-
Christian Beckmann authoredChristian Beckmann authored
melhlprfns.cc 28.32 KiB
/* MELODIC - Multivariate exploratory linear optimized decomposition into
independent components
melhlprfns.cc - misc functions
Christian F. Beckmann, FMRIB Image Analysis Group
Copyright (C) 1999-2008 University of Oxford */
/* Part of FSL - FMRIB's Software Library
http://www.fmrib.ox.ac.uk/fsl
fsl@fmrib.ox.ac.uk
Developed at FMRIB (Oxford Centre for Functional Magnetic Resonance
Imaging of the Brain), Department of Clinical Neurology, Oxford
University, Oxford, UK
LICENCE
FMRIB Software Library, Release 4.0 (c) 2007, The University of
Oxford (the "Software")
The Software remains the property of the University of Oxford ("the
University").
The Software is distributed "AS IS" under this Licence solely for
non-commercial use in the hope that it will be useful, but in order
that the University as a charitable foundation protects its assets for
the benefit of its educational and research purposes, the University
makes clear that no condition is made or to be implied, nor is any
warranty given or to be implied, as to the accuracy of the Software,
or that it will be suitable for any particular purpose or for use
under any specific conditions. Furthermore, the University disclaims
all responsibility for the use which is made of the Software. It
further disclaims any liability for the outcomes arising from using
the Software.
The Licensee agrees to indemnify the University and hold the
University harmless from and against any and all claims, damages and
liabilities asserted by third parties (including claims for
negligence) which arise directly or indirectly from the use of the
Software or the sale of any products based on the Software.
No part of the Software may be reproduced, modified, transmitted or
transferred in any form or by any means, electronic or mechanical,
without the express permission of the University. The permission of
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conditions of this Licence are imposed upon the receiver of the
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abide by these terms and conditions.
You are not permitted under this Licence to use this Software
commercially. Use for which any financial return is received shall be
defined as commercial use, and includes (1) integration of all or part
of the source code or the Software into a product for sale or license
by or on behalf of Licensee to third parties or (2) use of the
Software or any derivative of it for research with the final aim of
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(3) use of the Software or any derivative of it for research with the
final aim of developing non-software products for sale or license to a
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innovation@isis.ox.ac.uk quoting reference DE/1112. */
#include "melhlprfns.h"
#include "libprob.h"
#include "miscmaths/miscprob.h"
#include "miscmaths/t2z.h"
#include "miscmaths/f2z.h"
namespace Melodic{
void update_mask(volume<float>& mask, Matrix& Data)
{
Matrix DStDev=stdev(Data);
volume4D<float> tmpMask, RawData;
tmpMask.setmatrix(DStDev,mask);
