MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
posv: Solves Ax = b using Cholesky factorization (driver)

Functions

magma_int_t magma_cposv (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb, magma_int_t *info)
CPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_cposv_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)
CPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_dposv (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, double *A, magma_int_t lda, double *B, magma_int_t ldb, magma_int_t *info)
DPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_dposv_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t *info)
DPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_dsposv_gpu (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magmaDouble_ptr dX, magma_int_t lddx, magmaDouble_ptr dworkd, magmaFloat_ptr dworks, magma_int_t *iter, magma_int_t *info)
DSPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_sposv (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, float *A, magma_int_t lda, float *B, magma_int_t ldb, magma_int_t *info)
SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_sposv_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)
SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_zcposv_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, magmaDoubleComplex_ptr dX, magma_int_t lddx, magmaDoubleComplex_ptr dworkd, magmaFloatComplex_ptr dworks, magma_int_t *iter, magma_int_t *info)
ZCPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_zposv (magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *B, magma_int_t ldb, magma_int_t *info)
ZPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_zposv_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)
ZPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. More...

Function Documentation

 magma_int_t magma_cposv ( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaFloatComplex * A, magma_int_t lda, magmaFloatComplex * B, magma_int_t ldb, magma_int_t * info )

CPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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] 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 factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in,out] B COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the 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
 magma_int_t magma_cposv_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 )

CPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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 on the GPU, dimension (LDDA,N) On entry, the Hermitian matrix dA. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H*U or dA = L*L**H. [in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N). [in,out] dB COMPLEX array on the GPU, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_dposv ( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, double * A, magma_int_t lda, double * B, magma_int_t ldb, magma_int_t * info )

DPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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] A DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric 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 factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in,out] B DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the 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
 magma_int_t magma_dposv_gpu ( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t * info )

DPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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 DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the symmetric matrix dA. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H*U or dA = L*L**H. [in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N). [in,out] dB DOUBLE PRECISION array on the GPU, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_dsposv_gpu ( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dB, magma_int_t lddb, magmaDouble_ptr dX, magma_int_t lddx, magmaDouble_ptr dworkd, magmaFloat_ptr dworks, magma_int_t * iter, magma_int_t * info )

DSPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

DSPOSV first attempts to factorize the matrix in real SINGLE PRECISION and use this factorization within an iterative refinement procedure to produce a solution with real DOUBLE PRECISION norm-wise backward error quality (see below). If the approach fails the method switches to a real DOUBLE PRECISION factorization and solve.

The iterative refinement is not going to be a winning strategy if the ratio real SINGLE PRECISION performance over real DOUBLE PRECISION performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.

Parameters
 [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] dA DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the symmetric 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 iterative refinement has been successfully used (INFO.EQ.0 and ITER.GE.0, see description below), then A is unchanged, if double factorization has been used (INFO.EQ.0 and ITER.LT.0, see description below), then the array dA contains the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. [in] ldda INTEGER The leading dimension of the array dA. LDDA >= max(1,N). [in] dB DOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS) The N-by-NRHS right hand side matrix B. [in] lddb INTEGER The leading dimension of the array dB. LDDB >= max(1,N). [out] dX DOUBLE PRECISION array on the GPU, dimension (LDDX,NRHS) If INFO = 0, the N-by-NRHS solution matrix X. [in] lddx INTEGER The leading dimension of the array dX. LDDX >= max(1,N). dworkd (workspace) DOUBLE PRECISION array on the GPU, dimension (N*NRHS) This array is used to hold the residual vectors. dworks (workspace) SINGLE PRECISION array on the GPU, dimension (N*(N+NRHS)) This array is used to store the real single precision matrix and the right-hand sides or solutions in single precision. [out] iter INTEGER < 0: iterative refinement has failed, double precision factorization has been performed -1 : the routine fell back to full precision for implementation- or machine-specific reasons -2 : narrowing the precision induced an overflow, the routine fell back to full precision -3 : failure of SPOTRF -31: stop the iterative refinement after the 30th iteration > 0: iterative refinement has been successfully used. Returns the number of iterations [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i of (DOUBLE PRECISION) A is not positive definite, so the factorization could not be completed, and the solution has not been computed.
 magma_int_t magma_sposv ( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, float * A, magma_int_t lda, float * B, magma_int_t ldb, magma_int_t * info )

SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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] A REAL array, dimension (LDA,N) On entry, the symmetric 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 factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in,out] B REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the 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
 magma_int_t magma_sposv_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 )

SPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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 REAL array on the GPU, dimension (LDDA,N) On entry, the symmetric matrix dA. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H*U or dA = L*L**H. [in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N). [in,out] dB REAL array on the GPU, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
 magma_int_t magma_zcposv_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, magmaDoubleComplex_ptr dX, magma_int_t lddx, magmaDoubleComplex_ptr dworkd, magmaFloatComplex_ptr dworks, magma_int_t * iter, magma_int_t * info )

ZCPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

ZCPOSV first attempts to factorize the matrix in complex SINGLE PRECISION and use this factorization within an iterative refinement procedure to produce a solution with complex DOUBLE PRECISION norm-wise backward error quality (see below). If the approach fails the method switches to a complex DOUBLE PRECISION factorization and solve.

The iterative refinement is not going to be a winning strategy if the ratio complex SINGLE PRECISION performance over complex DOUBLE PRECISION performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement.

The iterative refinement process is stopped if ITER > ITERMAX or for all the RHS we have: RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX where o ITER is the number of the current iteration in the iterative refinement process o RNRM is the infinity-norm of the residual o XNRM is the infinity-norm of the solution o ANRM is the infinity-operator-norm of the matrix A o EPS is the machine epsilon returned by DLAMCH('Epsilon') The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.

Parameters
 [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] dA COMPLEX_16 array on the GPU, dimension (LDDA,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 iterative refinement has been successfully used (INFO.EQ.0 and ITER.GE.0, see description below), then A is unchanged, if double factorization has been used (INFO.EQ.0 and ITER.LT.0, see description below), then the array dA contains the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. [in] ldda INTEGER The leading dimension of the array dA. LDDA >= max(1,N). [in] dB COMPLEX_16 array on the GPU, dimension (LDDB,NRHS) The N-by-NRHS right hand side matrix B. [in] lddb INTEGER The leading dimension of the array dB. LDDB >= max(1,N). [out] dX COMPLEX_16 array on the GPU, dimension (LDDX,NRHS) If INFO = 0, the N-by-NRHS solution matrix X. [in] lddx INTEGER The leading dimension of the array dX. LDDX >= max(1,N). dworkd (workspace) COMPLEX_16 array on the GPU, dimension (N*NRHS) This array is used to hold the residual vectors. dworks (workspace) COMPLEX array on the GPU, dimension (N*(N+NRHS)) This array is used to store the complex single precision matrix and the right-hand sides or solutions in single precision. [out] iter INTEGER < 0: iterative refinement has failed, double precision factorization has been performed -1 : the routine fell back to full precision for implementation- or machine-specific reasons -2 : narrowing the precision induced an overflow, the routine fell back to full precision -3 : failure of SPOTRF -31: stop the iterative refinement after the 30th iteration > 0: iterative refinement has been successfully used. Returns the number of iterations [out] info INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i of (DOUBLE PRECISION) A is not positive definite, so the factorization could not be completed, and the solution has not been computed.
 magma_int_t magma_zposv ( magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex * A, magma_int_t lda, magmaDoubleComplex * B, magma_int_t ldb, magma_int_t * info )

ZPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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] A COMPLEX_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 factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [in,out] B COMPLEX_16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the 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
 magma_int_t magma_zposv_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 )

ZPOSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = MagmaUpper, or A = L * L**H, if UPLO = MagmaLower, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [in] uplo magma_uplo_t = MagmaUpper: Upper triangle of A is stored; = MagmaLower: Lower triangle of A is stored. [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_16 array on the GPU, dimension (LDDA,N) On entry, the Hermitian matrix dA. If UPLO = MagmaUpper, the leading N-by-N upper triangular part of dA contains the upper triangular part of the matrix dA, and the strictly lower triangular part of dA is not referenced. If UPLO = MagmaLower, the leading N-by-N lower triangular part of dA contains the lower triangular part of the matrix dA, and the strictly upper triangular part of dA is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization dA = U**H*U or dA = L*L**H. [in] ldda INTEGER The leading dimension of the array A. LDDA >= max(1,N). [in,out] dB COMPLEX_16 array on the GPU, 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 = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value