メイン power2.html Last modified: Sep 01, 2009
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<script language="JavaScript">
<!--
function sp(x, y, n)
{
var i, s
s = 0
for (i = 0; i < n; i++) {
s += x[i]*y[i]
}
return s
}
function normal(x, n)
{
var i, s
s = Math.sqrt(sp(x, x, n))
for (i = 0; i < n; i++) {
x[i] /= s
}
}
function inival(x, n)
{
var i
for (i = 0; i < n; i++) {
x[i] = Math.random()
}
normal(x, n)
}
function rat(x, y, arg, n)
{
var i, q, rmin, rmax
var eps = 1.0e-20, bignum = 1.0e20
rmin = bignum
rmax = -bignum
for (i = 0; i < n; i++) {
if (Math.abs(y[i]) < eps) {
rmin = eps
}
else {
if (Math.abs(x[i]) > eps) {
q = y[i]/x[i]
if (q < rmin) {
rmin = q
}
if (q > rmax) {
rmax = q
}
}
else {
rmax = bignum
}
}
}
arg[2] = sp(x, y, n)
arg[0] = rmin
arg[1] = rmax
}
function mtxv(a, x, y, n)
{
var i, j, s
for (i = 0; i < n; i++) {
s = 0.0
for (j = 0; j < n; j++) {
s += a[j][i]*x[j]
}
y[i] = s
}
}
function pivot(a, b, k, n)
{
var i, j, imax, g, aik, temp
g = Math.abs(a[k][k])
imax = k
for (i = k+1; i < n; i++) {
aik = Math.abs(a[i][k])
if (aik > g) {
g = aik
imax = i
}
}
if (imax == k) {
return
}
for (j = k; j < n; j++) {
temp = a[k][j]
a[k][j] = a[imax][j]
a[imax][j] = temp
}
temp = b[k]
b[k] = b[imax]
b[imax] = temp
}
function gauss(a, b, x, n)
{
var p, q, s, i, j, k
var eps = 1.0e-20
for (k = 0; k < n-1; k++) {
pivot(a, b, k, n)
p = a[k][k]
if (Math.abs(p) < eps) {
p = eps
}
for (j = k; j < n; j++) {
a[k][j] /= p
}
b[k] /= p
for (i = k+1; i < n; i++) {
q = a[i][k]
for (j = k; j < n; j++) {
a[i][j] -= q*a[k][j]
}
b[i] -= q*b[k]
}
}
x[n-1] = b[n-1]/a[n-1][n-1]
for (k = n-2; k >= 0; --k) {
s = b[k]
for (j = k+1; j < n; j++) {
s -= a[k][j]*x[j]
}
x[k] = s
}
}
function copyv(a, b, n)
{
var i
for (i = 0; i < n; i++) {
b[i] = a[i]
}
}
function atev(a, qev, x, n)
{
var i, j, k, y, xx, aa, b, rmax, rmin, rrq, arg
var eps = 0.0001, kmax = 753
y = makeVector(n)
xx = makeVector(n)
aa = makeMatrix(n, n)
b = makeVector(n)
arg = makeVector(3)
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
aa[i][j] = a[j][i]
}
aa[i][i] -= qev
b[i] = -aa[i][n-1]
}
gauss(aa, b, x, n-1)
x[n-1] = 1.0
normal(x, n)
for (k = 0; k < kmax; k++) {
mtxv(a, x, y, n)
rat(x, y, arg, n)
rmin = arg[0]
rmax = arg[1]
rrq = arg[2]
copyv(y, x, n)
normal(x, n)
if (rmax-rmin <= eps) {
return
}
}
}
function pm(a0, n)
{
var i, j, k, ban, kai, x, y, z, a, u, v, rmax, rmin, rrq, ev, s, t, evv, vv, arg, m, nagoya
var eps = 0.0001, kmax = 75
x = makeVector(n)
y = makeVector(n)
z = makeVector(n)
a = makeMatrix(n, n)
u = makeVector(n)
v = makeVector(n)
evv = makeVector(n)
vv = makeMatrix(n, n)
arg = makeVector(n)
m = n
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
a[i][j] = a0[i][j]
}
}
for (ban = 0; ban < m; ban++) {
nagoya = 0
for (kai = 0; kai < 10; kai++) {
inival(x, n)
for (k = 0; k < kmax; k++) {
for (i = 0; i < n; i++) {
s = 0.0
for (j = 0; j < n; j++) {
s += a[i][j]*x[j]
}
y[i] = s
}
rat(x, y, arg, n)
rmin = arg[0]
rmax = arg[1]
rrq = arg[2]
if (rmax-rmin <= eps) {
nagoya = 1
break
}
copyv(y, x, n)
normal(x, n)
}
if (nagoya == 1 ) {
break
}
}
copyv(y, u, n)
normal(u, n)
copyv(u, v, n)
atev(a, rrq, v, n)
if (sp(u, v, n) < 0.0) {
for (i = 0; i < n; i++) {
v[i] = -v[i]
}
}
s = t = 0.0
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
s += v[i]*a0[i][j]*u[j]
}
t += u[i]*v[i]
}
ev = s/t
evv[ban] = ev
for (i = 0; i < n; i++) {
vv[ban][i] = u[i]
}
printf("固有値 %17.8g\n", ev)
printf("固有ベクトル\n")
for (i = 0; i < n; i++) {
printf("%15.8g\n", u[i])
}
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
a[i][j] -= ev*u[i]*v[j]
}
}
}
}
function calc(data_string)
{
var i, j, nc, rank, r
if ((r = getdata(data_string, 0)) != false) {
nc = r.length
rank = r[0].length
if (nc != rank) {
printf("正方行列でなくてはなりません\n")
}
else {
printf("★ 入力された行列 ★\n\n")
for (i = 0; i < rank; i++) {
for (j = 0; j < rank; j++) {
printf("%12.6g", r[i][j])
}
printf("\n")
}
printf("\n★ 固有値・固有ベクトル ★\n\n")
pm(r, rank)
}
}
sep2(50)
printf("\n")
}
//-->
</script>
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<font size="+2"><b>パワー法による固有値・固有ベクトル</b></font> <a href="src/power.html"><img src="png/src.png" width=35 height=11 alt="src" align=top></a> Last modified: Jun 01, 2006<hr noshade><p>
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