sgtsl(3P)

NAME

sgtsl - solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.

SYNOPSIS

SUBROUTINE DGTSL (N, DSUBD, DDIAG, DSUPERD, DB, INFO)

SUBROUTINE SGTSL (N, SSUBD, SDIAG, SSUPERD, SB, INFO)

SUBROUTINE ZGTSL (N, ZSUBD, ZDIAG, ZSUPERD, ZB, INFO)

SUBROUTINE CGTSL (N, CSUBD, CDIAG, CSUPERD, BB, INFO)

#include <sunperf.h>

void dgtsl(int n, double ∗dc, double ∗d, double ∗e, double ∗db, int ∗info) ;

void sgtsl(int n, float ∗sc, float ∗d, float ∗e, float ∗sb, int ∗info) ;

void zgtsl(int n, doublecomplex ∗zc, doublecomplex ∗d, doublecomplex ∗e, doublecomplex ∗zb, int ∗info) ;

void cgtsl(int n, complex ∗cc, complex ∗d, complex ∗e, complex ∗cb, int ∗info) ;

ARGUMENTS

N Order of the matrix A. N >= 0.

xSUBD Subdiagonal of A. SUBD(2) through SUBD(N) contain the subdiagonal and SUBD(1) is not referenced.

xDIAG Diagonal of A.

xSUPERD Superdiagonal of A. SUPERD(1) through SUPERD(N-1) contain the superdiagonal and SUPERD(N) is not referenced.

xB On entry, the right-hand side vector b. On exit, the solution vector x.

INFO On exit:
INFO = 0Subroutine completed normally.
INFO ∗ 0Returns a value k when the kth element of the diagonal becomes exactly zero.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           N
      PARAMETER        (N = 5)
C
      DOUBLE PRECISION B(N), SUBD(N), DIAG(N), SUPERD(N)
      INTEGER           INFO
C
      EXTERNAL          DGTSL
C
C     Initialize the arrays SUBD, DIAG, and SUPERD to store
C     the subdiagonal, diagonal, and superdiagonal of the
C     tridiagonal matrix A shown below. Initialize the array
C     B to store the right hand side of Ax=b.
C
C         -3   1                     6
C          1 -2   1                12
C     A =      1 -2   1        b = 18
C                  1 -2   1        12
C                      1 -1         6
C
      DATA SUBD / 8D8, 4∗1.0D0 /
      DATA DIAG / -3.0D0, -2.0D0, -2.0D0, -2.0D0, -1.0D0 /
      DATA SUPERD / 4∗1.0D0, 8D8 /
      DATA B / 6.0D0, 1.2D1, 1.8D1, 1.2D1, 6.0D0 /
C
      PRINT 1000
      PRINT 1010, DIAG(1), SUPERD(1)
      PRINT 1020, SUBD(2), DIAG(2), SUPERD(2)
      PRINT 1030, SUBD(3), DIAG(3), SUPERD(3)
      PRINT 1040, SUBD(4), DIAG(4), SUPERD(4)
      PRINT 1050, SUBD(5), DIAG(5)
      PRINT 1060
      PRINT 1070, B
      CALL DGTSL (N, SUBD, DIAG, SUPERD, B, INFO)
      IF (INFO .EQ. 0) THEN
        PRINT 1080
        PRINT 1070, B
      ELSE
        PRINT 1090, INFO
      END IF
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (1X, 2(2X, F4.1))
1020 FORMAT (1X, 3(2X, F4.1))
1030 FORMAT (1X, 6X, 3(2X, F4.1))
1040 FORMAT (1X, 12X, 3(2X, F4.1))
1050 FORMAT (1X, 18X, 2(2X, F4.1))
1060 FORMAT (/1X, ’b:’)
1070 FORMAT (3X, F6.1)
1080 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1090 FORMAT (/1X, ’A appears singular at ’, I1)
C
      END

SAMPLE OUTPUT

A:
   -3.0   1.0
    1.0 -2.0   1.0
          1.0 -2.0   1.0
                1.0 -2.0   1.0
                      1.0 -1.0

b:
      6.0
     12.0
     18.0
     12.0
      6.0

A∗∗(-1) ∗ b:
    -27.0
    -75.0
   -111.0
   -129.0
   -135.0