The function may be called by the names: f07arc, nag_lapacklin_zgetrf or nag_zgetrf.
f07arc 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 function 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: – 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 number of rows of the matrix .
3: – IntegerInput
On entry: , the number of columns of the matrix .
4: – ComplexInput/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 matrix .
On exit: the factors and from the factorization ; the unit diagonal elements of are not stored.
5: – IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
if , .
6: – IntegerOutput
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.
7: – 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, .
On entry, . Constraint: .
On entry, and .
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 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.
f07arc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f07arc 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 real floating-point operations is approximately if (the usual case), if and if .
A call to this function with may be followed by calls to the functions: