NAG Library Routine Document
F03AEF computes a Cholesky factorization of a real symmetric positive definite matrix, and evaluates the determinant.
||N, LDA, ID, IFAIL
||A(LDA,*), P(N), D1
F03AEF computes the Cholesky factorization of a real symmetric positive definite matrix where is lower triangular. The determinant is the product of the squares of the diagonal elements of .
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: A(LDA,) – REAL (KIND=nag_wp) arrayInput/Output
the second dimension of the array A
must be at least
On entry: the upper triangle of the by positive definite symmetric matrix . The elements of the array below the diagonal need not be set.
On exit: the subdiagonal elements of the lower triangular matrix . The upper triangle of is unchanged.
- 3: LDA – INTEGERInput
: the first dimension of the array A
as declared in the (sub)program from which F03AEF is called.
- 4: P(N) – REAL (KIND=nag_wp) arrayOutput
On exit: the reciprocals of the diagonal elements of .
- 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: 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 not positive definite, 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 25 of Wilkinson and Reinsch (1971)
The time taken by F03AEF is approximately proportional to .
This example computes a Cholesky factorization and calculate the determinant of the real symmetric positive definite matrix
9.1 Program Text
Program Text (f03aefe.f90)
9.2 Program Data
Program Data (f03aefe.d)
9.3 Program Results
Program Results (f03aefe.r)