M(=3), 2M(=6) and min(N,3M)(=6).
 *** K must be 0 in the first step and nonzero afterwards.
 *** The results for MULTBQ = .TRUE. and .FALSE. must be equal
 *** since we chose Q=I.
 *** The U'SuSu'U matrices are meant for comparison with
 *** SRCF.
1*** First example : Square root information filter with
 *** A, B, C in (upper) controller Hessenberg form
 *** and upper triangular Q, R.
 
 
 *** Input SRIFCO
 
 
 
 
 *** Input COHESS
 
 
 *** N =  6 M =  2 P =   2
 
 
 *** UPPER = .TRUE.
 
 
 Ainv     ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.7560439D+00  0.2211346D-03  0.3303271D+00
  2    0.8497452D+00  0.6857310D+00  0.8782165D+00  0.6837404D-01
  3    0.7263507D+00  0.1985144D+00  0.5442573D+00  0.2320748D+00
  4    0.8833888D+00  0.6525135D+00  0.3076091D+00  0.9329616D+00
  5    0.3616361D+00  0.2922267D+00  0.5664249D+00  0.4826472D+00
  6    0.5015342D+00  0.4368588D+00  0.2693125D+00  0.6325745D+00
 
            5              6
  1    0.6653811D+00  0.6283918D+00
  2    0.5608486D+00  0.6623569D+00
  3    0.2312237D+00  0.2164633D+00
  4    0.2146008D+00  0.3126420D+00
  5    0.3321719D+00  0.5935095D+00
  6    0.4051954D+00  0.9184708D+00
 
 AinvB    ( 6X 2)
 
            1              2
  1   -0.8805479D+00  0.5207521D+00
  2   -0.6075187D+00  0.1168888D+01
  3    0.1325720D+01 -0.1693905D+00
  4    0.1038693D+01 -0.2305789D+00
  5    0.2103993D+01 -0.1115921D+01
  6   -0.8531301D+00  0.6597089D+00
 
 C matrix ( 2X 6)
 
            1              2              3              4
  1    0.4373343D-01  0.4818509D+00  0.2639556D+00  0.4148104D+00
  2    0.7783129D+00  0.2119030D+00  0.1121355D+00  0.6856896D+00
 
            5              6
  1    0.2806498D+00  0.1280058D+00
  2    0.1531217D+00  0.6970851D+00
 
 
 
 *** Output COHESS
 
 
 Ainvu    ( 6X 6)
 
            1              2              3              4
  1    0.2008873D+00 -0.4245205D+00 -0.2097518D+00 -0.3048541D+00
  2   -0.3163469D+00  0.1677275D+01  0.1466019D+01  0.1811058D+00
  3   -0.3222207D+00  0.1153122D+01  0.9599862D+00  0.4765324D+00
  4    0.0000000D+00  0.6345976D+00  0.4285850D+00  0.7299071D+00
  5    0.0000000D+00  0.0000000D+00 -0.1809051D+00 -0.2320514D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.2239701D+00
 
            5              6
  1    0.3711037D+00 -0.4634347D+00
  2   -0.6791964D+00  0.2697618D+00
  3   -0.7025880D-01 -0.5388063D+00
  4    0.2432710D+00  0.2488519D+00
  5   -0.4329501D-01  0.2608173D-01
  6    0.4072138D+00  0.1001569D+00
 
 AinvBu   ( 6X 2)
 
            1              2
  1    0.3022495D+01 -0.1503209D+01
  2    0.0000000D+00 -0.1067802D+01
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Cu matr. ( 2X 6)
 
            1              2              3              4
  1    0.3079669D+00 -0.6366799D+00 -0.1717533D+00 -0.1589127D+00
  2   -0.7468438D-01 -0.6111938D+00 -0.7937632D+00 -0.7348406D+00
 
            5              6
  1   -0.1254464D+00  0.1699368D-01
  2    0.2759580D+00 -0.1321099D+00
 
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.1000000D+01
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1000000D+01  0.0000000D+00
  6    0.0000000D+00  0.1000000D+01
 
 
 
 *** Additional input to SRIFCO
 
 
 QINV     ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.4498763D+00
  2    0.0000000D+00  0.7227253D+00
 
