def test_svd_c_rand():
for i in xrange(5):
full = mp.rand() > 0.5
m = 1 + int(mp.rand() * 10)
n = 1 + int(mp.rand() * 10)
A = (2 * mp.randmatrix(m, n) - 1) + 1j * (2 * mp.randmatrix(m, n) - 1)
if mp.rand() > 0.5:
A *= 10
for x in xrange(m):
for y in xrange(n):
A[x,y]=int(mp.re(A[x,y])) + 1j * int(mp.im(A[x,y]))
run_svd_c(A, full_matrices=full, verbose=False)
def test_eig_dyn():
v = 0
for i in xrange(5):
n = 1 + int(mp.rand() * 5)
if mp.rand() > 0.5:
# real
A = 2 * mp.randmatrix(n, n) - 1
if mp.rand() > 0.5:
A *= 10
for x in xrange(n):
for y in xrange(n):
A[x,y] = int(A[x,y])
else:
A = (2 * mp.randmatrix(n, n) - 1) + 1j * (2 * mp.randmatrix(n, n) - 1)
if mp.rand() > 0.5:
A *= 10
for x in xrange(n):
for y in xrange(n):
A[x,y] = int(mp.re(A[x,y])) + 1j * int(mp.im(A[x,y]))
run_hessenberg(A, verbose = v)
run_schur(A, verbose = v)
run_eig(A, verbose = v)
def _eigenvals_eigenvects_mpmath(M):
norm2 = lambda v: mp.sqrt(sum(i**2 for i in v))
v1 = None
prec = max([x._prec for x in M.atoms(Float)])
eps = 2**-prec
while prec < DEFAULT_MAXPREC:
with workprec(prec):
A = mp.matrix(M.evalf(n=prec_to_dps(prec)))
E, ER = mp.eig(A)
v2 = norm2([i for e in E for i in (mp.re(e), mp.im(e))])
if v1 is not None and mp.fabs(v1 - v2) < eps:
return E, ER
v1 = v2
prec *= 2
# we get here because the next step would have taken us
# past MAXPREC or because we never took a step; in case
# of the latter, we refuse to send back a solution since
# it would not have been verified; we also resist taking
# a small step to arrive exactly at MAXPREC since then
# the two calculations might be artificially close.
raise PrecisionExhausted
R = np.ndarray(f.size)
I = np.ndarray(f.size)
Gr = np.ndarray(f.size)
Gi = np.ndarray(f.size)
for n in range(f.size):
Zap[n] = ZapA[n]*( i0(gammac[n]*a) / i1(gammac[n]*a) )
Zbp[n] = ZbpA[n] * ((i0(gammac[n]*b) * k1(gammac[n]*c) + k0(gammac[n]*b)*i1(gammac[n]*c)) / ( i1(gammac[n]*c)*k1(gammac[n]*b) - i1(gammac[n]*b)*k1(gammac[n]*c) ) )
ZL[n] = 1j*omega[n]*Lp
YC[n] = 1j*omega[n]*Cp
Zp[n] = Zap[n] + Zbp[n] + ZL[n]
Yp[n] = YC[n] # + G[n]
Zc[n] = mp.sqrt(Zp[n]/Yp[n])
A[n] = mp.fabs(Zc[n])
R[n] = mp.re(Zc[n])
I[n] = mp.im(Zc[n])
Gr[n] = mp.re(mp.sqrt(Zp[n]*Yp[n]))
Gi[n] = mp.im(mp.sqrt(Zp[n]*Yp[n]))
fig = plt.figure()
plt.plot(f/10**6, A, label='Magnitude', color='red')
plt.xlabel('Frequency [MHz]')
plt.ylabel('Magnitude of Z$_{c}$ [$\Omega$]')
plt.legend()
plt.xlim([-0.3,100])
#plt.show()
fig2 = plt.figure()
plt.plot(f/10**6, R, label='Real Part', color='red')
plt.xlabel('Frequency [MHz]')
plt.ylabel('Real Part of Z$_{c}$ [$\Omega$]')
plt.legend()
from mpmath import mp
mp.dps = 5
wx = mp.mpf('9'); wy = mp.mpf('6')
phi = (1 + mp.sqrt(5)) / 2
phi = mp.power(phi, 2)
coeffs = [
6,
7 * wx + 2 * wy,
wx * ((3 - phi)*wy + 2*wx),
(1 - phi) * mp.power(wx, 2) * wy
]
roots = mp.polyroots(coeffs, 15)
b = [root for root in roots if mp.im(root) == mp.mpf(0)][0]
bottom = b + mp.power(b, 2) / (wx + b)
print(
"Print dimensions: {wx!s} x {wy!s}\n"
"Resulting border: {b!s}\n"
"Resulting bottom border: {bottom!s}"
.format(wx=wx, wy=wy, b=b, bottom=bottom)
)
v = dict(
mat_l=0 - b,
mat_t=b,
mat_w=wx + 2 * b,
mat_h=-1 * (wy + b + bottom),
)
def mp_to_complex(mpcplx):
mpreal = mp.re(mpcplx)
mpimag = mp.im(mpcplx)
flreal = np.float(mp.nstr(mpreal, mp.dps))
flimag = np.float(mp.nstr(mpimag, mp.dps))
return flreal + 1j * flimag
def mp_im(mpcarr):
imarr = mp.zero * np.zeros_like(mpcarr)
for i in range(len(mpcarr)):
imarr[i] = mp.im(mpcarr[i])
return imarr
def plots(self, re_lerp, im_lerp):
return [[(re_lerp(mp.re(z)), im_lerp(mp.im(z))) for z in zs]
for t, zs in self.pts]
