LFDQH
Computes the determinant of a complex Hermitian positive definite matrix given the RHR Cholesky factorization in band Hermitian storage mode.
Required Arguments
FACT — Complex NCODA + 1 by N array containing the RHR factorization of the Hermitian positive definite band matrix A. (Input)
FACT is obtained as output from routine LFCQH/DLFCQH or LFTQH/DLFTQH.
NCODA — Number of upper or lower codiagonals of A. (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 — 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 LFDQH (FACT, NCODA, DET1, DET2 [, …])
Specific: The specific interface names are S_LFDQH and D_LFDQH.
FORTRAN 77 Interface
Single: CALL LFDQH (N, FACT, LDFACT, NCODA, DET1, DET2)
Double: The double precision name is DLFDQH.
Description
Routine
LFDQH computes the determinant of a complex Hermitian positive definite band coefficient matrix. To compute the determinant, the coefficient matrix must first undergo an
RH R factorization. This may be done by calling either
LFCQH or
LFTQH. 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,
LFDQH is based on the LINPACK routine CPBDI; see Dongarra et al. (1979).
Example
The determinant is computed for a 5 × 5 complex Hermitian positive definite band matrix with one codiagonal.
USE LFDQH_INT
USE LFTQH_INT
USE UMACH_INT
! Declare variables
INTEGER LDA, LDFACT, N, NCODA, NOUT
PARAMETER (LDA=2, N=5, LDFACT=2, NCODA=1)
REAL DET1, DET2
COMPLEX A(LDA,N), FACT(LDFACT,N)
!
! Set values for A in band Hermitian form
!
! A = ( 0.0+0.0i -1.0+1.0i 1.0+2.0i 0.0+4.0i 1.0+1.0i )
! ( 2.0+0.0i 4.0+0.0i 10.0+0.0i 6.0+0.0i 9.0+0.0i )
!
DATA A/(0.0,0.0), (2.0,0.0), (-1.0,1.0), (4.0, 0.0), (1.0,2.0),&
(10.0,0.0), (0.0,4.0), (6.0,0.0), (1.0,1.0), (9.0,0.0)/
! Factor the matrix
CALL LFTQH (A, NCODA, FACT)
! Compute the determinant
CALL LFDQH (FACT, NCODA, 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 1.736 * 10**3.
Published date: 03/19/2020
Last modified date: 03/19/2020