RawData.setmatrix(Data,mask);
float tMmax;
volume<float> tmpMask2;
tmpMask2 = tmpMask[0];
tMmax = tmpMask2.max();
double st_mean = DStDev.Sum()/DStDev.Ncols();
double st_std = stdev(DStDev.t()).AsScalar();
mask = binarise(tmpMask2,(float) max((float) st_mean-3*st_std,(float) 0.01*st_mean),tMmax);
Data = RawData.matrix(mask);
}
void del_vols(volume4D<float>& in, int howmany)
{
for(int ctr=1; ctr<=howmany; ctr++){
in.deletevolume(ctr);
}
}
Matrix calc_FFT(const Matrix& Mat, const bool logpwr)
{
Matrix res;
for(int ctr=1; ctr <= Mat.Ncols(); ctr++){
ColumnVector tmpCol;
tmpCol=Mat.Column(ctr);
ColumnVector FtmpCol_real;
ColumnVector FtmpCol_imag;
ColumnVector tmpPow;
if(tmpCol.Nrows()%2 != 0){
Matrix empty(1,1); empty=0;
tmpCol &= empty;
}
RealFFT(tmpCol,FtmpCol_real,FtmpCol_imag);
tmpPow = pow(FtmpCol_real,2)+pow(FtmpCol_imag,2);
tmpPow = tmpPow.Rows(2,tmpPow.Nrows());
if(logpwr) tmpPow = log(tmpPow);
if(res.Storage()==0){res= tmpPow;}else{res|=tmpPow;}
}
return res;
} //Matrix calc_FFT()
Matrix smoothColumns(const Matrix& inp)
{
Matrix temp(inp);
int ctr1 = temp.Nrows();
Matrix temp2(temp);
temp2=0;
temp = temp.Row(4) & temp.Row(3) & temp.Row(2) & temp & temp.Row(ctr1-1)
& temp.Row(ctr1-2) &temp.Row(ctr1-3);
double kern[] ={0.0045 , 0.055, 0.25, 0.4, 0.25, 0.055, 0.0045};
double fac = 0.9090909;
for(int cc=1;cc<=temp2.Ncols();cc++){
for(int cr=1;cr<=temp2.Nrows();cr++){
temp2(cr,cc) = fac*( kern[0] * temp(cr,cc) + kern[1] * temp(cr+1,cc) +
kern[2] * temp(cr+2,cc) + kern[3] * temp(cr+3,cc) +
kern[4] * temp(cr+4,cc) + kern[5] * temp(cr+5,cc) +
kern[6] * temp(cr+6,cc));
}
}
return temp2;
} //Matrix smoothColumns()
Matrix convert_to_pbsc(Matrix& inp)
{
Matrix meanimg;
meanimg = mean(inp);
float eps = 0.00001;
for(int ctr=1; ctr <= inp.Ncols(); ctr++){
if(meanimg(1,ctr) < eps)
meanimg(1,ctr) = eps;
}
for(int ctr=1; ctr <= inp.Nrows(); ctr++){
Matrix tmp;
tmp << inp.Row(ctr);
inp.Row(ctr) << 100 * SP((tmp - meanimg),pow(meanimg,-1));
}
inp = remmean(inp);
return meanimg;
} //void convert_to_pbsc
RowVector varnorm(Matrix& in, int dim, float level)
{
Matrix Corr;
Corr = calc_corr(in);
RowVector out;
out = varnorm(in,Corr,dim,level);
return out;
} //RowVector varnorm
void varnorm(Matrix& in, const RowVector& vars)
{
Matrix tmp = vars;
in = SP(in,pow(ones(in.Nrows(),1) * tmp,-1));
}
RowVector varnorm(Matrix& in, Matrix& Corr, int dim, float level)
{
Matrix tmpE, white, dewhite;
RowVector tmpD, tmpD2;
std_pca(remmean(in,2), Corr, tmpE, tmpD);
calc_white(tmpE,tmpD, dim, white, dewhite);
Matrix ws = white * in;
for(int ctr1 = 1; ctr1<=ws.Ncols(); ctr1++)
for(int ctr2 = 1; ctr2<=ws.Nrows(); ctr2++)
if(std::abs(ws(ctr2,ctr1)) < level)
ws(ctr2,ctr1)=0;
tmpD = stdev(in - dewhite*ws);
for(int ctr1 = 1; ctr1<=tmpD.Ncols(); ctr1++)
if(tmpD(ctr1) < 0.01){
tmpD(ctr1) = 1.0;
in.Column(ctr1) = 0.0*in.Column(ctr1);
}
varnorm(in,tmpD);
return tmpD; } //RowVector varnorm
Matrix SP2(const Matrix& in, const Matrix& weights, bool econ)
{
Matrix Res;
Res = in;
if(econ){
ColumnVector tmp;
for(int ctr=1; ctr <= in.Ncols(); ctr++){
tmp = in.Column(ctr);
tmp = tmp * weights(1,ctr);
Res.Column(ctr) = tmp;
}
}
else{
