MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
 All Classes Files Functions Friends Groups Pages
lansy/he: Symmetric/Hermitian matrix norm

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

Functions

float magmablas_clanhe (magma_norm_t norm, magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dwork, magma_int_t lwork, magma_queue_t queue)
 CLANHE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix A. More...
 
double magmablas_dlansy (magma_norm_t norm, magma_uplo_t uplo, magma_int_t n, magmaDouble_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dwork, magma_int_t lwork, magma_queue_t queue)
 DLANSY returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A. More...
 
float magmablas_slansy (magma_norm_t norm, magma_uplo_t uplo, magma_int_t n, magmaFloat_const_ptr dA, magma_int_t ldda, magmaFloat_ptr dwork, magma_int_t lwork, magma_queue_t queue)
 SLANSY returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A. More...
 
double magmablas_zlanhe (magma_norm_t norm, magma_uplo_t uplo, magma_int_t n, magmaDoubleComplex_const_ptr dA, magma_int_t ldda, magmaDouble_ptr dwork, magma_int_t lwork, magma_queue_t queue)
 ZLANHE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix A. More...
 

Detailed Description

1, Frobenius, or Infinity norm; or largest element

Function Documentation

float magmablas_clanhe ( magma_norm_t  norm,
magma_uplo_t  uplo,
magma_int_t  n,
magmaFloatComplex_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dwork,
magma_int_t  lwork,
magma_queue_t  queue 
)

CLANHE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix A.

CLANHE = ( max(abs(A(i,j))), NORM = MagmaMaxNorm ( ( norm1(A), NORM = MagmaOneNorm ( ( normI(A), NORM = MagmaInfNorm ( ( normF(A), NORM = MagmaFrobeniusNorm ** not yet supported

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.

On error, returns CLANHE < 0: if CLANHE = -i, the i-th argument had an illegal value.

Arguments:

Parameters
[in]normmagma_norm_t Specifies the value to be returned in CLANHE as described above.
[in]uplomagma_uplo_t Specifies whether the upper or lower triangular part of the Hermitian matrix A is to be referenced.
  • = MagmaUpper: Upper triangular part of A is referenced
  • = MagmaLower: Lower triangular part of A is referenced
[in]nINTEGER The order of the matrix A. N >= 0. When N = 0, CLANHE is set to zero.
[in]dACOMPLEX array on the GPU, dimension (LDDA,N) The Hermitian matrix A. If UPLO = MagmaUpper, the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(N,1).
dwork(workspace) REAL array on the GPU, dimension (MAX(1,LWORK)), where LWORK >= N. NOTE: this is different than LAPACK, where WORK is required only for norm1 and normI. Here max-norm also requires WORK.
[in]lworkINTEGER The dimension of the array DWORK. LWORK >= max( 1, N ).
[in]queuemagma_queue_t Queue to execute in.
double magmablas_dlansy ( magma_norm_t  norm,
magma_uplo_t  uplo,
magma_int_t  n,
magmaDouble_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dwork,
magma_int_t  lwork,
magma_queue_t  queue 
)

DLANSY returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A.

DLANSY = ( max(abs(A(i,j))), NORM = MagmaMaxNorm ( ( norm1(A), NORM = MagmaOneNorm ( ( normI(A), NORM = MagmaInfNorm ( ( normF(A), NORM = MagmaFrobeniusNorm ** not yet supported

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.

On error, returns DLANSY < 0: if DLANSY = -i, the i-th argument had an illegal value.

Arguments:

Parameters
[in]normmagma_norm_t Specifies the value to be returned in DLANSY as described above.
[in]uplomagma_uplo_t Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced.
  • = MagmaUpper: Upper triangular part of A is referenced
  • = MagmaLower: Lower triangular part of A is referenced
[in]nINTEGER The order of the matrix A. N >= 0. When N = 0, DLANSY is set to zero.
[in]dADOUBLE PRECISION array on the GPU, dimension (LDDA,N) The symmetric matrix A. If UPLO = MagmaUpper, the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(N,1).
dwork(workspace) DOUBLE PRECISION array on the GPU, dimension (MAX(1,LWORK)), where LWORK >= N. NOTE: this is different than LAPACK, where WORK is required only for norm1 and normI. Here max-norm also requires WORK.
[in]lworkINTEGER The dimension of the array DWORK. LWORK >= max( 1, N ).
[in]queuemagma_queue_t Queue to execute in.
float magmablas_slansy ( magma_norm_t  norm,
magma_uplo_t  uplo,
magma_int_t  n,
magmaFloat_const_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dwork,
magma_int_t  lwork,
magma_queue_t  queue 
)

SLANSY returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A.

SLANSY = ( max(abs(A(i,j))), NORM = MagmaMaxNorm ( ( norm1(A), NORM = MagmaOneNorm ( ( normI(A), NORM = MagmaInfNorm ( ( normF(A), NORM = MagmaFrobeniusNorm ** not yet supported

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.

On error, returns SLANSY < 0: if SLANSY = -i, the i-th argument had an illegal value.

Arguments:

Parameters
[in]normmagma_norm_t Specifies the value to be returned in SLANSY as described above.
[in]uplomagma_uplo_t Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced.
  • = MagmaUpper: Upper triangular part of A is referenced
  • = MagmaLower: Lower triangular part of A is referenced
[in]nINTEGER The order of the matrix A. N >= 0. When N = 0, SLANSY is set to zero.
[in]dAREAL array on the GPU, dimension (LDDA,N) The symmetric matrix A. If UPLO = MagmaUpper, the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(N,1).
dwork(workspace) REAL array on the GPU, dimension (MAX(1,LWORK)), where LWORK >= N. NOTE: this is different than LAPACK, where WORK is required only for norm1 and normI. Here max-norm also requires WORK.
[in]lworkINTEGER The dimension of the array DWORK. LWORK >= max( 1, N ).
[in]queuemagma_queue_t Queue to execute in.
double magmablas_zlanhe ( magma_norm_t  norm,
magma_uplo_t  uplo,
magma_int_t  n,
magmaDoubleComplex_const_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dwork,
magma_int_t  lwork,
magma_queue_t  queue 
)

ZLANHE returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix A.

ZLANHE = ( max(abs(A(i,j))), NORM = MagmaMaxNorm ( ( norm1(A), NORM = MagmaOneNorm ( ( normI(A), NORM = MagmaInfNorm ( ( normF(A), NORM = MagmaFrobeniusNorm ** not yet supported

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.

On error, returns ZLANHE < 0: if ZLANHE = -i, the i-th argument had an illegal value.

Arguments:

Parameters
[in]normmagma_norm_t Specifies the value to be returned in ZLANHE as described above.
[in]uplomagma_uplo_t Specifies whether the upper or lower triangular part of the Hermitian matrix A is to be referenced.
  • = MagmaUpper: Upper triangular part of A is referenced
  • = MagmaLower: Lower triangular part of A is referenced
[in]nINTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHE is set to zero.
[in]dACOMPLEX*16 array on the GPU, dimension (LDDA,N) The Hermitian matrix A. If UPLO = MagmaUpper, the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
[in]lddaINTEGER The leading dimension of the array A. LDDA >= max(N,1).
dwork(workspace) DOUBLE PRECISION array on the GPU, dimension (MAX(1,LWORK)), where LWORK >= N. NOTE: this is different than LAPACK, where WORK is required only for norm1 and normI. Here max-norm also requires WORK.
[in]lworkINTEGER The dimension of the array DWORK. LWORK >= max( 1, N ).
[in]queuemagma_queue_t Queue to execute in.