lantr: Triangular matrix norm

1, Frobenius, or Infinity norm; or largest element More...

Functions
float	plasma_clantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, int m, int n, plasma_complex32_t *pA, int lda)
void	plasma_omp_clantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, plasma_desc_t A, float *work, float *value, plasma_sequence_t *sequence, plasma_request_t *request)
double	plasma_dlantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, int m, int n, double *pA, int lda)
void	plasma_omp_dlantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, plasma_desc_t A, double *work, double *value, plasma_sequence_t *sequence, plasma_request_t *request)
float	plasma_slantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, int m, int n, float *pA, int lda)
void	plasma_omp_slantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, plasma_desc_t A, float *work, float *value, plasma_sequence_t *sequence, plasma_request_t *request)
double	plasma_zlantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, int m, int n, plasma_complex64_t *pA, int lda)
void	plasma_omp_zlantr (plasma_enum_t norm, plasma_enum_t uplo, plasma_enum_t diag, plasma_desc_t A, double *work, double *value, plasma_sequence_t *sequence, plasma_request_t *request)

Detailed Description

1, Frobenius, or Infinity norm; or largest element

Function Documentation

float plasma_clantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		int	m,
		int	n,
		plasma_complex32_t *	pA,
		int	lda
	)

Returns the norm of a trapezoidal or triangular matrix as

clantr = ( max(abs(A(i,j))), NORM = PlasmaMaxNorm ( ( norm1(A), NORM = PlasmaOneNorm ( ( normI(A), NORM = PlasmaInfNorm ( ( normF(A), NORM = PlasmaFrobeniusNorm

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

[in]	norm	PlasmaMaxNorm: max norm PlasmaOneNorm: one norm PlasmaInfNorm: infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix A. m >= 0. When m = 0, the returned value is set to zero.
[in]	n	The number of columns of the matrix A. n >= 0. When n = 0, the returned value is set to zero.
[in]	pA	The m-by-n trapezoidal matrix A.
[in]	lda	The leading dimension of the array A. lda >= max(1,m).

Return values

float

The specified norm of the trapezoidal or triangular matrix A.

See also

plasma_omp_clantr

plasma_clantr

plasma_slantr

plasma_slantr

void plasma_omp_clantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		plasma_desc_t	A,
		float *	work,
		float *	value,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Calculates the max, one, infinity or Frobenius norm of a general matrix. Non-blocking equivalent of plasma_clantr(). May return before the computation is finished. Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	norm	PlasmaMaxNorm: Max norm PlasmaOneNorm: One norm PlasmaInfNorm: Infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	A	The descriptor of matrix A.
[out]	work	Workspace of size: PlasmaMaxNorm: A.mt*A.nt PlasmaOneNorm: A.mt*A.n + A.n PlasmaInfNorm: A.mt*A.n + A.n PlasmaFrobeniusNorm: 2*A.mt*A.nt
[out]	value	The calculated value of the norm requested.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes).
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_clantr

plasma_omp_clantr

plasma_omp_slantr

plasma_omp_slantr

double plasma_dlantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		int	m,
		int	n,
		double *	pA,
		int	lda
	)

Returns the norm of a trapezoidal or triangular matrix as

dlantr = ( max(abs(A(i,j))), NORM = PlasmaMaxNorm ( ( norm1(A), NORM = PlasmaOneNorm ( ( normI(A), NORM = PlasmaInfNorm ( ( normF(A), NORM = PlasmaFrobeniusNorm

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

[in]	norm	PlasmaMaxNorm: max norm PlasmaOneNorm: one norm PlasmaInfNorm: infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix A. m >= 0. When m = 0, the returned value is set to zero.
[in]	n	The number of columns of the matrix A. n >= 0. When n = 0, the returned value is set to zero.
[in]	pA	The m-by-n trapezoidal matrix A.
[in]	lda	The leading dimension of the array A. lda >= max(1,m).

Return values

double

The specified norm of the trapezoidal or triangular matrix A.

See also

plasma_omp_dlantr

plasma_clantr

plasma_dlantr

plasma_slantr

void plasma_omp_dlantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		plasma_desc_t	A,
		double *	work,
		double *	value,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Calculates the max, one, infinity or Frobenius norm of a general matrix. Non-blocking equivalent of plasma_dlantr(). May return before the computation is finished. Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	norm	PlasmaMaxNorm: Max norm PlasmaOneNorm: One norm PlasmaInfNorm: Infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	A	The descriptor of matrix A.
[out]	work	Workspace of size: PlasmaMaxNorm: A.mt*A.nt PlasmaOneNorm: A.mt*A.n + A.n PlasmaInfNorm: A.mt*A.n + A.n PlasmaFrobeniusNorm: 2*A.mt*A.nt
[out]	value	The calculated value of the norm requested.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes).
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_dlantr

plasma_omp_clantr

plasma_omp_dlantr

plasma_omp_slantr

float plasma_slantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		int	m,
		int	n,
		float *	pA,
		int	lda
	)

