MAGMA  2.0.2
Matrix Algebra for GPU and Multicore Architectures

Functions

magma_int_t magma_zhesv (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex *A, magma_int_t lda, magma_int_t *ipiv, magmaDoubleComplex *B, magma_int_t ldb, magma_int_t *info)
 ZHESV computes the solution to a complex system of linear equations A * X = B, where A is an n-by-n Hermitian matrix and X and B are n-by-nrhs matrices. More...
 
magma_int_t magma_zhesv_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex_ptr dB, magma_int_t lddb, magma_int_t *info)
 ZHESV solves a system of linear equations A * X = B where A is an n-by-n Hermitian matrix and X and B are n-by-nrhs matrices. More...
 

Detailed Description

Function Documentation

magma_int_t magma_zhesv ( magma_uplo_t  uplo,
magma_int_t  n,
magma_int_t  nrhs,
magmaDoubleComplex *  A,
magma_int_t  lda,
magma_int_t *  ipiv,
magmaDoubleComplex *  B,
magma_int_t  ldb,
magma_int_t *  info 
)

ZHESV computes the solution to a complex system of linear equations A * X = B, where A is an n-by-n Hermitian matrix and X and B are n-by-nrhs matrices.

The diagonal pivoting method is used to factor A as A = U * D * U**H, if uplo = MagmaUpper, or A = L * D * L**H, if uplo = MagmaLower, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
[in]uplomagma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The number of linear equations, i.e., the order of the matrix A. n >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]ACOMPLEX*16 array, dimension (lda,n) On entry, 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.

On exit, if info = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by ZHETRF.

Parameters
[in]ldaINTEGER The leading dimension of the array A. lda >= max(1,n).
[out]ipivINTEGER array, dimension (n) Details of the interchanges and the block structure of D, as determined by ZHETRF. If ipiv(k) > 0, then rows and columns k and ipiv(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If uplo = MagmaUpper and ipiv(k) = ipiv(k-1) < 0, then rows and columns k-1 and -ipiv(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If uplo = MagmaLower and ipiv(k) = ipiv(k+1) < 0, then rows and columns k+1 and -ipiv(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[in,out]B(input/output) COMPLEX*16 array, dimension (ldb,nrhs) On entry, the n-by-nrhs right hand side matrix B. On exit, if info = 0, the n-by-nrhs solution matrix X.
[in]ldbINTEGER The leading dimension of the array B. ldb >= max(1,n).
[out]infoINTEGER = 0: successful exit < 0: if info = -i, the i-th argument had an illegal value > 0: if info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.
magma_int_t magma_zhesv_nopiv_gpu ( magma_uplo_t  uplo,
magma_int_t  n,
magma_int_t  nrhs,
magmaDoubleComplex_ptr  dA,
magma_int_t  ldda,
magmaDoubleComplex_ptr  dB,
magma_int_t  lddb,
magma_int_t *  info 
)

ZHESV solves a system of linear equations A * X = B where A is an n-by-n Hermitian matrix and X and B are n-by-nrhs matrices.

The LU decomposition with no pivoting is used to factor A as The factorization has the form A = U^H * D * U, if UPLO = MagmaUpper, or A = L * D * L^H, if UPLO = MagmaLower, where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
[in]uplomagma_uplo_t
  • = MagmaUpper: Upper triangle of A is stored;
  • = MagmaLower: Lower triangle of A is stored.
[in]nINTEGER The order of the matrix A. n >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0.
[in,out]dACOMPLEX_16 array, dimension (ldda,n). On entry, the n-by-n matrix to be factored. On exit, the factors L and U from the factorization A = L*U; the unit diagonal elements of L are not stored.
[in]lddaINTEGER The leading dimension of the array A. ldda >= max(1,n).
[in,out]dBCOMPLEX_16 array, dimension (lddb,nrhs) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. lddb >= max(1,n).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value