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+/* Copyright (C) 2017 - IIT Bombay - FOSSEE
+
+ 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
+ Author: Sandeep Gupta
+ Organization: FOSSEE, IIT Bombay
+ Email: toolbox@scilab.in
+ */
+
+/* Householder orthogonal reflexion matrix */
+
+/*
+Syntax :-
+ //u=householder(v [,w])
+ //Description
+ //given 2 column vectors v w of same size householder(v,w) returns a unitary
+ //column vector u, such that (eye-2*u*u')*v is proportional to w.
+ //(eye-2*u*u') is the orthogonal Householder reflexion matrix
+ //
+ // w default value is eye(v). In this case vector (eye-2*u*u')*v is the
+ // vector eye(v)*(+-norm(v))
+*/
+#include <stdio.h>
+#include <stdlib.h>
+#include "householder.h"
+#include "eye.h"
+#include "matrixTranspose.h"
+#include "matrixMultiplication.h"
+#include <math.h>
+#include "norm.h"
+
+void dhouseholdera(int ninp,double *inp1,int row,double *inp2,double *out1){
+
+ int i,j;
+ double *x;
+ x = (double *)malloc(row*sizeof(double));
+
+ for(i=0;i<row;i++)
+ x[i] = inp1[i];
+
+ if(ninp < 2){
+ deyea(x,row,1);
+ }
+ else{
+ for(i=0;i<row;i++){
+ x[i] = inp2[i];
+ }
+ }
+
+ /* vt transpose of inp1 */
+
+ double *vt;
+ vt = (double *)malloc(row*sizeof(double));
+ dtransposea(inp1,row,1,vt);
+
+ /*wt transpose of inp2 */
+ double *wt;
+ wt = (double *)malloc(row*sizeof(double));
+ dtransposea(x,row,1,wt);
+
+ /* vvt = inp1*vt */
+ double *vvt;
+ vvt = (double *)malloc(1*1*sizeof(double));
+ dmulma(vt,1,row,inp1,row,1,vvt);
+
+ /* wwt = inp2*wt */
+ double *wwt;
+ wwt = (double *)malloc(1*1*sizeof(double));
+ dmulma(wt,1,row,x,row,1,wwt);
+
+ /* a=-sqrt((v'*v)/(w'*w)) */
+ double a;
+ //a = (double *)malloc(1*1*sizeof(double));
+ a = -sqrt(vvt[0]/wwt[0]);
+
+ for(i=0;i<row;i++){
+ out1[i] = x[i]*a+inp1[i];
+ }
+
+ /* norm of out1 */
+ double r;
+ r = dnorma(out1,row,1,2);
+
+ for(i=0;i<row;i++){
+ out1[i]=out1[i]/r;
+ }
+}