NAG Library Function Document

nag_complex_lu (f03ahc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     n – IntegerInput

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

Constraint: $\mathbf{n}\ge 1$.

2:     a[$\mathbf{n}\times \mathbf{tda}$] – ComplexInput/Output

Note: the $\left(i,j\right)$th element of the matrix $A$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{tda}+j-1\right]$.

On entry: the $n$ by $n$ matrix $A$.

On exit: $A$ is overwritten by the lower triangular matrix $L$ and the off-diagonal elements of the upper triangular matrix $U$. The unit diagonal elements of $U$ are not stored.

3:     tda – IntegerInput

On entry: the stride separating matrix column elements in the array a.

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

4:     pivot[n] – IntegerOutput

On exit: $\mathbf{pivot}\left[i-1\right]$ gives the row index of the $i$th pivot.

5:     det – Complex *Output

6:     dete – Integer *Output

On exit: the determinant of $A$ is given by $\left(\mathbf{det}\mathbf{.}\mathbf{re}+i\mathbf{det}\mathbf{.}\mathbf{im}\right)\times {2.0}^{\mathbf{dete}}$. It is given in this form to avoid overflow and underflow.

7:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{tda}=⟨\mathit{\text{value}}⟩$ while $\mathbf{n}=⟨\mathit{\text{value}}⟩$. The arguments must satisfy $\mathbf{tda}\ge \mathbf{n}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_INT_ARG_LT

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 1$.

NE_SINGULAR

The matrix $A$ is singular, possibly due to rounding errors. The factorization could not be completed. $\mathbf{det}\mathbf{.}\mathbf{re}$, $\mathbf{det}\mathbf{.}\mathbf{im}$ and dete are set to zero.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f03ahce.c)

10.2  Program Data

Program Data (f03ahce.d)

10.3  Program Results

Program Results (f03ahce.r)