Block matrix descriptors and linear algebra operations. More...

#include <cblas.h>

Classes
struct	aa_dvec
	Descriptor for a vector. More...

struct	aa_dmat
	Descriptor for a block matrix. More...

Macros
#define	AA_DVEC_REF(v, i) ((v)->data[(i) * (v)->inc])
	Return an element of a dvec. More...

#define	AA_DMAT_REF(M, i, j) (((M)->data)[(M)->ld*(j) + (i)])
	Reference a matrix entry. More...

#define	AA_VEC_ARGS(X) (X->data), ((int)(X->inc))
	BLAS arguments for a vector.

#define	AA_MAT_ARGS(X) (X->data), ((int)(X->ld))
	BLAS arguments for a matrix.

#define	AA_MAT_DIAG(VEC, MAT) aa_dvec_view((VEC), (MAT)->cols, (MAT)->data, 1+(MAT)->ld);
	Set VEC to a descriptor for the diagonal vector of MAT.

Typedefs
typedef size_t	aa_la_size
	Type for sizes of vectors and matrices.

typedef void()	aa_la_err_fun(const char *message)
	Callback type for linear algebra errors.

Functions
AA_API void	aa_la_err (const char *message)
	Default handler function for linear algebra errors.

AA_API void	aa_la_set_err (aa_la_err_fun *fun)
	Set the handler function for linear algebra errors.

static struct aa_dvec	AA_DVEC_INIT (aa_la_size len, double *data, aa_la_size inc)
	Fill in a vector descriptor. More...

static void	AA_DVEC_VIEW (struct aa_dvec vec, aa_la_size len, double data, aa_la_size inc)
	Fill in a vector descriptor. More...

AA_API void	aa_dvec_view (struct aa_dvec vec, aa_la_size len, double data, aa_la_size inc)
	Fill in a vector descriptor. More...

AA_API void	aa_dmat_view (struct aa_dmat mat, aa_la_size rows, aa_la_size cols, double data, aa_la_size ld)
	Fill in a matrix descriptor. More...

AA_API void	aa_dmat_view_block (struct aa_dmat dst, const struct aa_dmat src, aa_la_size row_start, aa_la_size col_start, aa_la_size rows, aa_la_size cols)
	View a block of a matrix.

AA_API void	aa_dvec_slice (const struct aa_dvec src, aa_la_size start, aa_la_size stop, aa_la_size step, struct aa_dvec dst)
	View a slice of a vector.

AA_API void	aa_dmat_block (const struct aa_dmat src, aa_la_size row_start, aa_la_size col_start, aa_la_size row_end, aa_la_size col_end, struct aa_dmat dst)
	View a block of a matrix.

AA_API void	aa_dmat_row_vec (const struct aa_dmat src, aa_la_size row, struct aa_dvec dst)
	View a row of a matrix as a vector.

AA_API void	aa_dmat_col_vec (const struct aa_dmat src, aa_la_size col, struct aa_dvec dst)
	View a column of a matrix as a vector.

AA_API void	aa_dmat_diag_vec (const struct aa_dmat src, struct aa_dvec dst)
	View the diagonal of a matrix as a vector.

static struct aa_dmat	AA_DMAT_INIT (aa_la_size rows, aa_la_size cols, double *data, aa_la_size ld)
	Fill in a matrix descriptor. More...

static void	AA_DMAT_VIEW (struct aa_dmat mat, aa_la_size rows, aa_la_size cols, double data, aa_la_size ld)
	Fill in a matrix descriptor. More...

AA_API struct aa_dvec *	aa_dvec_alloc (struct aa_mem_region *reg, aa_la_size len)
	Region-allocate a vector. More...

AA_API struct aa_dvec *	aa_dvec_dup (struct aa_mem_region reg, const struct aa_dvec src)
	Duplicate vector out of region. More...

AA_API struct aa_dvec *	aa_dvec_mdup (const struct aa_dvec *src)
	Duplicate vector in the heap. More...

AA_API struct aa_dmat *	aa_dmat_dup (struct aa_mem_region reg, const struct aa_dmat src)
	Duplicate matrix out of region. More...

AA_API struct aa_dmat *	aa_dmat_mdup (const struct aa_dmat *src)
	Duplicate matrix in the heap. More...

AA_API struct aa_dmat *	aa_dmat_alloc (struct aa_mem_region *reg, aa_la_size rows, aa_la_size cols)
	Region-allocate a matrix. More...

AA_API struct aa_dvec *	aa_dvec_malloc (aa_la_size len)
	Heap-allocate a vector. More...

AA_API struct aa_dmat *	aa_dmat_malloc (aa_la_size rows, aa_la_size cols)
	Heap-allocate a matrix. More...

