NAG Library Routine Document

F11MLF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     NORM – CHARACTER(1)Input

On entry: specifies the value to be returned in ANORM.

$\mathbf{NORM}=\text{'1'}$ or $\text{'O'}$

The $1$-norm ${‖A‖}_1$ of the matrix is computed, that is ${\displaystyle \underset{1\le j\le n}{\max }}{\displaystyle \sum _{i=1}^n}\left|A_{ij}\right|$.

$\mathbf{NORM}=\text{'I'}$

The $\infty$-norm ${‖A‖}_{\infty }$ of the matrix is computed, that is ${\displaystyle \underset{1\le i\le n}{\max }}{\displaystyle \sum _{j=1}^n}\left|A_{ij}\right|$.

$\mathbf{NORM}=\text{'M'}$

The value ${\displaystyle \underset{1\le i,j\le n}{\max }}\left|A_{ij}\right|$ (not a norm).

Constraint: $\mathbf{NORM}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$ or $\text{'M'}$.

2:     ANORM – REAL (KIND=nag_wp)Output

On exit: the computed quantity relating the matrix.

3:     N – INTEGERInput

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

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

4:     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.

5:     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 $A$.

6:     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 $A$.

7:     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,	$\mathbf{NORM}\ne \text{'1'}$, $\text{'O'}$, $\text{'I'}$ or $\text{'M'}$,
or	$\mathbf{N}<0$.

$\mathbf{IFAIL}=301$

Unable to allocate required internal workspace.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f11mlfe.f90)

9.2  Program Data

Program Data (f11mlfe.d)

9.3  Program Results

Program Results (f11mlfe.r)