Mcr

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Contents 1 Purpose 2 Synopsis 3 Description 3.1 Inputs 3.2 Outputs 4 Options 5 See Also

Purpose

Multivariate curve resolution with constraints.

Synopsis

model = mcr(x,ncomp,options)  %calibrate

model = mcr(x,c0,options)  %calibrate with explict initial guess

pred = mcr(x,model,options)  %predict

Description

MCR decomposes a matrix X as CS such that X = CS + E where E is minimized in a least squares sense. By default, this is done using the alternating least squares (ALS) algorithm. For details on the ALS algorithm and constraints available in MCR, see the als reference page.

When called with new data and a model structure, MCR performs a prediction (applies the model to the new data) returning the projection of the new data onto the previously recovered loadings (i.e. estimated spectra).

Inputs

• x = the matrix to be decomposed (size m by n)
• ncomp or c0 or model :
  • ncomp = the number of components to extract
  • c0 = the explicit initial guess where, if c0 is size m by k, where k is the number of factors, then it is assumed to be the initial guess for C. If c0 is size k by n then it is assumed to be the initial guess for S. If m=n then, c0 is assumed to be the initial guess for C. Optional input options is described below.
  • model = a previously calculated MCR model structure to apply to the data in input x.

Outputs

• model = a standard model structure containing the results of the analysis. The estimated contributions C are stored in model.loads{2} and the estimated spectra S in model.loads{1}. Sum-squared residuals for samples and variables can be found in model.ssqresiduals{1} and model.ssqresiduals{2}, respectively. See the chemometrics tutorial for more information on the MCR method and models. Note that the sum-squared captured table contains various statistics on the information captured by each component. Please see MCR and PARAFAC Variance Captured for details.

Options

• options = a structure array with the following fields:

• display: [ 'off' | {'on'} ] governs level of display to command window.

• plots: [ 'none' | {'final'} ] governs level of plotting.

• preprocessing: { [] } preprocessing to apply to x-block (see PREPROCESS).

• blockdetails: [ 'compact' | {'standard'} | 'all' ] Extent of predictions and raw residuals included in model. 'standard' = none, 'all' x-block.

• confidencelimit: [{0.95}] Confidence level for Q limits.

• alsoptions: ['options'] options passed to ALS subroutine (see ALS).

The default options can be retreived using: options = mcr('options');.

See Also

als, analysis, evolvfa, ewfa, fasternnls, fastnnls, fastnnls_sel, mlpca, parafac, plotloads, preprocess