AA_API void	aa_dvec_zero (struct aa_dvec *vec)
	Zero a vector.

AA_API void	aa_dvec_set (struct aa_dvec *vec, double alpha)
	Fill a vector.

AA_API void	aa_dmat_set (struct aa_dmat *A, double alpha, double beta)
	Fill a matrix diagonal and off-diagonal elements. More...

AA_API void	aa_dmat_zero (struct aa_dmat *mat)
	Zero a matrix.

AA_API void	aa_dvec_swap (struct aa_dvec x, struct aa_dvec y)
	Swap x and y. More...

AA_API void	aa_dvec_scal (double alpha, struct aa_dvec *x)
	Scale x by alpha. More...

AA_API void	aa_dvec_inc (double alpha, struct aa_dvec *x)
	Increment x by alpha. More...

AA_API void	aa_dvec_copy (const struct aa_dvec x, struct aa_dvec y)
	Copy x to y. More...

AA_API void	aa_dvec_axpy (double a, const struct aa_dvec x, struct aa_dvec y)
	Alpha x plus y. More...

AA_API double	aa_dvec_dot (const struct aa_dvec x, struct aa_dvec y)
	Dot product. More...

AA_API double	aa_dvec_nrm2 (const struct aa_dvec *x)
	Euclidean Norm. More...

AA_API void	aa_dmat_gemv (AA_CBLAS_TRANSPOSE trans, double alpha, const struct aa_dmat A, const struct aa_dvec x, double beta, struct aa_dvec *y)
	General Matrix-Vector multiply. More...

AA_API void	aa_dmat_gemm (AA_CBLAS_TRANSPOSE transA, AA_CBLAS_TRANSPOSE transB, double alpha, const struct aa_dmat A, const struct aa_dmat B, double beta, struct aa_dmat *C)
	General Matrix-Matrix multiply. More...

AA_API void	aa_dmat_lacpy (const char uplo[1], const struct aa_dmat A, struct aa_dmat B)
	Copies all or part of a two-dimensional matrix A to another matrix B. More...

AA_API double	aa_dvec_ssd (const struct aa_dvec x, const struct aa_dvec y)
	sum-square-differences of two vectors

AA_API void	aa_dmat_axpy (double alpha, const struct aa_dmat X, struct aa_dmat Y)
	Y += alpha * X.

AA_API double	aa_dmat_ssd (const struct aa_dmat x, const struct aa_dmat y)
	sum-square-differences of two matrices

AA_API void	aa_dmat_scal (struct aa_dmat *A, double alpha)
	Scale the matrix A by alpha.

AA_API void	aa_dmat_inc (struct aa_dmat *A, double alpha)
	Increment the matrix A by alpha.

AA_API double	aa_dmat_nrm2 (const struct aa_dmat *x)
	Euclidean Norm.

AA_API void	aa_dmat_trans (const struct aa_dmat A, struct aa_dmat At)
	Matrix transpose.

AA_API int	aa_dmat_inv (struct aa_dmat *A)
	Matrix inverse, in-place.

AA_API int	aa_dmat_pinv (const struct aa_dmat A, double tol, struct aa_dmat As)
	Pseudo-inverse. More...

AA_API int	aa_dmat_dpinv (const struct aa_dmat A, double k, struct aa_dmat As)
	Damped pseudo-inverse.

AA_API int	aa_dmat_dzdpinv (const struct aa_dmat A, double s_min, struct aa_dmat As)
	Dead-zone damped pseudo-inverse.

AA_API void	aa_dmat_copy (const struct aa_dmat A, struct aa_dmat B)
	Copy a matrix.

Detailed Description

Block matrix descriptors and linear algebra operations.

Definition in file mat.h.

Macro Definition Documentation

◆ AA_DMAT_REF

#define AA_DMAT_REF	(	M,
		i,
		j
	)	(((M)->data)[(M)->ld*(j) + (i)])

Reference a matrix entry.

Parameters

M	matrix
i	row
j	column

Definition at line 94 of file mat.h.

◆ AA_DVEC_REF

#define AA_DVEC_REF	(	v,
		i
	)	((v)->data[(i) * (v)->inc])

Return an element of a dvec.

Parameters

v	an aa_dvec
i	the index of the element in v to return

Definition at line 85 of file mat.h.

Function Documentation

◆ aa_dmat_alloc()

AA_API struct aa_dmat* aa_dmat_alloc	(	struct aa_mem_region *	reg,
		aa_la_size	rows,
		aa_la_size	cols
	)

Region-allocate a matrix.

When finished, pop the descriptor.

