cgefa(3P)

NAME

cgefa - compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A.

SYNOPSIS

SUBROUTINE DGEFA (DA, LDA, N, IPIVOT, INFO)

SUBROUTINE SGEFA (SA, LDA, N, IPIVOT, INFO)

SUBROUTINE ZGEFA (ZA, LDA, N, IPIVOT, INFO)

SUBROUTINE CGEFA (CA, LDA, N, IPIVOT, INFO)

#include <sunperf.h>

void dgefa(double ∗da, int lda, int n, int ∗ipivot, int ∗info) ;

void sgefa(float ∗sa, int lda, int n, int ∗ipivot, int ∗info) ;

void zgefa(doublecomplex ∗za, int lda, int n, int ∗ipivot, int ∗info) ;

void cgefa(complex ∗ca, int lda, int n, int ∗ipivot, int ∗info) ;

ARGUMENTS

xA On entry, the matrix A. On exit, an LU factorization of A.

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

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

IPIVOT On exit, a vector of pivot indices.

INFO On exit:
INFO = 0Subroutine completed normally.
INFO ∗ 0Returns a value k if U(k,k) = 0 to indicate that xGESL will divide by zero if called.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LDA, N
      PARAMETER        (N = 3)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N)
      INTEGER           ICOL, INFO, IPIVOT(N), IROW
C
      EXTERNAL          DGEFA
C
C     Initialize the array A to store the matrix A shown below.
C
C         100    2    3
C     A = 100 202    6
C         100 202 306
C
      DATA A / 1.0D2, 1.0D2, 1.0D2, 2.0D0, 2.02D2, 2.02D2,
     $         3.0D0, 6.0D0, 3.06D2 /
      PRINT 1000
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
      CALL DGEFA (A, LDA, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        PRINT 1020
        PRINT 1030, (A(1,ICOL), ICOL = 1, N)
        PRINT 1040, (A(2,ICOL), ICOL = 1, N)
        PRINT 1050, (A(3,ICOL), ICOL = 1, N)
      ELSE
        PRINT 1060, INFO
      END IF
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (3(3X, F5.1))
1020 FORMAT (/8X, ’Multipliers’, 19X, ’Upper’)
1030 FORMAT (3X, ’ 1.0’, 17X, 3(2X, F5.1))
1040 FORMAT (3X, F5.1, 2X, ’ 1.0’, 17X, 2(2X, F5.1))
1050 FORMAT (1X, 2(2X, F5.1), 2X, ’ 1.0’, 17X, 2X, F5.1)
1060 FORMAT (1X, ’A appears singular at ’, I2)
C
      END

SAMPLE OUTPUT

A:
   100.0     2.0     3.0
   100.0   202.0     6.0
   100.0   202.0   306.0

        Multipliers                   Upper
     1.0                   100.0    2.0    3.0
     1.0    1.0                   200.0    3.0
     1.0    1.0    1.0                   300.0