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//#define WANT_STREAM
#define WANT_MATH
#include "include.h"
#include "config.h"
#include "newmatap.h"
//#include "newmatio.h"
#include "tmt.h"
#ifdef use_namespace
using namespace NEWMAT;
#endif
static void SlowFT(const ColumnVector& a, const ColumnVector&b,
ColumnVector& x, ColumnVector& y)
{
int n = a.Nrows();
x.ReSize(n); y.ReSize(n);
Real f = 6.2831853071795864769/n;
for (int j=1; j<=n; j++)
{
Real sumx = 0.0; Real sumy = 0.0;
for (int k=1; k<=n; k++)
{
Real theta = - (j-1) * (k-1) * f;
Real c = cos(theta); Real s = sin(theta);
sumx += c * a(k) - s * b(k); sumy += s * a(k) + c * b(k);
}
x(j) = sumx; y(j) = sumy;
}
}
static void SlowDTT_II(const ColumnVector& a, ColumnVector& c, ColumnVector& s)
{
int n = a.Nrows(); c.ReSize(n); s.ReSize(n);
Real f = 6.2831853071795864769 / (4*n);
int k;
for (k=1; k<=n; k++)
{
Real sum = 0.0;
const int k1 = k-1; // otherwise Visual C++ 5 fails
for (int j=1; j<=n; j++) sum += cos(k1 * (2*j-1) * f) * a(j);
c(k) = sum;
}
for (k=1; k<=n; k++)
{
Real sum = 0.0;
for (int j=1; j<=n; j++) sum += sin(k * (2*j-1) * f) * a(j);
s(k) = sum;
}
}
static void SlowDTT(const ColumnVector& a, ColumnVector& c, ColumnVector& s)
{
int n1 = a.Nrows(); int n = n1 - 1;
c.ReSize(n1); s.ReSize(n1);
Real f = 6.2831853071795864769 / (2*n);
int k;
int sign = 1;
for (k=1; k<=n1; k++)
{
Real sum = 0.0;
for (int j=2; j<=n; j++) sum += cos((j-1) * (k-1) * f) * a(j);
c(k) = sum + (a(1) + sign * a(n1)) / 2.0;
sign = -sign;
}
for (k=2; k<=n; k++)
{
Real sum = 0.0;
for (int j=2; j<=n; j++) sum += sin((j-1) * (k-1) * f) * a(j);
s(k) = sum;
}
s(1) = s(n1) = 0;
}
static void test(int n)
{
Tracer et("Test FFT");
ColumnVector A(n), B(n), X, Y;
for (int i=0; i<n; i++)
{
Real f = 6.2831853071795864769*i/n;
A.element(i) = fabs(sin(7.0*f) + 0.5 * cos(19.0 * f)) + (Real)i/(Real)n;
B.element(i) = fabs(0.25 * cos(31.0 * f)) + (Real)i/(Real)n;
}
FFT(A, B, X, Y); FFTI(X, Y, X, Y);
X = X - A; Y = Y - B;
Clean(X,0.000000001); Clean(Y,0.000000001); Print(X); Print(Y);
}
static void test1(int n)
{
Tracer et("Test RealFFT");
ColumnVector A(n), B(n), X, Y;
for (int i=0; i<n; i++)
{
Real f = 6.2831853071795864769*i/n;
A.element(i) = fabs(sin(7.0*f) + 0.5 * cos(19.0 * f)) + (Real)i/(Real)n;
}
B = 0.0;
FFT(A, B, X, Y);
B.CleanUp(); // release some space
int n2 = n/2+1;
ColumnVector X1,Y1,X2,Y2;
RealFFT(A, X1, Y1);
X2 = X1 - X.Rows(1,n2); Y2 = Y1 - Y.Rows(1,n2);
Clean(X2,0.000000001); Clean(Y2,0.000000001); Print(X2); Print(Y2);
X2.CleanUp(); Y2.CleanUp(); // release some more space
RealFFTI(X1,Y1,B);
B = A - B;
Clean(B,0.000000001); Print(B);
}
static void test2(int n)
{
Tracer et("cf FFT and slow FT");
ColumnVector A(n), B(n), X, Y, X1, Y1;
for (int i=0; i<n; i++)
{
Real f = 6.2831853071795864769*i/n;
A.element(i) = fabs(sin(7.0*f) - 0.5 * cos(19.0 * f)) + (Real)i/(Real)n;
B.element(i) = fabs(0.25 * cos(31.0 * f)) - (Real)i/(Real)n;
}
FFT(A, B, X, Y);
SlowFT(A, B, X1, Y1);
X = X - X1; Y = Y - Y1;
Clean(X,0.000000001); Clean(Y,0.000000001); Print(X); Print(Y);
}
static void test3(int n)
