ctrsl(l) — SunSoft Performance Library

NAME

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

SYNOPSIS

CALL DTRSL (DA, LDA, N, DB, JOB, INFO)

CALL STRSL (SA, LDA, N, SB, JOB, INFO)

CALL ZTRSL (ZA, LDA, N, ZB, JOB, INFO)

CALL CTRSL (CA, LDA, N, CB, JOB, INFO)

ARGUMENTS

xAMatrix A.

LDALeading dimension of the array A as specified in a dimension or type statement. LDA >= max(1,N).

NOrder of the matrix A. N >= 0.

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

JOBDetermines which operation the subroutine will perform:
00 Solve Ax = b, A lower triangular.
01 Solve Ax = b, A upper triangular.
10 Solve AHx = b, A lower triangular.
11 Solve AHx = b, A upper triangular. Note that ATx = AHx for real matrices.

INFOOn exit:
INFO = 0Subroutine completed normally.
INFO ∗ 0Returns the index of the first zero diagonal element of A.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LDA, LOTRAN, N
      PARAMETER        (LOTRAN = 10)
      PARAMETER        (N = 5)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), B(N)
      INTEGER           ICOL, INFO, IROW, JOB
C
      EXTERNAL          DTRSL
C
C     Initialize the array A to store the 5x5 triangular matrix A
C     shown below.
C
C         1                    5
C         1 1                 4
C     A = 1 1 1          b = 3
C         1 1 1 1           2
C         1 1 1 1 1        1
C
      DATA A / 5∗1.0D0, 8D8, 4∗1.0D0, 2∗8D8, 3∗1.0D0, 3∗8D8,
     $         2∗1.0D0, 4∗8D8, 1.0D0 /
      DATA B / 5.0D0, 4.0D0, 3.0D0, 2.0D0, 1.0D0 /
C
C     Print the initial values of the arrays.
C
      PRINT 1000
      DO 100, IROW = 1, N
        PRINT 1010, (A(IROW,ICOL), ICOL = 1, IROW)
100 CONTINUE
      PRINT 1020
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)
      PRINT 1030
      PRINT 1040, B
C
C     Solve the matrix in banded form.
C
      JOB = LOTRAN
      CALL DTRSL (A, LDA, N, B, JOB, INFO)
      IF (INFO .EQ. 0) THEN
        PRINT 1050
        PRINT 1040, B
      ELSE
        PRINT 1060, INFO
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (5(3X, F4.1))
1020 FORMAT (/1X, ’A in triangular form: (∗ in unused elements)’)
1030 FORMAT (/1X, ’b:’)
1040 FORMAT (3X, F4.1)
1050 FORMAT (/1X, ’A”∗∗(-1) ∗ b:’)
1060 FORMAT (1X, ’A appears singular at ’, I2)
C
      END

SAMPLE OUTPUT

A in full form:
    1.0
    1.0    1.0
    1.0    1.0    1.0
    1.0    1.0    1.0    1.0
    1.0    1.0    1.0    1.0    1.0

A in triangular form: (∗ in unused elements)
    1.0   ∗∗∗∗   ∗∗∗∗   ∗∗∗∗   ∗∗∗∗
    1.0    1.0   ∗∗∗∗   ∗∗∗∗   ∗∗∗∗
    1.0    1.0    1.0   ∗∗∗∗   ∗∗∗∗
    1.0    1.0    1.0    1.0   ∗∗∗∗
    1.0    1.0    1.0    1.0    1.0

b:
    5.0
    4.0
    3.0
    2.0
    1.0

A’∗∗(-1) ∗ b:
    1.0
    1.0
    1.0
    1.0
    1.0