Representation of a matrix as an array in column-major order. More...

Data Structures
struct	_amatrix
	Representation of a matrix as an array in column-major order. More...

Typedefs
typedef struct _amatrix	amatrix
	Representation of a matrix as a column-order array.

typedef amatrix *	pamatrix
	Pointer to amatrix object.

typedef const amatrix *	pcamatrix
	Pointer to constant amatrix object.

Functions
pamatrix	init_amatrix (pamatrix a, uint rows, uint cols)
	Initialize an amatrix object. More...

pamatrix	init_sub_amatrix (pamatrix a, pamatrix src, uint rows, uint roff, uint cols, uint coff)
	Initialize an amatrix object to represent a submatrix. More...

pamatrix	init_vec_amatrix (pamatrix a, pavector src, uint rows, uint cols)
	Initialize an amatrix object by a vector. More...

pamatrix	init_pointer_amatrix (pamatrix a, pfield src, uint rows, uint cols)
	Initialize an amatrix object using a given array for the coefficients. More...

pamatrix	init_zero_amatrix (pamatrix a, uint rows, uint cols)
	Initialize an amatrix object and set it to zero. More...

pamatrix	init_identity_amatrix (pamatrix a, uint rows, uint cols)
	Initialize an amatrix object and set it to identity. More...

void	uninit_amatrix (pamatrix a)
	Uninitialize an amatrix object. More...

pamatrix	new_amatrix (uint rows, uint cols)
	Create a new amatrix object. More...

pamatrix	new_sub_amatrix (pamatrix src, uint rows, uint roff, uint cols, uint coff)
	Create a new amatrix object representing a submatrix. More...

pamatrix	new_pointer_amatrix (field *src, uint rows, uint cols)
	Create a new amatrix object using a given array for the coefficients. More...

pamatrix	new_zero_amatrix (uint rows, uint cols)
	Create a new amatrix object representing a zero matrix. More...

pamatrix	new_identity_amatrix (uint rows, uint cols)
	Create a new amatrix object representing the identity. More...

void	del_amatrix (pamatrix a)
	Delete an amatrix object. More...

void	resize_amatrix (pamatrix a, uint rows, uint cols)
	Change the dimensions of an amatrix object without preserving its coefficients. More...

void	resizecopy_amatrix (pamatrix a, uint rows, uint cols)
	Change the dimensions of an amatrix object while preserving as many of its coefficients as possible. More...

field	getentry_amatrix (pcamatrix a, uint row, uint col)
	Read a matrix entry $a_{ij}$ . More...

void	setentry_amatrix (pamatrix a, uint row, uint col, field x)
	Set a matrix entry, $a_{ij}\gets x$ . More...

field	addentry_amatrix (pamatrix a, uint row, uint col, field x)
	Add to a matrix entry, $a_{ij} \gets a_{ij} + x$ . More...

uint	getactives_amatrix ()
	Get number of currently initialized amatrix objects. More...

size_t	getsize_amatrix (pcamatrix a)
	Get size of a given amatrix object. More...

size_t	getsize_heap_amatrix (pcamatrix a)
	Get heap size of a given amatrix object. More...

void	clear_amatrix (pamatrix a)
	Set a matrix to zero. More...

void	clear_lower_amatrix (pamatrix a, bool strict)
	Set the lower triangular part of a matrix to zero. More...

void	clear_upper_amatrix (pamatrix a, bool strict)
	Set the upper triangular part of a matrix to zero. More...

void	identity_amatrix (pamatrix a)
	Set a matrix to identity. More...

void	random_amatrix (pamatrix a)
	Fill a matrix with random values. More...

void	random_invertible_amatrix (pamatrix a, real alpha)
	Fill a square matrix with random values and ensure that it is invertible. More...

void	random_selfadjoint_amatrix (pamatrix a)
	Fill a matrix with random values and ensure that it is self-adjoint. More...

void	random_spd_amatrix (pamatrix a, real alpha)
	Fill a matrix with random values and ensure that it is positive definite. More...

void	copy_amatrix (bool atrans, pcamatrix a, pamatrix b)
	Copy a matrix into another matrix, $B \gets A$ or $B \gets A^*$ . More...

void	copy_colpiv_amatrix (bool atrans, pcamatrix a, const uint *colpiv, pamatrix b)
	Copy a matrix into another matrix, permuting the columns, i.e., $B \gets A P_\pi$ or $B \gets (A P_\pi)^*$ . More...