 RINV     ( 2X 2)
 
            1              2
  1    0.1000000D+01  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01
 
 Z vector ( 2X 1)
 
            1
  1    0.1964506D-02
  2    0.5075221D+00
 
 XU vect. ( 6X 1)
 
            1
  1    0.2364137D+00
  2   -0.1298232D+01
  3   -0.4510789D+00
  4   -0.6043419D+00
  5    0.5162359D-01
  6   -0.5897994D-01
 
 Y vector ( 2X 1)
 
            1
  1    0.4304966D+00
  2    0.2280548D-01
 
 
 
 *** Output SRIFCO MULTRC=.TRUE.
 
 
 *** ISTEP =  1
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.4954922D+00  0.1491544D+01  0.9934062D+00  0.3466117D+00
  2    0.0000000D+00  0.1195245D+01  0.1244657D+01  0.9813114D+00
  3    0.0000000D+00  0.0000000D+00  0.3606548D+00 -0.8937117D-01
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.5934144D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.1046015D+00 -0.3082552D+00
  2   -0.2715828D+00  0.2137206D+00
  3   -0.3232653D+00 -0.3001329D+00
  4    0.1722770D+00 -0.1986063D+00
  5   -0.5425369D+00  0.2697796D-01
  6    0.0000000D+00 -0.3757088D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.1274126D+00
  2    0.5536566D+00
  3    0.3481973D+00
  4    0.5286097D+00
  5   -0.9193801D-02
  6   -0.3619102D+00
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.1714490D+01  0.1179989D+01  0.7484713D+00  0.1492071D+01
  2    0.1179989D+01  0.1510285D+01  0.7211262D+00  0.1389401D+01
  3    0.7484713D+00  0.7211262D+00  0.7282816D+00  0.5331254D+00
  4    0.1492071D+01  0.1389401D+01  0.5331254D+00  0.1918910D+01
  5    0.8377470D+00  0.1092735D+01  0.6115677D+00  0.9187512D+00
  6    0.1575671D+01  0.1424504D+01  0.8798712D+00  0.1673648D+01
 
            5              6
  1    0.8377470D+00  0.1575671D+01
  2    0.1092735D+01  0.1424504D+01
  3    0.6115677D+00  0.8798712D+00
  4    0.9187512D+00  0.1673648D+01
  5    0.9072298D+00  0.1207340D+01
  6    0.1207340D+01  0.2154303D+01
 
 *** ISTEP =  2
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.5600042D+00  0.2189154D+01  0.1616731D+01  0.7341513D+00
  2    0.0000000D+00  0.1268891D+01  0.1396050D+01  0.9516494D+00
  3    0.0000000D+00  0.0000000D+00 -0.2730230D+00  0.5158834D-01
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.3847519D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.1987942D+00 -0.1150981D+00
  2   -0.3759302D+00  0.1400333D+00
  3    0.2030325D+00  0.2147795D+00
  4   -0.2120656D-01 -0.3697130D-01
  5    0.1968868D+00  0.7024610D-01
  6    0.0000000D+00  0.1365539D+00
 
 X vector ( 6X 1)
 
            1
  1    0.5520679D+00
  2   -0.1257842D+01
  3    0.1402490D+01
  4    0.1279330D+01
  5    0.1134170D+01
  6   -0.2059006D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2806785D+01  0.2396039D+01  0.1379941D+01  0.2596905D+01
  2    0.2396039D+01  0.2517363D+01  0.1446374D+01  0.2387129D+01
  3    0.1379941D+01  0.1446374D+01  0.8766829D+00  0.1343175D+01
  4    0.2596905D+01  0.2387129D+01  0.1343175D+01  0.2626034D+01
  5    0.1767717D+01  0.1830545D+01  0.1081612D+01  0.1713753D+01
  6    0.2869676D+01  0.2544845D+01  0.1511130D+01  0.2715773D+01
 
            5              6
  1    0.1767717D+01  0.2869676D+01
  2    0.1830545D+01  0.2544845D+01
  3    0.1081612D+01  0.1511130D+01
  4    0.1713753D+01  0.2715773D+01
  5    0.1384126D+01  0.1939020D+01
  6    0.1939020D+01  0.3102934D+01
 