Res = ones(in.Nrows(),1)*weights.Row(1);
Res = SP(in,Res);
}
return Res;
} //Matrix SP
Matrix corrcoef(const Matrix& in1, const Matrix& in2){
Matrix tmp = in1;
tmp |= in2;
Matrix out;
out=MISCMATHS::corrcoef(tmp,0);
return out.SubMatrix(1,in1.Ncols(),in1.Ncols()+1,out.Ncols());
}
Matrix corrcoef(const Matrix& in1, const Matrix& in2, const Matrix& part){
Matrix tmp1 = in1, tmp2 = in2, out;
if(part.Storage()){
tmp1 = tmp1 - part * pinv(part) * tmp1;
tmp2 = tmp2 - part * pinv(part) * tmp2;
}
out = corrcoef(tmp1,tmp2);
return out;
}
Matrix calc_corr(const Matrix& in, bool econ)
{
Matrix Res;
Res = zeros(in.Nrows(),in.Nrows());
if(econ){
ColumnVector tmp;
for(int ctr=1; ctr <= in.Ncols(); ctr++){
tmp = in.Column(ctr);
tmp = tmp - mean(tmp).AsScalar();
Res += (tmp * tmp.t()) / in.Ncols();
}
}
else
Res = cov(in.t());
return Res;
} //Matrix calc_corr
Matrix calc_corr(const Matrix& in, const Matrix& weights, bool econ)
{
Matrix Res;
Res = zeros(in.Nrows(),in.Nrows());
Matrix localweights;
if(weights.Storage() == 0)
localweights = ones(1,in.Ncols());
else
localweights = weights;
if(econ){
ColumnVector tmp;
for(int ctr=1; ctr <= in.Ncols(); ctr++){
tmp = in.Column(ctr); tmp = tmp - mean(tmp).AsScalar();
tmp = tmp * localweights(1,ctr);
Res += (tmp * tmp.t()) / in.Ncols();
}
}
else{
Res = SP2(in,localweights);
Res = calc_corr(Res, 0);
}
return Res;
} //Matrix calc_corr
float calc_white(const Matrix& tmpE, const RowVector& tmpD, const RowVector& PercEV, int dim, Matrix& param, Matrix& paramS, Matrix& white, Matrix& dewhite)
{
// tmpD2= tmpD | tmpPD.AsRow().Columns(tmpPE.Ncols()-param.Ncols()+1,tmpPE.Ncols());
// cerr << tmpPD.AsRow().Columns(tmpPE.Ncols()-param.Ncols()+1,tmpPE.Ncols()) << endl;
//
// Matrix tmpPE;
// tmpPE = SP(param,ones(param.Nrows(),1)*pow(stdev(param,1)*std::sqrt((float)param.Nrows()),-1));
// RE |= tmpPE;
// RowVector tmpD2;
// tmpD2 = tmpD | stdev(param,1).AsRow()*std::sqrt((float)param.Nrows());
// RD << abs(diag(tmpD2.t()));
// RD << RD.SymSubMatrix(N-dim+1,N);
Matrix RE;
DiagonalMatrix RD;
int N = tmpE.Ncols();
dim = std::min(dim,N);
// cerr << stdev(param) << endl;
RE = tmpE.Columns(std::min(N-dim+1+param.Ncols(),N-2),N);
RE |= param;
// cerr << paramS.Nrows() << " x " << paramS.Ncols() << endl;
// cerr << paramS << endl;
RowVector tmpD2;
tmpD2 = tmpD | pow(paramS,2).AsRow();
RD << abs(diag(tmpD2.t()));
// cerr << " " <<tmpD2.Ncols() << " " << N << " " << dim << endl;
RD << RD.SymSubMatrix(N-dim+1+param.Ncols(),N+param.Ncols());
float res = 1.0;
white = sqrt(abs(RD.i()))*RE.t();
dewhite = RE*sqrt(RD);
if(dim < N)
res = PercEV(dim);
return res;
} //Matrix calc_white
float calc_white(const Matrix& tmpE, const RowVector& tmpD, const RowVector& PercEV, int dim, Matrix& white, Matrix& dewhite)
{
Matrix RE;
DiagonalMatrix RD;
int N = tmpE.Ncols();
dim = std::min(dim,N);
RE = tmpE.Columns(N-dim+1,N);
RD << abs(diag(tmpD.t()));
RD << RD.SymSubMatrix(N-dim+1,N);
float res = 1.0;
white = sqrt(abs(RD.i()))*RE.t();
dewhite = RE*sqrt(RD);
if(dim < N)
res = PercEV(dim);
return res;
} //Matrix calc_white
void calc_white(const Matrix& tmpE, const RowVector& tmpD, int dim, Matrix& white, Matrix& dewhite)
