NAG FL Interface
f07arf (zgetrf)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{m}$ – Integer Input

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

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

2: $\mathbf{n}$ – Integer Input

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

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

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

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

On entry: the $m\times n$ matrix $A$.

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

4: $\mathbf{lda}$ – Integer Input

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

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

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

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 $\mathit{i}=1,2,\dots ,\min (m,n)$. $\mathbf{ipiv}\left(i\right)\le i$ indicates that, at the $i$th step, a row interchange was not required.

6: $\mathbf{info}$ – Integer Output

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

10.2 Program Data

10.3 Program Results