pamatrix	clone_amatrix (pcamatrix src)
	Create a duplicate of an existing amatrix. More...

void	copy_sub_amatrix (bool atrans, pcamatrix a, pamatrix b)
	Copy a matrix into another matrix, $B \gets A$ or $B \gets A^*$ . More...

void	print_amatrix (pcamatrix a)
	Print a matrix. More...

void	print_matlab_amatrix (pcamatrix a)
	Print a matrix in Matlab format. More...

real	check_ortho_amatrix (bool atrans, pcamatrix a)
	Check whether a matrix or its adjoint is isometric. More...

void	scale_amatrix (field alpha, pamatrix a)
	Scale a matrix by a factor $\alpha$ , $A \gets \alpha A$ . More...

void	conjugate_amatrix (pamatrix a)
	compute the complex conjugate $\bar A$ of a matrix . More...

field	dotprod_amatrix (pcamatrix a, pcamatrix b)
	Compute the Frobenius inner product $\langle A, B \rangle_F$ of two matrices and . More...

real	norm2_amatrix (pcamatrix A)
	Approximate the spectral norm $\\|A\\|_2$ of a matrix . More...

real	normfrob_amatrix (pcamatrix a)
	Compute the Frobenius norm $\\|A\\|_F$ of a matrix . More...

real	normfrob2_amatrix (pcamatrix a)
	Compute the squared Frobenius norm $\\|A\\|_F^2$ of a matrix . More...

real	norm2diff_amatrix (pcamatrix a, pcamatrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

void	addeval_amatrix_avector (field alpha, pcamatrix a, pcavector src, pavector trg)
	Multiply a matrix by a vector , $y \gets y + \alpha A x$ . More...

void	addevaltrans_amatrix_avector (field alpha, pcamatrix a, pcavector src, pavector trg)
	Multiply the adjoint of a matrix by a vector , $y \gets y + \alpha A^* x$ . More...

void	mvm_amatrix_avector (field alpha, bool atrans, pcamatrix a, pcavector src, pavector trg)
	Multiply a matrix or its adjoint by a vector, $y \gets y + \alpha A x$ or $y \gets y + \alpha A^* x$ . More...

void	add_amatrix (field alpha, bool atrans, pcamatrix a, pamatrix b)
	Add two matrices, $B \gets B + \alpha A$ or $B \gets B + \alpha A^*$ . More...

void	addmul_amatrix (field alpha, bool atrans, pcamatrix a, bool btrans, pcamatrix b, pamatrix c)
	Multiply two matrices, $C \gets C + \alpha A B$ , $C \gets C + \alpha A^* B$ , $C \gets C + \alpha A B^$ or $C \gets C + \alpha A^ B^*$ . More...

void	bidiagmul_amatrix (field alpha, bool atrans, pamatrix a, pcavector d, pcavector l)
	Multiply a matrix by a bidiagonal matrix, $A \gets \alpha A L$ or $A \gets \alpha L^* A$ . More...

Detailed Description

Representation of a matrix as an array in column-major order.

The amatrix class is used to handle standard linear algebra operations like matrix multiplication, factorization, solving linear systems or eigenvalue problems.

Function Documentation

void add_amatrix	(	field	alpha,
		bool	atrans,
		pcamatrix	a,
		pamatrix	b
	)

Add two matrices, $B \gets B + \alpha A$ or $B \gets B + \alpha A^*$ .

Parameters

alpha	Scaling factor $\alpha$ .
atrans	Set if is to be added instead of .
a	Source matrix .
b	Target matrix .

field addentry_amatrix	(	pamatrix	a,
		uint	row,
		uint	col,
		field	x
	)

Add to a matrix entry, $a_{ij} \gets a_{ij} + x$ .

Parameters

a	Matrix .
row	Row index .
col	Column index .
x	Summand.

Returns: New value of $a_{ij}$ .

void addeval_amatrix_avector	(	field	alpha,
		pcamatrix	a,
		pcavector	src,
		pavector	trg
	)

Multiply a matrix $A$ by a vector $x$ , $y \gets y + \alpha A x$ .

The matrix $A$ is multiplied by the source vector $x$ , the result is scaled by $\alpha$ and added to the target vector $y$ .