{
RowVector tmp(tmpE.Ncols());
float tmp2;
tmp2 = calc_white(tmpE,tmpD, tmp, dim, white, dewhite);
} //Matrix calc_white
void calc_white(const Matrix& tmpE, const RowVector& tmpD, int dim, Matrix& param, Matrix& paramS, Matrix& white, Matrix& dewhite)
{
RowVector tmp(tmpE.Ncols());
float tmp2;
tmp2 = calc_white(tmpE,tmpD, tmp, dim, param, paramS, white, dewhite);
} //Matrix calc_white
void calc_white(const Matrix& Corr, int dim, Matrix& white, Matrix& dewhite)
{
Matrix RE;
DiagonalMatrix RD;
SymmetricMatrix tmp;
RowVector tmp2;
tmp << Corr;
EigenValues(tmp,RD,RE);
tmp2 = diag(RD).t();
calc_white(RE,tmp2, dim, white, dewhite);
} //Matrix calc_white
void std_pca(const Matrix& Mat, const Matrix& weights, Matrix& Corr, Matrix& evecs, RowVector& evals)
{
if(weights.Storage()>0)
Corr << calc_corr(Mat, weights);
else
Corr << calc_corr(Mat);
SymmetricMatrix tmp;
tmp << Corr;
DiagonalMatrix tmpD;
EigenValues(tmp,tmpD,evecs);
evals = tmpD.AsRow();
} //void std_pca
void std_pca(const Matrix& Mat, Matrix& Corr, Matrix& evecs, RowVector& evals)
{
Matrix weights;
std_pca(Mat,weights,Corr,evecs,evals);
} //void std_pca
void em_pca(const Matrix& Mat, Matrix& evecs, RowVector& evals, int num_pc, int iter)
{
Matrix guess;
guess = normrnd(Mat.Nrows(),num_pc);
em_pca(Mat,guess,evecs,evals,num_pc,iter);
} //void em_pca
void em_pca(const Matrix& Mat, Matrix& guess, Matrix& evecs, RowVector& evals, int num_pc, int iter)
{
Matrix C;
if(guess.Ncols() < num_pc){
C=normrnd(Mat.Nrows(),num_pc);
C.Columns(1,guess.Ncols()) = guess;
}
else
C = guess;
Matrix tmp, tmp2;
for(int ctr=1; ctr <= iter; ctr++){ // E-Step
tmp = C.t()*C;
tmp = tmp.i();
tmp = tmp * C.t();
tmp = tmp * Mat;
// M-Step
tmp2 = tmp * tmp.t();
tmp2 = tmp2.i();
tmp2 = Mat*tmp.t()*tmp2;
C = tmp2;
}
symm_orth(C);
Matrix Evc, tmpC;
RowVector Evl;
tmp = C.t() * Mat;
std_pca(tmp,tmpC,Evc,Evl);
evals = Evl;
evecs = C * Evc;
} //void em_pca
float rankapprox(const Matrix& Mat, Matrix& cols, Matrix& rows, int dim)
{
Matrix Corr, Evecs, tmpWM, tmpDWM, tmp;
RowVector Evals;
std_pca(Mat.t(), Corr, Evecs, Evals);
calc_white(Corr, dim, tmpWM, tmpDWM);
tmp = tmpWM * Mat.t();
cols = tmp.t();
rows << tmpDWM;
float res;
Evals=fliplr(Evals);
res = sum(Evals.Columns(1,dim),2).AsScalar()/sum(Evals,2).AsScalar()*100;
return res;
} // rankapprox
RowVector krfact(const Matrix& Mat, Matrix& cols, Matrix& rows)
{
Matrix out; RowVector res(Mat.Ncols());
for(int ctr1 = 1; ctr1 <= Mat.Ncols(); ctr1++){
Matrix tmpVals(cols.Nrows(),rows.Nrows());
for(int ctr2 = 1; ctr2 <= rows.Nrows(); ctr2++)
tmpVals.Column(ctr2) << Mat.SubMatrix(cols.Nrows() *
(ctr2 - 1) + 1,cols.Nrows()*ctr2 ,ctr1,ctr1);
Matrix tmpcols, tmprows;
res(ctr1) =rankapprox(tmpVals, tmpcols, tmprows);
cols.Column(ctr1) = tmpcols;
rows.Column(ctr1) = tmprows;
}
return res;
} // krfact
RowVector krfact(const Matrix& Mat, int colnum, Matrix& cols, Matrix& rows)
{
RowVector res;
cols = zeros(colnum,Mat.Ncols());
rows = zeros(int(Mat.Nrows() / colnum),Mat.Ncols());
res = krfact(Mat,cols,rows);
return res;
} // krfact
Matrix krprod(const Matrix& cols, const Matrix& rows)
{
Matrix out;
out = zeros(cols.Nrows()*rows.Nrows(),cols.Ncols());
