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 test_eighe_randmatrix():
N = 5
for a in xrange(10):
A = (2 * mp.randmatrix(N, N) - 1) + 1j * (2 * mp.randmatrix(N, N) - 1)
for i in xrange(0, N):
A[i,i] = mp.re(A[i,i])
for j in xrange(i + 1, N):
A[j,i] = mp.conj(A[i,j])
run_eighe(A)
def test_eighe_randmatrix():
N = 5
for a in xrange(10):
A = (2 * mp.randmatrix(N, N) - 1) + 1j * (2 * mp.randmatrix(N, N) - 1)
for i in xrange(0, N):
A[i, i] = mp.re(A[i, i])
for j in xrange(i + 1, N):
A[j, i] = mp.conj(A[i, j])
run_eighe(A)
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_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_gauss_quadrature_dynamic(verbose = False):
n = 5
A = mp.randmatrix(2 * n, 1)
def F(x):
r = 0
for i in xrange(len(A) - 1, -1, -1):
r = r * x + A[i]
return r
def run(qtype, FW, R, alpha = 0, beta = 0):
X, W = mp.gauss_quadrature(n, qtype, alpha = alpha, beta = beta)
a = 0
for i in xrange(len(X)):
a += W[i] * F(X[i])
b = mp.quad(lambda x: FW(x) * F(x), R)
c = mp.fabs(a - b)
if verbose:
print(qtype, c, a, b)
assert c < 1e-5
run("legendre", lambda x: 1, [-1, 1])
run("legendre01", lambda x: 1, [0, 1])
run("hermite", lambda x: mp.exp(-x*x), [-mp.inf, mp.inf])
run("laguerre", lambda x: mp.exp(-x), [0, mp.inf])
run("glaguerre", lambda x: mp.sqrt(x)*mp.exp(-x), [0, mp.inf], alpha = 1 / mp.mpf(2))
run("chebyshev1", lambda x: 1/mp.sqrt(1-x*x), [-1, 1])
run("chebyshev2", lambda x: mp.sqrt(1-x*x), [-1, 1])
run("jacobi", lambda x: (1-x)**(1/mp.mpf(3)) * (1+x)**(1/mp.mpf(5)), [-1, 1], alpha = 1 / mp.mpf(3), beta = 1 / mp.mpf(5) )
def test_eigsy_randmatrix():
N = 5
for a in xrange(10):
A = 2 * mp.randmatrix(N, N) - 1
for i in xrange(0, N):
for j in xrange(i + 1, N):
A[j, i] = A[i, j]
run_eigsy(A)
def test_eigsy_randmatrix():
N = 5
for a in xrange(10):
A = 2 * mp.randmatrix(N, N) - 1
for i in xrange(0, N):
for j in xrange(i + 1, N):
A[j,i] = A[i,j]
run_eigsy(A)
def test_svd_r_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
if mp.rand() > 0.5:
A *= 10
for x in xrange(m):
for y in xrange(n):
A[x, y] = int(A[x, y])
run_svd_r(A, full_matrices=full, verbose=False)
def test_svd_r_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
if mp.rand() > 0.5:
A *= 10
for x in xrange(m):
for y in xrange(n):
A[x,y]=int(A[x,y])
run_svd_r(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 test():
PF1,PF2 = mp.matrix(2, 1)
J1,J2 = mp.randmatrix(2,1)+1j*mp.randmatrix(2,1)
j1,j2 = mp.exp(-J1),mp.exp(-J2)
basis = spin_basis(3)
for i in range(len(basis)):
Z1,Z2,Z3 = basis[i]
PF1 += mp.exp(J1*Z1*Z2+J2*Z2*Z3)
jp,dF = L_transform(j1,j2)
Jp = -mp.log(jp)
basis = spin_basis(2)
for i in range(len(basis)):
Z1,Z2 = basis[i]
PF2 += mp.exp(dF+Jp*Z1*Z2)
