# NAG CL Interfacef16ufc (zsy_​norm)

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## 1Purpose

f16ufc calculates the value of the $1$-norm, the $\infty$-norm, the Frobenius norm or the maximum absolute value of the elements of a complex $n×n$ symmetric matrix.

## 2Specification

 #include
 void f16ufc (Nag_OrderType order, Nag_NormType norm, Nag_UploType uplo, Integer n, const Complex a[], Integer pda, double *r, NagError *fail)
The function may be called by the names: f16ufc, nag_blast_zsy_norm or nag_zsy_norm.

## 3Description

Given a complex $n×n$ symmetric matrix, $A$, f16ufc calculates one of the values given by
 $‖A‖1=maxj⁡∑i=1n|aij|,$
 $‖A‖∞=maxi⁡∑j= 1n|aij|,$
 $‖A‖F=(∑i=1n∑j=1n |aij|2)1/2$
or
 $maxi,j|aij|.$
Note that, since $A$ is symmetric, ${‖A‖}_{1}={‖A‖}_{\infty }$.

## 4References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee https://www.netlib.org/blas/blast-forum/blas-report.pdf

## 5Arguments

1: $\mathbf{order}$Nag_OrderType Input
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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ or $\mathrm{Nag_ColMajor}$.
2: $\mathbf{norm}$Nag_NormType Input
On entry: specifies the value to be returned.
${\mathbf{norm}}=\mathrm{Nag_OneNorm}$
The $1$-norm.
${\mathbf{norm}}=\mathrm{Nag_InfNorm}$
The $\infty$-norm.
${\mathbf{norm}}=\mathrm{Nag_FrobeniusNorm}$
The Frobenius (or Euclidean) norm.
${\mathbf{norm}}=\mathrm{Nag_MaxNorm}$
The value $\underset{i,j}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}|{a}_{ij}|$ (not a norm).
Constraint: ${\mathbf{norm}}=\mathrm{Nag_OneNorm}$, $\mathrm{Nag_InfNorm}$, $\mathrm{Nag_FrobeniusNorm}$ or $\mathrm{Nag_MaxNorm}$.
3: $\mathbf{uplo}$Nag_UploType Input
On entry: specifies whether the upper or lower triangular part of $A$ is stored.
${\mathbf{uplo}}=\mathrm{Nag_Upper}$
The upper triangular part of $A$ is stored.
${\mathbf{uplo}}=\mathrm{Nag_Lower}$
The lower triangular part of $A$ is stored.
Constraint: ${\mathbf{uplo}}=\mathrm{Nag_Upper}$ or $\mathrm{Nag_Lower}$.
4: $\mathbf{n}$Integer Input
On entry: $n$, the order of the matrix $A$.
If $n=0$, n is set to zero.
Constraint: ${\mathbf{n}}\ge 0$.
5: $\mathbf{a}\left[\mathit{dim}\right]$const Complex Input
Note: the dimension, dim, of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pda}}×{\mathbf{n}}\right)$.
On entry: the $n×n$ symmetric matrix $A$.
If ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(j-1\right)×{\mathbf{pda}}+i-1\right]$.
If ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(i-1\right)×{\mathbf{pda}}+j-1\right]$.
If ${\mathbf{uplo}}=\mathrm{Nag_Upper}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
If ${\mathbf{uplo}}=\mathrm{Nag_Lower}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.
6: $\mathbf{pda}$Integer Input
On entry: the stride separating row or column elements (depending on the value of order) of the matrix $A$ in the array a.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
7: $\mathbf{r}$double * Output
On exit: the value of the norm specified by norm.
8: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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_INT_2
On entry, ${\mathbf{pda}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

## 7Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).