[93] | 1 | #include <math.h> |
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| 2 | #include <stdio.h> |
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| 3 | #include <stdlib.h> |
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| 4 | #define ROTATE(a,i,j,k,l) g=a[i*n + j];h=a[k*n + l];a[i*n + j]=g-s*(h+g*tau);\ |
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| 5 | a[k*n + l]=h+s*(g-h*tau); |
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| 6 | |
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| 7 | /* |
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| 8 | Computes all eigenvalues and eigenvectors of a real symmetric matrix a[1..n][1..n]. On |
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| 9 | output, elements of a above the diagonal are destroyed. d[1..n] returns the eigenvalues of a. |
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| 10 | v[1..n][1..n] is a matrix whose columns contain, on output, the normalized eigenvectors of |
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| 11 | a. nrot returns the number of Jacobi rotations that were required. |
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| 12 | */ |
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| 13 | void jacobi(float *a, int n, float d[], float *v, int *nrot) |
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| 14 | { |
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| 15 | int j,iq,ip,i; |
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| 16 | float tresh,theta,tau,t,sm,s,h,g,c,*b,*z; |
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| 17 | |
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| 18 | b = (float *) malloc(n * sizeof(float)); |
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| 19 | z = (float *) malloc(n * sizeof(float)); |
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| 20 | |
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| 21 | for (ip=0;ip<n;ip++) { // Initialize to the identity matrix. |
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| 22 | for (iq=0;iq<n;iq++) v[ip*n + iq]=0.0; |
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| 23 | v[ip*n + ip]=1.0; |
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| 24 | } |
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| 25 | for (ip=0;ip<n;ip++) { // Initialize b and d to the diagonal of a. |
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| 26 | b[ip]=d[ip]=a[ip*n + ip]; |
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| 27 | z[ip]=0.0; // This vector will accumulate terms of the form t*a[pq] as in equation (11.1.14). |
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| 28 | } |
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| 29 | |
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| 30 | *nrot=0; |
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| 31 | for (i=1;i<=50;i++) { |
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| 32 | sm=0.0; |
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| 33 | for (ip=0;ip<n-1;ip++) { // Sum off-diagonal elements. |
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| 34 | for (iq=ip+1;iq<n;iq++) |
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| 35 | sm += fabs(a[ip*n + iq]); |
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| 36 | } |
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| 37 | if (sm == 0.0) { // The normal return, which relies on quadratic convergence to machine underflow. |
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| 38 | free(z); |
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| 39 | free(b); |
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| 40 | return; |
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| 41 | } |
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| 42 | if (i < 4) |
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| 43 | tresh=0.2*sm/(n*n); // ...on the first three sweeps. |
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| 44 | else |
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| 45 | tresh=0.0; // ...thereafter. |
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| 46 | for (ip=0;ip<n-1;ip++) { |
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| 47 | for (iq=ip+1;iq<n;iq++) { |
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| 48 | g=100.0*fabs(a[ip*n + iq]); |
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| 49 | if (i > 4 && (float)(fabs(d[ip])+g) == (float)fabs(d[ip]) // After four sweeps, skip the rotation if the off-diagonal element is small. |
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| 50 | && (float)(fabs(d[iq])+g) == (float)fabs(d[iq])) |
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| 51 | a[ip*n + iq]=0.0; |
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| 52 | else if (fabs(a[ip*n + iq]) > tresh) { |
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| 53 | h=d[iq]-d[ip]; |
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| 54 | if ((float)(fabs(h)+g) == (float)fabs(h)) |
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| 55 | t=(a[ip*n + iq])/h; // t = 1/(2*theta) |
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| 56 | else { |
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| 57 | theta=0.5*h/(a[ip*n + iq]); // Equation (11.1.10). |
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| 58 | t=1.0/(fabs(theta)+sqrt(1.0+theta*theta)); |
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| 59 | if (theta < 0.0) t = -t; |
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| 60 | } |
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| 61 | |
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| 62 | c=1.0/sqrt(1+t*t); |
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| 63 | s=t*c; |
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| 64 | tau=s/(1.0+c); |
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| 65 | h=t*a[ip*n + iq]; |
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| 66 | z[ip] -= h; |
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| 67 | z[iq] += h; |
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| 68 | d[ip] -= h; |
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| 69 | d[iq] += h; |
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| 70 | a[ip*n + iq]=0.0; |
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| 71 | |
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| 72 | for (j=0;j<=ip-1;j++) { // Case of rotations 1 <= j < p. |
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| 73 | ROTATE(a,j,ip,j,iq) |
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| 74 | } |
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| 75 | for (j=ip+1;j<=iq-1;j++) { // Case of rotations p < j < q. |
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| 76 | ROTATE(a,ip,j,j,iq) |
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| 77 | } |
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| 78 | for (j=iq+1;j<n;j++) { // Case of rotations q < j <= n. |
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| 79 | ROTATE(a,ip,j,iq,j) |
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| 80 | } |
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| 81 | for (j=0;j<n;j++) { |
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| 82 | ROTATE(v,j,ip,j,iq) |
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| 83 | } |
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| 84 | |
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| 85 | ++(*nrot); |
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| 86 | } |
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| 87 | } |
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| 88 | } |
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| 89 | |
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| 90 | for (ip=0;ip<n;ip++) { |
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| 91 | b[ip] += z[ip]; |
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| 92 | d[ip]=b[ip]; // Updte d with the sum of t*a[pq], |
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| 93 | z[ip]=0.0; // and reinitialize z. |
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| 94 | } |
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| 95 | } |
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| 96 | |
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| 97 | printf("Too many iterations in routine jacobi\n"); |
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| 98 | } |
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| 99 | |
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| 100 | /* |
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| 101 | Given the eigenvalues d[1..n] and eigenvectors v[1..n][1..n] as output from jacobi |
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| 102 | (x11.1) or tqli (x11.3), this routine sorts the eigenvalues into descending order, and rearranges |
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| 103 | the columns of v correspondingly. The method is straight insertion. |
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| 104 | */ |
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| 105 | void eigsrt(float d[], float **v, int n) |
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| 106 | { |
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| 107 | int k,j,i; |
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| 108 | float p; |
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| 109 | for (i=0;i<n-1;i++) { |
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| 110 | p=d[k=i]; |
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| 111 | for (j=i+1;j<n;j++) |
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| 112 | if (d[j] >= p) p=d[k=j]; |
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| 113 | if (k != i) { |
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| 114 | d[k]=d[i]; |
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| 115 | d[i]=p; |
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| 116 | for (j=0;j<n;j++) { |
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| 117 | p=v[j*n + i]; |
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| 118 | v[j*n + i]=v[j*n + k]; |
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| 119 | v[j*n + k]=p; |
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| 120 | } |
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| 121 | } |
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| 122 | } |
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| 123 | } |
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