for(int ctr1 = 1; ctr1 <= cols.Ncols(); ctr1++)
for(int ctr2 = 1; ctr2 <= rows.Nrows(); ctr2++)
{
out.SubMatrix(cols.Nrows()*(ctr2-1)+1,cols.Nrows()*ctr2,ctr1,ctr1) << cols.Column(ctr1) * rows(ctr2,ctr1); }
return out;
} // krprod
Matrix krapprox(const Matrix& Mat, int size_cols, int dim)
{
Matrix out, cols, rows;
out = zeros(Mat.Nrows(), Mat.Ncols());
cols = zeros(size_cols,Mat.Ncols());
rows = zeros(int(Mat.Nrows() / size_cols), Mat.Ncols());
krfact(Mat,cols,rows);
out = krprod(cols, rows);
return out;
} // krapprox
void adj_eigspec(const RowVector& in, RowVector& out1, RowVector& out2, RowVector& out3, int& out4, int num_vox, float resels)
{
RowVector AdjEV;
AdjEV << in.AsRow();
AdjEV = AdjEV.Columns(3,AdjEV.Ncols());
AdjEV = AdjEV.Reverse();
RowVector CircleLaw;
int NumVox = (int) floor(num_vox/(2.5*resels));
CircleLaw = Feta(int(AdjEV.Ncols()), NumVox);
for(int ctr=1;ctr<=CircleLaw.Ncols(); ctr++){
if(CircleLaw(ctr)<5*10e-10){CircleLaw(ctr) = 5*10e-10;}
}
/* float slope;
slope = CircleLaw.Columns(int(AdjEV.Ncols()/4),AdjEV.Ncols() -
int(AdjEV.Ncols()/4)).Sum() /
AdjEV.Columns(int(AdjEV.Ncols()/4),AdjEV.Ncols() -
int(AdjEV.Ncols()/4)).Sum();*/
RowVector PercEV(AdjEV);
PercEV = cumsum(AdjEV / sum(AdjEV,2).AsScalar());
AdjEV << SP(AdjEV,pow(CircleLaw.Columns(1,AdjEV.Ncols()),-1));
SortDescending(AdjEV);
int maxEV = 1;
float threshold = 0.98;
for(int ctr_i = 1; ctr_i < PercEV.Ncols(); ctr_i++){
if((PercEV(ctr_i)<threshold)&&(PercEV(ctr_i+1)>=threshold)){maxEV=ctr_i;}
}
if(maxEV<3){maxEV=PercEV.Ncols()/2;}
RowVector NewEV;
Matrix temp1;
temp1 = abs(AdjEV);
NewEV << temp1.SubMatrix(1,1,1,maxEV);
AdjEV = (AdjEV - min(AdjEV).AsScalar())/(max(AdjEV).AsScalar() - min(AdjEV).AsScalar());
out1 = AdjEV;
out2 = PercEV;
out3 = NewEV;
out4 = maxEV;
} //adj_eigspec
void adj_eigspec(const RowVector& in, RowVector& out1, RowVector& out2)
{
RowVector AdjEV, PercEV;
AdjEV = in.Reverse();
SortDescending(AdjEV);
PercEV = cumsum(AdjEV / sum(AdjEV,2).AsScalar()); AdjEV = (AdjEV - min(AdjEV).AsScalar())/(max(AdjEV).AsScalar() - min(AdjEV).AsScalar());
out1 = AdjEV;
out2 = PercEV;
} //adj_eigspec
RowVector Feta(int n1, int n2)
{
float nu = (float) n1/n2;
float bm = pow((1-sqrt(nu)),2.0);
float bp = pow((1+sqrt(nu)),2.0);
float lrange = 0.9*bm;
float urange = 1.1*bp;
RowVector eta(30*n1);
float rangestepsize = (urange - lrange) / eta.Ncols();
for(int ctr_i = 1; ctr_i <= eta.Ncols(); ctr_i++){
eta(ctr_i) = lrange + rangestepsize * (ctr_i);
}
RowVector teta(10*n1);
teta = 0;
float stepsize = (bp - bm) / teta.Ncols();
for(int ctr_i = 1; ctr_i <= teta.Ncols(); ctr_i++){
teta(ctr_i) = stepsize*(ctr_i);
}
RowVector feta(teta);
feta = SP(pow(2*M_PI*nu*(teta + bm),-1), pow(SP(teta, bp-bm-teta),0.5));
teta = teta + bm;
RowVector claw(eta);
claw = 0;
for(int ctr_i = 1; ctr_i <= eta.Ncols(); ctr_i++){
double tmpval = 0.0;
for(int ctr_j = 1; ctr_j <= teta.Ncols(); ctr_j++){
if(( double(teta(ctr_j))/double(eta(ctr_i)) )<1)
tmpval += feta(ctr_j);
}
claw(ctr_i) = n1*(1-stepsize*tmpval);
}
RowVector Res(n1); //invert the CDF
Res = 0;
for(int ctr_i = 1; ctr_i < eta.Ncols(); ctr_i++){ //Should this be <= instead of <?
if(floor(claw(ctr_i))>floor(claw(ctr_i+1))){
Res(int(floor(claw(ctr_i)))) = eta(ctr_i);
}
}
return Res;
} //RowVector Feta
RowVector cumsum(const RowVector& Inp)
{
UpperTriangularMatrix UT(Inp.Ncols());
UT=1.0;
RowVector Res;
Res = Inp * UT;
return Res;
} //RowVector cumsum
int ppca_dim(const Matrix& in, const Matrix& weights, Matrix& PPCA, RowVector& AdjEV, RowVector& PercEV, Matrix& Corr, Matrix& tmpE, RowVector &tmpD, float resels, string which)
{
std_pca(in,weights,Corr,tmpE,tmpD);
int maxEV = 1;
RowVector NewEV;
adj_eigspec(tmpD.AsRow(),AdjEV,PercEV,NewEV,maxEV,in.Ncols(),resels);
int res;
PPCA = ppca_est(NewEV, in.Ncols(),resels);
ColumnVector tmp = ppca_select(PPCA, res, maxEV, which);
PPCA = tmp | PPCA;
return res;
} //int ppca_dim
int ppca_dim(const Matrix& in, const Matrix& weights, Matrix& PPCA, RowVector& AdjEV, RowVector& PercEV, float resels, string which)
{
RowVector tmpD;
Matrix tmpE;
Matrix Corr;
int res = ppca_dim(in, weights, PPCA, AdjEV, PercEV, Corr, tmpE, tmpD, resels, which);
return res;
} //int ppca_dim
int ppca_dim(const Matrix& in, const Matrix& weights, float resels, string which)
{
ColumnVector PPCA;
RowVector AdjEV, PercEV;
int res = ppca_dim(in,weights,PPCA,AdjEV,PercEV,resels,which);
return res;
} //int ppca_dim
ColumnVector ppca_select(Matrix& PPCAest, int& dim, int maxEV, string which)
{
RowVector estimators(5);
estimators = 1.0;
for(int ctr=1; ctr<=PPCAest.Ncols(); ctr++){
PPCAest.Column(ctr) = (PPCAest.Column(ctr) -
min(PPCAest.Column(ctr)).AsScalar()) /
( max(PPCAest.Column(ctr)).AsScalar() -
min(PPCAest.Column(ctr)).AsScalar());
}
int ctr_i = 1;
while((ctr_i< PPCAest.Nrows()-1)&&
(PPCAest(ctr_i,2) < PPCAest(ctr_i+1,2))&&(ctr_i<maxEV))
{estimators(1)=ctr_i+1;ctr_i++;}
ctr_i = 1;
while((ctr_i< PPCAest.Nrows()-1)&&
(PPCAest(ctr_i,3) < PPCAest(ctr_i+1,3))&&(ctr_i<maxEV))
{estimators(2)=ctr_i+1;ctr_i++;}
ctr_i = 1;
while((ctr_i< PPCAest.Nrows()-1)&&
(PPCAest(ctr_i,4) < PPCAest(ctr_i+1,4))&&(ctr_i<maxEV))
{estimators(3)=ctr_i+1;ctr_i++;}
ctr_i = 1;
while((ctr_i< PPCAest.Nrows()-1)&&
(PPCAest(ctr_i,5) < PPCAest(ctr_i+1,5))&&(ctr_i<maxEV))
{estimators(4)=ctr_i+1;ctr_i++;}
ctr_i = 1;
while((ctr_i< PPCAest.Nrows()-1)&&
(PPCAest(ctr_i,6) < PPCAest(ctr_i+1,6))&&(ctr_i<maxEV))
{estimators(5)=ctr_i+1;ctr_i++;}
int res = 0;
ColumnVector PPCA;
RowVector PercEV(PPCAest.Column(1).t());
PercEV = cumsum(PercEV / sum(PercEV,2).AsScalar());
if(which == string("aut"))
if(int(estimators(2)) < int(estimators(1)) &&
float(PercEV(int(estimators(2))))>0.8){
res=int(estimators(2));
PPCA << PPCAest.Column(3); }else{
res = int(estimators(1));
PPCA << PPCAest.Column(2);
}
if(which == string("lap")){
res = int(estimators(1));
PPCA << PPCAest.Column(2);
}
if(which == string("bic")){
res = int(estimators(2));
PPCA << PPCAest.Column(3);
}
if(which == string("mdl")){
res = int(estimators(3));
PPCA << PPCAest.Column(4);
}
if(which == string("rrn")){
res = int(estimators(4));
PPCA << PPCAest.Column(5);
}
if(which == string("aic")){
res = int(estimators(5));
PPCA << PPCAest.Column(6);
}
if(which == string("median")){
RowVector unsorted(estimators);
