NAG CL Interface
f07crc (zgttrf)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the matrix $A$.

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

2: $\mathbf{dl}\left[\mathit{dim}\right]$ – Complex Input/Output

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

On entry: must contain the $\left(n-1\right)$ subdiagonal elements of the matrix $A$.

On exit: is overwritten by the $\left(n-1\right)$ multipliers that define the matrix $L$ of the $LU$ factorization of $A$.

3: $\mathbf{d}\left[\mathit{dim}\right]$ – Complex Input/Output

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

On entry: must contain the $n$ diagonal elements of the matrix $A$.

On exit: is overwritten by the $n$ diagonal elements of the upper triangular matrix $U$ from the $LU$ factorization of $A$.

4: $\mathbf{du}\left[\mathit{dim}\right]$ – Complex Input/Output

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

On entry: must contain the $\left(n-1\right)$ superdiagonal elements of the matrix $A$.

On exit: is overwritten by the $\left(n-1\right)$ elements of the first superdiagonal of $U$.

5: $\mathbf{du2}\left[\mathbf{n}-2\right]$ – Complex Output

On exit: contains the $\left(n-2\right)$ elements of the second superdiagonal of $U$.

6: $\mathbf{ipiv}\left[\mathbf{n}\right]$ – Integer Output

On exit: contains the $n$ pivot indices that define the permutation matrix $P$. At the $i$th step, row $i$ of the matrix was interchanged with row $\mathbf{ipiv}\left[i-1\right]$. $\mathbf{ipiv}\left[i-1\right]$ will always be either $i$ or $\left(i+1\right)$, $\mathbf{ipiv}\left[i-1\right]=i$ indicating that a row interchange was not performed.

7: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

NE_INTERNAL_ERROR

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.

NE_NO_LICENCE

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.

NE_SINGULAR

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