{
Tracer et("cf slow and fast DCT_II and DST_II");
ColumnVector A(n), X, Y, X1, Y1;
for (int i=0; i<n; i++)
{
Real f = 6.2831853071795864769*i/n;
A.element(i) = fabs(sin(7.0*f) - 0.55 * cos(19.0 * f)
+ .73 * sin(6.0 * f)) + (Real)i/(Real)n;
}
DCT_II(A, X); DST_II(A, Y);
SlowDTT_II(A, X1, Y1);
X -= X1; Y -= Y1;
Clean(X,0.000000001); Clean(Y,0.000000001); Print(X); Print(Y);
}
static void test4(int n)
{
Tracer et("Test DCT_II");
ColumnVector A1(n);
for (int i=0; i<n; i++)
{
Real f = 6.2831853071795864769*i/n;
A1.element(i) =
fabs(sin(7.0*f) + 0.7588 * cos(19.0 * f) + (Real)i/(Real)n);
}
// do DCT II by ordinary FFT
ColumnVector P(2*n), Q(2*n);
P = 0.0; Q = 0.0; P.Rows(1,n) = A1;
FFT(P, Q, P, Q);
ColumnVector B1(n);
for (int k=0; k<n; k++)
{
Real arg = k * 6.2831853071795864769 / (4 * n);
B1(k+1) = P(k+1) * cos(arg) + Q(k+1) * sin(arg);
}
// use DCT_II routine
ColumnVector B2;
DCT_II(A1,B2);
// test inverse
ColumnVector A2;
DCT_II_inverse(B2,A2);
A1 -= A2; B1 -= B2;
Clean(A1,0.000000001); Clean(B1,0.000000001); Print(A1); Print(B1);
}
static void test5(int n)
{
Tracer et("Test DST_II");
ColumnVector A1(n);
for (int i=0; i<n; i++)
{
Real f = 6.2831853071795864769*i/n;
A1.element(i) =
fabs(sin(11.0*f) + 0.7588 * cos(19.0 * f) + (Real)i/(Real)n);
}
// do DST II by ordinary FFT
ColumnVector P(2*n), Q(2*n);
P = 0.0; Q = 0.0; P.Rows(1,n) = A1;
FFT(P, Q, P, Q);
ColumnVector B1(n);
for (int k=1; k<=n; k++)
{
Real arg = k * 6.2831853071795864769 / (4 * n);
B1(k) = P(k+1) * sin(arg) - Q(k+1) * cos(arg);
}
// use DST_II routine
ColumnVector B2;
DST_II(A1,B2);
// test inverse
ColumnVector A2;
DST_II_inverse(B2,A2);
A1 -= A2; B1 -= B2;
Clean(A1,0.000000001); Clean(B1,0.000000001); Print(A1); Print(B1);
}
static void test6(int n)
{
Tracer et("Test DST");
ColumnVector A1(n+1);
A1(1) = A1(n+1) = 0;
for (int i=1; i<n; i++)
{
Real f = 6.2831853071795864769*i/n;
A1.element(i) =
fabs(sin(11.0*f) + 0.7588 * cos(19.0 * f) + (Real)i/(Real)n);
}
// do DST by ordinary FFT
ColumnVector P(2*n), Q(2*n); P = 0.0; Q = 0.0; P.Rows(1,n+1) = A1;
FFT(P, Q, P, Q);
ColumnVector B1 = -Q.Rows(1,n+1);
// use DST routine
ColumnVector B2;
DST(A1,B2);
// test inverse
ColumnVector A2;
DST_inverse(B2,A2);
A1 -= A2; B1 -= B2;
Clean(A1,0.000000001); Clean(B1,0.000000001); Print(A1); Print(B1);
}
static void test7(int n)
{
Tracer et("Test DCT");
ColumnVector A1(n+1);
for (int i=0; i<=n; i++)
{
Real f = 6.2831853071795864769*i/n;
A1.element(i) =
fabs(sin(17.0*f) + 0.6399 * cos(23.0 * f) + 1.32*(Real)i/(Real)n);
}
// do DCT by ordinary FFT
ColumnVector P(2*n), Q(2*n); P = 0.0; Q = 0.0; P.Rows(1,n+1) = A1;
P(1) /= 2.0; P(n+1) /= 2.0;
FFT(P, Q, P, Q);
ColumnVector B1 = P.Rows(1,n+1);
// use DCT routine
ColumnVector B2;
DCT(A1,B2);
// test inverse
ColumnVector A2;
DCT_inverse(B2,A2);
A1 -= A2; B1 -= B2;
Clean(A1,0.000000001); Clean(B1,0.000000001); Print(A1); Print(B1);
}
static void test8(int n)
{
Tracer et("cf slow and fast DCT and DST");
ColumnVector A(n+1), X, Y, X1, Y1;
for (int i=0; i<=n; i++)
{
Real f = 6.2831853071795864769*i/n;
A.element(i) = fabs(sin(7.0*f) - 0.5 * cos(19.0 * f) +