SortAscending(unsorted);
ctr_i=1;
res=int(unsorted(3));
while(res != int(estimators(ctr_i)))
ctr_i++;
PPCA << PPCAest.Column(ctr_i);
}
if(res==0 || which == string("mean")){//median estimator
PPCA = mean(PPCAest.Columns(2,6),2);
res=int(mean(estimators,2).AsScalar());
}
dim = res;
return PPCA;
} //RowVector ppca_select
Matrix ppca_est(const RowVector& eigenvalues, const int N1, const float N2)
{
Matrix Res;
Res = ppca_est(eigenvalues, (int) floor(N1/(2.5*N2)));
return Res;
} //Matrix ppca_est
Matrix ppca_est(const RowVector& eigenvalues, const int N)
{
RowVector logLambda(eigenvalues);
logLambda = log(eigenvalues);
int d = logLambda.Ncols();
RowVector k(d);
for(int ctr_i = 1; ctr_i <=d; ctr_i++){
k(ctr_i)=ctr_i;
}
RowVector m(d);
m=d*k-0.5*SP(k,k+1);
RowVector loggam(d);
loggam = 0.5*k.Reverse();
for(int ctr_i = 1; ctr_i <=d; ctr_i++){
loggam(ctr_i)=lgam(loggam(ctr_i));
}
loggam = cumsum(loggam);
RowVector l_probU(d);
l_probU = -log(2)*k + loggam - cumsum(0.5*log(M_PI)*k.Reverse());
RowVector tmp1;
tmp1 = -cumsum(eigenvalues).Reverse()+sum(eigenvalues,2).AsScalar();
tmp1(1) = 0.95*tmp1(2);
tmp1=tmp1.Reverse();
RowVector tmp2;
tmp2 = -cumsum(logLambda).Reverse()+sum(logLambda,2).AsScalar();
tmp2(1)=tmp2(2);
tmp2=tmp2.Reverse();
RowVector tmp3;
tmp3 = d-k;
tmp3(d) = 1.0;
RowVector tmp4;
tmp4 = SP(tmp1,pow(tmp3,-1));
for(int ctr_i = 1; ctr_i <=d; ctr_i++){
if(tmp4(ctr_i)<0.01){tmp4(ctr_i)=0.01;}
if(tmp3(ctr_i)<0.01){tmp3(ctr_i)=0.01;}
if(tmp1(ctr_i)<0.01){tmp1(ctr_i)=0.01;}
}
RowVector l_nu;
l_nu = SP(-N/2*(d-k),log(tmp4));
l_nu(d) = 0;
RowVector l_lam;
l_lam = -(N/2)*cumsum(logLambda);
RowVector l_lhood;
l_lhood = SP(pow(tmp3,-1),tmp2)-log(SP(pow(tmp3,-1),tmp1));
Matrix t1,t2, t3;
UpperTriangularMatrix triu(d);
triu = 1.0;
for(int ctr_i = 1; ctr_i <= triu.Ncols(); ctr_i++){
triu(ctr_i,ctr_i)=0.0;
}
t1 = (ones(d,1) * eigenvalues);
t1 = SP(triu,t1.t() - t1);
t2 = pow(tmp4,-1).t()*ones(1,d);
t3 = ones(d,1)*pow(eigenvalues,-1);
t2 = SP(triu, t2.t()-t3.t());
for(int ctr_i = 1; ctr_i <= t1.Ncols(); ctr_i++){
for(int ctr_j = 1; ctr_j <= t1.Nrows(); ctr_j++){
if(t1(ctr_j,ctr_i)<=0){t1(ctr_j,ctr_i)=1;}
}
}
for(int ctr_i = 1; ctr_i <= t2.Ncols(); ctr_i++){
for(int ctr_j = 1; ctr_j <= t2.Nrows(); ctr_j++){
if(t2(ctr_j,ctr_i)<=0){t2(ctr_j,ctr_i)=1;}
}
}
t1 = cumsum(sum(log(t1),2).AsRow());
t2 = cumsum(sum(log(t2),2).AsRow());
RowVector l_Az(d);
l_Az << (t1+t2);
RowVector l_lap;
l_lap = l_probU + l_nu +l_Az + l_lam + 0.5*log(2*M_PI)*(m+k)-0.5*log(N)*k;
RowVector l_BIC;
l_BIC = l_lam + l_nu - 0.5*log(N)*(m+k);
RowVector l_RRN; l_RRN = -0.5*N*SP(k,log(SP(cumsum(eigenvalues),pow(k,-1))))+l_nu;
RowVector l_AIC;
l_AIC = -2*N*SP(tmp3,l_lhood)+ 2*(1+d*k+0.5*(k-1));
l_AIC = -l_AIC;
RowVector l_MDL;
l_MDL = -N*SP(tmp3,l_lhood)+ 0.5*(1+d*k+0.5*(k-1))*log(N);
l_MDL = -l_MDL;
Matrix Res;
Res = eigenvalues.t();
Res |= l_lap.t();
Res |= l_BIC.t();
Res |= l_MDL.t();
Res |= l_RRN.t();
Res |= l_AIC.t();
return Res;
} //Matrix ppca_est
ColumnVector acf(const ColumnVector& in, int order)
{
double meanval;
meanval = mean(in).AsScalar();
int tpoints = in.Nrows();
