Matrix &Matrix::eigenSystem()
{
Matrix *values;
assertDefined("eigenSystem");
assertSquare("eigenSystem");
values = new Matrix(1, maxc); // allocates space for eigen values
{
double *d, *e;
tridiagonalize(d, e); // allocates space for 2 double arrays
eigen(d, e, maxc, m); // returns eigen values in d
delete values->m[0]; // save the eigen values from above routines
values->m[0] = d;
delete e;
}
transposeSelf(); // result was returned in columns so put it in rows
isort(values->m[0], m, maxc); // sort rows so vector with max eigenvalue is first
values->defined = true; // mark eigen value matrix as defined
return *values;
}
int main()
{
int i, j, k, n;
static matrix a, p;
static vector d, e, temp;
double s, t;
printf("n = "); scanf("%d", &n);
printf("乱数の種 (正の整数) = ");
scanf("%ul", &seed); seed |= 1;
a = new_matrix(n, n);
p = new_matrix(n, n);
d = new_vector(n);
e = new_vector(n);
temp = new_vector(n);
for (i = 0; i < n; i++)
for (j = 0; j <= i; j++)
a[i][j] = a[j][i] = p[i][j] = p[j][i]
= rnd() - rnd();
printf("A:\n");
matprint(a, n, 7, "%10.6f");
tridiagonalize(n, p, d, e);
printf("d:\n");
vecprint(d, n, 5, "% -14g");
printf("e:\n");
vecprint(e, n - 1, 5, "% -14g");
for (i = 0; i < n; i++) {
for (k = 0; k < n; k++)
temp[k] = a[i][k];
for (j = 0; j < n; j++) {
s = 0;
for (k = 0; k < n; k++)
s += temp[k] * p[j][k];
a[i][j] = s;
}
}
for (j = 0; j < n; j++) {
for (k = 0; k < n; k++)
temp[k] = a[k][j];
for (i = 0; i < n; i++) {
s = 0;
for (k = 0; k < n; k++)
s += p[i][k] * temp[k];
a[i][j] = s;
}
}
s = 0;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
if (i == j) {
t = a[i][j] - d[i]; s += t * t;
} else if (i + 1 == j) {
t = a[i][j] - e[i]; s += t * t;
} else if (i == j + 1) {
t = a[i][j] - e[j]; s += t * t;
} else {
t = a[i][j]; s += t * t;
}
printf("二乗平均誤差: %g\n", sqrt(s) / n);
return EXIT_SUCCESS;
}
double * symmetricQR(matrix A){
/*
Symmetric QR for computation of eigenvalues.
Source: Golub and Van Loan, Matrix Computations p. 421.
Input:
matrix A Square, symmetric matrix of which to compute eigenvalues
Output:
double *eigs (returned) Eigenvalues of the matrix
*/
double *eigs = (double *) malloc(A.n * sizeof(double)) ;
A = tridiagonalize(A) ;
int i, k;
int start;
int n = A.n ;
int maxIt = 10000;
int p,q = 0 ;
double tol = 1e-14 ;
int iteration = 0 ;
while(q < n-1){
for (i = 0; i<n-1; i++){
if ( fabs( A.values[i+1][i] ) <= tol * (fabs( A.values[i][i] ) + fabs( A.values[i+1][i+1] )) ) {
A.values[i+1][i] = 0.0;
A.values[i][i+1] = 0.0;
}
}
// find largest diagonal block in lower right of matrix
start = n-q; //loop index starts with previously found diagonal block
for( k = start - 1; k >= 0; k--){
//check off-diagonal entries
//only above diagonal is checked because of symmetry
if(k != 0){
if(A.values[k][k-1] == 0.0)
q++;
else
break ;
}
}
p = n - q - 1;
for (k = start - 1; k > 0; k--) {
if (A.values[k][k - 1] != 0)
p--;
else
break;
}
if (q < n - 1 ){
A = symmetricQRStep(A, p, n-q) ;
}
iteration++ ;
if (iteration > maxIt){
fprintf(stderr, "Max it reached. Returning.\n");
break ;
}
}
for(i=0; i<n; i++)
eigs[i] = A.values[i][i] ;
qsort(eigs, n, sizeof(double), compareDoubles) ;
return eigs ;
}