MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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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...
 

Detailed Description

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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]ACOMPLEX 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER 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]BCOMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]ldbINTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]infoINTEGER
  • = 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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dACOMPLEX 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]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]ipivINTEGER 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]dBCOMPLEX array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]infoINTEGER
  • = 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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]ADOUBLE 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER 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]BDOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]ldbINTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]infoINTEGER
  • = 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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dADOUBLE 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]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]ipivINTEGER 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]dBDOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]infoINTEGER
  • = 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]transmagma_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]nINTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dADOUBLE 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]lddaINTEGER The leading dimension of the array dA. ldda >= max(1,N).
[out]ipivINTEGER 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]dipivINTEGER 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]dBDOUBLE PRECISION array on the GPU, dimension (lddb,NRHS) The N-by-NRHS right hand side matrix B.
[in]lddbINTEGER The leading dimension of the array dB. lddb >= max(1,N).
[out]dXDOUBLE PRECISION array on the GPU, dimension (lddx,NRHS) If info = 0, the N-by-NRHS solution matrix X.
[in]lddxINTEGER 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]iterINTEGER
  • < 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]infoINTEGER
  • = 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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]AREAL 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER 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]BREAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]ldbINTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]infoINTEGER
  • = 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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dAREAL 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]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]ipivINTEGER 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]dBREAL array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]infoINTEGER
  • = 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]transmagma_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]nINTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dACOMPLEX_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]lddaINTEGER The leading dimension of the array dA. ldda >= max(1,N).
[out]ipivINTEGER 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]dipivINTEGER 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]dBCOMPLEX_16 array on the GPU, dimension (lddb,NRHS) The N-by-NRHS right hand side matrix B.
[in]lddbINTEGER The leading dimension of the array dB. lddb >= max(1,N).
[out]dXCOMPLEX_16 array on the GPU, dimension (lddx,NRHS) If info = 0, the N-by-NRHS solution matrix X.
[in]lddxINTEGER 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]iterINTEGER
  • < 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]infoINTEGER
  • = 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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]ACOMPLEX_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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]ipivINTEGER 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]BCOMPLEX_16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]ldbINTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]infoINTEGER
  • = 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]nINTEGER The order of the matrix A. N >= 0.
[in]nrhsINTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]dACOMPLEX_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]lddaINTEGER The leading dimension of the array A. LDDA >= max(1,N).
[out]ipivINTEGER 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]dBCOMPLEX_16 array on the GPU, dimension (LDDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]lddbINTEGER The leading dimension of the array B. LDDB >= max(1,N).
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value