0.3 * (Real)i/(Real)n);
}
DCT(A, X); DST(A, Y);
SlowDTT(A, X1, Y1);
X -= X1; Y -= Y1;
Clean(X,0.000000001); Clean(Y,0.000000001); Print(X); Print(Y);
}
void trymatf()
{
Tracer et("Fifteenth test of Matrix package");
Tracer::PrintTrace();
int i;
ColumnVector A(12), B(12);
for (i = 1; i <=12; i++)
{
Real i1 = i - 1;
A(i) = .7
+ .2 * cos(6.2831853071795864769 * 4.0 * i1 / 12)
+ .3 * sin(6.2831853071795864769 * 3.0 * i1 / 12);
B(i) = .9
+ .5 * sin(6.2831853071795864769 * 2.0 * i1 / 12)
+ .4 * cos(6.2831853071795864769 * 1.0 * i1 / 12);
}
FFT(A, B, A, B);
A(1) -= 8.4; A(3) -= 3.0; A(5) -= 1.2; A(9) -= 1.2; A(11) += 3.0;
B(1) -= 10.8; B(2) -= 2.4; B(4) += 1.8; B(10) -= 1.8; B(12) -= 2.4;
Clean(A,0.000000001); Clean(B,0.000000001); Print(A); Print(B);
// test FFT
test(2048); test(2000); test(27*81); test(2310); test(49*49);
test(13*13*13); test(43*47);
test(16*16*3); test(16*16*5); test(16*16*7);
test(8*8*5);
// test realFFT
test1(2); test1(98); test1(22); test1(100);
test1(2048); test1(2000); test1(35*35*2);
// compare FFT and slowFFT
test2(1); test2(13); test2(12); test2(9); test2(16); test2(30); test2(42);
test2(24); test2(8); test2(40); test2(48); test2(4); test2(3); test2(5);
test2(32); test2(2);
// compare DCT_II, DST_II and slow versions
test3(2); test3(26); test3(32); test3(18);
// test DCT_II and DST_II
test4(2); test5(2);
test4(202); test5(202);
test4(1000); test5(1000);
// test DST and DCT
test6(2); test7(2);
test6(274); test7(274);
test6(1000); test7(1000);
// compare DCT, DST and slow versions
test8(2); test8(26); test8(32); test8(18);
// now do the same thing all over again forcing use of old FFT
FFT_Controller::OnlyOldFFT = true;
for (i = 1; i <=12; i++)
{
Real i1 = i - 1;
A(i) = .7
+ .2 * cos(6.2831853071795864769 * 4.0 * i1 / 12)
+ .3 * sin(6.2831853071795864769 * 3.0 * i1 / 12);
B(i) = .9
+ .5 * sin(6.2831853071795864769 * 2.0 * i1 / 12)
+ .4 * cos(6.2831853071795864769 * 1.0 * i1 / 12);
}
FFT(A, B, A, B);
A(1) -= 8.4; A(3) -= 3.0; A(5) -= 1.2; A(9) -= 1.2; A(11) += 3.0;
B(1) -= 10.8; B(2) -= 2.4; B(4) += 1.8; B(10) -= 1.8; B(12) -= 2.4;
Clean(A,0.000000001); Clean(B,0.000000001); Print(A); Print(B);
// test FFT
test(2048); test(2000); test(27*81); test(2310); test(49*49);
test(13*13*13); test(43*47);
test(16*16*3); test(16*16*5); test(16*16*7);
test(8*8*5);
// test realFFT
test1(2); test1(98); test1(22); test1(100);
test1(2048); test1(2000); test1(35*35*2);
// compare FFT and slowFFT
test2(1); test2(13); test2(12); test2(9); test2(16); test2(30); test2(42);
test2(24); test2(8); test2(40); test2(48); test2(4); test2(3); test2(5);
test2(32); test2(2);
// compare DCT_II, DST_II and slow versions
test3(2); test3(26); test3(32); test3(18);
// test DCT_II and DST_II
test4(2); test5(2);
test4(202); test5(202);
test4(1000); test5(1000);
// test DST and DCT
test6(2); test7(2);
test6(274); test7(274);
test6(1000); test7(1000);
// compare DCT, DST and slow versions
test8(2); test8(26); test8(32); test8(18);
FFT_Controller::OnlyOldFFT = false;
}
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