MAGMA  2.3.0 Matrix Algebra for GPU and Multicore Architectures
gerfs: Refine solution - no pivoting

## Functions

magma_int_t magma_cgerfs_nopiv_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dB, magma_int_t lddb, magmaFloatComplex_ptr dX, magma_int_t lddx, magmaFloatComplex_ptr dworkd, magmaFloatComplex_ptr dAF, magma_int_t *iter, magma_int_t *info)
CGERFS improves the computed solution to a system of linear equations. More...

magma_int_t magma_dgerfs_nopiv_gpu (magma_trans_t trans, 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, magmaDouble_ptr dAF, magma_int_t *iter, magma_int_t *info)
DGERFS improves the computed solution to a system of linear equations. More...

magma_int_t magma_sgerfs_nopiv_gpu (magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magmaFloat_ptr dX, magma_int_t lddx, magmaFloat_ptr dworkd, magmaFloat_ptr dAF, magma_int_t *iter, magma_int_t *info)
SGERFS improves the computed solution to a system of linear equations. More...

magma_int_t magma_zgerfs_nopiv_gpu (magma_trans_t trans, 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, magmaDoubleComplex_ptr dAF, magma_int_t *iter, magma_int_t *info)
ZGERFS improves the computed solution to a system of linear equations. More...

## Function Documentation

 magma_int_t magma_cgerfs_nopiv_gpu ( magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex_ptr dB, magma_int_t lddb, magmaFloatComplex_ptr dX, magma_int_t lddx, magmaFloatComplex_ptr dworkd, magmaFloatComplex_ptr dAF, magma_int_t * iter, magma_int_t * info )

CGERFS improves the computed solution to a system of linear equations.

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 SLAMCH('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] dA COMPLEX array on the GPU, dimension (ldda,N) the N-by-N coefficient matrix A. [in] ldda INTEGER The leading dimension of the array dA. ldda >= max(1,N). [in] dB COMPLEX 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). [in,out] dX COMPLEX array on the GPU, dimension (lddx,NRHS) On entry, the solution matrix X, as computed by CGETRS_NOPIV. On exit, the improved solution matrix X. [in] lddx INTEGER The leading dimension of the array dX. lddx >= max(1,N). dworkd (workspace) COMPLEX array on the GPU, dimension (N*NRHS) This array is used to hold the residual vectors. dAF COMPLEX array on the GPU, dimension (ldda,n) The factors L and U from the factorization A = L*U as computed by CGETRF_NOPIV. [out] iter INTEGER < 0: iterative refinement has failed, real 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 REAL 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_dgerfs_nopiv_gpu ( magma_trans_t trans, 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, magmaDouble_ptr dAF, magma_int_t * iter, magma_int_t * info )

DGERFS improves the computed solution to a system of linear equations.

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] dA DOUBLE PRECISION array on the GPU, dimension (ldda,N) the N-by-N coefficient matrix A. [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). [in,out] dX DOUBLE PRECISION array on the GPU, dimension (lddx,NRHS) On entry, the solution matrix X, as computed by DGETRS_NOPIV. On exit, the improved 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. dAF DOUBLE PRECISION array on the GPU, dimension (ldda,n) The factors L and U from the factorization A = L*U as computed by DGETRF_NOPIV. [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_sgerfs_nopiv_gpu ( magma_trans_t trans, magma_int_t n, magma_int_t nrhs, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dB, magma_int_t lddb, magmaFloat_ptr dX, magma_int_t lddx, magmaFloat_ptr dworkd, magmaFloat_ptr dAF, magma_int_t * iter, magma_int_t * info )

SGERFS improves the computed solution to a system of linear equations.

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 SLAMCH('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] dA REAL array on the GPU, dimension (ldda,N) the N-by-N coefficient matrix A. [in] ldda INTEGER The leading dimension of the array dA. ldda >= max(1,N). [in] dB REAL 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). [in,out] dX REAL array on the GPU, dimension (lddx,NRHS) On entry, the solution matrix X, as computed by SGETRS_NOPIV. On exit, the improved solution matrix X. [in] lddx INTEGER The leading dimension of the array dX. lddx >= max(1,N). dworkd (workspace) REAL array on the GPU, dimension (N*NRHS) This array is used to hold the residual vectors. dAF REAL array on the GPU, dimension (ldda,n) The factors L and U from the factorization A = L*U as computed by SGETRF_NOPIV. [out] iter INTEGER < 0: iterative refinement has failed, real 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 REAL 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_zgerfs_nopiv_gpu ( magma_trans_t trans, 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, magmaDoubleComplex_ptr dAF, magma_int_t * iter, magma_int_t * info )

ZGERFS improves the computed solution to a system of linear equations.

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] dA COMPLEX_16 array on the GPU, dimension (ldda,N) the N-by-N coefficient matrix A. [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). [in,out] dX COMPLEX_16 array on the GPU, dimension (lddx,NRHS) On entry, the solution matrix X, as computed by ZGETRS_NOPIV. On exit, the improved 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. dAF COMPLEX*16 array on the GPU, dimension (ldda,n) The factors L and U from the factorization A = L*U as computed by ZGETRF_NOPIV. [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.