NAG FL Interface
f11mlf (direct_​real_​gen_​norm)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{norm}$ – 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: $\mathbf{anorm}$ – Real (Kind=nag_wp) Output

On exit: the computed quantity relating the matrix.

3: $\mathbf{n}$ – Integer Input

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

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

4: $\mathbf{icolzp}\left(*\right)$ – Integer array Input

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

On entry: the new column index array of sparse matrix $A$. See Section 2.1.3 in the F11 Chapter Introduction.

5: $\mathbf{irowix}\left(*\right)$ – Integer array Input

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 $A$. See Section 2.1.3 in the F11 Chapter Introduction.

6: $\mathbf{a}\left(*\right)$ – Real (Kind=nag_wp) array Input

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: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{norm}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{norm}=\text{'1'}$, $\text{'O'}$, $\text{'I'}$ or $\text{'M'}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results