 *** ISTEP =  3
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.5727249D+00  0.2252770D+01  0.1678496D+01  0.7472376D+00
  2    0.0000000D+00  0.1223992D+01  0.1402922D+01  0.9061091D+00
  3    0.0000000D+00  0.0000000D+00 -0.1691888D+00  0.1156678D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.3032936D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.2228587D+00 -0.1224291D+00
  2   -0.4055155D+00  0.9745773D-01
  3    0.1890428D+00  0.1886359D+00
  4   -0.2190216D-01 -0.2409197D-01
  5    0.8434041D-01 -0.3608466D-01
  6    0.0000000D+00  0.8033827D-01
 
 X vector ( 6X 1)
 
            1
  1    0.2315943D+01
  2   -0.6344640D+01
  3    0.3674095D+00
  4    0.3464291D+01
  5    0.9289437D+01
  6   -0.6222618D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2845387D+01  0.2445634D+01  0.1453194D+01  0.2581864D+01
  2    0.2445634D+01  0.2564556D+01  0.1522925D+01  0.2393434D+01
  3    0.1453194D+01  0.1522925D+01  0.9288272D+00  0.1393814D+01
  4    0.2581864D+01  0.2393434D+01  0.1393814D+01  0.2523690D+01
  5    0.1857170D+01  0.1917774D+01  0.1158272D+01  0.1778605D+01
  6    0.2970545D+01  0.2662904D+01  0.1604467D+01  0.2741235D+01
 
            5              6
  1    0.1857170D+01  0.2970545D+01
  2    0.1917774D+01  0.2662904D+01
  3    0.1158272D+01  0.1604467D+01
  4    0.1778605D+01  0.2741235D+01
  5    0.1460172D+01  0.2050080D+01
  6    0.2050080D+01  0.3203283D+01
 
 *** ISTEP =  4
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.5728085D+00  0.2248477D+01  0.1676872D+01  0.7430241D+00
  2    0.0000000D+00  0.1211081D+01  0.1398611D+01  0.8950997D+00
  3    0.0000000D+00  0.0000000D+00 -0.1533516D+00  0.1371711D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.2578394D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.2255999D+00 -0.1242387D+00
  2   -0.4131405D+00  0.8473244D-01
  3    0.1745024D+00  0.1684401D+00
  4   -0.3799774D-01  0.1555136D-02
  5    0.6998405D-01 -0.2422438D-01
  6    0.0000000D+00  0.5378133D-01
 
 X vector ( 6X 1)
 
            1
  1    0.4516508D+01
  2   -0.1027816D+02
  3   -0.5650702D+00
  4    0.5048174D+01
  5    0.1620299D+02
  6   -0.1035923D+02
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2812466D+01  0.2418079D+01  0.1448061D+01  0.2546146D+01
  2    0.2418079D+01  0.2538357D+01  0.1517679D+01  0.2362428D+01
  3    0.1448061D+01  0.1517679D+01  0.9277794D+00  0.1392069D+01
  4    0.2546146D+01  0.2362428D+01  0.1392069D+01  0.2466339D+01
  5    0.1850907D+01  0.1910269D+01  0.1159255D+01  0.1767893D+01
  6    0.2961227D+01  0.2652733D+01  0.1609743D+01  0.2711900D+01
 
            5              6
  1    0.1850907D+01  0.2961227D+01
  2    0.1910269D+01  0.2652733D+01
  3    0.1159255D+01  0.1609743D+01
  4    0.1767893D+01  0.2711900D+01
  5    0.1459398D+01  0.2048311D+01
  6    0.2048311D+01  0.3189095D+01
 
1*** In both these tests we start with Sinvu=I and perform
 *** four iterations of the filter.
 *** The Sinv'Sinv matrices and X vectors are meant for
 *** comparison with SRIF.
1*** Second example : Square root information filter with
 *** A, B, C in (upper) controller Hessenberg form
 *** and upper triangular Q, R.
 
