Contents

• NAME
• SYNOPSIS
  • F95 INTERFACE
  • C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

     dgbtrs - solve a system of linear equations  A * X = B or A'
     * X = B with a general band matrix A using the LU factoriza-
     tion computed by DGBTRF

SYNOPSIS

     SUBROUTINE DGBTRS(TRANSA, N, KL, KU, NRHS, A, LDA, IPIVOT, B,
           LDB, INFO)

     CHARACTER * 1 TRANSA
     INTEGER N, KL, KU, NRHS, LDA, LDB, INFO
     INTEGER IPIVOT(*)
     DOUBLE PRECISION A(LDA,*), B(LDB,*)

     SUBROUTINE DGBTRS_64(TRANSA, N, KL, KU, NRHS, A, LDA, IPIVOT,
           B, LDB, INFO)

     CHARACTER * 1 TRANSA
     INTEGER*8 N, KL, KU, NRHS, LDA, LDB, INFO
     INTEGER*8 IPIVOT(*)
     DOUBLE PRECISION A(LDA,*), B(LDB,*)

  F95 INTERFACE
     SUBROUTINE GBTRS([TRANSA], [N], KL, KU, [NRHS], A, [LDA],
            IPIVOT, B, [LDB], [INFO])

     CHARACTER(LEN=1) :: TRANSA
     INTEGER :: N, KL, KU, NRHS, LDA, LDB, INFO
     INTEGER, DIMENSION(:) :: IPIVOT
     REAL(8), DIMENSION(:,:) :: A, B

     SUBROUTINE GBTRS_64([TRANSA], [N], KL, KU, [NRHS], A, [LDA],
            IPIVOT, B, [LDB], [INFO])

     CHARACTER(LEN=1) :: TRANSA
     INTEGER(8) :: N, KL, KU, NRHS, LDA, LDB, INFO
     INTEGER(8), DIMENSION(:) :: IPIVOT
     REAL(8), DIMENSION(:,:) :: A, B

  C INTERFACE
     #include <sunperf.h>

     void dgbtrs(char transa, int n, int kl, int  ku,  int  nrhs,
               double  *a,  int  lda, int *ipivot, double *b, int
               ldb, int *info);
     void dgbtrs_64(char transa, long n, long kl, long  ku,  long
               nrhs,  double  *a,  long lda, long *ipivot, double
               *b, long ldb, long *info);

PURPOSE

     dgbtrs solves a system of linear equations
        A * X = B  or  A' * X = B with a general  band  matrix  A
     using the LU factorization computed by DGBTRF.

ARGUMENTS

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

               TRANSA is defaulted to 'N' for F95 INTERFACE.

     N (input) The order of the matrix A.  N >= 0.

     KL (input)
               The number of subdiagonals within the band  of  A.
               KL >= 0.

     KU (input)
               The number of superdiagonals within the band of A.
               KU >= 0.

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

     A (input) Details of the LU factorization of the band matrix
               A, as computed by DGBTRF.  U is stored as an upper
               triangular band matrix with  KL+KU  superdiagonals
               in  rows  1  to  KL+KU+1, and the multipliers used
               during  the  factorization  are  stored  in   rows
               KL+KU+2 to 2*KL+KU+1.

     LDA (input)
               The leading dimension of  the  array  A.   LDA  >=
               2*KL+KU+1.
     IPIVOT (input)
               The pivot indices; for 1 <= i <= N, row i  of  the
               matrix was interchanged with row IPIVOT(i).

     B (input/output)
               On entry, the right hand side matrix B.  On  exit,
               the solution matrix X.

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

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