Returns the norm of a trapezoidal or triangular matrix as

slantr = ( max(abs(A(i,j))), NORM = PlasmaMaxNorm ( ( norm1(A), NORM = PlasmaOneNorm ( ( normI(A), NORM = PlasmaInfNorm ( ( normF(A), NORM = PlasmaFrobeniusNorm

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

[in]	norm	PlasmaMaxNorm: max norm PlasmaOneNorm: one norm PlasmaInfNorm: infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix A. m >= 0. When m = 0, the returned value is set to zero.
[in]	n	The number of columns of the matrix A. n >= 0. When n = 0, the returned value is set to zero.
[in]	pA	The m-by-n trapezoidal matrix A.
[in]	lda	The leading dimension of the array A. lda >= max(1,m).

Return values

float

The specified norm of the trapezoidal or triangular matrix A.

See also

plasma_omp_slantr

plasma_clantr

plasma_slantr

plasma_slantr

void plasma_omp_slantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		plasma_desc_t	A,
		float *	work,
		float *	value,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Calculates the max, one, infinity or Frobenius norm of a general matrix. Non-blocking equivalent of plasma_slantr(). May return before the computation is finished. Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	norm	PlasmaMaxNorm: Max norm PlasmaOneNorm: One norm PlasmaInfNorm: Infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	A	The descriptor of matrix A.
[out]	work	Workspace of size: PlasmaMaxNorm: A.mt*A.nt PlasmaOneNorm: A.mt*A.n + A.n PlasmaInfNorm: A.mt*A.n + A.n PlasmaFrobeniusNorm: 2*A.mt*A.nt
[out]	value	The calculated value of the norm requested.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes).
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_slantr

plasma_omp_clantr

plasma_omp_slantr

plasma_omp_slantr

double plasma_zlantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		int	m,
		int	n,
		plasma_complex64_t *	pA,
		int	lda
	)

Returns the norm of a trapezoidal or triangular matrix as

zlantr = ( max(abs(A(i,j))), NORM = PlasmaMaxNorm ( ( norm1(A), NORM = PlasmaOneNorm ( ( normI(A), NORM = PlasmaInfNorm ( ( normF(A), NORM = PlasmaFrobeniusNorm

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

[in]	norm	PlasmaMaxNorm: max norm PlasmaOneNorm: one norm PlasmaInfNorm: infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	m	The number of rows of the matrix A. m >= 0. When m = 0, the returned value is set to zero.
[in]	n	The number of columns of the matrix A. n >= 0. When n = 0, the returned value is set to zero.
[in]	pA	The m-by-n trapezoidal matrix A.
[in]	lda	The leading dimension of the array A. lda >= max(1,m).

Return values

double

The specified norm of the trapezoidal or triangular matrix A.

See also

plasma_omp_zlantr

plasma_clantr

plasma_dlantr

plasma_slantr

void plasma_omp_zlantr	(	plasma_enum_t	norm,
		plasma_enum_t	uplo,
		plasma_enum_t	diag,
		plasma_desc_t	A,
		double *	work,
		double *	value,
		plasma_sequence_t *	sequence,
		plasma_request_t *	request
	)

Calculates the max, one, infinity or Frobenius norm of a general matrix. Non-blocking equivalent of plasma_zlantr(). May return before the computation is finished. Operates on matrices stored by tiles. All matrices are passed through descriptors. All dimensions are taken from the descriptors. Allows for pipelining of operations at runtime.

Parameters

[in]	norm	PlasmaMaxNorm: Max norm PlasmaOneNorm: One norm PlasmaInfNorm: Infinity norm PlasmaFrobeniusNorm: Frobenius norm
[in]	uplo	PlasmaUpper: Upper triangle of A is stored; PlasmaLower: Lower triangle of A is stored.
[in]	diag	PlasmaNonUnit: A has non-unit diagonal, PlasmaUnit: A has unit diagonal.
[in]	A	The descriptor of matrix A.
[out]	work	Workspace of size: PlasmaMaxNorm: A.mt*A.nt PlasmaOneNorm: A.mt*A.n + A.n PlasmaInfNorm: A.mt*A.n + A.n PlasmaFrobeniusNorm: 2*A.mt*A.nt
[out]	value	The calculated value of the norm requested.
[in]	sequence	Identifies the sequence of function calls that this call belongs to (for completion checks and exception handling purposes).
[out]	request	Identifies this function call (for exception handling purposes).

Return values

void	Errors are returned by setting sequence->status and request->status to error values. The sequence->status and request->status should never be set to PlasmaSuccess (the initial values) since another async call may be setting a failure value at the same time.

See also

plasma_zlantr

plasma_omp_clantr

plasma_omp_dlantr

plasma_omp_slantr