NAG Library Function Document

nag_superlu_lu_factorize (f11mec)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{n}$ – IntegerInput

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

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

2:    $\mathbf{irowix}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array irowix must be at least $\mathit{nnz}$, the number of nonzeros of the sparse matrix $A$.

On entry: the row index array of sparse matrix $A$.

3:    $\mathbf{a}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array a must be at least $\mathit{nnz}$, the number of nonzeros of the sparse matrix $A$.

On entry: the array of nonzero values in the sparse matrix $A$.

4:    $\mathbf{iprm}\left[7\times \mathbf{n}\right]$ – IntegerInput/Output

On entry: contains the column permutation which defines the permutation $P_c$ and associated data structures as computed by function nag_superlu_column_permutation (f11mdc).

On exit: part of the array is modified to record the row permutation $P_r$ determined by pivoting.

5:    $\mathbf{thresh}$ – doubleInput

On entry: the diagonal pivoting threshold, $t$. At step $j$ of the Gaussian elimination, if $\left|A_{jj}\right|\ge t\left({\displaystyle \underset{i\ge j}{\max }}\left|A_{ij}\right|\right)$, use $A_{jj}$ as a pivot, otherwise use ${\displaystyle \underset{i\ge j}{\max }}\left|A_{ij}\right|$. A value of $t=1$ corresponds to partial pivoting, a value of $t=0$ corresponds to always choosing the pivot on the diagonal (unless it is zero).

Suggested value: $\mathbf{thresh}=1.0$. Smaller values may result in a faster factorization, but the benefits are likely to be small in most cases. It might be possible to use $\mathbf{thresh}=0.0$ if you are confident about the stability of the factorization, for example, if $A$ is diagonally dominant.

Constraint: $0.0\le \mathbf{thresh}\le 1.0$.

6:    $\mathbf{nzlmx}$ – IntegerInput

On entry: indicates the available size of array il. The dimension of il should be at least $7\times \mathbf{n}+\mathbf{nzlmx}+4$. A good range for nzlmx that works for many problems is $\mathit{nnz}$ to $8\times \mathit{nnz}$, where $\mathit{nnz}$ is the number of nonzeros in the sparse matrix $A$. If, on exit, $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NZLMX_TOO_SMALL, the given nzlmx was too small and you should attempt to provide more storage and call the function again.

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

7:    $\mathbf{nzlumx}$ – Integer *Input/Output

On entry: indicates the available size of array lval. The dimension of lval should be at least nzlumx.

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

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NZLUMX_TOO_SMALL, the given nzlumx was too small and is reset to a value that will be sufficient. You should then provide the indicated storage and call the function again.

8:    $\mathbf{nzumx}$ – IntegerInput

On entry: indicates the available sizes of arrays iu and uval. The dimension of iu should be at least $2\times \mathbf{n}+\mathbf{nzumx}+1$ and the dimension of uval should be at least nzumx. A good range for nzumx that works for many problems is $\mathit{nnz}$ to $8\times \mathit{nnz}$, where $\mathit{nnz}$ is the number of nonzeros in the sparse matrix $A$. If, on exit, $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NZUMX_TOO_SMALL, the given nzumx was too small and you should attempt to provide more storage and call the function again.

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

9:    $\mathbf{il}\left[7\times \mathbf{n}+\mathbf{nzlmx}+4\right]$ – IntegerOutput

On exit: encapsulates the sparsity pattern of matrix $L$.

10:  $\mathbf{lval}\left[\mathbf{nzlumx}\right]$ – doubleOutput

On exit: records the nonzero values of matrix $L$ and some of the nonzero values of matrix $U$.

11:  $\mathbf{iu}\left[2\times \mathbf{n}+\mathbf{nzumx}+1\right]$ – IntegerOutput

On exit: encapsulates the sparsity pattern of matrix $U$.

12:  $\mathbf{uval}\left[\mathbf{nzumx}\right]$ – doubleOutput

On exit: records some of the nonzero values of matrix $U$.

13:  $\mathbf{nnzl}$ – Integer *Output

On exit: the number of nonzero values in the matrix $L$.

14:  $\mathbf{nnzu}$ – Integer *Output

On exit: the number of nonzero values in the matrix $U$.

15:  $\mathbf{flop}$ – double *Output

On exit: the number of floating-point operations performed.

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

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

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction 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: $\mathbf{n}\ge 0$.

On entry, $\mathbf{nzlmx}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nzlmx}\ge 1$.

On entry, $\mathbf{nzlumx}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nzlumx}\ge 1$.

On entry, $\mathbf{nzumx}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nzumx}\ge 1$.

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

NE_NZLMX_TOO_SMALL

Insufficient nzlmx.

NE_NZLUMX_TOO_SMALL

Insufficient nzlumx.

NE_NZUMX_TOO_SMALL

Insufficient nzumx.

NE_REAL

On entry, $\mathbf{thresh}=〈\mathit{\text{value}}〉$.
Constraint: $0.0\le \mathbf{thresh}\le 1.0$.

NE_SINGULAR_MATRIX

The matrix is singular – no factorization possible.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f11mece.c)

10.2  Program Data

Program Data (f11mece.d)

10.3  Program Results

Program Results (f11mece.r)