SUBROUTINE ZGESVX( FACT, TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, * EQUED, ROWSC, COLSC, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, * WORK2, INFO) CHARACTER * 1 FACT, TRANSA, EQUED DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER IPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION ROWSC(*), COLSC(*), FERR(*), BERR(*), WORK2(*) SUBROUTINE ZGESVX_64( FACT, TRANSA, N, NRHS, A, LDA, AF, LDAF, * IPIVOT, EQUED, ROWSC, COLSC, B, LDB, X, LDX, RCOND, FERR, BERR, * WORK, WORK2, INFO) CHARACTER * 1 FACT, TRANSA, EQUED DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION ROWSC(*), COLSC(*), FERR(*), BERR(*), WORK2(*)
SUBROUTINE GESVX( FACT, [TRANSA], [N], [NRHS], A, [LDA], AF, [LDAF], * IPIVOT, EQUED, ROWSC, COLSC, B, [LDB], X, [LDX], RCOND, FERR, * BERR, [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: FACT, TRANSA, EQUED COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: ROWSC, COLSC, FERR, BERR, WORK2 SUBROUTINE GESVX_64( FACT, [TRANSA], [N], [NRHS], A, [LDA], AF, * [LDAF], IPIVOT, EQUED, ROWSC, COLSC, B, [LDB], X, [LDX], RCOND, * FERR, BERR, [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: FACT, TRANSA, EQUED COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: ROWSC, COLSC, FERR, BERR, WORK2
void zgesvx(char fact, char transa, int n, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, int *ipivot, char equed, double *rowsc, double *colsc, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *rcond, double *ferr, double *berr, int *info);
void zgesvx_64(char fact, char transa, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, char equed, double *rowsc, double *colsc, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *rcond, double *ferr, double *berr, long *info);
Error bounds on the solution and a condition estimate are also provided.
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B Whether or not the system will be equilibrated depends on the scaling of the matrix A, but if equilibration is used, A is overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the matrix A (after equilibration if FACT = 'E') as
A = P * L * U, where P is a permutation matrix, L is a unit lower triangular matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form of A.
5. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.
6. If equilibration was used, the matrix X is premultiplied by diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so that it solves the original system before equilibration.
On exit, if EQUED .ne. 'N', A is scaled as follows: EQUED = 'ROWSC': A := diag(ROWSC) * A
EQUED = 'COLSC': A := A * diag(COLSC)
EQUED = 'B': A := diag(ROWSC) * A * diag(COLSC).
If FACT = 'N', then AF is an output argument and on exit returns the factors L and U from the factorization A = P*L*U of the original matrix A.
If FACT = 'E', then AF is an output argument and on exit returns the factors L and U from the factorization A = P*L*U of the equilibrated matrix A (see the description of A for the form of the equilibrated matrix).
If FACT = 'N', then IPIVOT is an output argument and on exit contains the pivot indices from the factorization A = P*L*U of the original matrix A.
If FACT = 'E', then IPIVOT is an output argument and on exit contains the pivot indices from the factorization A = P*L*U of the equilibrated matrix A.