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_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))
