Computes the determinant of a real symmetric matrix given the U DUT factorization of the matrix.

Required Arguments

FACT — N by N matrix containing the factored matrix A as output from subroutine LFTSF/DLFTSF or LFCSF/DLFCSF.   (Input)

IPVT — Vector of length N containing the pivoting information for the U DUT factorization as output from routine LFTSF/DLFTSF or LFCSF/DLFCSF.   (Input)

DET1 — Scalar containing the mantissa of the determinant.   (Output)
The value DET1 is normalized so that, 1.0 ≤ |DET1| < 10.0 or DET1 = 0.0.

DET2 — Scalar containing the exponent of the determinant.   (Output)
The determinant is returned in the form, det(A) = DET1 * 10^DET2.

Optional Arguments

N — Order of the matrix.   (Input)
Default: N = size (FACT,2).

LDFACT — Leading dimension of FACT exactly as specified in the dimension statement of the calling program.   (Input)
Default: LDFACT = size (FACT,1).

FORTRAN 90 Interface

Generic:                              CALL LFDSF (FACT, IPVT, DET1, DET2 [,…])

Specific:                             The specific interface names are S_LFDSF and D_LFDSF.

FORTRAN 77 Interface

Single:                                CALL LFDSF (N, FACT, LDFACT, IPVT, DET1, DET2)

Double:                              The double precision name is DLFDSF.

Description

Routine LFDSF computes the determinant of a real symmetric indefinite coefficient matrix. To compute the determinant, the coefficient matrix must first undergo a U DUT factorization. This may be done by calling either LFCSF or LFTSF. Since det U = ±1, the formula
det A = det U det D det UT = det D is used to compute the determinant. Next det D is computed as the product of the determinants of its blocks.

LFDSF is based on the LINPACK routine SSIDI; see Dongarra et al. (1979).

Example

The determinant is computed for a real symmetric 3 × 3 matrix.

 

      USE LFDSF_INT
      USE LFTSF_INT
      USE UMACH_INT

!                                 Declare variables

      PARAMETER  (LDA=3, N=3)

      INTEGER    IPVT(N), NOUT

      REAL       A(LDA,LDA), FACT(LDA,LDA), DET1, DET2

!

!                                 Set values for A

!                                 A = (  1.0  -2.0   1.0)

!                                     ( -2.0   3.0  -2.0)

!                                     (  1.0  -2.0   3.0)

!

      DATA A/1.0, -2.0, 1.0, -2.0, 3.0, -2.0, 1.0, -2.0, 3.0/

!                                 Factor A

      CALL LFTSF (A, FACT, IPVT)

!                                 Compute the determinant

      CALL LFDSF (FACT, IPVT, DET1, DET2)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) DET1, DET2

99999 FORMAT (' The determinant of A is ', F6.3, ' * 10**', F2.0)

      END

Output

 

The determinant of A is -2.000 * 10**0.

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