DEFINITION MODULE CanCor;
(*******************************************************************
Module CanCor (Version 1.0)
Copyright (c) 1993-2006 by Dimitrios Gyalistras and ETH Zurich.
Purpose Perform Canonical Correlation Analysis (CCA)
of two data matrices in the sub-spaces spanned
by their empirical orthogonal functions (EOFs).
Remarks Requires input data as calculated by means of
procedure PrinComp.MakePCA.
Programming
o Design
Dimitrios Gyalistras 27/07/1993
o Implementation
Dimitrios Gyalistras 27/07/1993
ETH Zurich
Systems Ecology
CHN E 35.1
Universitaetstrasse 16
8092 Zurich
SWITZERLAND
URLs:
<mailto:RAMSES@env.ethz.ch>
<http://www.sysecol.ethz.ch>
<http://www.sysecol.ethz.ch/SimSoftware/RAMSES>
Last revision of definition: 24/05/2002 AF
*******************************************************************)
FROM DMFiles IMPORT TextFile;
IMPORT Errors;
FROM LgMatrices IMPORT LMatrix, LVector;
FROM PrinComp IMPORT WeightingType;
(******************************************************************)
CONST (* result codes returned *)
allOk = Errors.allOk;
notDone = Errors.onlyAnInsert;
CONST (* types of matrices supported *)
ccCoeffSqMatType = 201; (* squared canonical correlation coefficients *)
tvxXMatType = 202; (* X total variances explained by canonical modes *)
tvxYMatType = 203; (* Y total variances explained by canonical modes *)
mapXMatType = 210; (* X canonical maps *)
lvxXMatType = 211; (* X local variances explained by canonical modes *)
cmpXMatType = 212; (* X components of canonical modes *)
mapYMatType = 220; (* Y canonical maps *)
lvxYMatType = 221; (* Y local variances explained by canonical modes *)
cmpYMatType = 222; (* Y components of canonical modes *)
xEstCmpMatType = 230; (* X estimated components from CCA model application *)
yEstMatType = 231; (* Y estimated variables from CCA model application *)
yCrossVldMatType = 232; (* Y estimated variables from CCA model cross-validation *)
(*
Note: the dimensions of all LVector and LMatrix objects used below
are determined automatically via procedures LgMatrices.NElems,
LgMatrices.NRows and LgMatrices.NCols.
*)
(*********************************)
(*##### Main procedures #####*)
(*********************************)
PROCEDURE MakeCCA(
(* in: input data sets and their means *)
xDat : LMatrix;
yDat : LMatrix;
(* in, or in/out: numbers of EOFs to use *)
VAR nXEofs : INTEGER; (* if = 0, minXCumulV or maxXEigValREB is considered *)
VAR nYEofs : INTEGER; (* if = 0, minYCumulV or maxYEigValREB is considered *)
(* in: criteria used to automatically determine number of EOFs (used only if n*Eofs=0) *)
minXCumulV : LONGREAL; (* if undefined or = 0, maxXEigValREB is considered *)
minYCumulV : LONGREAL; (* if undefined or = 0, maxYEigValREB is considered *)
maxXEigValREB : LONGREAL;
maxYEigValREB : LONGREAL;
(* in: results of PC analyses (see module PrinComp) *)
muX : LMatrix; (* 1 x NCols(X) *)
wghtX : LMatrix; (* 1 x NCols(X) *)
eigValX : LMatrix; (* 1 x NEofs(X) *)
pcX : LMatrix; (* NRows(X) x NCols(X) *)
muY : LMatrix; (* 1 x NCols(Y) *)
wghtY : LMatrix; (* 1 x NCols(Y) *)
eigValY : LMatrix; (* 1 x NEofs(Y) *)
pcY : LMatrix; (* NRows(Y) x NCols(Y) *)
(* out: results of CCA *)
ccCoeffSq : LMatrix; (* 1 x NCCCoeffs *)
mapX : LMatrix; (* NCCCoeffs x NCols(X) *)
cmpX : LMatrix; (* NRows(X) x NCols(X) *)
tvxX : LMatrix; (* 1 x NCols(X) *)
lvxX : LMatrix; (* NCCCoeffs x NCols(X) *)
mapY : LMatrix; (* NCCCoeffs x NCols(Y) *)
cmpY : LMatrix; (* NRows(Y) x NCols(Y) *)
tvxY : LMatrix; (* 1 x NCols(Y) *)
lvxY : LMatrix; (* NCCCoeffs x NCols(Y) *)
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
PROCEDURE ApplyCCA(
(* in: independent data *)
xDat : LMatrix;
areAnomalies : BOOLEAN; (* if FALSE, X data are converted to anomalies first *)
(* in, or in/out: specification of canonical modes to use *)
VAR nCanModes : INTEGER; (* if = 0, taken are all modes for which ccCoeffSq is above ccCfSqTrshld *)
ccCfSqTrshld : LONGREAL; (* considered only if nCanModes = 0 *)
(* in: CCA model parameters *)
ccCoeffSq : LMatrix;
muX : LMatrix;
wghtX : LMatrix;
mapX : LMatrix;
muY : LMatrix;
wghtY : LMatrix;
mapY : LMatrix;
(* out: estimated components and y-values *)
xEstCmp : LMatrix;
yEst : LMatrix;
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
TYPE
PCAResultsProc = PROCEDURE ( (* resultNr *) INTEGER,
VAR (* mu *) LMatrix,
VAR (* wght *) LMatrix,
