dgtsl(3P)

NAME

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

SYNOPSIS

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

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

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

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

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

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

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

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

ARGUMENTS

NOrder of the matrix A. N >= 0.

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

xDIAGDiagonal of A.

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

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

INFOOn 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