SUBROUTINE CGTSVX( FACT, TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, * DIAGF, UPF1, UPF2, IPIVOT, B, LDB, X, LDX, RCOND, FERR, BERR, * WORK, WORK2, INFO) CHARACTER * 1 FACT, TRANSA COMPLEX LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*) REAL RCOND REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CGTSVX_64( FACT, TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, * DIAGF, UPF1, UPF2, IPIVOT, B, LDB, X, LDX, RCOND, FERR, BERR, * WORK, WORK2, INFO) CHARACTER * 1 FACT, TRANSA COMPLEX LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*) REAL RCOND REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE GTSVX( FACT, [TRANSA], [N], [NRHS], LOW, DIAG, UP, LOWF, * DIAGF, UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], RCOND, FERR, BERR, * [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: FACT, TRANSA COMPLEX, DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL :: RCOND REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE GTSVX_64( FACT, [TRANSA], [N], [NRHS], LOW, DIAG, UP, * LOWF, DIAGF, UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], RCOND, FERR, * BERR, [WORK], [WORK2], [INFO]) CHARACTER(LEN=1) :: FACT, TRANSA COMPLEX, DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL :: RCOND REAL, DIMENSION(:) :: FERR, BERR, WORK2
void cgtsvx(char fact, char transa, int n, int nrhs, complex *low, complex *diag, complex *up, complex *lowf, complex *diagf, complex *upf1, complex *upf2, int *ipivot, complex *b, int ldb, complex *x, int ldx, float *rcond, float *ferr, float *berr, int *info);
void cgtsvx_64(char fact, char transa, long n, long nrhs, complex *low, complex *diag, complex *up, complex *lowf, complex *diagf, complex *upf1, complex *upf2, long *ipivot, complex *b, long ldb, complex *x, long ldx, float *rcond, float *ferr, float *berr, long *info);
Error bounds on the solution and a condition estimate are also provided.
The following steps are performed:
1. If FACT = 'N', the LU decomposition is used to factor the matrix A as A = L * U, where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.
2. 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.
3. The system of equations is solved for X using the factored form of A.
4. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.
If FACT = 'N', then LOWF is an output argument and on exit contains the (n-1) multipliers that define the matrix L from the LU factorization of A.
If FACT = 'N', then DIAGF is an output argument and on exit contains the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
If FACT = 'N', then UPF1 is an output argument and on exit contains the (n-1) elements of the first superdiagonal of U.
If FACT = 'N', then UPF2 is an output argument and on exit contains the (n-2) elements of the second superdiagonal of U.
If FACT = 'N', then IPIVOT is an output argument and on exit contains the pivot indices from the LU factorization of A; row i of the matrix was interchanged with row IPIVOT(i). IPIVOT(i) will always be either i or i+1; IPIVOT(i) = i indicates a row interchange was not required.