zgeco(3P)

NAME

zgeco - compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A.

SYNOPSIS

CALL DGECO (DA, LDA, N, IPIVOT, DRCOND, DWORK)

void zgeco(doublecomplex ∗za, long int lda,
long int n, long int ∗ipivot, double ∗rcond)

CALL SGECO (SA, LDA, N, IPIVOT, SRCOND, SWORK)

CALL ZGECO (ZA, LDA, N, IPIVOT, DRCOND, ZWORK)

CALL CGECO (CA, LDA, N, IPIVOT, SRCOND, CWORK)

void dgeco(double ∗da, long int lda, long int n, long int ∗ipivot,
double ∗rcond)

void sgeco(float ∗sa, long int lda, long int n, long int ∗ipivot,
float ∗rcond)

void zgeco(doublecomplex ∗za, long int lda,
long int n, long int ∗ipivot, double ∗rcond)

void cgeco(complex ∗ca, long int lda, long int n,
long int ∗ipivot, float ∗rcond)

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.

xRCONDOn exit, an estimate of the reciprocal condition number of A.
0.0 <= RCOND <= 1.0. As the value of RCOND gets smaller, operations with A such as solving Ax = b may become less stable. If RCOND satisfies RCOND + 1.0 = 1.0 then A may be singular to working precision.

xWORKScratch array with a dimension of N.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           IAXEQB, LDA, LDB, N
      PARAMETER        (IAXEQB = 0)
      PARAMETER        (N = 3)
      PARAMETER        (LDA = N)
      PARAMETER        (LDB = LDA)
      DOUBLE PRECISION A(LDA,N), B(LDB), RCOND, WORK(N)
      INTEGER           ICOL, IPIVOT(N), IROW, JOB
C
      EXTERNAL          DGECO, 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 /
      PRINT 1000
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
      PRINT 1020
      PRINT 1030, B
      CALL DGECO (A, LDA, N, IPIVOT, RCOND, WORK)
      PRINT 1040, RCOND
      IF ((RCOND + 1.0D0) .EQ. 1.0D0) THEN
        PRINT 1060
      END IF
      JOB = IAXEQB
      CALL DGESL (A, LDA, N, IPIVOT, B, JOB)
      PRINT 1050
      PRINT 1030, B
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (3(3X, F4.1))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, F4.1)
1040 FORMAT (/1X, ’Estimated reciprocal condition number:’, F7.4)
1050 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1060 FORMAT (1X, ’A may be singular to working precision.’)
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

Estimated reciprocal condition number: 0.1429

A∗∗(-1) ∗ b:
    3.0
    3.0
    3.0