sgtsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B,
SUBROUTINE SGTSVX( 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 INTEGER N, NRHS, LDB, LDX, INFO INTEGER IPIVOT(*), WORK2(*) REAL RCOND REAL LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE SGTSVX_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 INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 IPIVOT(*), WORK2(*) REAL RCOND REAL LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
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 INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT, WORK2 REAL :: RCOND REAL, DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X
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 INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2 REAL :: RCOND REAL, DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X
#include <sunperf.h>
void sgtsvx(char fact, char transa, int n, int nrhs, float *low, float *diag, float *up, float *lowf, float *diagf, float *upf1, float *upf2, int *ipivot, float *b, int ldb, float *x, int ldx, float *rcond, float *ferr, float *berr, int *info);
void sgtsvx_64(char fact, char transa, long n, long nrhs, float *low, float *diag, float *up, float *lowf, float *diagf, float *upf1, float *upf2, long *ipivot, float *b, long ldb, float *x, long ldx, float *rcond, float *ferr, float *berr, long *info);
sgtsvx uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N and X and B are N-by-NRHS matrices.
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.
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose = Transpose)
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.
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
dimension(3*N)
dimension(N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
< = N: U(i,i) is exactly zero. The factorization has not been completed unless i = N, but the factor U is exactly singular, so the solution and error bounds could not be computed. RCOND = 0 is returned. = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest.