Linear Algebra

Linear algebra utility for matrix and vector computations. More...

Macros
#define	FSB_MAX(a, b)   (((a) > (b)) ? (a) : (b))
#define	FSB_MIN(a, b)   (((a) < (b)) ? (a) : (b))

Typedefs
typedef double	double_t
	Floating point type.
typedef enum FsbLapackErrorType	FsbLinalgErrorType
	Error codes for linear algebra functions.

Enumerations
enum	FsbLapackErrorType {   EFSB_LAPACK_ERROR_NONE = 0 , EFSB_LAPACK_ERROR_INPUT = 1 , EFSB_LAPACK_ERROR_MEMORY = 2 , EFSB_LAPACK_ERROR_CONVERGE = 3 ,   EFSB_LAPACK_ERROR_QUERY = 4 , EFSB_LAPACK_NOT_POSITIVE_DEFINITE = 5 , EFSB_LAPACK_SINGULAR = 6 , EFSB_LAPACK_ERROR_NOT_FULL_RANK = 7 }
	Error codes for linear algebra functions. More...

Functions
FsbLinalgErrorType	fsb_linalg_svd (const double_t mat[], size_t rows, size_t cols, bool u_full, bool v_full, size_t work_len, double_t work[], double_t unitary_u[], double_t sing_val[], double_t unitary_vt[])
	SVD decomposition.
FsbLinalgErrorType	fsb_linalg_matrix_eig (const double_t mat[], size_t dim, size_t work_len, double_t work[], double_t val_real[], double_t val_imag[], double_t vec_real[], double_t vec_imag[])
	Eigenvalue decomposition.
FsbLinalgErrorType	fsb_linalg_sym_lt_eig (const double_t mat[], size_t dim, size_t work_len, double_t work[], double_t val[], double_t vec[])
	Eigenvalue decomposition for symmetric lower triangular matrix.
FsbLinalgErrorType	fsb_linalg_cholesky_decomposition (const double_t mat[], size_t dim, double_t mat_chol[])
	Cholesky factorization for symmetric positive definite matrix.
FsbLinalgErrorType	fsb_linalg_cholesky_solve (const double_t mat[], const double_t b_vec[], size_t nrhs, size_t dim, size_t work_len, double_t work[], double_t x_vec[])
	Cholesky solve.
bool	fsb_linalg_is_posdef (const double_t mat[], size_t dim, size_t work_len, double_t work[])
	Check if lower triangular symmetric matrix is positive definite.
FsbLinalgErrorType	fsb_linalg_matrix_sqr_solve (const double_t mat[], const double_t y_vec[], size_t nrhs, size_t dim, size_t work_len, size_t iwork_len, double_t work[], int iwork[], double_t x_vec[])
FsbLinalgErrorType	fsb_linalg_pseudoinverse (const double_t mat[], size_t rows, size_t columns, size_t work_len, double_t work[], double_t inv_mat[])
	Inverse of a matrix where number of columns are great er than or equal to number of rows.
FsbLinalgErrorType	fsb_linalg_leastsquares_solve (const double_t mat[], size_t rows, size_t columns, const double_t b_vec[], size_t nrhs, size_t work_len, double_t work[], double_t x_vec[])
	Solve overdetermined or underdetermined system using least squares.
void	sample_dgels_example (void)

Detailed Description

Linear algebra utility for matrix and vector computations.

Enumeration Type Documentation

FsbLapackErrorType

enum FsbLapackErrorType

Error codes for linear algebra functions.

Enumerator
EFSB_LAPACK_ERROR_NONE	No error.
EFSB_LAPACK_ERROR_INPUT	Input value error.
EFSB_LAPACK_ERROR_MEMORY	Not enough memory.
EFSB_LAPACK_ERROR_CONVERGE	Solution did not converge.
EFSB_LAPACK_ERROR_QUERY	Work query failed.
EFSB_LAPACK_NOT_POSITIVE_DEFINITE	Matrix not positive definite.
EFSB_LAPACK_SINGULAR	Input matrix is singular.
EFSB_LAPACK_ERROR_NOT_FULL_RANK	Matrix is not full rank.

Function Documentation

fsb_linalg_cholesky_decomposition()

FsbLinalgErrorType fsb_linalg_cholesky_decomposition	(	const double_t	mat[],
		size_t	dim,
		double_t	mat_chol[]
	)

Cholesky factorization for symmetric positive definite matrix.

Parameters

mat	Input matrix (dim x dim)
dim	Matrix A dimension s
mat_chol	Cholesky factorization of input matrix A (dim x dim)

Returns

Error code

fsb_linalg_cholesky_solve()

FsbLinalgErrorType fsb_linalg_cholesky_solve	(	const double_t	mat[],
		const double_t	b_vec[],
		size_t	nrhs,
		size_t	dim,
		size_t	work_len,
		double_t	work[],
		double_t	x_vec[]
	)

Cholesky solve.

square symmetric positive-definite matrix cholesky solve. solve for b from x = A b Variable x is overwritten by b on exit

Parameters

mat
b_vec
nrhs
dim
work_len
work
x_vec

Returns

fsb_linalg_is_posdef()

bool fsb_linalg_is_posdef	(	const double_t	mat[],
		size_t	dim,
		size_t	work_len,
		double_t	work[]
	)

Check if lower triangular symmetric matrix is positive definite.

