#!/usr/bin/env python2.3import mathimport sysimport randompi=math.pie=math.ej=complex(0,1)def fft(f,inv):    n=len(f)    if n==1:        return f    for p in 2,3,5:        if n%p==0:            break    else:        raise Exception('%s not factorable ' % n)    m = n/p    Fout=[]    for q in range(p): # 0,1        fp = f[q::p]        Fp = fft( fp ,inv)        Fout.extend( Fp )    for u in range(m):        scratch = Fout[u::m] # u to end in strides of m        for q1 in range(p):            k = q1*m + u  # indices to Fout above that became scratch            Fout[ k ] = scratch[0] # cuz e**0==1 in loop below            for q in range(1,p):                if inv:                    t = e ** ( j*2*pi*k*q/n )                else:                                        t = e ** ( -j*2*pi*k*q/n )                Fout[ k ] += scratch[q] * t    return Foutdef rifft(F):    N = len(F) - 1    Z = [0] * (N)    for k in range(N):        Fek = ( F[k] + F[-k-1].conjugate() )        Fok = ( F[k] - F[-k-1].conjugate() ) * e ** (j*pi*k/N)        Z[k] = Fek + j*Fok    fp = fft(Z , 1)    f = []    for c in fp:        f.append(c.real)        f.append(c.imag)    return fdef real_fft( f,inv ):    if inv:        return rifft(f)    N = len(f) / 2    res = f[::2]    ims = f[1::2]    fp = [ complex(r,i) for r,i in zip(res,ims) ]    print 'fft input ', fp    Fp = fft( fp ,0 )    print 'fft output ', Fp    F = [ complex(0,0) ] * ( N+1 )        F[0] = complex( Fp[0].real + Fp[0].imag , 0 )     for k in range(1,N/2+1):        tw = e ** ( -j*pi*(.5+float(k)/N ) )                F1k = Fp[k] + Fp[N-k].conjugate()        F2k = Fp[k] - Fp[N-k].conjugate()        F2k *= tw        F[k] = ( F1k + F2k ) * .5        F[N-k] = ( F1k - F2k ).conjugate() * .5        #F[N-k] = ( F1kp + e ** ( -j*pi*(.5+float(N-k)/N ) ) * F2kp ) * .5        #F[N-k] = ( F1k.conjugate() - tw.conjugate() * F2k.conjugate() ) * .5    F[N] = complex( Fp[0].real - Fp[0].imag , 0 )     return Fdef main():    #fft_func = fft    fft_func = real_fft    tvec = [0.309655,0.815653,0.768570,0.591841,0.404767,0.637617,0.007803,0.012665]    Ftvec = [ complex(r,i) for r,i in zip(                [3.548571,-0.378761,-0.061950,0.188537,-0.566981,0.188537,-0.061950,-0.378761],                [0.000000,-1.296198,-0.848764,0.225337,0.000000,-0.225337,0.848764,1.296198] ) ]    F = fft_func( tvec,0 )    nerrs= 0    for i in range(len(Ftvec)/2 + 1):        if abs( F[i] - Ftvec[i] )> 1e-5:            print 'F[%d]: %s != %s' % (i,F[i],Ftvec[i])            nerrs += 1    print '%d errors in forward fft' % nerrs    if nerrs:        return    trec = fft_func( F , 1 )    for i in range(len(trec) ):        trec[i] /= len(trec)    for i in range(len(tvec) ):        if abs( trec[i] - tvec[i] )> 1e-5:            print 't[%d]: %s != %s' % (i,tvec[i],trec[i])            nerrs += 1    print '%d errors in reverse fft' % nerrsdef make_random(dims=[1]):    import Numeric     res = []    for i in range(dims[0]):        if len(dims)==1:            r=random.uniform(-1,1)            i=random.uniform(-1,1)            res.append( complex(r,i) )        else:            res.append( make_random( dims[1:] ) )    return Numeric.array(res)def flatten(x):    import Numeric    ntotal = Numeric.product(Numeric.shape(x))    return Numeric.reshape(x,(ntotal,))def randmat( ndims ):    dims=[]    for i in range( ndims ):        curdim = int( random.uniform(2,4) )        dims.append( curdim )    return make_random(dims )def test_fftnd(ndims=3):    import FFT    import Numeric    x=randmat( ndims )    print 'dimensions=%s' % str( Numeric.shape(x) )    #print 'x=%s' %str(x)    xver = FFT.fftnd(x)    x2=myfftnd(x)    err = xver - x2    errf = flatten(err)    xverf = flatten(xver)    errpow = Numeric.vdot(errf,errf)+1e-10    sigpow = Numeric.vdot(xverf,xverf)+1e-10    snr = 10*math.log10(abs(sigpow/errpow) )    if snr<80:        print xver        print x2    print 'SNR=%sdB' % str( snr ) def myfftnd(x):    import Numeric    xf = flatten(x)    Xf = fftndwork( xf , Numeric.shape(x) )    return Numeric.reshape(Xf,Numeric.shape(x) )def fftndwork(x,dims):    import Numeric    dimprod=Numeric.product( dims )    for k in range( len(dims) ):        cur_dim=dims[ k ]        stride=dimprod/cur_dim        next_x = [complex(0,0)]*len(x)        for i in range(stride):            next_x[i*cur_dim:(i+1)*cur_dim] = fft(x[i:(i+cur_dim)*stride:stride],0)        x = next_x    return xif __name__ == "__main__":    try:        nd = int(sys.argv[1])    except:        nd=None    if nd:            test_fftnd( nd )    else:            sys.exit(0)