NAG Library Function Document

nag_superlu_refine_lu (f11mhc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{trans}$ – Nag_TransTypeInput

On entry: specifies whether $AX=B$ or $A^{\mathrm{T}}X=B$ is solved.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$

$AX=B$ is solved.

$\mathbf{trans}=\mathrm{Nag\_Trans}$

$A^{\mathrm{T}}X=B$ is solved.

Constraint: $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ or $\mathrm{Nag\_Trans}$.

3:    $\mathbf{n}$ – IntegerInput

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

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

4:    $\mathbf{icolzp}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array icolzp must be at least $\mathbf{n}+1$.

On entry: $\mathbf{icolzp}\left[i-1\right]$ contains the index in $A$ of the start of a new column. See Section 2.1.3 in the f11 Chapter Introduction.

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

Note: the dimension, dim, of the array irowix must be at least $\mathbf{icolzp}\left[\mathbf{n}\right]-1$, the number of nonzeros of the sparse matrix $A$.

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

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

Note: the dimension, dim, of the array a must be at least $\mathbf{icolzp}\left[\mathbf{n}\right]-1$, the number of nonzeros of the sparse matrix $A$.

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

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

On entry: the column permutation which defines $P_c$, the row permutation which defines $P_r$, plus associated data structures as computed by nag_superlu_lu_factorize (f11mec).

8:    $\mathbf{il}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array il must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records the sparsity pattern of matrix $L$ as computed by nag_superlu_lu_factorize (f11mec).

9:    $\mathbf{lval}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array lval must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records the nonzero values of matrix $L$ and some nonzero values of matrix $U$ as computed by nag_superlu_lu_factorize (f11mec).

10:  $\mathbf{iu}\left[\mathit{dim}\right]$ – const IntegerInput

Note: the dimension, dim, of the array iu must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records the sparsity pattern of matrix $U$ as computed by nag_superlu_lu_factorize (f11mec).

11:  $\mathbf{uval}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array uval must be at least as large as the dimension of the array of the same name in nag_superlu_lu_factorize (f11mec).

On entry: records some nonzero values of matrix $U$ as computed by nag_superlu_lu_factorize (f11mec).

12:  $\mathbf{nrhs}$ – IntegerInput

On entry: $\mathit{nrhs}$, the number of right-hand sides in $B$.

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

13:  $\mathbf{b}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array b must be at least

• $\max \left(1,\mathbf{pdb}\times \mathbf{nrhs}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdb}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $B$ is stored in

• $\mathbf{b}\left[\left(j-1\right)\times \mathbf{pdb}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{b}\left[\left(i-1\right)\times \mathbf{pdb}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $\mathit{nrhs}$ right-hand side matrix $B$.

14:  $\mathbf{pdb}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array b.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdb}\ge \max \left(1,\mathbf{nrhs}\right)$.

15:  $\mathbf{x}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array x must be at least

• $\max \left(1,\mathbf{pdx}\times \mathbf{nrhs}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdx}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

The $\left(i,j\right)$th element of the matrix $X$ is stored in

• $\mathbf{x}\left[\left(j-1\right)\times \mathbf{pdx}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{x}\left[\left(i-1\right)\times \mathbf{pdx}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $n$ by $\mathit{nrhs}$ solution matrix $X$, as returned by nag_superlu_solve_lu (f11mfc).

On exit: the $n$ by $\mathit{nrhs}$ improved solution matrix $X$.

16:  $\mathbf{pdx}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array x.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdx}\ge \max \left(1,\mathbf{n}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdx}\ge \max \left(1,\mathbf{nrhs}\right)$.

17:  $\mathbf{ferr}\left[\mathbf{nrhs}\right]$ – doubleOutput

On exit: $\mathbf{ferr}\left[\mathit{j}-1\right]$ contains an estimated error bound for the $\mathit{j}$th solution vector, that is, the $\mathit{j}$th column of $X$, for $\mathit{j}=1,2,\dots ,\mathit{nrhs}$.

18:  $\mathbf{berr}\left[\mathbf{nrhs}\right]$ – doubleOutput

On exit: $\mathbf{berr}\left[\mathit{j}-1\right]$ contains the component-wise backward error bound $\beta$ for the $\mathit{j}$th solution vector, that is, the $\mathit{j}$th column of $X$, for $\mathit{j}=1,2,\dots ,\mathit{nrhs}$.

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

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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, $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nrhs}\ge 0$.

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

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

NE_INT_2

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{pdb}=〈\mathit{\text{value}}〉$ and $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{nrhs}\right)$.

On entry, $\mathbf{pdx}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdx}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{pdx}=〈\mathit{\text{value}}〉$ and $\mathbf{nrhs}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdx}\ge \max \left(1,\mathbf{nrhs}\right)$.

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_PERM_COL

Incorrect column permutations in array iprm.

NE_INVALID_PERM_ROW

Incorrect row permutations in array iprm.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f11mhce.c)

10.2

Program Data

Program Data (f11mhce.d)

10.3

Program Results

Program Results (f11mhce.r)