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Scripts for generating positive definiton inputs #23

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Scripts for generating positive definiton inputs #23

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80f980a
generate positive definiton inputs
hcq9102 Dec 1, 2023
41c9f81
update script
hcq9102 Dec 1, 2023
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40 changes: 40 additions & 0 deletions apps/choleskey/generateInputMatrix.py
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#!/usr/bin/env python
# coding: utf-8

# This is an Jupyter Script for generating the Input Positive Definition(PD) Matrix for Cholesky decomposition.
# The generated .txt file stores the entire PD matrix with the matrix elems row by row.
# This input.txt file can be used directly In benchmark part in each cpp file.


import numpy as np

#enter matrix size
matrixSize = 4
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Hardcoding this is not a good idea. Consider using argparse module and use that to take input from the user on the matrix size to generate.


#1. Generates a random matrix A of size matrixSize x matrixSize.
A = np.random.rand(matrixSize, matrixSize)
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I would recommend not generating matrices using rand here as the probability of generating a wrong matrix may get increasingly higher for larger matrices. Instead I would recommend looking into methods to generate positive definitive matrices with high probability such as translating this matlab code to python: https://math.stackexchange.com/questions/357980/how-to-generate-random-symmetric-positive-definite-matrices-using-matlab

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@hcq9102 hcq9102 Dec 2, 2023 •
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agree, I have another helper function in tiled_cholesky implementation which can generate the pd matrix using blas lib.
I suggest to leave this PR alone at this moment(I usually use this when i did performance test before).
And we can close this pr when get the better method.

print(A)
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print(A) for large matrixSize would just flood the console


#2. Computes the product of matrix A and its transpose, i.e., A * A^T, storing the result in matrix B.
B = np.dot(A, A.transpose())
print("B")
print(B)
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Same comment for large matrixSize for B


#3. Adds the transpose of matrix B to itself, generating a symmetric matrix C.
C = B + B.T # Ensure it's symmetric

print("C")
print(C)

try:
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It looks like the script will either generate or not generate a positive definitive matrix when run so that should be in a loop until we do get a correct solution.

Also using Cholesky transformation itself to check if the generated matrix is positive definitive doesn't seem to be the correct solution especially for larger matrices. I would recommend using a cheaper (eigen value based or Gershgorin circle theorem to verify this). You can refer to Gilbert Strang's book/videos or online resources for this.

D = np.linalg.cholesky(C)
print("Matrix C is positive definite.")

# Write the Cholesky decomposition result to a text file
with open(f"cholesky_result_{matrixSize}.txt", "w") as file:
for row in C:
for value in row:
file.write(f"{value}\n")
except np.linalg.LinAlgError:
print("Matrix C is not positive definite.")