Parameters

alpha	Scaling factor $\alpha$ .
a	Matrix .
src	Source vector .
trg	Target vector .

void addevaltrans_amatrix_avector	(	field	alpha,
		pcamatrix	a,
		pcavector	src,
		pavector	trg
	)

Multiply the adjoint of a matrix $A$ by a vector $x$ , $y \gets y + \alpha A^* x$ .

The adjoint $A^*$ is multiplied by the source vector $x$ , the result is scaled by $\alpha$ and added to the target vector $y$ .

Parameters

alpha	Scaling factor $\alpha$ .
a	Matrix .
src	Source vector .
trg	Target vector .

void addmul_amatrix	(	field	alpha,
		bool	atrans,
		pcamatrix	a,
		bool	btrans,
		pcamatrix	b,
		pamatrix	c
	)

Multiply two matrices, $C \gets C + \alpha A B$ , $C \gets C + \alpha A^* B$ , $C \gets C + \alpha A B^*$ or $C \gets C + \alpha A^* B^*$ .

The matrices $A$ (or $A^*$ ) and $B$ (or $B^*$ ) are multiplied, the result is scaled by $\alpha$ and added to the target matrix $C$ .

Parameters

alpha	Scaling factor $\alpha$ .
atrans	Set if is to be used instead of .
a	Left factor .
btrans	Set if is to be used instead of .
b	Right factor .
c	Target matrix .

void bidiagmul_amatrix	(	field	alpha,
		bool	atrans,
		pamatrix	a,
		pcavector	d,
		pcavector	l
	)

Multiply a matrix by a bidiagonal matrix, $A \gets \alpha A L$ or $A \gets \alpha L^* A$ .

The matrix $A$ (or $A^*$ ) is multiplied by the lower bidiagonal matrix $L$ described by the diagonal vector $d$ and the subdiagonal vector $l$ , the result is scaled by $\alpha$ and written back into $A$ , i.e., $a_{ij} \gets \alpha (a_{ij} d_j + a_{i,j+1} l_j)$ or $a_{ij} \gets \alpha (\bar d_i a_{ij} + \bar l_i a_{i,j+1})$ (adding zeros to $b$ for the last column or row).

Parameters

alpha	Scaling factor $\alpha$ .
atrans	Set if is to be used instead of .
a	Matrix .
d	Diagonal entries of .
l	Subdiagonal entries of .

real check_ortho_amatrix	(	bool	atrans,
		pcamatrix	a
	)

Check whether a matrix $A$ or its adjoint $A^*$ is isometric.

Compute either $I-A^*A$ or $I-AA^*$ . If the return value is small, $A$ or $A^*$ are isometric matrices. For square matrices, this also means that they are orthogonal.

Parameters

atrans	Set if is to be checked, otherwise is used.
a	Matrix .

Returns: if atrans==false and otherwise.

void clear_amatrix ( pamatrix a )

Set a matrix to zero.

Parameters

a	Target matrix.

void clear_lower_amatrix	(	pamatrix	a,
		bool	strict
	)

Set the lower triangular part of a matrix to zero.

Parameters

a	Target matrix.
strict	If set, only the strict lower triangular part should be cleared.

void clear_upper_amatrix	(	pamatrix	a,
		bool	strict
	)

Set the upper triangular part of a matrix to zero.

Parameters

a	Target matrix.
strict	If set, only the strict upper triangular part should be cleared.

pamatrix clone_amatrix ( pcamatrix src )

Create a duplicate of an existing amatrix.

Parameters

src	Matrix to be duplicated.

Returns: Copy of src.

void conjugate_amatrix ( pamatrix a )

compute the complex conjugate $\bar A$ of a matrix $ A $ .

Parameters

a	Matrix that will be conjugated.

void copy_amatrix	(	bool	atrans,
		pcamatrix	a,
		pamatrix	b
	)

Copy a matrix into another matrix, $B \gets A$ or $B \gets A^*$ .

The numbers of rows and columns have to match.

Parameters

atrans	Set if is to be used instead of .
a	Source matrix.
b	Target matrix.

void copy_colpiv_amatrix	(	bool	atrans,
		pcamatrix	a,
		const uint *	colpiv,
		pamatrix	b
	)

Copy a matrix into another matrix, permuting the columns, i.e., $B \gets A P_\pi$ or $B \gets (A P_\pi)^*$ .

The numbers of rows and columns have to match.

