LFDCT
Computes the determinant of a complex triangular matrix.
Required Arguments
A — Complex N by N matrix containing the triangular matrix.(Input)
DET1 — Complex 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 (A,2).
LDA — Leading dimension of A exactly as specified in the dimension statement of the calling program. (Input)
Default: LDA = size (A,1).
FORTRAN 90 Interface
Generic: CALL LFDCT (A, DET1, DET2 [,…])
Specific: The specific interface names are S_LFDCT and D_LFDCT.
FORTRAN 77 Interface
Single: CALL LFDCT (N, A, LDA, DET1, DET2)
Double: The double precision name is DLFDCT.
Description
Routine LFDCT computes the determinant of a complex triangular coefficient matrix. The determinant of a triangular matrix is the product of the diagonal elements
LFDCT is based on the LINPACK routine CTRDI; see Dongarra et al. (1979).
Comments
Informational error
Type | Code | Description |
|---|
3 | 1 | The input triangular matrix is singular. |
Example
The determinant is computed for a 3 × 3 complex lower triangular matrix.
USE LFDCT_INT
USE UMACH_INT
! Declare variables
INTEGER LDA, N
PARAMETER (LDA=3, N=3)
INTEGER NOUT
REAL DET2
COMPLEX A(LDA,LDA), DET1
! Set values for A
!
! A = ( -3.0+2.0i )
! ( -2.0-1.0i 0.0+6.0i )
! ( -1.0+3.0i 1.0-5.0i -4.0+0.0i )
!
DATA A/(-3.0,2.0), (-2.0,-1.0), (-1.0, 3.0), (0.0,0.0), (0.0,6.0),&
(1.0,-5.0), (0.0,0.0), (0.0,0.0), (-4.0,0.0)/
!
! Compute the determinant of A
CALL LFDCT (A, DET1, DET2)
! Print results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) DET1, DET2
99999 FORMAT (’ The determinant of A is (’,F4.1,’,’,F4.1,’) * 10**’,&
F2.0)
END
Output
The determinant of A is ( 0.5, 0.7) * 10**2.
