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MAGMA
1.6.3
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_ssytrf (magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info) |
SSYTRF computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. More... | |
magma_int_t | magma_ssytrf_aasen (magma_uplo_t uplo, magma_int_t cpu_panel, magma_int_t n, float *A, magma_int_t lda, magma_int_t *ipiv, magma_int_t *info) |
SSYTRF_AASEN computes the factorization of a real symmetric matrix A based on a communication-avoiding variant of the Aasen's algorithm . More... | |
magma_int_t | magma_ssytrf_nopiv (magma_uplo_t uplo, magma_int_t n, float *A, magma_int_t lda, magma_int_t *info) |
SSYTRF_nopiv computes the LDLt factorization of a real symmetric matrix A. More... | |
magma_int_t | magma_ssytrf_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *info) |
SSYTRF_nopiv_gpu computes the LDLt factorization of a real symmetric matrix A. More... | |
magma_int_t | magma_ssytrs_nopiv_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t *info) |
SSYTRS solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U * D * U**H or A = L * D * L**H computed by SSYTRF_NOPIV_GPU. More... | |
magma_int_t magma_ssytrf | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
float * | A, | ||
magma_int_t | lda, | ||
magma_int_t * | ipiv, | ||
magma_int_t * | info | ||
) |
SSYTRF computes the factorization of a real symmetric 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 symmetric 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
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[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | REAL array, dimension (LDA,N) On entry, the symmetric 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
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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_ssytrf_aasen | ( | magma_uplo_t | uplo, |
magma_int_t | cpu_panel, | ||
magma_int_t | n, | ||
float * | A, | ||
magma_int_t | lda, | ||
magma_int_t * | ipiv, | ||
magma_int_t * | info | ||
) |
SSYTRF_AASEN computes the factorization of a real symmetric matrix A based on a communication-avoiding variant of the Aasen's algorithm .
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 symmetric and banded matrix of the band width equal to the block size.
[in] | uplo | CHARACTER*1
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[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | REAL array, dimension (LDA,N) On entry, the symmetric 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 banded matrix D and the triangular factor U or L. |
[in] | lda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | ipiv | INTEGER array, dimension (N) Details of the interchanges. |
[out] | info | INTEGER
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magma_int_t magma_ssytrf_nopiv | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
float * | A, | ||
magma_int_t | lda, | ||
magma_int_t * | info | ||
) |
SSYTRF_nopiv computes the LDLt factorization of a real symmetric 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
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[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | A | REAL array, dimension (LDA,N) On entry, the symmetric 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
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magma_int_t magma_ssytrf_nopiv_gpu | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magmaFloat_ptr | dA, | ||
magma_int_t | ldda, | ||
magma_int_t * | info | ||
) |
SSYTRF_nopiv_gpu computes the LDLt factorization of a real symmetric 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
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[in] | n | INTEGER The order of the matrix A. N >= 0. |
[in,out] | dA | REAL array on the GPU, dimension (LDDA,N) On entry, the symmetric 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] | ldda | INTEGER The leading dimension of the array A. LDDA >= max(1,N). |
[out] | info | INTEGER
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magma_int_t magma_ssytrs_nopiv_gpu | ( | magma_uplo_t | uplo, |
magma_int_t | n, | ||
magma_int_t | nrhs, | ||
magmaFloat_ptr | dA, | ||
magma_int_t | ldda, | ||
magmaFloat_ptr | dB, | ||
magma_int_t | lddb, | ||
magma_int_t * | info | ||
) |
SSYTRS solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U * D * U**H or A = L * D * L**H computed by SSYTRF_NOPIV_GPU.
[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] | dA | REAL 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 SSYTRF_NOPIV_GPU. |
[in] | ldda | INTEGER The leading dimension of the array A. LDA >= max(1,N). |
param[in,out] dB REAL 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
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