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MAGMA
2.0.0
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_chesv (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloatComplex *A, magma_int_t lda, magma_int_t *ipiv, magmaFloatComplex *B, magma_int_t ldb, magma_int_t *info) |
CHESV 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_chesv_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dB, magma_int_t lddb, magma_int_t *info) |
CHESV 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... | |
magma_int_t magma_chesv | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magma_int_t | nrhs, | ||
magmaFloatComplex * | A, | ||
magma_int_t | lda, | ||
magma_int_t * | ipiv, | ||
magmaFloatComplex * | B, | ||
magma_int_t | ldb, | ||
magma_int_t * | info | ||
) |
CHESV 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.
[in] | uplo | magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. |
[in] | n | INTEGER The number of linear equations, i.e., the order of the matrix A. n >= 0. |
[in] | nrhs | INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0. |
[in,out] | A | COMPLEX 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 CHETRF.
[in] | lda | INTEGER The leading dimension of the array A. lda >= max(1,n). |
[out] | ipiv | INTEGER array, dimension (n) Details of the interchanges and the block structure of D, as determined by CHETRF. 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 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] | ldb | INTEGER The leading dimension of the array B. ldb >= max(1,n). |
[out] | info | INTEGER = 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_chesv_nopiv_gpu | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magma_int_t | nrhs, | ||
magmaFloatComplex_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloatComplex_ptr | dB, | ||
magma_int_t | lddb, | ||
magma_int_t * | info | ||
) |
CHESV 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.
[in] | uplo | magma_uplo_t
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[in] | n | INTEGER The order of the matrix A. n >= 0. |
[in] | nrhs | INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. nrhs >= 0. |
[in,out] | dA | COMPLEX 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] | ldda | INTEGER The leading dimension of the array A. ldda >= max(1,n). |
[in,out] | dB | COMPLEX array, dimension (lddb,nrhs) On entry, the right hand side matrix B. On exit, the solution matrix X. |
[in] | lddb | INTEGER The leading dimension of the array B. lddb >= max(1,n). |
[out] | info | INTEGER
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