NAME

SYNOPSIS

  SUBROUTINE ZGTRFS( TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, DIAGF, 
 *      UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, 
 *      INFO)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NRHS, LDB, LDX, INFO
  INTEGER IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
 
  SUBROUTINE ZGTRFS_64( TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, DIAGF, 
 *      UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, 
 *      INFO)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX LOW(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)
 

F95 INTERFACE

  SUBROUTINE GTRFS( [TRANSA], [N], [NRHS], LOW, DIAG, UP, LOWF, DIAGF, 
 *       UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8), DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, WORK
  COMPLEX(8), DIMENSION(:,:) :: B, X
  INTEGER :: N, NRHS, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
 
  SUBROUTINE GTRFS_64( [TRANSA], [N], [NRHS], LOW, DIAG, UP, LOWF, 
 *       DIAGF, UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8), DIMENSION(:) :: LOW, DIAG, UP, LOWF, DIAGF, UPF1, UPF2, WORK
  COMPLEX(8), DIMENSION(:,:) :: B, X
  INTEGER(8) :: N, NRHS, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2
 

C INTERFACE

void zgtrfs(char transa, int n, int nrhs, doublecomplex *low, doublecomplex *diag, doublecomplex *up, doublecomplex *lowf, doublecomplex *diagf, doublecomplex *upf1, doublecomplex *upf2, int *ipivot, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info);

void zgtrfs_64(char transa, long n, long nrhs, doublecomplex *low, doublecomplex *diag, doublecomplex *up, doublecomplex *lowf, doublecomplex *diagf, doublecomplex *upf1, doublecomplex *upf2, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);

PURPOSE

ARGUMENTS

* 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 diagonal elements of A.

* UP (input)

The (n-1) superdiagonal elements of A.

* LOWF (input)

The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.

* DIAGF (input)

The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

* UPF1 (input)

The (n-1) elements of the first superdiagonal of U.

* UPF2 (input)

The (n-2) elements of the second superdiagonal of U.

* IPIVOT (input)

The pivot indices; for 1 <= i <= n, 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 right hand side matrix B.

* LDB (input)

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

* X (input/output)

On entry, the solution matrix X, as computed by CGTTRS. On exit, the improved solution matrix X.

* LDX (input)

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

* 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)