NAG FL Interface
f03bnf (complex_​gen)

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1 Purpose

f03bnf computes the determinant of a complex n×n matrix A. f07arf must be called first to supply the matrix A in factorized form.

2 Specification

Fortran Interface
Subroutine f03bnf ( n, a, lda, ipiv, d, id, ifail)
Integer, Intent (In) :: n, lda, ipiv(n)
Integer, Intent (Inout) :: ifail
Integer, Intent (Out) :: id(2)
Complex (Kind=nag_wp), Intent (In) :: a(lda,*)
Complex (Kind=nag_wp), Intent (Out) :: d
C Header Interface
#include <nag.h>
void  f03bnf_ (const Integer *n, const Complex a[], const Integer *lda, const Integer ipiv[], Complex *d, Integer id[], Integer *ifail)
The routine may be called by the names f03bnf or nagf_det_complex_gen.

3 Description

f03bnf computes the determinant of a complex n×n matrix A that has been factorized by a call to f07arf. The determinant of A is the product of the diagonal elements of U with the correct sign determined by the row interchanges.

4 References

Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag

5 Arguments

1: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n>0.
2: a(lda,*) Complex (Kind=nag_wp) array Input
Note: the second dimension of the array a must be at least n.
On entry: the n×n matrix A in factorized form as returned by f07arf.
3: lda Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f03bnf is called.
Constraint: ldan.
4: ipiv(n) Integer array Input
On entry: the row interchanges used to factorize matrix A as returned by f07arf.
5: d Complex (Kind=nag_wp) Output
On exit: the mantissa of the real and imaginary parts of the determinant.
6: id(2) Integer array Output
On exit: the exponents for the real and imaginary parts of the determinant. The determinant, d=(dr,di), is returned as dr=Dr×2j and di=Di×2k, where d=(Dr,Di) and j and k are stored in the first and second elements respectively of the array id on successful exit.
7: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, n=value.
Constraint: n1.
On entry, lda=value and n=value.
Constraint: ldan.
The matrix A is approximately singular.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The accuracy of the determinant depends on the conditioning of the original matrix. For a detailed error analysis, see page 107 of Wilkinson and Reinsch (1971).

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f03bnf is not threaded in any implementation.

9 Further Comments

The time taken by f03bnf is approximately proportional to n.

10 Example

This example calculates the determinant of the complex matrix
( 1 1+2i 2+10i 1+i 3i −5+14i 1+i 5i −8+20i ) .  

10.1 Program Text

Program Text (f03bnfe.f90)

10.2 Program Data

Program Data (f03bnfe.d)

10.3 Program Results

Program Results (f03bnfe.r)