NAG Library Routine Document

f07arf  (zgetrf)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $A$.

Constraint: $\mathbf{m}\ge 0$.

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $A$.

Constraint: $\mathbf{n}\ge 0$.

3:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array a must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $m$ by $n$ matrix $A$.

On exit: the factors $L$ and $U$ from the factorization $A=PLU$; the unit diagonal elements of $L$ are not stored.

4:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f07arf (zgetrf) is called.

Constraint: $\mathbf{lda}\ge \max \left(1,\mathbf{m}\right)$.

5:     $\mathbf{ipiv}\left(\min \left(\mathbf{m},\mathbf{n}\right)\right)$ – Integer arrayOutput

On exit: the pivot indices that define the permutation matrix. At the $\mathit{i}$th step, if $\mathbf{ipiv}\left(\mathit{i}\right)>\mathit{i}$ then row $\mathit{i}$ of the matrix $A$ was interchanged with row $\mathbf{ipiv}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\min \left(m,n\right)$. $\mathbf{ipiv}\left(i\right)\le i$ indicates that, at the $i$th step, a row interchange was not required.

6:     $\mathbf{info}$ – IntegerOutput

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6

Error Indicators and Warnings

$\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{info}>0$

Element $〈\mathit{\text{value}}〉$ of the diagonal is exactly zero. The factorization has been completed, but the factor $U$ is exactly singular, and division by zero will occur if it is used to solve a system of equations.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f07arfe.f90)

10.2

Program Data

Program Data (f07arfe.d)

10.3

Program Results

Program Results (f07arfe.r)