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authoryash11122017-07-07 21:20:49 +0530
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+/*
+ * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ * Copyright (C) 2008 - INRIA - Arnaud TORSET
+ *
+ * This file must be used under the terms of the CeCILL.
+ * This source file is licensed as described in the file COPYING, which
+ * you should have received as part of this distribution. The terms
+ * are also available at
+ * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ */
+
+#include <stdlib.h>
+#include "levin.h"
+#include "levinUtils.h"
+#include "matrixInversion.h"
+#include "matrixMultiplication.h"
+#include "zeros.h"
+
+void slevina (int n, float* cov, int lCov, int cCov, float* la, float* sig, float* lb){
+/*
+ [la and lb]
+ In Scilab, the return value la is a list of n elements. Each element is a matrix cCov*cCov,
+ and each element of the matrix is a polynome whose degree is n, so the polynome got n+1 elements.
+ The greatest size of a element of the list is : (n+1)*cCov*cCov.
+
+ Here, la is a matrix which contain all elements of the list, its size is n*(n+1)*cCov*cCov. We take the
+ maximum size for all elements.
+ The first element of the list is the first (n+1)*cCov*cCov elements of la, namely la[0] to la[(n+1)*cCov*cCov-1].
+ The second element of the list is the elements of la between (n+1)*cCov*cCov and 2*(n+1)*cCov*cCov,namely la[(n+1)*cCov*cCov]
+ to la[2*(n+1)*cCov*cCov-1],...
+
+ Enter now in a element of the list. Take the first for example.
+ This is, like said before, a cCov*cCov matrix. In la, it contains (n+1)*cCov*cCov. Each element of the matrix contains (n+1)
+ elements. As it's stocked by columns, if we represent a matrix like [a c], for example, the elements 0 to n of la represent
+ [b d]
+ a, the elements (n+1) to 2(n+1)-1 represent b,...
+
+ To finish, look at the elements of the matrix, the polynomes. The coefficients of the polynomes are stocked in increasing order.
+
+ For example, if la in Scilab is : list( [3+2x 5-2x ])
+ ( [-5+x -2+4x])
+ ([3+x-x^2 -1+2x ])
+ ([1+6x+3x^2 -2x-x^2 ])
+ the result in dlevin will be :
+ -la is a table of 2*3*2*2 elements(n=2,cCov=2);
+ -la[]={3,2,0, -5,1,0, 5,-2,0, -2,4,0, 3,1,-1, 1,6,3 -1,2,0, 0,-2,-1}.
+
+ It's the same for lb.
+
+ [sig]
+ In Scilab, the return value sig is a list of n elements. Each element is a matrix cCov*cCov,
+ and each element of the matrix is a scalar, so 1 element.
+ The greatest size of a element of the list is : cCov*cCov.
+
+ Let see an example so know how it's stocked.
+ In Scilab, if sig is : list( [1 3])
+ ( [2 4])
+ ( [5 7])
+ ( [6 8])
+ the result in dlevin will be :
+ -sig={1,2, 5,6, 3,4, 7,8}.
+ It's as if we put the matrix the ones under the others and we take the first column, the second,...
