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. | |
magma_int_t | magma_chetrf (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info) |
CHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. | |
magma_int_t | magma_chetrf_nopiv (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magma_int_t *info) |
CHETRF_nopiv computes the LDLt factorization of a complex Hermitian matrix A. | |
magma_int_t | magma_chetrf_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t *info) |
CHETRF_nopiv_gpu computes the LDLt factorization of a complex Hermitian matrix A. | |
magma_int_t | magma_chetrs_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) |
Solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF_NOPIV_GPU. |
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 = 'U', or A = L * D * L**H, if uplo = 'L', 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 | CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': 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 = 'U', 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 = 'L', 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 = 'U' 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 = 'L' 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_chetrf | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaFloatComplex * | A, | |||
magma_int_t | lda, | |||
magma_int_t * | ipiv, | |||
magma_int_t * | info | |||
) |
CHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.
The form of the factorization is
A = U*D*U**H or A = L*D*L**H
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.
This is the blocked version of the algorithm, calling Level 3 BLAS.
[in] | UPLO | CHARACTER*1
|
[in] | N | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', 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 = 'L', 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L (see below for further details). |
[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. 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 = 'U' 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 = 'L' 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. |
[out] | INFO | INTEGER
|
Further Details =============== If UPLO = 'U', then A = U*D*U', where U = P(n)*U(n)* ... *P(k)U(k)* ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then
( I v 0 ) k-s U(k) = ( 0 I 0 ) s ( 0 0 I ) n-k k-s s n-k
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-1:k).
If UPLO = 'L', then A = L*D*L', where L = P(1)*L(1)* ... *P(k)*L(k)* ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then
( I 0 0 ) k-1 L(k) = ( 0 I 0 ) s ( 0 v I ) n-k-s+1 k-1 s n-k-s+1
If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
magma_int_t magma_chetrf_nopiv | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaFloatComplex * | A, | |||
magma_int_t | lda, | |||
magma_int_t * | info | |||
) |
CHETRF_nopiv computes the LDLt factorization of a complex Hermitian matrix A.
This version does not require work space on the GPU passed as input. GPU memory is allocated in the routine.
The factorization has the form A = U^H * D * U, if UPLO = 'U', or A = L * D * L^H, if UPLO = 'L', where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.
This is the block version of the algorithm, calling Level 3 BLAS.
[in] | UPLO | CHARACTER*1
|
[in] | N | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', 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 = 'L', 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 factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory. |
[in] | LDA | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | INFO | INTEGER
|
magma_int_t magma_chetrf_nopiv_gpu | ( | magma_uplo_t | uplo, | |
magma_int_t | n, | |||
magmaFloatComplex_ptr | dA, | |||
magma_int_t | ldda, | |||
magma_int_t * | info | |||
) |
CHETRF_nopiv_gpu computes the LDLt factorization of a complex Hermitian matrix A.
The factorization has the form A = U^H * D * U, if UPLO = 'U', or A = L * D * L^H, if UPLO = 'L', where U is an upper triangular matrix, L is lower triangular, and D is a diagonal matrix.
This is the block version of the algorithm, calling Level 3 BLAS.
[in] | UPLO | CHARACTER*1
|
[in] | N | INTEGER The order of the matrix A. N >= 0. |
[in,out] | dA | COMPLEX array on the GPU, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', 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 = 'L', 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 factor U or L from the Cholesky factorization A = U^H D U or A = L D L^H. Higher performance is achieved if A is in pinned memory, e.g. allocated using cudaMallocHost. |
[in] | LDA | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | INFO | INTEGER
|
magma_int_t magma_chetrs_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 | |||
) |
Solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF_NOPIV_GPU.
[in] | uplo | magma_uplo_t
|
[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] | dA | COMPLEX array on the GPU, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_NOPIV_GPU. |
[in] | ldda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
param[in,out] dB COMPLEX array on the GPU, dimension (LDB,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. LDB >= max(1,N). |
[out] | info | INTEGER
|