◆ aa_dmat_dup()

AA_API struct aa_dmat* aa_dmat_dup	(	struct aa_mem_region *	reg,
		const struct aa_dmat *	src
	)

Duplicate matrix out of region.

When finished, pop the descriptor.

◆ aa_dmat_gemm()

AA_API void aa_dmat_gemm	(	AA_CBLAS_TRANSPOSE	transA,
		AA_CBLAS_TRANSPOSE	transB,
		double	alpha,
		const struct aa_dmat *	A,
		const struct aa_dmat *	B,
		double	beta,
		struct aa_dmat *	C
	)

General Matrix-Matrix multiply.

\[ \mathbf{y} \leftarrow \alpha \mathbf{A}^{\rm opA} \mathbf{B}^\rm{opB} + \beta \mathbf{C} \]

◆ aa_dmat_gemv()

AA_API void aa_dmat_gemv	(	AA_CBLAS_TRANSPOSE	trans,
		double	alpha,
		const struct aa_dmat *	A,
		const struct aa_dvec *	x,
		double	beta,
		struct aa_dvec *	y
	)

General Matrix-Vector multiply.

\[ \mathbf{y} \leftarrow \alpha \mathbf{A}^{\rm op} \mathbf{x} + \beta \mathbf{y} \]

◆ AA_DMAT_INIT()

static struct aa_dmat AA_DMAT_INIT	(	aa_la_size	rows,
		aa_la_size	cols,
		double *	data,
		aa_la_size	ld
	)

inlinestatic

Fill in a matrix descriptor.

Parameters

rows	Number of rows in matrix
cols	Number of colums in matrix
data	Pointer to vector data
ld	Leading dimension of matrix

Definition at line 225 of file mat.h.

◆ aa_dmat_lacpy()

AA_API void aa_dmat_lacpy	(	const char	uplo[1],
		const struct aa_dmat *	A,
		struct aa_dmat *	B
	)

Copies all or part of a two-dimensional matrix A to another matrix B.

Parameters

[in]	uplo	Specifies the part of the matrix A to be copied to B. = 'U': Upper triangular part = 'L': Lower triangular part Otherwise: All of the matrix A
[in]	A	dimension (LDA,N) The m by n matrix A. If UPLO = 'U', only the upper triangle or trapezoid is accessed; if UPLO = 'L', only the lower triangle or trapezoid is accessed.
[out]	B	dimension (LDB,N) On exit, B = A in the locations specified by UPLO.

◆ aa_dmat_malloc()

AA_API struct aa_dmat* aa_dmat_malloc	(	aa_la_size	rows,
		aa_la_size	cols
	)

Heap-allocate a matrix.

The descriptor and data are contained in a single malloc()'ed block. When finished, call free() on the descriptor.

◆ aa_dmat_mdup()

AA_API struct aa_dmat* aa_dmat_mdup ( const struct aa_dmat * src )

Duplicate matrix in the heap.

When finished, free the descriptor.

◆ aa_dmat_pinv()

AA_API int aa_dmat_pinv	(	const struct aa_dmat *	A,
		double	tol,
		struct aa_dmat *	As
	)

Pseudo-inverse.

Singular values less than tol are ignored. If tol < 0, then a sane default is used.

◆ aa_dmat_set()

AA_API void aa_dmat_set	(	struct aa_dmat *	A,
		double	alpha,
		double	beta
	)

Fill a matrix diagonal and off-diagonal elements.

Parameters

[in]	A	The matrix to fill
[in]	alpha	off-diagonal entries of A
[in]	beta	diagonal entries of A

◆ aa_dmat_view()

AA_API void aa_dmat_view	(	struct aa_dmat *	mat,
		aa_la_size	rows,
		aa_la_size	cols,
		double *	data,
		aa_la_size	ld
	)

Fill in a matrix descriptor.

Parameters

mat	Pointer to descriptor
rows	Number of rows in matrix
cols	Number of colums in matrix
data	Pointer to vector data
ld	Leading dimension of matrix

◆ AA_DMAT_VIEW()

static void AA_DMAT_VIEW	(	struct aa_dmat *	mat,
		aa_la_size	rows,
		aa_la_size	cols,
		double *	data,
		aa_la_size	ld
	)

inlinestatic

Fill in a matrix descriptor.

Parameters

mat	Pointer to descriptor
rows	Number of rows in matrix
cols	Number of colums in matrix
data	Pointer to vector data
ld	Leading dimension of matrix

Definition at line 257 of file mat.h.

◆ aa_dvec_alloc()

AA_API struct aa_dvec* aa_dvec_alloc	(	struct aa_mem_region *	reg,
		aa_la_size	len
	)

Region-allocate a vector.