Parameters

atrans	Set if is to be used instead of .
a	Source matrix.
colpiv	Array of dimension `a->cols` containing the column indices.
b	Target matrix.

void copy_sub_amatrix	(	bool	atrans,
		pcamatrix	a,
		pamatrix	b
	)

Copy a matrix into another matrix, $B \gets A$ or $B \gets A^*$ .

If $B$ is smaller than $A$ (or $A^*$ ), only the upper left part of $A$ is copied. If $A$ (or $A^*$ ) is smaller than $B$ , only the upper left part of $B$ is filled.

Parameters

atrans	Set if is to be used instead of .
a	Source matrix.
b	Target matrix.

void del_amatrix ( pamatrix a )

Delete an amatrix object.

Releases the storage corresponding to the object.

Attention: Make sure that there are no submatrix objects referring to this object, since they will otherwise keep using pointers to invalid storage.

Parameters

a	Object to be deleted.

field dotprod_amatrix	(	pcamatrix	a,
		pcamatrix	b
	)

Compute the Frobenius inner product $\langle A, B \rangle_F$ of two matrices $A$ and $B$ .

The Frobenius inner product is given by $\langle A, B \rangle_F = \sum_{i,j} \bar a_{ij} b_{ij}$ .

Parameters

a	Matrix .
b	Matrix .

Returns: Frobenius inner product $\langle A, B \rangle_F$ .

uint getactives_amatrix ( )

Get number of currently initialized amatrix objects.

Calls to initialization functions like init_amatrix and constructors like new_amatrix increase an internal counter, while uninit_amatrix and del_amatrix decrease it.

Remarks: Use this function to check whether a program correctly cleans up temporary variables.

Returns: Number of currently initialized amatrix objects.

field getentry_amatrix	(	pcamatrix	a,
		uint	row,
		uint	col
	)

Read a matrix entry $a_{ij}$ .

Parameters

a	Matrix .
row	Row index .
col	Column index .

Returns: Matrix entry $a_{ij}$ .

size_t getsize_amatrix ( pcamatrix a )

Get size of a given amatrix object.

Computes the size of the amatrix object and the storage allocated for the coefficients. If the object uses the coefficients of another object (e.g., if it was created using new_sub_amatrix), no coefficient storage is added.

Parameters

a	Matrix object.

Returns: Size of allocated storage in bytes.

size_t getsize_heap_amatrix ( pcamatrix a )

Get heap size of a given amatrix object.

Computes the size of storage allocated for the coefficients on the heap, but not for the amatrix object itself. If the object uses the coefficients of another object (e.g., if it was created using new_sub_amatrix), no storage is required.

Parameters

a	Matrix object.

Returns: Size of allocated heap storage in bytes.

void identity_amatrix ( pamatrix a )

Set a matrix to identity.

Sets all diagonal entries to one and all off-diagonal entries to zero. For square matrices, this yields an identity matrix.

Parameters

a	Target matrix.

pamatrix init_amatrix	(	pamatrix	a,
		uint	rows,
		uint	cols
	)

Initialize an amatrix object.

Sets up the components of the object and allocates storage for the coefficient array.

Remarks: Should always be matched by a call to uninit_amatrix.

Parameters

a	Object to be initialized.
rows	Number of rows.
cols	Number of columns.

Returns: Initialized amatrix object.

pamatrix init_identity_amatrix	(	pamatrix	a,
		uint	rows,
		uint	cols
	)

Initialize an amatrix object and set it to identity.

Sets up the components of the object, allocates storage for the coefficient array, sets the diagonal to one and all off-diagonal entries to zero. For square matrices, this yields an identity matrix.

Remarks: Should always be matched by a call to uninit_amatrix.

Parameters

a	Object to be initialized.
rows	Number of rows.
cols	Number of columns.

Returns: Initialized amatrix object.

pamatrix init_pointer_amatrix	(	pamatrix	a,
		pfield	src,
		uint	rows,
		uint	cols
	)

Initialize an amatrix object using a given array for the coefficients.

Sets up the components of the object and uses the given array to represent the coefficients.

Remarks: Should always be matched by a call to uninit_amatrix that will not release the coefficient storage.

Parameters

a	Object to be initialized.
src	Source array, should contain at least `rows * cols` elements.
rows	Number of rows.
cols	Number of columns.

