LFDDH
Computes the determinant of a complex Hermitian positive definite matrix given the RHR Cholesky factorization of the matrix.
Required Arguments
FACT — Complex N by N matrix containing the RHR factorization of the coefficient matrix A as output from routine LFCDH/DLFCDH or LFTDH/DLFTDH. (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 * 10DET2.
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 LFDDH (FACT, DET1, DET2 [, …])
Specific: The specific interface names are S_LFDDH and D_LFDDH.
FORTRAN 77 Interface
Single: CALL LFDDH (N, FACT, LDFACT, DET1, DET2)
Double: The double precision name is DLFDDH.
Description
Routine LFDDH computes the determinant of a complex Hermitian positive definite coefficient matrix. To compute the determinant, the coefficient matrix must first undergo an RH R factorization. This may be done by calling either LFCDH or LFTDH. The formula det A = det RH det R = (det R)2 is used to compute the determinant. Since the determinant of a triangular matrix is the product of the diagonal elements,
(The matrix R is stored in the upper triangle of FACT.)
LFDDH is based on the LINPACK routine CPODI; see Dongarra et al. (1979).
Example
The determinant is computed for a complex Hermitian positive definite 3 × 3 matrix.
USE LFDDH_INT
USE LFTDH_INT
USE UMACH_INT
! Declare variables
INTEGER LDA, LDFACT, NOUT
PARAMETER (LDA=3, LDFACT=3)
REAL DET1, DET2
COMPLEX A(LDA,LDA), FACT(LDFACT,LDFACT)
!
! Set values for A
!
! A = ( 6.0+0.0i 1.0-1.0i 4.0+0.0i )
! ( 1.0+1.0i 7.0+0.0i -5.0+1.0i )
! ( 4.0+0.0i -5.0-1.0i 11.0+0.0i )
!
DATA A /(6.0,0.0), (1.0,1.0), (4.0,0.0), (1.0,-1.0), (7.0,0.0),&
(-5.0,-1.0), (4.0,0.0), (-5.0,1.0), (11.0,0.0)/
! Factor the matrix
CALL LFTDH (A, FACT)
! Compute the determinant
CALL LFDDH (FACT, DET1, DET2)
! Print 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 1.400 * 10**2.
