NAG Library Routine Document
F03AFF computes an factorization of a real matrix, with partial pivoting, and evaluates the determinant.
||N, LDA, ID, IFAIL
||EPS, A(LDA,*), D1, P(N)
F03AFF computes an factorization of a real matrix with partial pivoting: , where is a permutation matrix, is lower triangular and is unit upper triangular. The determinant of is the product of the diagonal elements of with the correct sign determined by the row interchanges.
Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag
- 1: N – INTEGERInput
On entry: , the order of the matrix .
- 2: EPS – REAL (KIND=nag_wp)Input
On entry: is no longer required by F03AFF but is retained for backwards compatibility.
- 3: A(LDA,) – REAL (KIND=nag_wp) arrayInput/Output
the second dimension of the array A
must be at least
On entry: the by matrix .
On exit: is overwritten by the lower triangular matrix and the off-diagonal elements of the upper triangular matrix . The unit diagonal elements of are not stored.
- 4: LDA – INTEGERInput
: the first dimension of the array A
as declared in the (sub)program from which F03AFF is called.
- 5: D1 – REAL (KIND=nag_wp)Output
- 6: ID – INTEGEROutput
On exit: the determinant of is given by . It is given in this form to avoid overflow or underflow.
- 7: P(N) – REAL (KIND=nag_wp) arrayOutput
On exit: gives the row index of the th pivot.
- 8: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
is singular, possibly due to rounding errors. The factorization could not be completed. D1
are set to zero.
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)
The time taken by F03AFF is approximately proportional to .
This example computes the
factorization with partial pivoting, and calculates the determinant, of the real matrix
9.1 Program Text
Program Text (f03affe.f90)
9.2 Program Data
Program Data (f03affe.d)
9.3 Program Results
Program Results (f03affe.r)