NAME

SYNOPSIS

  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(*)
 

F95 INTERFACE

  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
 

C INTERFACE

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);

PURPOSE

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.

ARGUMENTS

* FACT (input)

Specifies whether or not the factored form of A has been supplied on entry.

* TRANSA (input)

Specifies the form of the system of equations:

* N (input)

The order of the matrix A. N >= 0.

* NRHS (input)

The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

* LOW (input)

The (n-1) subdiagonal elements of A.

* DIAG (input)

The n diagonal elements of A.

* UP (input/output)

The (n-1) superdiagonal elements of A.

* LOWF (input/output)

If FACT = 'F', then LOWF is an input argument and on entry contains the (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.

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.

* DIAGF (input/output)

If FACT = 'F', then DIAGF is an input argument and on entry contains the n diagonal elements of the upper triangular matrix U 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.

* UPF1 (input/output)

If FACT = 'F', then UPF1 is an input argument and on entry contains the (n-1) elements of the first superdiagonal of U.

If FACT = 'N', then UPF1 is an output argument and on exit contains the (n-1) elements of the first superdiagonal of U.

* UPF2 (input/output)

If FACT = 'F', then UPF2 is an input argument and on entry contains the (n-2) elements of the second 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.

* IPIVOT (input/output)

If FACT = 'F', then IPIVOT is an input argument and on entry contains the pivot indices from the LU factorization of A as computed by SGTTRF.

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.

* B (input)

The N-by-NRHS right hand side matrix B.

* LDB (input)

The leading dimension of the array B. LDB >= max(1,N).

* X (output)

If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.

* LDX (input)

The leading dimension of the array X. LDX >= max(1,N).

* RCOND (output)

The estimate of the reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condition is indicated by a return code of INFO > 0.

* FERR (output)

The estimated forward error bound for each solution vector 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.

* BERR (output)

The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).

* WORK (workspace)

dimension(2*N)

* WORK2 (workspace)

* INFO (output)