+
+
+ >>>CAREFUL<<<
+ la/lb and sig are stored differently
+
+*/
+
+
+ int i=0;
+
+
+/*version ISO C99
+ double tmp1[n*cCov*cCov], tmp2[n*cCov*cCov];
+ double sig1[cCov], gam[cCov];
+ double R1[n*cCov],R2[n*cCov],R3[n*cCov],R4[n*cCov];
+*/
+/*version pas ISO C99 */
+ float *tmp1, *tmp2;
+ float *sig1, *gam;
+ float *R1,*R2,*R3,*R4;
+
+ /* FIXME : malloc here */
+
+ tmp1=(float*)malloc((unsigned int)((n+1)*cCov*cCov)*sizeof(float));
+ tmp2=(float*)malloc((unsigned int)((n+1)*cCov*cCov)*sizeof(float));
+ sig1=(float*)malloc((unsigned int)(cCov*cCov)*sizeof(float));
+ gam=(float*)malloc((unsigned int)(cCov*cCov)*sizeof(float));
+ R1=(float*)malloc((unsigned int)(n*cCov*cCov)*sizeof(float));
+ R2=(float*)malloc((unsigned int)(n*cCov*cCov)*sizeof(float));
+ R3=(float*)malloc((unsigned int)(n*cCov*cCov)*sizeof(float));
+ R4=(float*)malloc((unsigned int)(n*cCov*cCov)*sizeof(float));
+
+
+
+ /*
+ * Initializations
+ * */
+ szerosa(sig,n*cCov*cCov,1);
+ szerosa(la,n*(n+1)*cCov*cCov,1);
+ szerosa(lb,n*(n+1)*cCov*cCov,1);
+
+ /*equal to eye(la) and eye(lb)
+ but we can't use eye cause to the indexation*/
+ for (i=0;i<cCov;i++){
+ la[i*((n+1)*(cCov+1))]=1;
+ lb[i*((n+1)*(cCov+1))]=1;
+ }
+
+ sr1(cov,lCov,cCov,n,R1);
+ sr2(cov,lCov,cCov,n,R2);
+ sr3(cov,lCov,cCov,n,R3);
+ sr4(cov,lCov,cCov,n,R4);
+
+/* case i=0 */
+
+
+ /*computation of sig */
+ slevinmul(la,R4,n,cCov,0,sig,n*cCov,0,'d');
+ /*computation of gam1 */
+ slevinmul(lb,R2,n,cCov,0,gam,cCov,0,'u');
+ /*computation of c1*r1 */
+ slevinmul(la,R1,n,cCov,0,tmp1,cCov,0,'u');
+ /*computation of inv(gam1) */
+ sinverma(gam,sig1,cCov);
+ /*computation of k1 = c1*r1*inv(gam1) */
+ smulma(tmp1,cCov,cCov,sig1,cCov,cCov,tmp2);
+ /*computation of k1*lb */
+ slevinmul2(tmp2,lb,0,n,cCov,tmp1);
+ /*computation of k1*lb*z */
+ sdecalage(tmp1,0,n,cCov,tmp1);
+ /*computation of la */
+ slevinsub(la,tmp1,n,cCov,0,0,la);
+
+ /*computation of sig1 (we extract the value if sig at time 0)*/
+ slevinsig(sig,0,cCov,n*cCov,sig1);
+ /*computation of c2*r3 */
+ slevinmul(lb,R3,n,cCov,0,tmp1,cCov,0,'d');
+ /*computation of inv(sig1)*/
+ sinverma(sig1,gam,cCov);
+ /*computation of k2 = c2*r3*inv(sig1) */
+ smulma(tmp1,cCov,cCov,gam,cCov,cCov,tmp2);
+ /*computation of k2*la (here it's lb cause la have been modified
+ and the precedent values hadn't been saved)*/
+ slevinmul2(tmp2,lb,0,n,cCov,tmp1);
+ /*computation of lb*z */
+ sdecalage(lb,0,n,cCov,lb);
+ /*computation of lb */
+ slevinsub(lb,tmp1,n,cCov,0,0,lb);
+
+
+ for (i=1;i<n;i++){
+ slevinmul(la,R4,n,cCov,i,sig,n*cCov,1,'d');
+ slevinmul(lb,R2,n,cCov,i,gam,cCov,0,'u');
+ slevinmul(la,R1,n,cCov,i,tmp1,cCov,0,'u');
+ sinverma(gam,sig1,cCov);
+ smulma(tmp1,cCov,cCov,sig1,cCov,cCov,tmp2);
+
+ slevinmul2(tmp2,lb,i-1,n,cCov,tmp1);
+ sdecalage(tmp1,0,n,cCov,tmp1);
+ slevinsub(la,tmp1,n,cCov,i,i,la);/*a*/
+
+ /*computation of sig1 (we extract the value if sig at time i)*/
+ slevinsig(sig,i,cCov,n*cCov,sig1);
+ slevinmul(lb,R3,n,cCov,i,tmp1,cCov,0,'d');
+ sinverma(sig1,gam,cCov);
+ smulma(tmp1,cCov,cCov,gam,cCov,cCov,tmp2);
+ /*computation of k2*la (now it's la at time (i-1))*/
+ slevinmul2(tmp2,la,i-1,n,cCov,tmp1);
+ sdecalage(lb,(i-1)*(n+1)*cCov*cCov,n,cCov,tmp2);
+ slevinsub(tmp2,tmp1,n,cCov,0,i,lb);
+ }
+
+
+ free(R4);
+ free(R3);
+ free(R2);
+ free(R1);
+ free(gam);
+ free(sig1);
+ free(tmp2);
+ free(tmp1);
+}