NAG Library Routine Document

F11MHF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     TRANS – CHARACTER(1)Input

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

$\mathbf{TRANS}=\text{'N'}$

$AX=B$ is solved.

$\mathbf{TRANS}=\text{'T'}$

$A^{\mathrm{T}}X=B$ is solved.

Constraint: $\mathbf{TRANS}=\text{'N'}$ or $\text{'T'}$.

2:     N – INTEGERInput

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

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

3:     ICOLZP($*$) – INTEGER arrayInput

Note: the dimension of the array ICOLZP must be at least $\mathbf{N}+1$.

On entry: $\mathbf{ICOLZP}\left(i\right)$ contains the index in $A$ of the start of a new column. See Section 2.1.3 in the F11 Chapter Introduction.

4:     IROWIX($*$) – INTEGER arrayInput

Note: the dimension of the array IROWIX must be at least $\mathbf{ICOLZP}\left(\mathbf{N}+1\right)-1$, the number of nonzeros of the sparse matrix $A$.

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

5:     A($*$) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array A must be at least $\mathbf{ICOLZP}\left(\mathbf{N}+1\right)-1$, the number of nonzeros of the sparse matrix $A$.

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

6:     IPRM($7\times \mathbf{N}$) – INTEGER arrayInput

On entry: the column permutation which defines $P_c$, the row permutation which defines $P_r$, plus associated data structures as computed by F11MEF.

7:     IL($*$) – INTEGER arrayInput

Note: the dimension of the array IL must be at least as large as the dimension of the array of the same name in F11MEF.

On entry: records the sparsity pattern of matrix $L$ as computed by F11MEF.

8:     LVAL($*$) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array LVAL must be at least as large as the dimension of the array of the same name in F11MEF.

On entry: records the nonzero values of matrix $L$ and some nonzero values of matrix $U$ as computed by F11MEF.

9:     IU($*$) – INTEGER arrayInput

Note: the dimension of the array IU must be at least as large as the dimension of the array of the same name in F11MEF.

On entry: records the sparsity pattern of matrix $U$ as computed by F11MEF.

10:   UVAL($*$) – REAL (KIND=nag_wp) arrayInput

Note: the dimension of the array UVAL must be at least as large as the dimension of the array of the same name in F11MEF.

On entry: records some nonzero values of matrix $U$ as computed by F11MEF.

11:   NRHS – INTEGERInput

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

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

12:   B(LDB,$*$) – REAL (KIND=nag_wp) arrayInput

Note: the second dimension of the array B must be at least $\max \left(1,\mathbf{NRHS}\right)$.

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

13:   LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F11MHF is called.

Constraint: $\mathbf{LDB}\ge \max \left(1,\mathbf{N}\right)$.

14:   X(LDX,$*$) – REAL (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array X must be at least $\max \left(1,\mathbf{NRHS}\right)$.

On entry: the $n$ by $\mathit{nrhs}$ solution matrix $X$, as returned by F11MFF.

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

15:   LDX – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which F11MHF is called.

Constraint: $\mathbf{LDX}\ge \max \left(1,\mathbf{N}\right)$.

16:   FERR(NRHS) – REAL (KIND=nag_wp) arrayOutput

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

17:   BERR(NRHS) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{BERR}\left(\mathit{j}\right)$ 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 $\mathit{j}=1,2,\dots ,\mathit{nrhs}$.

18:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{TRANS}\ne \text{'N'}$ or $\text{'T'}$,
or	$\mathbf{N}<0$,
or	$\mathbf{NRHS}<0$,
or	$\mathbf{LDB}<\max \left(1,\mathbf{N}\right)$,
or	$\mathbf{LDX}<\max \left(1,\mathbf{N}\right)$.

$\mathbf{IFAIL}=2$

Ill-defined row permutation in array $\mathbf{IPRM}$. Internal checks have revealed that the $\mathbf{IPRM}$ array is corrupted.

$\mathbf{IFAIL}=3$

Ill-defined column permutations in array $\mathbf{IPRM}$. Internal checks have revealed that the $\mathbf{IPRM}$ array is corrupted.

$\mathbf{IFAIL}=301$

Unable to allocate required internal workspace.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f11mhfe.f90)

9.2  Program Data

Program Data (f11mhfe.d)

9.3  Program Results

Program Results (f11mhfe.r)