Returns: Initialized amatrix object.

pamatrix init_sub_amatrix	(	pamatrix	a,
		pamatrix	src,
		uint	rows,
		uint	roff,
		uint	cols,
		uint	coff
	)

Initialize an amatrix object to represent a submatrix.

Sets up the components of the object and uses part of the storage of another amatrix for the coefficient array, leading to a new matrix representing a submatrix of the source. Changes to the coefficients of the new matrix also change coefficients of the source matrix.

Remarks: Should always be matched by a call to uninit_amatrix that will not release the coefficient storage.

Parameters

a	Object to be initialized.
src	Source matrix.
rows	Number of rows.
roff	Row offset, should satisfy `rows+roff<=src->rows`.
cols	Number of columns.
coff	Column offset, should satisfy `cols+coff<=src->cols`.

Returns: Initialized amatrix object.

pamatrix init_vec_amatrix	(	pamatrix	a,
		pavector	src,
		uint	rows,
		uint	cols
	)

Initialize an amatrix object by a vector.

Sets up the components of the object and uses part of the storage of an avector in order to represent the matrix.

Remarks: Should always be matched by a call to uninit_amatrix that will not release the coefficient storage.

Parameters

a	Object to be initialized.
src	Source vector.
rows	Number of rows.
cols	Number of columns.

Returns: Initialized amatrix object.

pamatrix init_zero_amatrix	(	pamatrix	a,
		uint	rows,
		uint	cols
	)

Initialize an amatrix object and set it to zero.

Sets up the components of the object, allocates storage for the coefficient array, and sets it to zero.

Remarks: Should always be matched by a call to uninit_amatrix.

Parameters

a	Object to be initialized.
rows	Number of rows.
cols	Number of columns.

Returns: Initialized amatrix object.

void mvm_amatrix_avector	(	field	alpha,
		bool	atrans,
		pcamatrix	a,
		pcavector	src,
		pavector	trg
	)

Multiply a matrix $A$ or its adjoint $A^*$ by a vector, $y \gets y + \alpha A x$ or $y \gets y + \alpha A^* x$ .

The matrix or its adjoint is multiplied by the source vector $x$ , the result is scaled by $\alpha$ and added to the target vector $y$ .

Parameters

alpha	Scaling factor $\alpha$ .
atrans	Set if is to be used instead of .
a	Matrix .
src	Source vector .
trg	Target vector .

pamatrix new_amatrix	(	uint	rows,
		uint	cols
	)

Create a new amatrix object.

Allocates storage for the object and sets up its components.

Remarks: Should always be matched by a call to del_amatrix.

Parameters

rows	Number of rows.
cols	Number of columns.

Returns: New amatrix object.

pamatrix new_identity_amatrix	(	uint	rows,
		uint	cols
	)

Create a new amatrix object representing the identity.

Allocates storage for the object and sets diagonal entries to one and off-diagonal entries to zero. For square matrices, this yields an identity matrix.

Remarks: Should always be matched by a call to del_amatrix.

Parameters

rows	Number of rows.
cols	Number of columns.

Returns: New amatrix object.

pamatrix new_pointer_amatrix	(	field *	src,
		uint	rows,
		uint	cols
	)

Create a new amatrix object using a given array for the coefficients.

Parameters

src	Source array, should contain at least `rows * cols` elements.
rows	Number of rows for the new matrix.
cols	Number of columns for the new matrix.

Returns: New amatrix object.

pamatrix new_sub_amatrix	(	pamatrix	src,
		uint	rows,
		uint	roff,
		uint	cols,
		uint	coff
	)

Create a new amatrix object representing a submatrix.

Allocates storage for the object, but uses part of the storage of another amatrix object to keep the coefficients. Since the leading dimension of the source matrix is used, this allows us to work with a rectangular submatrix of the original matrix.

Remarks: Should always be matched by a call to del_amatrix that will not release the coefficient storage.

Parameters

src	Source matrix.
rows	Number of rows.
roff	Row offset, should satisfy `rows+roff<=src->rows`.
cols	Number of columns.
coff	Column offset, should satisfy `cols+coff<=src->cols`.

Returns: New amatrix object.

pamatrix new_zero_amatrix	(	uint	rows,
		uint	cols
	)

Create a new amatrix object representing a zero matrix.

Allocates storage for the object and sets all coefficients to zero.

Remarks: Should always be matched by a call to del_amatrix.

Parameters

rows	Number of rows.
cols	Number of columns.