Parameters

mat	Input lower triangular matrix (sxs)
dim	Matrix A dimension
work_len	Work vector length
work	Work vector

Returns

true

false

fsb_linalg_leastsquares_solve()

FsbLinalgErrorType fsb_linalg_leastsquares_solve	(	const double_t	mat[],
		size_t	rows,
		size_t	columns,
		const double_t	b_vec[],
		size_t	nrhs,
		size_t	work_len,
		double_t	work[],
		double_t	x_vec[]
	)

Solve overdetermined or underdetermined system using least squares.

Solves min ||A*X - B|| for X where A is an M-by-N matrix using the singular value decomposition (SVD) approach. This method handles rank-deficient least squares problems more robustly than the QR approach.

Parameters

mat	Input matrix A (rows x columns)
rows	Number of rows in A
columns	Number of columns in A
b_vec	Right-hand side matrix B (rows x nrhs)
nrhs	Number of right-hand side vectors
work_len	Length of work vector
work	Work vector
x_vec	Output solution matrix X (columns x nrhs).

Returns

Error code

fsb_linalg_matrix_eig()

FsbLinalgErrorType fsb_linalg_matrix_eig	(	const double_t	mat[],
		size_t	dim,
		size_t	work_len,
		double_t	work[],
		double_t	val_real[],
		double_t	val_imag[],
		double_t	vec_real[],
		double_t	vec_imag[]
	)

Eigenvalue decomposition.

Parameters

[in]	mat	input matrix (sxs)
[in]	dim	matrix A dimension
[in]	work_len	buffer
[in,out]	work	buffer
[out]	val_real	real components of the eigenvalues (sx1)
[out]	val_imag	imaginary components of the eigenvalues (sx1)
[out]	vec_real	real components of the eigenvectors (sxs)
[out]	vec_imag	imaginary components of the eigenvectors (sxs)

Returns

error code

fsb_linalg_matrix_sqr_solve()

FsbLinalgErrorType fsb_linalg_matrix_sqr_solve	(	const double_t	mat[],
		const double_t	y_vec[],
		size_t	nrhs,
		size_t	dim,
		size_t	work_len,
		size_t	iwork_len,
		double_t	work[],
		int	iwork[],
		double_t	x_vec[]
	)

@biref Solve linear system of equations with a square matrix

Parameters

mat	Matrix to solve (dim x dim)
y_vec	Right-hand side vector (dim x nrhs)
nrhs	Number of right-hand side vectors
dim	Matrix A dimension (s)
work_len	Work vector length
iwork_len	Integer work vector length
work	Work vector
iwork	Integer work vector
x_vec	Output Solution vector (dim x nrhs)

Returns

Error code

fsb_linalg_pseudoinverse()

FsbLinalgErrorType fsb_linalg_pseudoinverse	(	const double_t	mat[],
		size_t	rows,
		size_t	columns,
		size_t	work_len,
		double_t	work[],
		double_t	inv_mat[]
	)

Inverse of a matrix where number of columns are great er than or equal to number of rows.

Work length must be at least rows * MIN(rows, columns) + MIN(rows, columns) + MIN(rows, columns) * columns and additional length required by the fsb_linalg_svd function.

Parameters

mat	Input matrix (rows x columns)
rows	Number of rows in matrix
columns	Number of columns in matrix
work_len	Length of work vector
work	Work vector
inv_mat	Output inverse matrix (columns x rows)

Returns

Error code

fsb_linalg_svd()

FsbLinalgErrorType fsb_linalg_svd	(	const double_t	mat[],
		size_t	rows,
		size_t	cols,
		bool	u_full,
		bool	v_full,
		size_t	work_len,
		double_t	work[],
		double_t	unitary_u[],
		double_t	sing_val[],
		double_t	unitary_vt[]
	)

SVD decomposition.

u_full and v_full affect the output matrices as follows: if (m < n) then s = m else s = n if (u_full, v_full) == (0, 0) then U(m,s), S(s,s), VT(s,n) if (u_full, v_full) == (1, 0) then U(m,m), S(m,s), VT(s,n) if (u_full, v_full) == (0, 1) then U(m,s), S(s,n), VT(n,n) if (u_full, v_full) == (1, 1) then U(m,m), S(m,n), VT(n,n)

Parameters

[in]	mat	matrix to perform SVD
[in]	rows	rows of A
[in]	cols	columns of A
[in]	u_full	Boolean for full U matrix
[in]	v_full	Boolean for full V matrix
[in]	work_len	buffer
[in,out]	work	buffer
[out]	unitary_u	Unitary matrix U (m x m)
[out]	sing_val	Singular values array S (s x 1)
[out]	unitary_vt	Transpose of unitary matrix V (n x n)

fsb_linalg_sym_lt_eig()

FsbLinalgErrorType fsb_linalg_sym_lt_eig	(	const double_t	mat[],
		size_t	dim,
		size_t	work_len,
		double_t	work[],
		double_t	val[],
		double_t	vec[]
	)

Eigenvalue decomposition for symmetric lower triangular matrix.

Parameters

[in]	mat	input matrix (sxs)
[in]	dim	matrix A dimension
[in]	work_len	buffer
[in,out]	work	buffer
[out]	val	eigenvalues (sx1)
[out]	vec	column eigenvectors (sxs)