BOOST_FORCEINLINE void
combine_eigens(const T& wr, const T& wi, A0& w)
{
typedef typename A0::value_type type_t;
int n = numel(wr);
w.resize(of_size(n, 1));
nt2::container::table<type_t, nt2::shared_> sw(of_size(n, 1), share(w.data(), w.data()+n));
sw = tocomplex(wr, wi);
}
BOOST_FORCEINLINE void
combine_vects(const T1& rv, const T2& wi, A0& v)
{
typedef typename A0::value_type type_t;
int n = height(rv);
v.resize(of_size(n, n));
nt2::container::table<type_t, nt2::shared_> sv(of_size(n, n), share(v.data(), v.data()+numel(v)));
for(int j=1; j <= n; ++j)
{
if(wi(j))
{
sv(nt2::_, j ) = tocomplex(rv(nt2::_, j), rv(nt2::_, j+1));
sv(nt2::_, j+1) = conj(sv(nt2::_, j));
++j;
}
else
sv(nt2::_, j) = rv(nt2::_, j);
}
}
void cgauj(Complex a[], int l, int m, int n, double eps)
{
int c, i, iw, j, k, mm1, *p, r, *work;
double api, w, wmax;
Complex pivot, *q, *q1, wk, wk1;
if(l < n || m < 2 || m >= n || eps <= 0.)
{
fprintf(stderr, "Error : Illegal parameter in cgauj()\n");
return;
}
work = (int *)malloc(m * sizeof(int));
if(work == NULL)
{
fprintf(stderr, "Error : Out of memory in cgauj()\n");
return;
}
for(i = 0, p = work; i < m; i++) *p++ = i;
for(k = 0; k < m; k++)
{
wmax = 0.;
for(i = k; i < m; i++)
{
for(j = k, q = a + i * l + k; j < m; j++)
{
w = cabslt(*q++);
if(w > wmax)
{
wmax = w;
r = i;
c = j;
}
}
}
pivot = *(a + r * l + c);
api = cabslt(pivot);
if(api < eps)
{
fprintf(stderr, "Error : api < eps in cgauj()\n");
free((char *)work);
return;
}
if(c != k)
{
iw = *(work + k);
*(work + k) = *(work + c);
*(work + c) = iw;
for(i = 0, q = a + i * l; i < m; i++, q += l)
{
wk = *(q + k);
*(q + k) = *(q + c);
*(q + c) = wk;
}
}
if(r != k)
{
for(j = k; j < n; j++)
{
wk = *(a + r * l + j);
*(a + r * l + j) = *(a + k * l + j);
*(a + k * l + j) = wk;
}
}
*(a + k * l + k) = tocomplex(1., 0.);
for(i = k + 1, q = a + k * l + k + 1; i < n; i++, q++)
*q = cdiv(*q, pivot);
for(i = 0; i < m; i++)
{
if(i != k)
{
wk = *(a + i * l + k);
for(j = k; j < n; j++)
{
wk1 = cmul(wk, *(a + k * l + j));
*(a + i * l + j) = csub(*(a + i * l + j), wk1);
}
}
}
}
mm1 = m - 1;
for(i = 0; i < mm1; i++)
{
for(;;)
{
k = *(work + i);
if(k == i) break;
iw = *(work + k);
*(work + k) = *(work + i);
*(work + i) = iw;
for(j = m, q = a + k * l + m, q1 = a + i * l + m; j < n; j++)
{
wk = *q;
*q++ = *q1;
*q1++ = wk;
}
}
}
free((char *)work);
return;
}
int main(void)
{
static double ar[8] = { 0., 0., 0., 1., 1., 0., 0., 0.};
static double ai[8] = { 0., 0., 0., 0., 0., 0., 0., 0.};
static double ar2[16] = { 0., 0., 0., 0., 0., 1., 1., 0.,
0., 1., 1., 0., 0., 0., 0., 0.};
static double ai2[16] = { 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0.};
Complex a[8], a2[16];
int flag, i, iter, j, k, n, nmax;
iter = 0;
n = 8;
#ifndef CPX
for(i = 0; i < n; i++)
a[i] = tocomplex(ar[i], ai[i]);
print(ar, ai, n);
#else
printx(a, n);
#endif
/* forward FFT */
flag = 0;
#ifndef CPX
fft1(ar, ai, n, iter, flag);
print(ar, ai, n);
#else
fft1x(a, n, iter, flag);
printx(a, n);
#endif
/* reverse FFT */
flag = 1;
#ifndef CPX
fft1(ar, ai, n, iter, flag);
print(ar, ai, n);
#else
fft1x(a, n, iter, flag);
printx(a, n);
#endif
n = nmax = 4;
for(i = k = 0; i < n; i++)
for(j = 0; j < n; j++, k++)
a2[k] = tocomplex(ar2[k], ai2[k]);
#ifndef CPX
print2(ar2, ai2, n, nmax);
#else
print2x(a2, n, nmax);
#endif
flag = 0;
#ifndef CPX
fft2(ar2, ai2, n, nmax, flag);
print2(ar2, ai2, n, nmax);
#else
fft2x(a2, n, nmax, flag);
print2x(a2, n, nmax);
#endif
flag = 1;
#ifndef CPX
fft2(ar2, ai2, n, nmax, flag);
print2(ar2, ai2, n, nmax);
#else
fft2x(a2, n, nmax, flag);
print2x(a2, n, nmax);
#endif
return 1;
}
void fft1x(Complex a[], int n, int iter, int flag)
{
int i, it, j, j1, j2, k, xp, xp2;
double arg, sign, w;
Complex d1, d2, *p, *q, t, ww;
if(n < 2)
{
fprintf(stderr, "Error : n < 2 in fft1()\n");
return;
}
if(iter <= 0)
{
iter = 0;
i = n;
while((i /= 2) != 0) iter++;
}
j = 1;
for(i = 0; i < iter; i++) j *= 2;
if(n != j)
{
fprintf(stderr, "Error : n != 2 ^ k in fft1()\n");
return;
}
sign = (flag == 1)? 1.: -1.;
xp2 = n;
for(it = 0; it < iter; it++)
{
xp = xp2;
xp2 = xp / 2;
w = M_PI / xp2;
for(k = 0; k < xp2; k++)
{
arg = k * w;
ww = tocomplex(cos(arg), sign * sin(arg));
i = k - xp;
for(j = xp, p = a + i + xp, q = a + i + xp + xp2;
j <= n; j += xp, p += xp, q += xp)
{
t = csub(*p, *q);
*p = cadd(*p, *q);
*q = cmul(t, ww);
}
}
}
j1 = n / 2;
j2 = n - 1;
j = 1;
for(i = 1, p = a; i <= j2; i++, p++)
{
if(i < j) swapx(p, a + j - 1);
k = j1;
while(k < j)
{
j -= k;
k /= 2;
}
j += k;
}
if(flag == 0) return;
w = n;
for(i = 0, p = a; i < n; i++, p++) *p = cdiv1(*p, w);
return;
}
