## [6164d0]: mp_mysvd.m Maximize Restore History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297``` ```function [U,S,V]=mp_mysvd(A,dummy) %function [U,S,V]=mysvd(A,dummy) %svd: singular value decomposition %Outputs should verify that U*S*V'==A %The case with two arguments is considered as an "economy size" request % Based upon FORTRAN 77 routine at NUMERICAL RECIPES, monkey-modified to run in Matlab % also taking into consideration the C implementation (due to the GOTO hell!) % Given a matrix A(1:m,1:n),with physical dimensions mp by np this routine computes its % singular value decomposition,A = U * W * V' .The matrix U replaces A on output.The % diagonal matrix of singular values W is output as a vector w(1:n). The matrix V (not the % transpose V') is output as v(1:n,1:n). % NOTICE that direct comparison with the matlab svd is possible only for the singular values, % but for the left and right matrix you should be prepared to consider some possible % sign differences. The verification should be instead that norm(U*S*V'-A) is small, and % that norm(S-Smatlab) is also small % %source in FORTRAN 77 at http://cc.oulu.fi/~tf/tiedostot/pub/nrf/svdcmp.f %source in C at http://www.cs.utah.edu/~tch/classes/cs4550/code/Numerical-Recipes/sources-used/svdcmp.c [m,n]=size(A); a_zero=A(1)*0;%a zero of the same data type as input matrix A a_one=1+a_zero;%a one of the same data type as input matrix A g=a_zero; scale=a_zero; anorm=a_zero; for i=1:n %do 25 i=1,n L=i+1; rv1(i)=scale*g; g=a_zero; s=a_zero; scale=a_zero; if(i<=m) for k=i:m %do 11 k=i,m scale=scale+abs(A(k,i)); end %enddo 11 if (scale~=0) for k=i:m%do 12 k=i,m A(k,i)=A(k,i)/scale; s=s+A(k,i)*A(k,i); end %enddo 12 f=A(i,i); g=-signtransf(sqrt(s),f); h=f*g-s; A(i,i)=f-g; if i~=n for j=L:n %do 15 j=l,n s=a_zero; for k=i:m %do 13 k=i,m s=s+A(k,i)*A(k,j); end %enddo 13 f=s/h; for k=i:m %do 14 k=i,m A(k,j)=A(k,j)+f*A(k,i); end %enddo 14 end %enddo 15 end for k=i:m %do 16 k=i,m A(k,i)=scale*A(k,i); end %enddo 16 end end w(i)=scale *g; g=a_zero; s=a_zero; scale=a_zero; if((i<=m) & (i~=n)) for k=L:n %do 17 k=l,n scale=scale+abs(A(i,k)); end %enddo 17 if(scale~=a_zero) for k=L:n %do 18 k=l,n A(i,k)=A(i,k)/scale; s=s+A(i,k)*A(i,k); end %enddo 18 f=A(i,L); g=-signtransf(sqrt(s),f); h=f*g-s; A(i,L)=f-g; for k=L:n %do 19 k=l,n rv1(k)=A(i,k)/h; end %enddo 19 for j=L:m %do 23 j=l,m s=a_zero; for k=L:n %do 21 k=l,n s=s+A(j,k)*A(i,k); end %enddo 21 for k=L:n %do 22 k=l,n A(j,k)=A(j,k)+s*rv1(k); end %enddo 22 end %enddo 23 for k=L:n %do 24 k=l,n A(i,k)=scale*A(i,k); end %enddo 24 end end anorm=max(anorm,(abs(w(i))+abs(rv1(i)))); end %enddo 25 v=repmat(a_zero,n,n);%Preallocate space for i=n:-1:1 %do 32 i=n,1,-1 Accumulation of right-hand transformations. if(i 1 s=a_one; for i=L:k %do 43 i=l,k f=s*rv1(i); rv1(i)=c*rv1(i); if((abs(f)+anorm)==anorm) break end g=w(i); h=pythag(f,g); w(i)=h; h=a_one/h; c= (g*h); s=-(f*h); for j=1:m %do 42 j=1,m y=A(j,nm); z=A(j,i); A(j,nm)=(y*c)+(z*s); A(j,i)=-(y*s)+(z*c); end %enddo 42 end %enddo 43 end %del goto 1 %2 z=w(k); if(L==k)%then Convergence. if(z<=a_zero)% Singular value is made nonnegative. w(k)=-z; for j=1:n %do 44 j=1,n v(j,k)=-v(j,k); end %enddo 44 end break end if(its==30) error('no convergence in 30 iterations of svdcmp') end x=w(L);% Shift from bottom 2-by-2 minor. nm=k-1; y=w(nm); g=rv1(nm); h=rv1(k); f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y); g=pythag(f,a_one); f=((x-z)*(x+z)+h*((y/(f+signtransf(g,f)))-h))/x; c=a_one; %Next QR transformation: s=a_one; for j=L:nm %do 47 j=l,nm i=j+1; g=rv1(i); y=w(i); h=s*g; g=c*g; z=pythag(f,h); rv1(j)=z; c=f/z; s=h/z; f= (x*c)+(g*s); g=-(x*s)+(g*c); h=y*s; y=y*c; for jj=1:n %do 45 jj=1,n x=v(jj,j); z=v(jj,i); v(jj,j)= (x*c)+(z*s); v(jj,i)=-(x*s)+(z*c); end %enddo 45 z=pythag(f,h); w(j)=z;% Rotation can be arbitrary if z =0 if(z~=a_zero) z=a_one/z; c=f*z; s=h*z; end f= (c*g)+(s*y); x=-(s*g)+(c*y); for jj=1:m %do 46 jj=1,m y=A(jj,j); z=A(jj,i); A(jj,j)= (y*c)+(z*s); A(jj,i)=-(y*s)+(z*c); end %enddo 46 end %enddo 47 rv1(L)=a_zero; rv1(k)=f; w(k)=x; end %enddo 48 %3 continue end %enddo 49 [dummy,I]=sort(-w(1:n));%Sort in decreasing order S=diag(w(I)); if nargin<2 %fill in with zeros in order to satisfy dimension requirements if nabsb) py=absa*sqrt(1.+(absb/absa)^2); else if(absb==0) py=absb; else py=absb*sqrt(1.+(absa/absb)^2); end end function c=signtransf(A1,A2) %C = SIGNTRANSF(A1,A2) performs sign transfer: if A2 is negative the result is -abs(A1), %if A2 is zero or positive the result is abs(A1). %It is the fortran equivalent of SIGN(A1,A2) % (see http://www.math.hawaii.edu/lab/197/fortran/fort4.htm#sign) c=abs(A1); q=find(A2<0);c(q)=-abs(A1(q)); ```