Norm Class Reference

Norm: Static class for commonly used norms on sets of vectors. More...

Detailed Description

Norm: Static class for commonly used norms on sets of vectors.

All norm functions perform their respective computations on each column of a given matrix!

Author

Daniel Wirtz

Date

2012-03-29

New in 0.6:

(Daniel Wirtz, 2012-03-29) Added this class.

This class is part of the framework

KerMor - Model Order Reduction using Kernels

• Homepage http://www.morepas.org/software/index.html
• Documentation http://www.morepas.org/software/kermor/index.html
• License KerMor license conditions

Definition at line 17 of file Norm.m.

Static Public Member Functions
static function rowvec < double > n =	L2 (matrix< double > x)
	Returns the discrete \(L^2\) norm for each column vector in x. More...
static function vecs =	normalizeL2 (vecs)
static function rowvec < double > n =	L1 (matrix< double > x)
	Returns the discrete \(L^1\) norm for each column vector in x. More...
static function rowvec < double > n =	Linf (matrix< double > x)
	Returns the discrete \(L^\infty\) norm for each column vector in x. More...
static function rowvec < double > n =	LG (matrix< double > x, G)
	Returns the \(\vG\)-induced norm for each column vector in \(\vX\). More...

Member Function Documentation

function rowvec< double > n = Norm.L1 ( matrix< double >  x )

static

Returns the discrete \(L^1\) norm for each column vector in x.

Parameters

x	A matrix \(\vX\) containing column vectors \(\vx_i\)

Return values

n	The \(L^1\) norm \(\norm{\vx}{1} = \sum\limits_{i=1}^d|x_i|\) for each column vector \(\vx\in\R^d\) in \(\vX\)

Definition at line 59 of file Norm.m.

Referenced by data.ApproxTrainData.getErrorsFor().

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function rowvec< double > n = Norm.L2 ( matrix< double >  x )

static

Returns the discrete \(L^2\) norm for each column vector in x.

Parameters

x	A matrix \(\vX\) containing column vectors \(\vx_i\)

Return values

n	The \(L^2\) norm \(\norm{\vx}{2} = \sqrt{\sum\limits_{i=1}^dx_i^2}\) for each column vector \(\vx\in\R^d\) in \(\vX\)

Definition at line 39 of file Norm.m.

Referenced by ModelAnalyzer.analyzeError(), testing.DEIM.compareDEIM_Full_Jacobian(), ModelAnalyzer.compareRedFull(), testing.DEIM.computeDEIMErrors(), testing.DEIM.effectivityAnalysis(), models.muscle.AMuscleConfig.geta0(), testing.DEIM.getApproxErrorFullRed(), ModelAnalyzer.getATDError(), testing.DEIM.getDEIMErrorsAtXForParams_plots(), testing.DEIM.getDEIMReducedModelErrors(), data.ApproxTrainData.getErrorsFor(), ModelAnalyzer.getRedErrForParamSamples(), ModelAnalyzer.getTrajApproxError(), testing.DEIM.getTrajApproxErrorDEIMEstimates(), Utils.getTube(), models.motorunit.experiments.InitialConditions(), general.interpolation.KernelInterpol.interpolate(), demos.VKOGA.IterationPlots(), testing.Speed.KernelExpCustomBaseEval(), DEIMEstimatorAnalyzer>pushbutton5_Callback(), DEIMEstimatorAnalyzer>rePlot(), normalizeL2(), ParamSweep(), error.DefaultEstimator.postProcess(), approx.BaseApprox.test_ApproxProjections(), testing.DEIM.test_DEIMNoSpatialDependence(), sampling.RandomSampler.test_DomainSampling(), data.FileMatrix.test_Times_MTimes(), Utils.test_Tube(), approx.TPWLApprox.test_TWPLApprox(), and models.muscle.System.test_UnassembledEvaluation().

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function rowvec< double > n = Norm.LG ( matrix< double >  x,   G  )

static

Returns the \(\vG\)-induced norm for each column vector in \(\vX\).

Parameters

x	A matrix \(\vX\) containing column vectors \(\vx_i\)
G	A positive definite matrix \(\vG\)

Return values

n	The G-norm \(\noG{\vx} = \sqrt{\vx^T\vG\vx}\) for each column vector \(\vx\) in \(\vX\)

Definition at line 87 of file Norm.m.

Referenced by error.DEIMEstimator.getAlpha(), error.initial.AffineParametric.getE0(), error.DefaultEstimator.postProcess(), and error.initial.Constant.prepareForReducedModel().

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function rowvec< double > n = Norm.Linf ( matrix< double >  x )

static

Returns the discrete \(L^\infty\) norm for each column vector in x.

Parameters

x	A matrix \(\vX\) containing column vectors \(\vx_i\)

Return values

n	The \(L^\infty\) norm \(\norm{\vx}{\infty} = \max\limits_{i=1}^d|x_i|\) for each column vector \(\vx\in\R^d\) in \(\vX\)

Definition at line 73 of file Norm.m.

Referenced by ModelAnalyzer.compareRedFull(), ModelAnalyzer.getATDError(), ModelAnalyzer.getRedErrForParamSamples(), ModelAnalyzer.getTrajApproxError(), and models.motorunit.experiments.InitialConditions().

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static function vecs = Norm.normalizeL2 (   vecs )

static

Definition at line 53 of file Norm.m.

References L2(), and t.

Referenced by fem.BaseFEM.init().

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The documentation for this class was generated from the following file:

• core/tools/Norm.m