 
 *** Input SRIFCO
 
 
 
 
 *** Input COHESS
 
 
 *** N =  6 M =  2 P =   3
 
 
 *** UPPER = .TRUE.
 
 
 Ainv     ( 6X 6)
 
            1              2              3              4
  1    0.2113249D+00  0.7560439D+00  0.2211346D-03  0.3303271D+00
  2    0.8497452D+00  0.6857310D+00  0.8782165D+00  0.6837404D-01
  3    0.7263507D+00  0.1985144D+00  0.5442573D+00  0.2320748D+00
  4    0.8833888D+00  0.6525135D+00  0.3076091D+00  0.9329616D+00
  5    0.3616361D+00  0.2922267D+00  0.5664249D+00  0.4826472D+00
  6    0.5015342D+00  0.4368588D+00  0.2693125D+00  0.6325745D+00
 
            5              6
  1    0.6653811D+00  0.6283918D+00
  2    0.5608486D+00  0.6623569D+00
  3    0.2312237D+00  0.2164633D+00
  4    0.2146008D+00  0.3126420D+00
  5    0.3321719D+00  0.5935095D+00
  6    0.4051954D+00  0.9184708D+00
 
 AinvB    ( 6X 2)
 
            1              2
  1   -0.8805479D+00  0.5207521D+00
  2   -0.6075187D+00  0.1168888D+01
  3    0.1325720D+01 -0.1693905D+00
  4    0.1038693D+01 -0.2305789D+00
  5    0.2103993D+01 -0.1115921D+01
  6   -0.8531301D+00  0.6597089D+00
 
 C matrix ( 3X 6)
 
            1              2              3              4
  1    0.4373343D-01  0.4818509D+00  0.2639556D+00  0.4148104D+00
  2    0.7783129D+00  0.2119030D+00  0.1121355D+00  0.6856896D+00
  3    0.8415518D+00  0.4062025D+00  0.4094825D+00  0.8784126D+00
 
            5              6
  1    0.2806498D+00  0.1280058D+00
  2    0.1531217D+00  0.6970851D+00
  3    0.1138360D+00  0.1998338D+00
 
 
 
 *** Output COHESS
 
 
 Ainvu    ( 6X 6)
 
            1              2              3              4
  1    0.2008873D+00 -0.4245205D+00 -0.2097518D+00 -0.3048541D+00
  2   -0.3163469D+00  0.1677275D+01  0.1466019D+01  0.1811058D+00
  3   -0.3222207D+00  0.1153122D+01  0.9599862D+00  0.4765324D+00
  4    0.0000000D+00  0.6345976D+00  0.4285850D+00  0.7299071D+00
  5    0.0000000D+00  0.0000000D+00 -0.1809051D+00 -0.2320514D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.2239701D+00
 
            5              6
  1    0.3711037D+00 -0.4634347D+00
  2   -0.6791964D+00  0.2697618D+00
  3   -0.7025880D-01 -0.5388063D+00
  4    0.2432710D+00  0.2488519D+00
  5   -0.4329501D-01  0.2608173D-01
  6    0.4072138D+00  0.1001569D+00
 
 AinvBu   ( 6X 2)
 
            1              2
  1    0.3022495D+01 -0.1503209D+01
  2    0.0000000D+00 -0.1067802D+01
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00
 
 Cu matr. ( 3X 6)
 
            1              2              3              4
  1    0.3079669D+00 -0.6366799D+00 -0.1717533D+00 -0.1589127D+00
  2   -0.7468438D-01 -0.6111938D+00 -0.7937632D+00 -0.7348406D+00
  3    0.1774969D+00 -0.8547973D+00 -0.5709496D+00 -0.6186294D+00
 
            5              6
  1   -0.1254464D+00  0.1699368D-01
  2    0.2759580D+00 -0.1321099D+00
  3    0.1794903D+00 -0.6019142D+00
 
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.1000000D+01
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1    0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00
  4    0.0000000D+00  0.0000000D+00
  5    0.1000000D+01  0.0000000D+00
  6    0.0000000D+00  0.1000000D+01
 
 
 
 *** Additional input to SRIFCO
 
 
 QINV     ( 2X 2)
 
            1              2
  1    0.8813348D-01  0.4498763D+00
  2    0.0000000D+00  0.7227253D+00
 
 RINV     ( 3X 3)
 
            1              2              3
  1    0.1000000D+01  0.0000000D+00  0.0000000D+00
  2    0.0000000D+00  0.1000000D+01  0.0000000D+00
  3    0.0000000D+00  0.0000000D+00  0.1000000D+01
 
 Z vector ( 2X 1)
 
            1
  1    0.1964506D-02
  2    0.5075221D+00
 
 XU vect. ( 6X 1)
 
            1
  1    0.9726275D+00
  2   -0.8550479D+00
  3   -0.5702739D+00
  4   -0.2509331D-01
  5    0.2138843D+00
  6    0.1132806D-01
 
 Y vector ( 3X 1)
 
            1
  1    0.5591451D+00
  2    0.4304966D+00
  3    0.2280548D-01
 
 
 
 *** Output SRIFCO MULTRC=.TRUE.
 
 
 *** ISTEP =  1
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.5263247D+00  0.1692439D+01  0.1127758D+01  0.5349325D+00
  2    0.0000000D+00  0.1232738D+01  0.1256361D+01  0.1065398D+01
  3    0.0000000D+00  0.0000000D+00 -0.3765657D+00  0.1463274D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00 -0.6191167D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.1590049D+00 -0.8720884D-01
  2   -0.2960462D+00  0.3713540D+00
  3    0.2914402D+00  0.4594150D+00
  4   -0.1213648D+00  0.5169148D-01
  5    0.5769305D+00 -0.2031667D+00
  6    0.0000000D+00  0.6114634D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.2569291D+00
  2   -0.7735836D+00
  3    0.9761830D-01
  4    0.5768679D+00
  5    0.1493255D+01
  6   -0.1070294D+00
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.2422699D+01  0.1521830D+01  0.1093072D+01  0.2231301D+01
  2    0.1521830D+01  0.1675285D+01  0.8874590D+00  0.1746214D+01
  3    0.1093072D+01  0.8874590D+00  0.8959575D+00  0.8928200D+00
  4    0.2231301D+01  0.1746214D+01  0.8928200D+00  0.2690518D+01
  5    0.9335458D+00  0.1138976D+01  0.6581816D+00  0.1018746D+01
  6    0.1743842D+01  0.1505677D+01  0.9616997D+00  0.1849185D+01
 
            5              6
  1    0.9335458D+00  0.1743842D+01
  2    0.1138976D+01  0.1505677D+01
  3    0.6581816D+00  0.9616997D+00
  4    0.1018746D+01  0.1849185D+01
  5    0.9201884D+00  0.1230088D+01
  6    0.1230088D+01  0.2194236D+01
 
 *** ISTEP =  2
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.5881623D+00  0.2358934D+01  0.1725129D+01  0.8909403D+00
  2    0.0000000D+00  0.1297859D+01  0.1404894D+01  0.9850048D+00
  3    0.0000000D+00  0.0000000D+00 -0.2998004D+00  0.1218702D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.4590046D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.2307777D+00  0.8009653D-01
  2   -0.3336009D+00  0.2367807D+00
  3    0.2189869D+00  0.4366601D+00
  4   -0.1678586D+00  0.1696023D+00
  5    0.3465299D+00 -0.1896643D-01
  6    0.0000000D+00  0.4593957D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.1456113D+01
  2   -0.4309217D-01
  3    0.5894792D-01
  4    0.1416551D+01
  5   -0.8426659D+00
  6    0.7265106D+00
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.3580686D+01  0.2832780D+01  0.1706668D+01  0.3400289D+01
  2    0.2832780D+01  0.2819464D+01  0.1586885D+01  0.2836624D+01
  3    0.1706668D+01  0.1586885D+01  0.1049222D+01  0.1685414D+01
  4    0.3400289D+01  0.2836624D+01  0.1685414D+01  0.3460296D+01
  5    0.1906616D+01  0.1939049D+01  0.1116499D+01  0.1855839D+01
  6    0.3033008D+01  0.2619028D+01  0.1594275D+01  0.2886584D+01
 
            5              6
  1    0.1906616D+01  0.3033008D+01
  2    0.1939049D+01  0.2619028D+01
  3    0.1116499D+01  0.1594275D+01
  4    0.1855839D+01  0.2886584D+01
  5    0.1425362D+01  0.1958594D+01
  6    0.1958594D+01  0.3143224D+01
 
