Computes the determinant of a complex Hermitian matrix given the U DUH factorization of the matrix.

Required Arguments

FACT — Complex N by N matrix containing the factorization of the coefficient matrix A as output from routine LFCHF/DLFCHF or LFTHF/DLFTHF.   (Input)
Only the upper triangle of FACT is used.

IPVT — Vector of length N containing the pivoting information for the factorization of A as output from routine LFCHF/DLFCHF or LFTHF/DLFTHF.   (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 — Number of equations.   (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 LFDHF (FACT, IPVT, DET1, DET2 [,…])

Specific:                             The specific interface names are S_LFDHF and D_LFDHF.

FORTRAN 77 Interface

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

Double:                              The double precision name is DLFDHF.

Description

Routine LFDHF computes the determinant of a complex Hermitian indefinite coefficient matrix. To compute the determinant, the coefficient matrix must first undergo a U DUH factorization. This may be done by calling either LFCHF or LFTHF since det U = ±1, the formula
det A = det U det D det UH = det D is used to compute the determinant. det D is computed as the product of the determinants of its blocks.

LFDHF is based on the LINPACK routine CSIDI; see Dongarra et al. (1979).

Example

The determinant is computed for a complex Hermitian 3 × 3 matrix.

 

      USE LFDHF_INT
      USE LFTHF_INT
      USE UMACH_INT

!                                 Declare variables

      INTEGER    LDA, N

      PARAMETER  (LDA=3, N=3)

      INTEGER    IPVT(N), NOUT

      REAL       DET1, DET2

      COMPLEX    A(LDA,LDA), FACT(LDA,LDA)

!

!                               Set values for A

!

!                               A = ( 3.0+0.0i   1.0-1.0i   4.0+0.0i )

!                                   ( 1.0+1.0i   2.0+0.0i  -5.0+1.0i )

!                                   ( 4.0+0.0i  -5.0-1.0i  -2.0+0.0i )

!

      DATA A/(3.0,0.0), (1.0,1.0), (4.0,0.0), (1.0,-1.0), (2.0,0.0),&

            (-5.0,-1.0), (4.0,0.0), (-5.0,1.0), (-2.0,0.0)/

!                                 Factor A

      CALL LFTHF (A, FACT, IPVT)

!                                 Compute the determinant

      CALL LFDHF (FACT, IPVT, DET1, DET2)

!                                 Print the results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,99999) DET1, DET2

!

99999 FORMAT (' The determinant is', F5.1, ' * 10**', F2.0)

      END

Output

 

The determinant is -1.5 * 10**2.

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