The routine may be called by the names f07arf, nagf_lapacklin_zgetrf or its LAPACK name zgetrf.
f07arf forms the factorization of a complex matrix as , where is a permutation matrix, is lower triangular with unit diagonal elements (lower trapezoidal if ) and is upper triangular (upper trapezoidal if ). Usually is square , and both and are triangular. The routine uses partial pivoting, with row interchanges.
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
1: – IntegerInput
On entry: , the number of rows of the matrix .
2: – IntegerInput
On entry: , the number of columns of the matrix .
3: – Complex (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a
must be at least
On entry: the matrix .
On exit: the factors and from the factorization ; the unit diagonal elements of are not stored.
4: – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f07arf is called.
5: – Integer arrayOutput
On exit: the pivot indices that define the permutation matrix. At the
th step, if then row of the matrix was interchanged with row , for . indicates that, at the th step, a row interchange was not required.
6: – 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 exactly zero.
The factorization has been completed, but the factor
is exactly singular, and division by zero will occur if it is used to solve
a system of equations.
The computed factors and are the exact factors of a perturbed matrix , where
is a modest linear function of , and is the machine precision.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f07arf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f07arf 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 real floating-point operations is approximately if (the usual case), if and if .
A call to this routine with may be followed by calls to the routines: