# hub.darcs.net :: basilisk -> basilisk -> files

Basilisk source code

## root / src / lambda2.h

 ```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 ``` ``````static void eigsrt (double d[dimension], double v[dimension][dimension]) { int k, j, i; double p; for (i = 0; i < dimension - 1; i++) { p = d[k = i]; for (j = i + 1; j < dimension; j++) if (d[j] >= p) p = d[k = j]; if (k != i) { d[k] = d[i]; d[i] = p; for (j = 0; j < dimension; j++) { p = v[j][i]; v[j][i] = v[j][k]; v[j][k] = p; } } } } #define ROTATE(a,i,j,k,l) {\ g=a[i][j];h=a[k][l];a[i][j]=g-s*(h+g*tau);a[k][l]=h+s*(g-h*tau);} /** * eigenvalues: * @a: a symmetric matrix. * @d: a vector. * @v: another matrix. * * Fills @d (resp. @v) with the eigenvalues (resp. eigenvectors) of * matrix @a. */ void eigenvalues (double a[dimension][dimension], double d[dimension], double v[dimension][dimension]) { int j, iq, ip, i; double tresh, theta, tau, t, sm, s, h, g, c, b[dimension], z[dimension]; for (ip = 0; ip < dimension; ip++) { for (iq = 0; iq < dimension; iq++) v[ip][iq] = 0.0; v[ip][ip] = 1.0; } for (ip = 0; ip < dimension; ip++) { b[ip] = d[ip] = a[ip][ip]; z[ip] = 0.0; } for (i = 1; i <= 50; i++) { sm = 0.0; for (ip = 0; ip < dimension - 1; ip++) { for (iq = ip + 1; iq < dimension; iq++) sm += fabs (a[ip][iq]); } if (sm == 0.0) { eigsrt (d, v); return; } if (i < 4) tresh = 0.2*sm/(dimension*dimension); else tresh = 0.0; for (ip = 0; ip < dimension - 1; ip++) { for (iq = ip + 1; iq < dimension; iq++) { g = 100.0*fabs (a[ip][iq]); if (i > 4 && fabs(d[ip]) + g == fabs(d[ip]) && fabs(d[iq]) + g == fabs(d[iq])) a[ip][iq] = 0.0; else if (fabs (a[ip][iq]) > tresh) { h = d[iq] - d[ip]; if (fabs(h) + g == fabs(h)) t = a[ip][iq]/h; else { theta = 0.5*h/a[ip][iq]; t = 1.0/(fabs (theta) + sqrt (1.0 + theta*theta)); if (theta < 0.0) t = -t; } c = 1.0/sqrt (1 + t*t); s = t*c; tau = s/(1.0 + c); h = t*a[ip][iq]; z[ip] -= h; z[iq] += h; d[ip] -= h; d[iq] += h; a[ip][iq] = 0.0; for (j = 0; j <= ip - 1; j++) ROTATE (a, j, ip, j, iq); for (j = ip + 1; j <= iq - 1; j++) ROTATE (a, ip, j, j, iq); for (j = iq + 1; j < dimension; j++) ROTATE(a, ip, j, iq, j); for (j = 0; j < dimension; j++) ROTATE(v, j, ip, j, iq); } } } for (ip = 0; ip < dimension; ip++) { b[ip] += z[ip]; d[ip] = b[ip]; z[ip] = 0.0; } } /* Too many iterations */ for (i = 0; i < dimension; i++) { for (j = 0; j < dimension; j++) fprintf (stderr, "%10.3g ", a[i][j]); fprintf (stderr, "\n"); } assert (false); } void lambda2 (const vector u, scalar l2) { foreach() { double JJ[dimension][dimension]; scalar s = u.x; int i = 0; foreach_dimension() JJ[0][i++] = (s[1] - s[-1])/(2.*Delta); s = u.y; i = 0; foreach_dimension() JJ[1][i++] = (s[1] - s[-1])/(2.*Delta); s = u.z; i = 0; foreach_dimension() JJ[2][i++] = (s[1] - s[-1])/(2.*Delta); double S2O2[dimension][dimension]; for (int i = 0; i < dimension; i++) for (int j = 0; j < dimension; j++) { S2O2[i][j] = 0.; for (int k = 0; k < dimension; k++) S2O2[i][j] += JJ[i][k]*JJ[k][j] + JJ[k][i]*JJ[j][k]; } double lambda[dimension], ev[dimension][dimension]; eigenvalues (S2O2, lambda, ev); l2[] = lambda[1]/2.; } boundary ({l2}); }``````