print("--------------------------------------")
print("L-transform test:")
print("Original: ", PF1)
print("Renormalized:", PF2)
print("--------------------------------------")
PF1,PF2 = mp.matrix(2, 1)
J0,J1,J2,J3 = mp.randmatrix(4,1)+1j*mp.randmatrix(4,1)
j0,j1,j2,j3 = mp.exp(-J0),mp.exp(-J1),mp.exp(-J2),mp.exp(-J3)
j1p,j2p,j3p,dF = Y_transform(j0,j1,j2,j3)
J1p,J2p,J3p = -mp.log(j1p),-mp.log(j2p),-mp.log(j3p)
basis = spin_basis(4)
for i in range(len(basis)):
Z1,Z2,Z3,Z4 = basis[i]
PF1 += mp.exp(J0*Z1*Z2+J1*Z1*Z3+J2*Z2*Z3+J3*Z3*Z4)
PF2 += mp.exp(dF+J1p*Z1*Z3+J2p*Z2*Z3+J3p*Z3*Z4)
print("--------------------------------------")
print("Y-transform test:")
print("Original: ", PF1)
print("Renormalized:", PF2)
print("--------------------------------------")
PF1,PF2 = mp.matrix(2, 1)
J0,J1,J2 = mp.randmatrix(3,1)+1j*mp.randmatrix(3,1)
j0,j1,j2 = mp.exp(-J0),mp.exp(-J1),mp.exp(-J2)
j1p,j2p,dF = D_transform(j0,j1,j2)
J1p,J2p = -mp.log(j1p),-mp.log(j2p)
basis = spin_basis(3)
for i in range(len(basis)):
Z1,Z2,Z3 = basis[i]
PF1 += mp.exp(J0*Z1*Z2+J1*Z1*Z3+J2*Z2*Z3)
PF2 += mp.exp(dF+J1p*Z1*Z3+J2p*Z2*Z3)
print("--------------------------------------")
print("D-transform test:")
print("Original: ", PF1)
print("Renormalized:", PF2)
print("--------------------------------------")
#------------------------------------------------------------------------------
PF1,PF2 = mp.matrix(2, 1)
J0,J1,J2,J3,J4 = mp.randmatrix(5,1)+1j*mp.randmatrix(5,1)
J1=0
j0,j1,j2,j3,j4 = mp.exp(-J0),mp.exp(-J1),mp.exp(-J2),mp.exp(-J3),mp.exp(-J4)
j1p,j2p,j3p,j4p,j5p,dF = X_transform(j0,j1,j2,j3,j4)
J1p,J2p,J3p,J4p,J5p = -mp.log(j1p),-mp.log(j2p),-mp.log(j3p),-mp.log(j4p),-mp.log(j5p)
basis = spin_basis(5)
for i in range(len(basis)):
Z1,Z2,Z3,Z4,Z5 = basis[i]
PF1 += mp.exp(J0*Z1*Z2+J1*Z1*Z3+J2*Z2*Z3+J3*Z3*Z5+J4*Z3*Z4)
PF2 += mp.exp(dF+J1p*Z1*Z3+J2p*Z2*Z3+J3p*Z3*Z5+J4p*Z3*Z4+J5p*Z4*Z5)
print("--------------------------------------")
print("X-transform test:")
print("Original: ", PF1)
print("Renormalized:", PF2)
print("--------------------------------------")
return 0
# reajuste 0
d0 = np.identity(100)
d0[d0 == 1.0] = abs(-0.00000062521499573893501604735293439538)
d2 = mp.matrix(d0)
BBT1 = BBT0 + d2
E1 = mp.eig(BBT1, left=False, right=False)
E1 = mp.eig_sort(E1)
# choslesky
B0 = mp.cholesky(BBT0)
B1 = mp.cholesky(BBT1)
# el modelo
x_ant = Feb_80W.T[0, :].T
x0 = x_ant - M_Feb
alea = mp.randmatrix(100, 1)
med_sim = M_Mar
mes_sim = ((A * x0) + (B1 * alea)) + med_sim
s0 = mp.chop(BBT0 - B1 * B1.H)
s1 = mp.chop(BBT1 - B1 * B1.H)
Z_ant = np.array(x_ant, dtype=float)
Z_sim = np.array(mes_sim, dtype=float)
SK = st.ks_2samp(Z_ant, Z_sim)
# funciones
def parametros(Y, X):
M0_act = ((Y * Y.T) / 100)
