dgesl(l) — SunSoft Performance Library

NAME

dgesl - solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x.

SYNOPSIS

CALL DGESL (DA, LDA, N, IPIVOT, DB, JOB)

CALL SGESL (SA, LDA, N, IPIVOT, SB, JOB)

CALL ZGESL (ZA, LDA, N, IPIVOT, ZB, JOB)

CALL CGESL (CA, LDA, N, IPIVOT, CB, JOB)

ARGUMENTS

xALU factorization of the matrix A, as computed by xGECO or xGEFA.

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.

IPIVOTPivot vector as computed by xGECO or xGEFA.

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

JOBDetermines which operation the subroutine will perform:
0 Solve the system Ax = b.
not 0 Solve the linear system AHx = b. Note that ATx = AHx for real matrices.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           IAXEQB, LDA, LDB, N
      PARAMETER        (IAXEQB = 0)
      PARAMETER        (N = 3)
      PARAMETER        (LDA = N)
      PARAMETER        (LDB = LDA)
C
      DOUBLE PRECISION A(LDA,N), B(LDB)
      INTEGER           ICOL, INFO, IPIVOT(N), IROW, JOB
C
      EXTERNAL          DGEFA, DGESL
C
C     Initialize the array A to store the matrix A shown below.
C     Initialize the array B to store the vector b shown below.
C
C         1 2 2        15
C     A = 2 1 2    b = 15
C         2 2 1        15
C
      DATA A / 1.0D0, 3∗2.0D0, 1.0D0, 3∗2.0D0, 1.0D0 /
      DATA B / 3∗1.5D1 /
C
      PRINT 1000
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
      PRINT 1020
      PRINT 1030, B
      CALL DGEFA (A, LDA, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        JOB = IAXEQB
        CALL DGESL (A, LDA, N, IPIVOT, B, JOB)
        PRINT 1040
        PRINT 1030, B
      ELSE
        PRINT 1050, INFO
      END IF
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (3(3X, F4.1))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (1X, 2X, F4.1)
1040 FORMAT (/1X, ’A∗∗(-1)∗b’)
1050 FORMAT (1X, ’A appears singular at ’, I2)
C
      END

SAMPLE OUTPUT

A:
    1.0    2.0    2.0
    2.0    1.0    2.0
    2.0    2.0    1.0

b:
   15.0
   15.0
   15.0

A∗∗(-1)∗b
    3.0
    3.0
    3.0