MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS 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 NbyN matrix and X and B are NbyNRHS matrices. More...  
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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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

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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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

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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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

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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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

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 NbyN matrix and X and B are NbyNRHS 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 normwise 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 righthand 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 infinitynorm of the residual o XNRM is the infinitynorm of the solution o ANRM is the infinityoperatornorm 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.
[in]  trans  magma_trans_t Specifies the form of the system of equations:

[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 NbyN 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 oneafteranother. 
[in]  dB  DOUBLE PRECISION array on the GPU, dimension (lddb,NRHS) The NbyNRHS 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 NbyNRHS 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 righthand sides or solutions in single precision.  
[out]  iter  INTEGER

[out]  info  INTEGER

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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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

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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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

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 NbyN matrix and X and B are NbyNRHS 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 normwise 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 righthand 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 infinitynorm of the residual o XNRM is the infinitynorm of the solution o ANRM is the infinityoperatornorm 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.
[in]  trans  magma_trans_t Specifies the form of the system of equations:

[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 NbyN 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 oneafteranother. 
[in]  dB  COMPLEX_16 array on the GPU, dimension (lddb,NRHS) The NbyNRHS 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 NbyNRHS 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 righthand sides or solutions in single precision.  
[out]  iter  INTEGER

[out]  info  INTEGER

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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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

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 NbyN matrix and X and B are NbyNRHS 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.
[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 MbyN 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
