NAG Library Function Document

nag_superlu_matrix_norm (f11mlc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     norm – Nag_NormTypeInput

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

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

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

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

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

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

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

Constraint: $\mathbf{norm}=\mathrm{Nag\_RealOneNorm}$, $\mathrm{Nag\_RealInfNorm}$ or $\mathrm{Nag\_RealMaxNorm}$.

2:     anorm – double *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[$\mathit{dim}$] – 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:     irowix[$\mathit{dim}$] – 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:     a[$\mathit{dim}$] – 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:     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, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 0$.

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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f11mlce.c)

10.2  Program Data

Program Data (f11mlce.d)

10.3  Program Results

Program Results (f11mlce.r)