NAG Library Routine Document
F01ADF calculates the approximate inverse of a real symmetric positive definite matrix, using a Cholesky factorization.
||N, LDA, IFAIL
To compute the inverse of a real symmetric positive definite matrix , F01ADF first computes a Cholesky factorization of as , where is lower triangular. It then computes and finally forms as the product .
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 lower triangle of the inverse matrix is stored in the elements of the array below the diagonal, in rows to ; is stored in for . The upper triangle of the original matrix is unchanged.
- 3: LDA – INTEGERInput
: the first dimension of the array A
as declared in the (sub)program from which F01ADF is called.
- 4: 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:
The matrix is not positive definite, possibly due to rounding errors.
The accuracy of the computed inverse depends on the conditioning of the original matrix. For a detailed error analysis see page 39 of Wilkinson and Reinsch (1971)
The time taken by F01ADF is approximately proportional to
. F01ADF calls routines F07FDF (DPOTRF)
and F07FJF (DPOTRI)
This example finds the inverse of the
9.1 Program Text
Program Text (f01adfe.f90)
9.2 Program Data
Program Data (f01adfe.d)
9.3 Program Results
Program Results (f01adfe.r)