When finished, pop the descriptor.

◆ aa_dvec_axpy()

AA_API void aa_dvec_axpy	(	double	a,
		const struct aa_dvec *	x,
		struct aa_dvec *	y
	)

Alpha x plus y.

\[ \mathbf{y} \leftarrow \alpha \mathbf{x} + \mathbf{y} \]

◆ aa_dvec_copy()

AA_API void aa_dvec_copy	(	const struct aa_dvec *	x,
		struct aa_dvec *	y
	)

Copy x to y.

\[ \mathbf{y} \leftarrow \mathbf{x} \]

◆ aa_dvec_dot()

AA_API double aa_dvec_dot	(	const struct aa_dvec *	x,
		struct aa_dvec *	y
	)

Dot product.

\[ \mathbf{x}^T \mathbf{y} \]

◆ aa_dvec_dup()

AA_API struct aa_dvec* aa_dvec_dup	(	struct aa_mem_region *	reg,
		const struct aa_dvec *	src
	)

Duplicate vector out of region.

When finished, pop the descriptor.

◆ aa_dvec_inc()

AA_API void aa_dvec_inc	(	double	alpha,
		struct aa_dvec *	x
	)

Increment x by alpha.

\[ \mathbf{x} \leftarrow \alpha + \mathbf{x} \]

◆ AA_DVEC_INIT()

static struct aa_dvec AA_DVEC_INIT	(	aa_la_size	len,
		double *	data,
		aa_la_size	inc
	)

inlinestatic

Fill in a vector descriptor.

Parameters

len	Number of elements in vector
data	Pointer to vector data
inc	Increment between sucessive elements

Definition at line 113 of file mat.h.

◆ aa_dvec_malloc()

AA_API struct aa_dvec* aa_dvec_malloc ( aa_la_size len )

Heap-allocate a vector.

The descriptor and data are contained in a single malloc()'ed block. When finished, call free() on the descriptor.

◆ aa_dvec_mdup()

AA_API struct aa_dvec* aa_dvec_mdup ( const struct aa_dvec * src )

Duplicate vector in the heap.

When finished, free the descriptor.

◆ aa_dvec_nrm2()

AA_API double aa_dvec_nrm2 ( const struct aa_dvec * x )

Euclidean Norm.

\[ \left\Vert \mathbf{x} \right\Vert_2 \]

◆ aa_dvec_scal()

AA_API void aa_dvec_scal	(	double	alpha,
		struct aa_dvec *	x
	)

Scale x by alpha.

\[ \mathbf{x} \leftarrow \alpha \mathbf{x} \]

◆ aa_dvec_swap()

AA_API void aa_dvec_swap	(	struct aa_dvec *	x,
		struct aa_dvec *	y
	)

Swap x and y.

\[ \mathbf{x} \leftrightarrow \mathbf{y} \]

◆ AA_DVEC_VIEW()

static void AA_DVEC_VIEW	(	struct aa_dvec *	vec,
		aa_la_size	len,
		double *	data,
		aa_la_size	inc
	)

inlinestatic

Fill in a vector descriptor.

Parameters

vec	Pointer to descriptor
len	Number of elements in vector
data	Pointer to vector data
inc	Increment between sucessive elements

Definition at line 151 of file mat.h.

◆ aa_dvec_view()

AA_API void aa_dvec_view	(	struct aa_dvec *	vec,
		aa_la_size	len,
		double *	data,
		aa_la_size	inc
	)

Fill in a vector descriptor.

Parameters

vec	Pointer to descriptor
len	Number of elements in vector
data	Pointer to vector data
inc	Increment between sucessive elements

Classes

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

◆ AA_DMAT_REF

◆ AA_DVEC_REF

Function Documentation

◆ aa_dmat_alloc()

◆ aa_dmat_dup()

◆ aa_dmat_gemm()

◆ aa_dmat_gemv()

◆ AA_DMAT_INIT()

◆ aa_dmat_lacpy()

◆ aa_dmat_malloc()

◆ aa_dmat_mdup()

◆ aa_dmat_pinv()

◆ aa_dmat_set()

◆ aa_dmat_view()

◆ AA_DMAT_VIEW()

◆ aa_dvec_alloc()

◆ aa_dvec_axpy()

◆ aa_dvec_copy()

◆ aa_dvec_dot()

◆ aa_dvec_dup()

◆ aa_dvec_inc()

◆ AA_DVEC_INIT()

◆ aa_dvec_malloc()

◆ aa_dvec_mdup()

◆ aa_dvec_nrm2()

◆ aa_dvec_scal()

◆ aa_dvec_swap()

◆ AA_DVEC_VIEW()

◆ aa_dvec_view()