MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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trtri: Triangular inverse; used in getri, potri

\( A = A^{-1} \) where \( A \) is triangular More...

Functions

magma_int_t magma_ctrtri (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *info)
 CTRTRI computes the inverse of a real upper or lower triangular matrix A. More...
 
magma_int_t magma_ctrtri_gpu (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t *info)
 CTRTRI computes the inverse of a real upper or lower triangular matrix dA. More...
 
magma_int_t magma_dtrtri (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, double *A, magma_int_t lda, magma_int_t *info)
 DTRTRI computes the inverse of a real upper or lower triangular matrix A. More...
 
magma_int_t magma_dtrtri_gpu (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t *info)
 DTRTRI computes the inverse of a real upper or lower triangular matrix dA. More...
 
magma_int_t magma_strtri (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info)
 STRTRI computes the inverse of a real upper or lower triangular matrix A. More...
 
magma_int_t magma_strtri_gpu (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *info)
 STRTRI computes the inverse of a real upper or lower triangular matrix dA. More...
 
magma_int_t magma_ztrtri (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *info)
 ZTRTRI computes the inverse of a real upper or lower triangular matrix A. More...
 
magma_int_t magma_ztrtri_gpu (magma_uplo_t uplo, magma_diag_t diag, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *info)
 ZTRTRI computes the inverse of a real upper or lower triangular matrix dA. More...
 

Detailed Description

\( A = A^{-1} \) where \( A \) is triangular

Function Documentation

magma_int_t magma_ctrtri ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
magma_int_t *  info 
)

CTRTRI computes the inverse of a real upper or lower triangular matrix A.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX array, dimension (LDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed.
magma_int_t magma_ctrtri_gpu ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaFloatComplex_ptr  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

CTRTRI computes the inverse of a real upper or lower triangular matrix dA.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dACOMPLEX array ON THE GPU, dimension (LDDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array dA contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array dA contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, dA(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed. (Singularity check is currently disabled.)
magma_int_t magma_dtrtri ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
double *  A,
magma_int_t  lda,
magma_int_t *  info 
)

DTRTRI computes the inverse of a real upper or lower triangular matrix A.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ADOUBLE PRECISION array, dimension (LDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed.
magma_int_t magma_dtrtri_gpu ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaDouble_ptr  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

DTRTRI computes the inverse of a real upper or lower triangular matrix dA.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dADOUBLE PRECISION array ON THE GPU, dimension (LDDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array dA contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array dA contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, dA(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed. (Singularity check is currently disabled.)
magma_int_t magma_strtri ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
float *  A,
magma_int_t  lda,
magma_int_t *  info 
)

STRTRI computes the inverse of a real upper or lower triangular matrix A.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed.
magma_int_t magma_strtri_gpu ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

STRTRI computes the inverse of a real upper or lower triangular matrix dA.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dAREAL array ON THE GPU, dimension (LDDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array dA contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array dA contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, dA(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed. (Singularity check is currently disabled.)
magma_int_t magma_ztrtri ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaDoubleComplex *  A,
magma_int_t  lda,
magma_int_t *  info 
)

ZTRTRI computes the inverse of a real upper or lower triangular matrix A.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX_16 array, dimension (LDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed.
magma_int_t magma_ztrtri_gpu ( magma_uplo_t  uplo,
magma_diag_t  diag,
magma_int_t  n,
magmaDoubleComplex_ptr  dA,
magma_int_t  ldda,
magma_int_t *  info 
)

ZTRTRI computes the inverse of a real upper or lower triangular matrix dA.

This is the Level 3 BLAS version of the algorithm.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: A is upper triangular;
  • = MagmaLower: A is lower triangular.
[in]diagmagma_diag_t
  • = MagmaNonUnit: A is non-unit triangular;
  • = MagmaUnit: A is unit triangular.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]dACOMPLEX_16 array ON THE GPU, dimension (LDDA,N) On entry, the triangular matrix A. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of the array dA contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of the array dA contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = MagmaUnit, the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.
[in]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, dA(i,i) is exactly zero. The triangular matrix is singular and its inverse cannot be computed. (Singularity check is currently disabled.)