VAR (* eigVal *) LMatrix,
VAR (* pcX *) LMatrix,
VAR (* resCode *) INTEGER,
VAR (* errTxt *) ARRAY OF CHAR );
PROCEDURE EmptyPCAResultsProc( resultNr : INTEGER;
VAR mu : LMatrix;
VAR wght : LMatrix;
VAR eigVal : LMatrix;
VAR pc : LMatrix;
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
PROCEDURE CrossValidCCA(
(* in: independent data *)
xDat : LMatrix;
yDat : LMatrix;
xWType : WeightingType;
yWType : WeightingType;
(* in, or in/out: numbers of EOFs to use *)
VAR nXEofs : INTEGER; (* if = 0, minXCumulV or maxXEigValREB is considered *)
VAR nYEofs : INTEGER; (* if = 0, minYCumulV or maxYEigValREB is considered *)
(* in: criteria used to automatically determine number of EOFs (used only if n*Eofs=0) *)
minXCumulV : LONGREAL; (* if undefined or = 0, maxXEigValREB is considered *)
minYCumulV : LONGREAL; (* if undefined or = 0, maxYEigValREB is considered *)
maxXEigValREB : LONGREAL;
maxYEigValREB : LONGREAL;
(* in: procedures for geting pre-calculated eofs *)
getXPCAResults : PCAResultsProc;
getYPCAResults : PCAResultsProc;
(* in: specification of canonical modes to use *)
nCanModes : INTEGER; (* if = 0, taken are all modes for which ccCoeffSq is above ccCfSqTrshld *)
ccCfSqTrshld : LONGREAL; (* considered only if nCanModes = 0 *)
(* in: procedure called to signify progress report *)
progrReport : PROC;
(* out: results from cross-validation *)
yCrossVld : LMatrix;
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
(**************************)
(*##### Auxilary #####*)
(**************************)
PROCEDURE InDataMatsOK( xDat : LMatrix;
yDat : LMatrix;
xGenericDescr : ARRAY OF CHAR; (* used if xDat has no descriptor attached to it *)
yGenericDescr : ARRAY OF CHAR; (* used if yDat has no descriptor attached to it *)
callee : ARRAY OF CHAR;
VAR errTxt : ARRAY OF CHAR ): BOOLEAN;
PROCEDURE NCanModesOK( ccCoeffSq : LMatrix;
nCanModes : INTEGER;
genericDescr : ARRAY OF CHAR; (* used if ccCoeffSq has no descriptor attached to it *)
callee : ARRAY OF CHAR;
VAR errTxt : ARRAY OF CHAR ): BOOLEAN;
PROCEDURE GetNumCanModes( ccCoeffSq : LMatrix;
ccCfSqTrshld : LONGREAL;
VAR nCanModes : INTEGER;
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
(*
Returns the number of canonical modes for which ccCoeffSq is above ccCfSqTrshld.
*)
PROCEDURE AllocCCAResVars( nXEofs : INTEGER;
nYEofs : INTEGER;
xDat : LMatrix;
yDat : LMatrix;
VAR ccCoeffSq : LMatrix;
VAR mapX, cmpX, tvxX, lvxX : LMatrix;
VAR mapY, cmpY, tvxY, lvxY : LMatrix;
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
PROCEDURE DeallocCCAResVars( VAR ccCoeffSq : LMatrix;
VAR mapX, cmpX, tvxX, lvxX : LMatrix;
VAR mapY, cmpY, tvxY, lvxY : LMatrix );
(************************************)
(*##### I/O of CCA results #####*)
(************************************)
PROCEDURE WriteCCAResults( VAR outF : TextFile;
(* main results *)
wrCcCoeffSq : BOOLEAN; ccCoeffSq : LMatrix;
wrTvxX : BOOLEAN; tvxX : LMatrix;
wrTvxY : BOOLEAN; tvxY : LMatrix;
(* X model parameters *)
wrMuX : BOOLEAN; muX : LMatrix;
wrWghtX : BOOLEAN; wghtX : LMatrix;
wrMapX : BOOLEAN; mapX : LMatrix;
(* Y model parameters *)
wrMuY : BOOLEAN; muY : LMatrix;
wrWghtY : BOOLEAN; wghtY : LMatrix;
wrMapY : BOOLEAN; mapY : LMatrix;
(* X local explained variances and components *)
wrLvxX : BOOLEAN; lvxX : LMatrix;
wrCmpX : BOOLEAN; cmpX : LMatrix;
(* Y local explained variances and components *)
wrLvxY : BOOLEAN; lvxY : LMatrix;
wrCmpY : BOOLEAN; cmpY : LMatrix;
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
PROCEDURE ReadCCAResults( inFName : ARRAY OF CHAR;
tryOpenFile : BOOLEAN;
keepFileOpen : BOOLEAN;
(* main results *)
rdCcCoeffSq : BOOLEAN; VAR ccCoeffSq : LMatrix;
rdTvxX : BOOLEAN; VAR tvxX : LMatrix;
rdTvxY : BOOLEAN; VAR tvxY : LMatrix;
(* X model parameters *)
rdMuX : BOOLEAN; VAR muX : LMatrix;
rdWghtX : BOOLEAN; VAR wghtX : LMatrix;
rdMapX : BOOLEAN; VAR mapX : LMatrix;
(* Y model parameters *)
rdMuY : BOOLEAN; VAR muY : LMatrix;
rdWghtY : BOOLEAN; VAR wghtY : LMatrix;
rdMapY : BOOLEAN; VAR mapY : LMatrix;
(* X local explained variances and components *)
rdLvxX : BOOLEAN; VAR lvxX : LMatrix;
rdCmpX : BOOLEAN; VAR cmpX : LMatrix;
(* Y local explained variances and components *)
rdLvxY : BOOLEAN; VAR lvxY : LMatrix;
rdCmpY : BOOLEAN; VAR cmpY : LMatrix;
VAR endOfFile : BOOLEAN;
VAR resCode : INTEGER;
VAR errTxt : ARRAY OF CHAR );
END CanCor.
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