dgefa(3P)

NAME

dgefa - 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

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

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

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

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

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

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

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

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

ARGUMENTS

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

IPIVOTOn exit, a vector of pivot indices.

INFOOn 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