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

## Functions

magma_int_t magma_cgesv (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)
CGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_cgesv_gpu (magma_int_t n, magma_int_t nrhs, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloatComplex_ptr dB, magma_int_t lddb, magma_int_t *info)
CGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_dgesv (magma_int_t n, magma_int_t nrhs, double *A, magma_int_t lda, magma_int_t *ipiv, double *B, magma_int_t ldb, magma_int_t *info)
DGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_dgesv_gpu (magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t *info)
DGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_dsgesv_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaInt_ptr dipiv, 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)
DSGESV computes the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_sgesv (magma_int_t n, magma_int_t nrhs, float *A, magma_int_t lda, magma_int_t *ipiv, float *B, magma_int_t ldb, magma_int_t *info)
SGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_sgesv_gpu (magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t *info)
SGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_zcgesv_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaInt_ptr dipiv, 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)
ZCGESV computes the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_zgesv (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)
ZGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

magma_int_t magma_zgesv_gpu (magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *ipiv, magmaDoubleComplex_ptr dB, magma_int_t lddb, magma_int_t *info)
ZGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices. More...

## Function Documentation

 magma_int_t magma_cgesv ( 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 )

CGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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_cgesv_gpu ( magma_int_t n, magma_int_t nrhs, magmaFloatComplex_ptr dA, magma_int_t ldda, magma_int_t * ipiv, magmaFloatComplex_ptr dB, magma_int_t lddb, magma_int_t * info )

CGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*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). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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_dgesv ( magma_int_t n, magma_int_t nrhs, double * A, magma_int_t lda, magma_int_t * ipiv, double * B, magma_int_t ldb, magma_int_t * info )

DGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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_dgesv_gpu ( magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t * ipiv, magmaDouble_ptr dB, magma_int_t lddb, magma_int_t * info )

DGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*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). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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_dsgesv_gpu ( magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaDouble_ptr dA, magma_int_t ldda, magma_int_t * ipiv, magmaInt_ptr dipiv, 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 )

DSGESV computes the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

DSGESV 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] trans magma_trans_t Specifies the form of the system of equations: = MagmaNoTrans: A * X = B (No transpose) = MagmaTrans: A**T * X = B (Transpose) = MagmaConjTrans: A**H * X = B (Conjugate transpose) [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 N-by-N coefficient matrix A. On exit, if iterative refinement has been successfully used (info.EQ.0 and ITER.GE.0, see description below), A is unchanged. If double precision factorization has been used (info.EQ.0 and ITER.LT.0, see description below), then the array dA contains the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [in] ldda INTEGER The leading dimension of the array dA. ldda >= max(1,N). [out] ipiv INTEGER array, dimension (N) The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i). Corresponds either to the single precision factorization (if info.EQ.0 and ITER.GE.0) or the double precision factorization (if info.EQ.0 and ITER.LT.0). [out] dipiv INTEGER array on the GPU, dimension (N) The pivot indices; for 1 <= i <= N, after permuting, row i of the matrix was moved to row dIPIV(i). Note this is different than IPIV, where interchanges are applied one-after-another. [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 SGETRF -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, U(i,i) computed in DOUBLE PRECISION is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.
 magma_int_t magma_sgesv ( magma_int_t n, magma_int_t nrhs, float * A, magma_int_t lda, magma_int_t * ipiv, float * B, magma_int_t ldb, magma_int_t * info )

SGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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_sgesv_gpu ( magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magma_int_t * ipiv, magmaFloat_ptr dB, magma_int_t lddb, magma_int_t * info )

SGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*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). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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_zcgesv_gpu ( magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t * ipiv, magmaInt_ptr dipiv, 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 )

ZCGESV computes the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

ZCGESV 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] trans magma_trans_t Specifies the form of the system of equations: = MagmaNoTrans: A * X = B (No transpose) = MagmaTrans: A**T * X = B (Transpose) = MagmaConjTrans: A**H * X = B (Conjugate transpose) [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 N-by-N coefficient matrix A. On exit, if iterative refinement has been successfully used (info.EQ.0 and ITER.GE.0, see description below), A is unchanged. If double precision factorization has been used (info.EQ.0 and ITER.LT.0, see description below), then the array dA contains the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [in] ldda INTEGER The leading dimension of the array dA. ldda >= max(1,N). [out] ipiv INTEGER array, dimension (N) The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i). Corresponds either to the single precision factorization (if info.EQ.0 and ITER.GE.0) or the double precision factorization (if info.EQ.0 and ITER.LT.0). [out] dipiv INTEGER array on the GPU, dimension (N) The pivot indices; for 1 <= i <= N, after permuting, row i of the matrix was moved to row dIPIV(i). Note this is different than IPIV, where interchanges are applied one-after-another. [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 SGETRF -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, U(i,i) computed in DOUBLE PRECISION is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.
 magma_int_t magma_zgesv ( 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 )

ZGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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_zgesv_gpu ( magma_int_t n, magma_int_t nrhs, magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t * ipiv, magmaDoubleComplex_ptr dB, magma_int_t lddb, magma_int_t * info )

ZGESV solves a system of linear equations A * X = B where A is a general N-by-N matrix and X and B are N-by-NRHS matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters
 [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 M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*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). [out] ipiv INTEGER array, dimension (min(M,N)) The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i). [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