The function may be called by the names: f07ajc, nag_lapacklin_dgetri or nag_dgetri.
f07ajc is used to compute the inverse of a real matrix , the function must be preceded by a call to f07adc, 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: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
2: – IntegerInput
On entry: , the order of the matrix .
3: – doubleInput/Output
Note: the dimension, dim, of the array a
must be at least
The th element of the matrix is stored in
On entry: the factorization of , as returned by f07adc.
On exit: the factorization is overwritten by the matrix .
4: – IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
5: – const IntegerInput
Note: the dimension, dim, of the array ipiv
must be at least
On entry: the pivot indices, as returned by f07adc.
6: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
On entry, . Constraint: .
On entry, and .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.
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.
f07ajc 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The total number of floating-point operations is approximately .