The routine may be called by the names f07ajf, nagf_lapacklin_dgetri or its LAPACK name dgetri.
f07ajf is used to compute the inverse of a real matrix , the routine must be preceded by a call to f07adf, which computes the factorization of as . The inverse of is computed by forming and then solving the equation for .
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal.12 1–19
1: – IntegerInput
On entry: , the order of the matrix .
2: – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a
must be at least
On entry: the factorization of , as returned by f07adf.
On exit: the factorization is overwritten by the matrix .
3: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f07ajf is called.
4: – Integer arrayInput
Note: the dimension of the array ipiv
must be at least
On entry: the pivot indices, as returned by f07adf.
5: – Real (Kind=nag_wp) arrayWorkspace
On exit: if , contains the minimum value of lwork required for optimum performance.
6: – IntegerInput
On entry: the dimension of the array work as declared in the (sub)program from which f07ajf is called, unless , in which case a workspace query is assumed and the routine only calculates the optimal dimension of work (using the formula given below).
for optimum performance lwork should be at least , where is the block size.
7: – IntegerOutput
On exit: unless the routine detects an error (see Section 6).
6Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
Element of the diagonal is zero.
is singular, and the inverse of cannot be computed.
The computed inverse satisfies a bound of the form:
where is a modest linear function of , and is the machine precision.
Background information to multithreading can be found in the Multithreading documentation.
f07ajf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The total number of floating-point operations is approximately .