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Updated: June 2017
 
 

dgtrfs (3p)

Name

dgtrfs - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, provide error bounds and backward error estimates for the solution

Synopsis

SUBROUTINE DGTRFS(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF, UPF1,
UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER*1 TRANSA
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*), WORK2(*)
DOUBLE PRECISION LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*),
B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

SUBROUTINE DGTRFS_64(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF,
UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2,
INFO)

CHARACTER*1 TRANSA
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*), WORK2(*)
DOUBLE PRECISION LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*),
B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)




F95 INTERFACE
SUBROUTINE GTRFS(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF,
UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK,
WORK2, INFO)

CHARACTER(LEN=1) :: TRANSA
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT, WORK2
REAL(8),  DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR,
WORK
REAL(8), DIMENSION(:,:) :: B, X

SUBROUTINE GTRFS_64(TRANSA, N, NRHS, LOW, D, UP, LOWF,
DF, UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK,
WORK2, INFO)

CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
REAL(8), DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR,  BERR,
WORK
REAL(8), DIMENSION(:,:) :: B, X




C INTERFACE
#include <sunperf.h>

void  dgtrfs(char transa, int n, int nrhs, double *low, double *d, dou-
ble *up, double  *lowf,  double  *df,  double  *upf1,  double
*upf2,  int  *ipivot, double *b, int ldb, double *x, int ldx,
double *ferr, double *berr, int *info);

void dgtrfs_64(char transa, long n, long nrhs, double *low, double  *d,
double  *up,  double  *lowf, double *df, double *upf1, double
*upf2, long *ipivot, double *b, long  ldb,  double  *x,  long
ldx, double *ferr, double *berr, long *info);

Description

Oracle Solaris Studio Performance Library                           dgtrfs(3P)



NAME
       dgtrfs  - improve the computed solution to a system of linear equations
       when the coefficient matrix is tridiagonal, provide  error  bounds  and
       backward error estimates for the solution


SYNOPSIS
       SUBROUTINE DGTRFS(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF, UPF1,
             UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER*1 TRANSA
       INTEGER N, NRHS, LDB, LDX, INFO
       INTEGER IPIVOT(*), WORK2(*)
       DOUBLE PRECISION LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*),
       B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

       SUBROUTINE DGTRFS_64(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF,
             UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2,
             INFO)

       CHARACTER*1 TRANSA
       INTEGER*8 N, NRHS, LDB, LDX, INFO
       INTEGER*8 IPIVOT(*), WORK2(*)
       DOUBLE PRECISION LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*),
       B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)




   F95 INTERFACE
       SUBROUTINE GTRFS(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF,
              UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK,
              WORK2, INFO)

       CHARACTER(LEN=1) :: TRANSA
       INTEGER :: N, NRHS, LDB, LDX, INFO
       INTEGER, DIMENSION(:) :: IPIVOT, WORK2
       REAL(8),  DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR,
       WORK
       REAL(8), DIMENSION(:,:) :: B, X

       SUBROUTINE GTRFS_64(TRANSA, N, NRHS, LOW, D, UP, LOWF,
              DF, UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK,
              WORK2, INFO)

       CHARACTER(LEN=1) :: TRANSA
       INTEGER(8) :: N, NRHS, LDB, LDX, INFO
       INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
       REAL(8), DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR,  BERR,
       WORK
       REAL(8), DIMENSION(:,:) :: B, X




   C INTERFACE
       #include <sunperf.h>

       void  dgtrfs(char transa, int n, int nrhs, double *low, double *d, dou-
                 ble *up, double  *lowf,  double  *df,  double  *upf1,  double
                 *upf2,  int  *ipivot, double *b, int ldb, double *x, int ldx,
                 double *ferr, double *berr, int *info);

       void dgtrfs_64(char transa, long n, long nrhs, double *low, double  *d,
                 double  *up,  double  *lowf, double *df, double *upf1, double
                 *upf2, long *ipivot, double *b, long  ldb,  double  *x,  long
                 ldx, double *ferr, double *berr, long *info);



PURPOSE
       dgtrfs  improves  the computed solution to a system of linear equations
       when the coefficient matrix is tridiagonal, and provides  error  bounds
       and backward error estimates for the solution.


ARGUMENTS
       TRANSA (input)
                 Specifies the form of the system of equations:
                 = 'N':  A * X = B     (No transpose)
                 = 'T':  A**T * X = B  (Transpose)
                 = 'C':  A**H * X = B  (Conjugate transpose = Transpose)


       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.


       D (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 DGTTRF.


       DF (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 DGTTRS.  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  esti-
                 mated upper bound for the magnitude of the largest element in
                 (X(j) - XTRUE) divided by the magnitude of the  largest  ele-
                 ment  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  ele-
                 ment of A or B that makes X(j) an exact solution).


       WORK (workspace)
                 dimension(3*N)

       WORK2 (workspace)
                 dimension(N)


       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value




                                  7 Nov 2015                        dgtrfs(3P)