linalg_custom.h File Reference

Simple linear algebra routines. More...

#include "matrix.h"

Go to the source code of this file.

int	clap_MatrixAddition (Matrix *A, Matrix *B, double alpha)
	Add two matrices of the same size, storing the result in B. More...
int	clap_MatrixScale (Matrix *A, double alpha)
	Scale a matrix by a constant. More...
int	clap_MatrixMultiply (Matrix *A, Matrix *B, Matrix *C, bool tA, bool tB, double alpha, double beta)
	Matrix multiplication. More...
int	clap_MatrixTransposeMultiply (Matrix *A, Matrix *B, Matrix *C)
	A shortcut to perform transposed matrix multiplication. More...
int	clap_SymmetricMatrixMultiply (Matrix *Asym, Matrix *B, Matrix *C, double alpha, double beta)
	Matrix multiplication with a symmetric matrix A. More...
int	clap_AddDiagonal (Matrix *A, double alpha)
	Add a constant value to the diagonal of a matrix. More...
int	clap_CholeskyFactorize (Matrix *A)
	Perform a Cholesky decomposition. More...
int	clap_CholeskySolve (Matrix *A, Matrix *b)
	Solve a linear system of equation with a precomputed Cholesky decomposition. More...
int	clap_LowerTriBackSub (Matrix *L, Matrix *b, bool istransposed)
	Solve a linear system of equation for a lower triangular matrix. More...

Detailed Description

Simple linear algebra routines.

Author

Brian Jackson (bjack.nosp@m.205@.nosp@m.gmail.nosp@m..com)

Version

0.1

Date

2022-01-31

Copyright

Copyright (c) 2022

Function Documentation

clap_AddDiagonal()

int clap_AddDiagonal	(	Matrix *	A,
		double	alpha
	)

Add a constant value to the diagonal of a matrix.

Parameters

[in,out]	A	a matrix of size (n,m) where n <= m
[in]	alpha	scalar to add to the diagonal

Returns

0 if successful

clap_CholeskyFactorize()

int clap_CholeskyFactorize

(

Matrix *

A

)

Perform a Cholesky decomposition.

Performs a Cholesky decomposition on the square matrix A, storing the result in the lower triangular portion of A.

Parameters

A	a square symmetric matrix

Returns

clap_kCholeskySuccess if successful, and clap_kCholeskyFail if not.

clap_CholeskySolve()

int clap_CholeskySolve	(	Matrix *	A,
		Matrix *	b
	)

Solve a linear system of equation with a precomputed Cholesky decomposition.

Parameters

[in]	A	A square matrix whose Cholesky decomposition is stored in the lower triangular portion of the matrix
[in,out]	b	The right-hand-side vector. Stores the solution upon completion of the function.

Returns

0 if successful

clap_LowerTriBackSub()

int clap_LowerTriBackSub	(	Matrix *	L,
		Matrix *	b,
		bool	istransposed
	)

Solve a linear system of equation for a lower triangular matrix.

Uses backsubstitution to solve a system of equations of the following form:

\[ L x = b \]

for a lower-triangular matrix \( L \), or

\[ L^T x = b \]

if istransposed is true.

Parameters

[in]	L	A lower-triangular matrix
[in,out]	b	The right-hand-side vector. Stores the solution upon completion.
	istransposed	Should L be transposed when solving the system of equations.

Returns

0 if successful

clap_MatrixAddition()

int clap_MatrixAddition	(	Matrix *	A,
		Matrix *	B,
		double	alpha
	)

Add two matrices of the same size, storing the result in B.

Performs the following operation:

\[ B = B + \alpha A \]

Parameters

[in]	A	any matrix of size (m,n)
[in,out]	B	any matrix of size (m,n)
[in]	alpha	scalar factor on A

Returns

0 if successful

clap_MatrixMultiply()

int clap_MatrixMultiply	(	Matrix *	A,
		Matrix *	B,
		Matrix *	C,
		bool	tA,
		bool	tB,
		double	alpha,
		double	beta
	)

Matrix multiplication.

\[ C = \alpha A B + \beta C \]

Parameters

[in]	A	Matrix of size (m,n)
[in]	B	Matrix of size (n,p)
[in,out]	C	Output matrix of size (m,p)
[in]	tA	Should A be transposed
[in]	tB	Should B be transposed
[in]	alpha	scalar on the \( A B \) term
[in]	beta	scalar on the \( C \) term. Set to zero for pure matrix multiplication.

clap_MatrixScale()

int clap_MatrixScale	(	Matrix *	A,
		double	alpha
	)

Scale a matrix by a constant.

Parameters

A	any matrix of non-zero size
alpha	scalar multiplier

Returns

0 if successful

clap_MatrixTransposeMultiply()

int clap_MatrixTransposeMultiply	(	Matrix *	A,
		Matrix *	B,
		Matrix *	C
	)

A shortcut to perform transposed matrix multiplication.

Calculates

\[ C = A^T B \]

Parameters

[in]	A	any matrix of size (n,m)
[in]	B	any matrix of size (n,p)
[out]	C	any matrix of size (m,p)

Returns

clap_SymmetricMatrixMultiply()

int clap_SymmetricMatrixMultiply	(	Matrix *	Asym,
		Matrix *	B,
		Matrix *	C,
		double	alpha,
		double	beta
	)

Matrix multiplication with a symmetric matrix A.

Perform the following computation

\[ C = \alpha A B + \beta C \]

For a symmetric matrix \( A \).

Parameters

[in]	Asym
[in]	B
[in,out]	C
[in]	alpha
[in]	beta