Returns: New amatrix object.

real norm2_amatrix ( pcamatrix A )

Approximate the spectral norm $\|A\|_2$ of a matrix $A$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $A^* A$ and computing the square root of the resulting eigenvalue approximation.

Parameters

A	Dense matrix .

Returns: Approximation of $\|A\|_2$ .

real norm2diff_amatrix	(	pcamatrix	a,
		pcamatrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	Dense matrix .
b	Dense matrix .

Returns: Approximation of $\|A-B\|_2$ .

real normfrob2_amatrix ( pcamatrix a )

Compute the squared Frobenius norm $\|A\|_F^2$ of a matrix $A$ .

The Frobenius norm is given by $\|A\|_F^2 = \sum_{i,j} |a_{ij}|^2$ .

Parameters

a Matrix .

Returns: Squared Frobenius norm $\|A\|_F^2$ .

real normfrob_amatrix ( pcamatrix a )

Compute the Frobenius norm $\|A\|_F$ of a matrix $A$ .

The Frobenius norm is given by $\|A\|_F = \left( \sum_{i,j} |a_{ij}|^2 \right)^{1/2}$ .

Parameters

a Matrix .

Returns: Frobenius norm $\|A\|_F$ .

void print_amatrix ( pcamatrix a )

Print a matrix.

Parameters

a	Matrix object.

void print_matlab_amatrix ( pcamatrix a )

Print a matrix in Matlab format.

Parameters

a	Matrix object.

void random_amatrix ( pamatrix a )

Fill a matrix with random values.

Parameters

a	Target matrix.

void random_invertible_amatrix	(	pamatrix	a,
		real	alpha
	)

Fill a square matrix with random values and ensure that it is invertible.

First the matrix is filled with random values, then the diagonal elements are set to $a_{ii} \gets \alpha + \sum_{j=1}^n |a_{ij}|$ , ensuring that $A$ is diagonal dominant and therefore invertible.

Parameters

a	Target matrix.
alpha	Diagonal shift $\alpha$ , should be a positive number.

void random_selfadjoint_amatrix ( pamatrix a )

Fill a matrix with random values and ensure that it is self-adjoint.

Parameters

a	Target matrix.

void random_spd_amatrix	(	pamatrix	a,
		real	alpha
	)

Fill a matrix with random values and ensure that it is positive definite.

First the matrix is filled with random values, ensuring that it becomes self-adjoint. Then the diagonal elements are set to $a_{ii} \gets \alpha + \sum_{j=1}^n |a_{ij}|$ , ensuring that $A$ is diagonal dominant and therefore positiv definite.

Parameters

a	Target matrix.
alpha	Diagonal shift $\alpha$ , should be a positiv number.

void resize_amatrix	(	pamatrix	a,
		uint	rows,
		uint	cols
	)

Change the dimensions of an amatrix object without preserving its coefficients.

Allocates new storage for the coefficients and releases the old storage.

Attention: Make sure that there are no submatrix objects referring to this object, since they might otherwise keep using pointers to invalid storage.

Parameters

a	Matrix to be resized.
rows	New number of rows.
cols	New number of columns.

void resizecopy_amatrix	(	pamatrix	a,
		uint	rows,
		uint	cols
	)

Change the dimensions of an amatrix object while preserving as many of its coefficients as possible.

Allocates new storage for the coefficients and copies as many of the old coefficients into it. If there are more rows or columns in the new matrix, the additional coefficients are left unintialized.

Attention: Make sure that there are no submatrix objects referring to this object, since they might otherwise keep using pointers to invalid storage.

Parameters

a	Matrix to be resized.
rows	New number of rows.
cols	New number of columns.

void scale_amatrix	(	field	alpha,
		pamatrix	a
	)

Scale a matrix $A$ by a factor $\alpha$ , $A \gets \alpha A$ .

Parameters

alpha	Scaling factor $\alpha$ .
a	Target matrix .

void setentry_amatrix	(	pamatrix	a,
		uint	row,
		uint	col,
		field	x
	)

Set a matrix entry, $a_{ij}\gets x$ .

Parameters

a	Matrix .
row	Row index .
col	Column index .
x	New value of $a_{ij}$ .

void uninit_amatrix ( pamatrix a )

Uninitialize an amatrix object.

Invalidates pointers, freeing corresponding storage if appropriate, and prepares the object for deletion.

Parameters

a	Object to be uninitialized.

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation