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lnDiffErfs.c
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lnDiffErfs.c
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#include <math.h>
#include "mex.h"
#include "matrix.h"
/*
* This function is based on cleaning up f2c translation of Fortran
* code found at Netlib/Specfun. The original Fortran code was
* written by W. J. Cody, 1990. The translation was performed by
* Antti Honkela, 2008.
*/
double calerf(double x, int jint)
{
/* constants */
double sqrpi = 5.6418958354775628695E-1; /* 1 / sqrt(M_PI); */
double xinf = 1.79e308;
double xneg = -26.628;
double xsmall = 1.11e-16;
double xbig = 26.543;
double xhuge = 6.71e7;
double xmax = 2.53e307;
static double a[] = {3.16112374387056560e00,1.13864154151050156e02,
3.77485237685302021e02,3.20937758913846947e03,
1.85777706184603153e-1};
static double b[] = {2.36012909523441209e01,2.44024637934444173e02,
1.28261652607737228e03,2.84423683343917062e03};
static double c[] = {5.64188496988670089E-1,8.88314979438837594E0,
6.61191906371416295E01,2.98635138197400131E02,
8.81952221241769090E02,1.71204761263407058E03,
2.05107837782607147E03,1.23033935479799725E03,
2.15311535474403846E-8};
static double d[] = {1.57449261107098347E01,1.17693950891312499E02,
5.37181101862009858E02,1.62138957456669019E03,
3.29079923573345963E03,4.36261909014324716E03,
3.43936767414372164E03,1.23033935480374942E03};
static double p[] = {3.05326634961232344E-1,3.60344899949804439E-1,
1.25781726111229246E-1,1.60837851487422766E-2,
6.58749161529837803E-4,1.63153871373020978E-2};
static double q[] = {2.56852019228982242E00,1.87295284992346047E00,
5.27905102951428412E-1,6.05183413124413191E-2,
2.33520497626869185E-3};
/* Local variables */
double r__1, r__2;
double xden;
double xnum;
double y, del, ysq;
double result;
int i;
/* ------------------------------------------------------------------ */
/* This packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x) */
/* for a real argument x. It contains three FUNCTION type */
/* subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX), */
/* and one SUBROUTINE type subprogram, CALERF. The calling */
/* statements for the primary entries are: */
/* Y=ERF(X) (or Y=DERF(X)), */
/* Y=ERFC(X) (or Y=DERFC(X)), */
/* and */
/* Y=ERFCX(X) (or Y=DERFCX(X)). */
/* The routine CALERF is intended for internal packet use only, */
/* all computations within the packet being concentrated in this */
/* routine. The function subprograms invoke CALERF with the */
/* statement */
/* CALL CALERF(ARG,RESULT,JINT) */
/* where the parameter usage is as follows */
/* Function Parameters for CALERF */
/* call ARG Result JINT */
/* ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0 */
/* ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1 */
/* ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2 */
/* The main computation evaluates near-minimax approximations */
/* from "Rational Chebyshev approximations for the error function" */
/* by W. J. Cody, Math. Comp., 1969, PP. 631-638. This */
/* transportable program uses rational functions that theoretically */
/* approximate erf(x) and erfc(x) to at least 18 significant */
/* decimal digits. The accuracy achieved depends on the arithmetic */
/* system, the compiler, the intrinsic functions, and proper */
/* selection of the machine-dependent constants. */
/* ******************************************************************* */
/* ******************************************************************* */
/* Explanation of machine-dependent constants */
/* XMIN = the smallest positive floating-point number. */
/* XINF = the largest positive finite floating-point number. */
/* XNEG = the largest negative argument acceptable to ERFCX; */
/* the negative of the solution to the equation */
/* 2*exp(x*x) = XINF. */
/* XSMALL = argument below which erf(x) may be represented by */
/* 2*x/sqrt(pi) and above which x*x will not underflow. */
/* A conservative value is the largest machine number X */
/* such that 1.0 + X = 1.0 to machine precision. */
/* XBIG = largest argument acceptable to ERFC; solution to */
/* the equation: W(x) * (1-0.5/x**2) = XMIN, where */
/* W(x) = exp(-x*x)/[x*sqrt(pi)]. */
/* XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to */
/* machine precision. A conservative value is */
/* 1/[2*sqrt(XSMALL)] */
/* XMAX = largest acceptable argument to ERFCX; the minimum */
/* of XINF and 1/[sqrt(pi)*XMIN]. */
/* ******************************************************************* */
/* Error returns */
/* The program returns ERFC = 0 for ARG .GE. XBIG; */
/* ERFCX = XINF for ARG .LT. XNEG; */
/* and */
/* ERFCX = 0 for ARG .GE. XMAX. */
/* Author: W. J. Cody */
/* Mathematics and Computer Science Division */
/* Argonne National Laboratory */
/* Argonne, IL 60439 */
/* Latest modification: March 19, 1990 */
/* ------------------------------------------------------------------ */
/* S REAL */
/* D DOUBLE PRECISION */
/* ------------------------------------------------------------------ */
y = fabs(x);
if (y <= 0.46875) {
/* ------------------------------------------------------------------ */
/* Evaluate erf for |X| <= 0.46875 */
/* ------------------------------------------------------------------ */
ysq = 0.0;
if (y > xsmall) {
ysq = y * y;
}
xnum = a[4] * ysq;
xden = ysq;
for (i = 0; i < 3; ++i) {
xnum = (xnum + a[i]) * ysq;
xden = (xden + b[i]) * ysq;
/* L20: */
}
result = x * (xnum + a[3]) / (xden + b[3]);
if (jint != 0) {
result = 1.0 - result;
}
if (jint == 2) {
result = exp(ysq) * result;
}
goto L800;
/* ------------------------------------------------------------------ */
/* Evaluate erfc for 0.46875 <= |X| <= 4.0 */
/* ------------------------------------------------------------------ */
} else if (y <= 4.0) {
xnum = c[8] * y;
xden = y;
for (i = 0; i < 7; ++i) {
xnum = (xnum + c[i]) * y;
xden = (xden + d[i]) * y;
/* L120: */
}
result = (xnum + c[7]) / (xden + d[7]);
if (jint != 2) {
ysq = rint(y * 16.0) / 16.0;
del = (y - ysq) * (y + ysq);
result = exp(-ysq * ysq) * exp(-del) * result;
}
/* ------------------------------------------------------------------ */
/* Evaluate erfc for |X| > 4.0 */
/* ------------------------------------------------------------------ */
} else {
result = 0.0;
if (y >= xbig) {
if (jint != 2 || y >= xmax) {
goto L300;
}
if (y >= xhuge) {
result = sqrpi / y;
goto L300;
}
}
ysq = 1.0 / (y * y);
xnum = p[5] * ysq;
xden = ysq;
for (i = 0; i < 4; ++i) {
xnum = (xnum + p[i]) * ysq;
xden = (xden + q[i]) * ysq;
/* L240: */
}
result = ysq * (xnum + p[4]) / (xden + q[4]);
result = (sqrpi - result) / y;
if (jint != 2) {
ysq = rint(y * 16.0) / 16.0;
del = (y - ysq) * (y + ysq);
result = exp(-ysq * ysq) * exp(-del) * result;
}
}
/* ------------------------------------------------------------------ */
/* Fix up for negative argument, erf, etc. */
/* ------------------------------------------------------------------ */
L300:
if (jint == 0) {
result = 0.5 - result + 0.5;
if (x < 0.0) {
result = -(result);
}
} else if (jint == 1) {
if (x < 0.0) {
result = 2.0 - result;
}
} else {
if (x < 0.0) {
if (x < xneg) {
result = xinf;
} else {
ysq = rint(x * 16.0) / 16.0;
del = (x - ysq) * (x + ysq);
y = exp(ysq * ysq) * exp(del);
result = y + y - result;
}
}
}
L800:
return result;
/* ---------- Last card of CALERF ---------- */
} /* calerf_ */
void
mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
int dim1, dim2, dim1_1, dim2_1, dim1_2, dim2_2, i;
int inc1, inc2;
double *in1, *in2, *out, *signs;
double v1, v2, temp;
/******************** input variables ********************/
in1 = mxGetPr(prhs[0]);
in2 = mxGetPr(prhs[1]);
dim1_1 = (int)mxGetM(prhs[0]);
dim2_1 = (int)mxGetN(prhs[0]);
dim1_2 = (int)mxGetM(prhs[1]);
dim2_2 = (int)mxGetN(prhs[1]);
dim1 = fmax(dim1_1, dim1_2);
dim2 = fmax(dim2_1, dim2_2);
/* Check that inputs are either a scalar and a matrix or matrices of
the same size */
if (!(((dim1_1 == 1 && dim2_1 == 1) || ((dim1_1 == dim1 && dim2_1 == dim2))) &&
((dim1_2 == 1 && dim2_2 == 1) || ((dim1_2 == dim1 && dim2_2 == dim2)))))
mexErrMsgTxt("lnDiffErfs: invalid input sizes");
/* Increments to walk through the inputs */
if (dim1_1 == 1 && dim2_1 == 1)
inc1 = 0;
else
inc1 = 1;
if (dim1_2 == 1 && dim2_2 == 1)
inc2 = 0;
else
inc2 = 1;
/* Create outputs, complex if single output, real otherwise */
if (nlhs < 2) {
plhs[0] = mxCreateDoubleMatrix(dim1, dim2, mxCOMPLEX);
out = mxGetPr(plhs[0]);
signs = mxGetPi(plhs[0]);
}
else {
plhs[0] = mxCreateDoubleMatrix(dim1, dim2, mxREAL);
plhs[1] = mxCreateDoubleMatrix(dim1, dim2, mxREAL);
out = mxGetPr(plhs[0]);
signs = mxGetPr(plhs[1]);
}
/* Do the hard work */
for (i=0; i<dim1*dim2; i++) {
v1 = *in1;
in1 += inc1;
v2 = *in2;
in2 += inc2;
if (v1 < v2) {
temp = v1;
v1 = v2;
v2 = temp;
*signs++ = -1;
}
else
*signs++ = 1;
if (v1 * v2 < 0)
*out++ = log(erf(v1) - erf(v2));
else if (v1 == v2)
*out++ = -mxGetInf();
else if (v1 > 0)
*out++ = log(calerf(v2, 2) - calerf(v1, 2) * exp(v2*v2 - v1*v1)) - v2*v2;
else
*out++ = log(calerf(-v1, 2) - calerf(-v2, 2) * exp(v1*v1 - v2*v2)) - v1*v1;
}
/* Return complex result instead of signs if just one output argument */
if (nlhs < 2) {
signs = mxGetPi(plhs[0]);
for (i=0; i<dim1*dim2; i++) {
signs[i] = 0.5 * (1 - signs[i]) * M_PI;
}
}
return;
}