NAG FL Interface
f03baf (real_​gen)

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1 Purpose

f03baf computes the determinant of a real n×n matrix A. f07adf must be called first to supply the matrix A in factorized form.

2 Specification

Fortran Interface
Subroutine f03baf ( n, a, lda, ipiv, d, id, ifail)
Integer, Intent (In) :: n, lda, ipiv(n)
Integer, Intent (Inout) :: ifail
Integer, Intent (Out) :: id
Real (Kind=nag_wp), Intent (In) :: a(lda,*)
Real (Kind=nag_wp), Intent (Out) :: d
C Header Interface
#include <nag.h>
void  f03baf_ (const Integer *n, const double a[], const Integer *lda, const Integer ipiv[], double *d, Integer *id, Integer *ifail)
The routine may be called by the names f03baf or nagf_det_real_gen.

3 Description

f03baf computes the determinant of a real n×n matrix A that has been factorized by a call to f07adf. 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,*) Real (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 f07adf.
3: lda Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f03baf is called.
Constraint: ldan.
4: ipiv(n) Integer array Input
On entry: the row interchanges used to factorize matrix A as returned by f07adf.
5: d Real (Kind=nag_wp) Output
6: id Integer Output
On exit: the determinant of A is given by d×2.0id. It is given in this form to avoid overflow or underflow.
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.
f03baf is not threaded in any implementation.

9 Further Comments

The time taken by f03baf is approximately proportional to n.

10 Example

This example computes the LU factorization with partial pivoting, and calculates the determinant, of the real matrix
( 33 16 72 −24 −10 −57 −8 −4 −17 ) .  

10.1 Program Text

Program Text (f03bafe.f90)

10.2 Program Data

Program Data (f03bafe.d)

10.3 Program Results

Program Results (f03bafe.r)