 *** ISTEP =  3
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.6001270D+00  0.2404979D+01  0.1770721D+01  0.8902379D+00
  2    0.0000000D+00  0.1250899D+01  0.1406348D+01  0.9464549D+00
  3    0.0000000D+00  0.0000000D+00 -0.2239961D+00  0.1785637D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.4119673D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.2683656D+00  0.6074122D-01
  2   -0.3617494D+00  0.1976607D+00
  3    0.2270893D+00  0.5170292D+00
  4   -0.1581758D+00  0.1487360D+00
  5    0.3033280D+00 -0.1437781D+00
  6    0.0000000D+00  0.3296338D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.2360051D+01
  2    0.5336696D+01
  3   -0.2252791D+00
  4    0.4210842D+00
  5   -0.8901653D+01
  6    0.3138066D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.3582605D+01  0.2835907D+01  0.1777583D+01  0.3350927D+01
  2    0.2835907D+01  0.2812484D+01  0.1660539D+01  0.2795164D+01
  3    0.1777583D+01  0.1660539D+01  0.1122809D+01  0.1720830D+01
  4    0.3350927D+01  0.2795164D+01  0.1720830D+01  0.3337550D+01
  5    0.1969028D+01  0.1992116D+01  0.1196833D+01  0.1892063D+01
  6    0.3118870D+01  0.2710456D+01  0.1698934D+01  0.2897519D+01
 
            5              6
  1    0.1969028D+01  0.3118870D+01
  2    0.1992116D+01  0.2710456D+01
  3    0.1196833D+01  0.1698934D+01
  4    0.1892063D+01  0.2897519D+01
  5    0.1482826D+01  0.2061537D+01
  6    0.2061537D+01  0.3256908D+01
 
 *** ISTEP =  4
 Sinvu    ( 6X 6)
 
            1              2              3              4
  1   -0.6000943D+00  0.2402587D+01  0.1770673D+01  0.8908128D+00
  2    0.0000000D+00  0.1242993D+01  0.1402091D+01  0.9396790D+00
  3    0.0000000D+00  0.0000000D+00 -0.2222093D+00  0.1837065D+00
  4    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.3882191D+00
  5    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
  6    0.0000000D+00  0.0000000D+00  0.0000000D+00  0.0000000D+00
 
            5              6
  1   -0.2706509D+00  0.5917622D-01
  2   -0.3631891D+00  0.1897784D+00
  3    0.2324745D+00  0.5126829D+00
  4   -0.1797033D+00  0.1682731D+00
  5    0.2886708D+00 -0.1336111D+00
  6    0.0000000D+00  0.3205551D+00
 
 X vector ( 6X 1)
 
            1
  1   -0.2525420D+01
  2    0.9904315D+01
  3    0.1568047D+00
  4   -0.1263859D+01
  5   -0.1548146D+02
  6    0.4935227D+01
 
 Sin'Sin ( 6X 6)
 
            1              2              3              4
  1    0.3558236D+01  0.2817693D+01  0.1771960D+01  0.3329810D+01
  2    0.2817693D+01  0.2796224D+01  0.1653642D+01  0.2780394D+01
  3    0.1771960D+01  0.1653642D+01  0.1119838D+01  0.1720891D+01
  4    0.3329810D+01  0.2780394D+01  0.1720891D+01  0.3304554D+01
  5    0.1965507D+01  0.1986326D+01  0.1196543D+01  0.1888306D+01
  6    0.3115443D+01  0.2704655D+01  0.1704280D+01  0.2882543D+01
 
            5              6
  1    0.1965507D+01  0.3115443D+01
  2    0.1986326D+01  0.2704655D+01
  3    0.1196543D+01  0.1704280D+01
  4    0.1888306D+01  0.2882543D+01
  5    0.1482010D+01  0.2062778D+01
  6    0.2062778D+01  0.3254345D+01
 
1*** In both these tests we start with Sinvu=I and perform
 *** four iterations of the filter.
 *** The Sinv'Sinv matrices and X vectors are meant for
 *** comparison with SRIF.