68 Chapter 2. Solution of Linear Algebraic Equations for (k=l;k<=n;k++){ a[i][k]/scale; s+=a[i][k]*a[i][k]; d f=a[i][1]: g =-SIGN(sqrt(s),f); h=f*g-s; a[i][1]=f-g; for (k=1;k<=n;k++)rvi[k]=a[i][k]/h; for(j=1;j<=m;j++){ for(s=0.0,k=1;k<=n;k+)8+=a[j][k]*a[1][k]; for (k=l;k<=n;k++)a[j][k]+s*rvi[k]; http://www.n Permission is read able files for (k=l;k<=n;k++)a[i][k]*scale; 83 2 (including this one) granted for 198891992 anorm=FMAX(anorm,(fabs(w [i])+fabs(rv1[i]))); 11600 for(1=n;1>=1;i--)[ Accumulation of right-hand transformations. if (i <n){ 1f(g)[ for (j=l;j<=n;j++) Double division to avoid possible underflow to any v[1][i]=(a[i][j]/a[1][1])/g; for(j=1;j<=n;j++){ for(s=0.0,k=1;k<=n;k++)s+=a[i][]*v[k][j]; for(k=1;k<=n;k++)v[k][j]+=s*v[k][i]; (North America server computer, users to make one paper by Cambridge University Press. from NUMERICAL RECIPES IN THE 是 ART for(j1;j<=n;j+)v[i][j]=v[j][i]=0.0; v[i][i]=1.0; Programs g=rv1[i]; send 1=1; for (i=IMIN(m,n);i>=1;i--){ Accumulation of left-hand transformations. Copyright (C) 1=1+1; g=w[1]; for(j=1;j<=n;j++)a[1][j]=0.0; 1f(g) g=1.0/g; for (i=1ii<=n;i++) for(s=0.0,k=1;k<=m;k++)s+=a[k][i]*ak][j]; f=(s/a[i][1])*g; v@cambri for (k=i;k<=m;k++)a[k][j]+f*a[k][i]; for (j=i;j<=m;j++)a[j][i]*g; gercal pecpeonco personal use.Further reproduction, 1988-1992 by Numerical Recipes OF SCIENTIFIC COMPUTING (ISBN 0-521 else for (j=i;j<=m;j++)a[j][i]=0.0; -431085 ++a[i][i]: (outside for(k=n;k>=1;k--){ Diagonalization of the bidiagonal form:Loop over for(1ts=1;1tg<=30;1ts++)[ singular values,and over allowed iterations. North Software. flag=1; for(1=k;1>=1;1--) Test for splitting. nm-】-1; Note that rv1[1]is always zero if ((float)(fabs(rv1[1])+anorm)==anorm) flag=0; break; if ((float)(fabs(w[nm])+anorm)==anorm)break; if (flag){ c=0.0; Cancellation of rv1[1],if 11. s=1.0; for (i=l;i<-k;i++){68 Chapter 2. Solution of Linear Algebraic Equations Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin Copyright (C) 1988-1992 by Cambridge University Press. Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) g of machine￾readable files (including this one) to any server computer, is strictly prohibited. To order Numerical Recipes books or CDROMs, visit website http://www.nr.com or call 1-800-872-7423 (North America only), or send email to directcustserv@cambridge.org (outside North America). for (k=l;k<=n;k++) { a[i][k] /= scale; s += a[i][k]*a[i][k]; } f=a[i][l]; g = -SIGN(sqrt(s),f); h=f*g-s; a[i][l]=f-g; for (k=l;k<=n;k++) rv1[k]=a[i][k]/h; for (j=l;j<=m;j++) { for (s=0.0,k=l;k<=n;k++) s += a[j][k]*a[i][k]; for (k=l;k<=n;k++) a[j][k] += s*rv1[k]; } for (k=l;k<=n;k++) a[i][k] *= scale; } } anorm=FMAX(anorm,(fabs(w[i])+fabs(rv1[i]))); } for (i=n;i>=1;i--) { Accumulation of right-hand transformations. if (i < n) { if (g) { for (j=l;j<=n;j++) Double division to avoid possible underflow. v[j][i]=(a[i][j]/a[i][l])/g; for (j=l;j<=n;j++) { for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j]; for (k=l;k<=n;k++) v[k][j] += s*v[k][i]; } } for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0; } v[i][i]=1.0; g=rv1[i]; l=i; } for (i=IMIN(m,n);i>=1;i--) { Accumulation of left-hand transformations. l=i+1; g=w[i]; for (j=l;j<=n;j++) a[i][j]=0.0; if (g) { g=1.0/g; for (j=l;j<=n;j++) { for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j]; f=(s/a[i][i])*g; for (k=i;k<=m;k++) a[k][j] += f*a[k][i]; } for (j=i;j<=m;j++) a[j][i] *= g; } else for (j=i;j<=m;j++) a[j][i]=0.0; ++a[i][i]; } for (k=n;k>=1;k--) { Diagonalization of the bidiagonal form: Loop over for (its=1;its<=30;its++) { singular values, and over allowed iterations. flag=1; for (l=k;l>=1;l--) { Test for splitting. nm=l-1; Note that rv1[1] is always zero. if ((float)(fabs(rv1[l])+anorm) == anorm) { flag=0; break; } if ((float)(fabs(w[nm])+anorm) == anorm) break; } if (flag) { c=0.0; Cancellation of rv1[l], if l > 1. s=1.0; for (i=l;i<=k;i++) {