ColumnVector y, res;
Matrix X, tmp;
y = in.Rows(order+1,tpoints) - meanval;
X = zeros(order + 1, order);
for(int ctr1 = 1; ctr1 <= order; ctr1++)
X.Column(ctr1) = in.Rows(order + 1 - ctr1, tpoints - ctr1) - meanval;
tmp = X.t()*X;
tmp = tmp.i();
tmp = tmp * X.t();
res << tmp * y;
return res;
} //ColumnVector acf
ColumnVector pacf(const ColumnVector& in, int maxorder)
{
int tpoint = in.Nrows();
ColumnVector res;
res = acf(in, maxorder);
for(int ctr1 = 1; ctr1 <= maxorder; ctr1++)
if ( res.Column(ctr1).AsScalar() < (1/tpoint) + 2/(float)std::pow(tpoint,0.5))
res.Column(ctr1) = 0;
return res;
} //ColumnVector pacf
Matrix est_ar(const Matrix& Mat, int maxorder)
{
Matrix res;
res = zeros(maxorder, Mat.Ncols());
ColumnVector tmp;
for (int ctr = 1; ctr <= Mat.Ncols(); ctr++){
tmp = pacf(Mat.Column(ctr));
res.Column(ctr) = tmp;
}
return res;
} //Matrix est_ar
ColumnVector gen_ar(const ColumnVector& in, int maxorder)
{
float sdev;
sdev = stdev(in).AsScalar(); ColumnVector x, arcoeff, scaled;
scaled = in / sdev;
arcoeff = pacf( scaled, maxorder);
x = normrnd(in.Nrows(),1).AsColumn() * sdev;
for(int ctr1=2; ctr1 <= in.Nrows(); ctr1++)
for(int ctr2 = 1; ctr2 <= maxorder; ctr2++)
x(ctr1) = arcoeff(ctr2) * x(std::max(1,int(ctr1-ctr2))) + x(ctr1);
return x;
} //ColumnVector gen_ar
Matrix gen_ar(const Matrix& in, int maxorder)
{
Matrix res;
res = in;
ColumnVector tmp;
for(int ctr=1; ctr <= in.Ncols(); ctr++){
tmp = in.Column(ctr);
res.Column(ctr) = gen_ar(tmp, maxorder);
}
return res;
} //Matrix gen_ar
Matrix gen_arCorr(const Matrix& in, int maxorder)
{
Matrix res;
res = zeros(in.Nrows(), in.Nrows());
ColumnVector tmp;
for(int ctr=1; ctr<= in.Ncols(); ctr++){
tmp = in.Column(ctr);
tmp = gen_ar(tmp, maxorder);
res += tmp * tmp.t();
}
return res;
} //Matrix gen_arCorr
void basicGLM::olsfit(const Matrix& data, const Matrix& design,
const Matrix& contrasts, int DOFadjust)
{
beta = zeros(design.Ncols(),1);
residu = zeros(1); sigsq = -1.0*ones(1); varcb = -1.0*ones(1);
t = zeros(1); z = zeros(1); p=-1.0*ones(1);
dof = (int)-1; cbeta = -1.0*ones(1);
if(data.Nrows()==design.Nrows()){
Matrix dat = data;
Matrix tmp = design.t()*design;
Matrix pinvdes = tmp.i()*design.t();
beta = pinvdes * dat;
residu = dat - design*beta;
dof = design.Nrows() - design.Ncols()-1;
sigsq = sum(SP(residu,residu))/dof;
float fact = float(dof) / design.Ncols();
f_fmf = SP(sum(SP(design*beta,design*beta)),pow(sum(SP(residu,residu)),-1)) * fact;
pf_fmf = f_fmf.Row(1);
for(int ctr1=1;ctr1<=f_fmf.Ncols();ctr1++)
pf_fmf(1,ctr1) = 1.0-MISCMATHS::fdtr(design.Ncols(),
int(design.Nrows() -1 -design.Ncols()),f_fmf.Column(ctr1).AsScalar());
if(contrasts.Storage()>0 && contrasts.Ncols()==beta.Nrows()){
cbeta = contrasts*beta;
Matrix tmp = contrasts*pinvdes*pinvdes.t()*contrasts.t();
varcb = diag(tmp)*sigsq;
t = SP(cbeta,pow(varcb,-0.5));
z = t; p=t;
for(int ctr1=1;ctr1<=t.Ncols();ctr1++){
ColumnVector tmp = t.Column(ctr1); T2z::ComputeZStats(varcb.Column(ctr1),cbeta.Column(ctr1),dof, tmp);
z.Column(ctr1) << tmp;
T2z::ComputePs(varcb.Column(ctr1),cbeta.Column(ctr1),dof, tmp);
p.Column(ctr1) << exp(tmp);
}
}
}
}
}