linear-algebra.c File Reference

Various linear algebra routines needed for the Carathéodory-Fejér method. More...

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <float.h>
#include <string.h>
#include <complex.h>

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Functions
void	getInverseComplex (int n, double complex *A)
	Interface function to LAPACK matrix inversion subroutine. More...
void	linSolveComplex (int n, double complex *A, double complex *B, double complex *x)
	Solves the complex linear system Ax = B. More...
void	roots (int n, double *v, double complex *rt)
	Polynomial root finding function. More...
void	svd (int n, double *A, double *S, double *U, double *V)
	Singular value decomposition function. More...

Detailed Description

Various linear algebra routines needed for the Carathéodory-Fejér method.

Definition in file linear-algebra.c.

Function Documentation

getInverseComplex()

void getInverseComplex	(	int	n,
		double complex *	A
	)

Interface function to LAPACK matrix inversion subroutine.

Performs inversion of square matrix. Uses LAPACK subroutines DGETRF and DGETRI.

Parameters

[in]	n	order of matrix
[in]	A	the input matrix, size n*n

Returns

info success/fail integer flag

Definition at line 23 of file linear-algebra.c.

linSolveComplex()

void linSolveComplex	(	int	n,
		double complex *	A,
		double complex *	B,
		double complex *	x
	)

Solves the complex linear system Ax = B.

Performs inversion of square matrix. Uses LAPACK subroutines DGETRF and DGETRI.

Parameters

[in]	n	order of matrix
[in]	A	the LHS matrix, size n*n
[in]	B	the RHS matrix, size n*n
[out]	x	the solved vector, size n*1

Definition at line 88 of file linear-algebra.c.

roots()

void roots	(	int	n,
		double *	v,
		double complex *	rt
	)

Polynomial root finding function.

This function calculates the roots of a polynomial represented by its coefficients in the array v. This is done by constructing a companion matrix out of the polynomial coefficients, then using the LAPACK subroutine DGEEV to calculate its eigenvalues. These are the roots of the polynomial.

Parameters

[in]	n	size of v;
[in]	v	array of polynomial coefficients (real)
[out]	rt	array of polynomial roots (complex), size n - 1

Definition at line 141 of file linear-algebra.c.

svd()

void svd	(	int	n,
		double *	A,
		double *	S,
		double *	U,
		double *	V
	)

Singular value decomposition function.

Decomposes a matrix A into U * S * V', where S (here an array, really a diagonal matrix) holds the singular values. The function uses the LAPACK subroutine DGESVD.

Parameters

[in]	n	leading dimension of array
[in]	A	array to be decomposed, size n * n
[out]	S	array with singular values, size n
[out]	U	array with left singular vectors, size n * n
[out]	V	array with right singular vectors, size n * n

Definition at line 215 of file linear-algebra.c.