NAG Library Function Document

nag_zgb_norm (f16ubc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     norm – Nag_NormTypeInput

On entry: specifies the value to be returned. The integer codes shown below can be replaced by the equivalent named constants of the form NAG_?_NORM. These named constants are available via the nag_library module and are also used in the example program for clarity.

$\mathbf{norm}=\mathrm{Nag\_OneNorm}$

The $1$-norm.

$\mathbf{norm}=\mathrm{Nag\_FrobeniusNorm}$

The Frobenius (or Euclidean) norm.

$\mathbf{norm}=\mathrm{Nag\_InfNorm}$

The $\infty$-norm.

$\mathbf{norm}=\mathrm{Nag\_MaxNorm}$

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

Constraint: $\mathbf{norm}=\mathrm{Nag\_OneNorm}$, $\mathrm{Nag\_TwoNorm}$, $\mathrm{Nag\_FrobeniusNorm}$, $\mathrm{Nag\_InfNorm}$ or $\mathrm{Nag\_MaxNorm}$.

3:     m – IntegerInput

On entry: $m$, the number of rows of the matrix $A$.

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

4:     n – IntegerInput

On entry: $n$, the number of columns of the matrix $A$.

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

5:     kl – IntegerInput

On entry: $k_l$, the number of subdiagonals within the band of $A$.

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

6:     ku – IntegerInput

On entry: $k_u$, the number of superdiagonals within the band of $A$.

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

7:     ab[$\mathit{dim}$] – const ComplexInput

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

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

On entry: the $m$ by $n$ band matrix $A$.

This is stored as a notional two-dimensional array with row elements or column elements stored contiguously. The storage of elements $A_{ij}$, for row $i=1,\dots ,m$ and column $j=\max \left(1,i-k_l\right),\dots ,\min \left(n,i+k_u\right)$, depends on the order argument as follows:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $A_{ij}$ is stored as $\mathbf{ab}\left[\left(j-1\right)\times \mathbf{pdab}+\mathbf{ku}+i-j\right]$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $A_{ij}$ is stored as $\mathbf{ab}\left[\left(i-1\right)\times \mathbf{pdab}+\mathbf{kl}+j-i\right]$.

8:     pdab – IntegerInput

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

Constraint: $\mathbf{pdab}\ge \mathbf{kl}+\mathbf{ku}+1$.

9:     r – double *Output

On exit: the value of the norm specified by norm.

10:   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.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INT

On entry, $\mathbf{kl}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{kl}\ge 0$.

On entry, $\mathbf{ku}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ku}\ge 0$.

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 0$.

NE_INT_3

On entry, $\mathbf{pdab}=⟨\mathit{\text{value}}⟩$, $\mathbf{kl}=⟨\mathit{\text{value}}⟩$, $\mathbf{ku}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdab}\ge \mathbf{kl}+\mathbf{ku}+1$.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f16ubce.c)

10.2  Program Data

Program Data (f16ubce.d)

10.3  Program Results

Program Results (f16ubce.r)