naginterfaces.library.blas.dlansf

naginterfaces.library.blas.dlansf(norm, transr, uplo, n, a)

dlansf returns the value of the $1$-norm, the $\infty$-norm, the Frobenius norm, or the maximum absolute value of the elements of a real symmetric matrix $A$ stored in Rectangular Full Packed (RFP) format.

For full information please refer to the NAG Library document for f06wa

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06waf.html

Parameters

normstr, length 1

Specifies the value to be returned.

$norm=\text{'1'}$ or $\text{'O'}$

The $1$-norm.

$norm=\text{'I'}$

The $\infty$-norm.

$norm=\text{'F'}$ or $\text{'E'}$

The Frobenius (or Euclidean) norm.

$norm=\text{'M'}$

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

transrstr, length 1

Specifies whether the RFP representation of $A$ is normal or transposed.

$transr=\text{'N'}$

The matrix $A$ is stored in normal RFP format.

$transr=\text{'T'}$

The matrix $A$ is stored in transposed RFP format.

uplostr, length 1

Specifies whether the upper or lower triangular part of $A$ is stored.

$uplo=\text{'U'}$

The upper triangular part of $A$ is stored.

$uplo=\text{'L'}$

The lower triangular part of $A$ is stored.

nint

$n$, the order of the matrix $A$.

When $n=0$, dlansf returns zero.

afloat, array-like, shape $(n\times (n+1)/2)$

The upper or lower triangular part (as specified by $uplo$) of the $n\times n$ symmetric matrix $A$, in either normal or transposed RFP format (as specified by $transr$). The storage format is described in detail in the F07 Introduction.

Returns

nrmfloat

The $\infty$-norm, the Frobenius norm, or the maximum absolute value of the elements of the real symmetric matrix $A$ stored in Rectangular Full Packed (RFP) format.

Raises

NagValueError

(errno $1$)

On entry, error in parameter $norm$.

Constraint: $norm=\text{'1'}$, $\text{'O'}$, $\text{'I'}$, $\text{'F'}$, $\text{'E'}$ or $\text{'M'}$.

(errno $2$)

On entry, error in parameter $transr$.

Constraint: $transr=\text{'N'}$ or $\text{'T'}$.

(errno $3$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(errno $4$)

On entry, error in parameter $n$.

Constraint: $n\ge 0$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

Given a real $n\times n$ symmetric matrix, $A$, dlansf calculates one of the values given by

${\parallel A\parallel }_1={max}_j\left({\sum }_{i=1}^n\left|a_{ij}\right|\right)$	(the $1$-norm of $A$),
${\parallel A\parallel }_{\infty }={max}_i\left({\sum }_{j=1}^n\left|a_{ij}\right|\right)$	(the $\infty$-norm of $A$),
${\parallel A\parallel }_F={\left({\sum }_{i=1}^n{\sum }_{j=1}^n{\left|a_{ij}\right|}^2\right)}^{1/2}$	(the Frobenius norm of $A$), or
${max}_{i,j}\left(\left|a_{ij}\right|\right)$	(the maximum absolute element value of $A$).

$A$ is stored in compact form using the RFP format. The RFP storage format is described in the F07 Introduction.

References

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

Gustavson, F G, Waśniewski, J, Dongarra, J J and Langou, J, 2010, Rectangular full packed format for Cholesky’s algorithm: factorization, solution, and inversion, ACM Trans. Math. Software (37, 2)