def test_nsolve():
# onedimensional
x = Symbol('x')
assert nsolve(sin(x), 2) - pi.evalf() < 1e-15
assert nsolve(Eq(2 * x, 2), x, -10) == nsolve(2 * x - 2, -10)
# Testing checks on number of inputs
raises(TypeError, lambda: nsolve(Eq(2 * x, 2)))
raises(TypeError, lambda: nsolve(Eq(2 * x, 2), x, 1, 2))
# issue 4829
assert nsolve(x**2 / (1 - x) / (1 - 2 * x)**2 - 100, x, 0) # doesn't fail
# multidimensional
x1 = Symbol('x1')
x2 = Symbol('x2')
f1 = 3 * x1**2 - 2 * x2**2 - 1
f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8
f = Matrix((f1, f2)).T
F = lambdify((x1, x2), f.T, modules='mpmath')
for x0 in [(-1, 1), (1, -2), (4, 4), (-4, -4)]:
x = nsolve(f, (x1, x2), x0, tol=1.e-8)
assert mnorm(F(*x), 1) <= 1.e-10
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago (z was added to make it 3-dimensional)
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
f1 = -x + 2 * y
f2 = (x**2 + x * (y**2 - 2) - 4 * y) / (x + 4)
f3 = sqrt(x**2 + y**2) * z
f = Matrix((f1, f2, f3)).T
F = lambdify((x, y, z), f.T, modules='mpmath')
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
assert list(map(round, getroot((1, 1, 1)))) == [2.0, 1.0, 0.0]
assert nsolve([Eq(f1), Eq(f2), Eq(f3)], [x, y, z],
(1, 1, 1)) # just see that it works
a = Symbol('a')
assert abs(
nsolve(1 / (0.001 + a)**3 - 6 /
(0.9 - a)**3, a, 0.3) - mpf('0.31883011387318591')) < 1e-15
def test_nsolve():
# onedimensional
x = Symbol('x')
assert nsolve(sin(x), 2) - pi.evalf() < 1e-15
assert nsolve(Eq(2*x, 2), x, -10) == nsolve(2*x - 2, -10)
# Testing checks on number of inputs
raises(TypeError, lambda: nsolve(Eq(2*x, 2)))
raises(TypeError, lambda: nsolve(Eq(2*x, 2), x, 1, 2))
# issue 4829
assert nsolve(x**2/(1 - x)/(1 - 2*x)**2 - 100, x, 0) # doesn't fail
# multidimensional
x1 = Symbol('x1')
x2 = Symbol('x2')
f1 = 3 * x1**2 - 2 * x2**2 - 1
f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8
f = Matrix((f1, f2)).T
F = lambdify((x1, x2), f.T, modules='mpmath')
for x0 in [(-1, 1), (1, -2), (4, 4), (-4, -4)]:
x = nsolve(f, (x1, x2), x0, tol=1.e-8)
assert mnorm(F(*x), 1) <= 1.e-10
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago (z was added to make it 3-dimensional)
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
f1 = -x + 2*y
f2 = (x**2 + x*(y**2 - 2) - 4*y) / (x + 4)
f3 = sqrt(x**2 + y**2)*z
f = Matrix((f1, f2, f3)).T
F = lambdify((x, y, z), f.T, modules='mpmath')
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
assert list(map(round, getroot((1, 1, 1)))) == [2.0, 1.0, 0.0]
assert nsolve([Eq(
f1), Eq(f2), Eq(f3)], [x, y, z], (1, 1, 1)) # just see that it works
a = Symbol('a')
assert nsolve(1/(0.001 + a)**3 - 6/(0.9 - a)**3, a, 0.3).ae(
mpf('0.31883011387318591'))
def cond(_matrix):
return mnorm(_matrix, 1)
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
def getroot(x0):
root = nsolve(f, (x, y, z), x0)
assert mnorm(F(*root), 1) <= 1.e-8
return root
],
'agm': [
'primitive',
[lambda x, y: mp.agm(x) if y is None else mp.agm(x, y[0]), None]
],
#
'matrix': [
'primitive',
[
lambda x, y: mp.matrix(x) if isa(x, Vector) else mp.matrix(x)
if y is None else mp.matrix(x, y[0]), None
]
],
'matrix-ref': ['primitive', [lambda x, y: x[y[0], y[1], [0]], None]],
'matrix-set': [
'primitive',
[lambda x, y: matrix_set(x, y[0], y[1][0], y[1][1][0]), None]
],
'zeros': ['primitive', [lambda x, y: mp.zeros(x), None]],
'ones': ['primitive', [lambda x, y: mp.ones(x), None]],
'eye': ['primitive', [lambda x, y: mp.eye(x), None]],
'diag': ['primitive', [lambda x, y: mp.diag(x), None]],
'randmatrix': ['primitive', [lambda x, y: mp.randmatrix(x), None]],
'matrix-inv': ['primitive', [lambda x, y: x**(-1), None]],
'norm': [
'primitive',
[lambda x, y: mp.norm(x) if y is None else mp.norm(x, y[0]), None]
],
'mnorm': ['primitive', [lambda x, y: mp.mnorm(x, y[0]), None]],
}
if i > j:
d_mat_b[ij_index] = float(mpfr_sqrt3 * (i + 1))
mp_mat_b[ij_index] = mp_sqrt3 * mpmath.mp.mpf(i + 1)
mpfr_mat_b[ij_index] = mpfr_sqrt3 * gmpy2.mpfr(i + 1)
else:
d_mat_b[ij_index] = float(mpfr_sqrt3 * (j + 1))
mp_mat_b[ij_index] = mp_sqrt3 * mpmath.mp.mpf(j + 1)
mpfr_mat_b[ij_index] = mpfr_sqrt3 * gmpy2.mpfr(j + 1)
mpmat_b[i, j] = mp_mat_b[ij_index]
print('double= ', xd_norm_fro(d_mat_a, row_dim, mid_dim, d_zero),
xd_norm_fro(d_mat_b, mid_dim, col_dim, d_zero))
print('mp = ', xd_norm_fro(mp_mat_a, row_dim, mid_dim, mp_zero),
xd_norm_fro(mp_mat_b, mid_dim, col_dim, mp_zero))
print('mpmat = ', mpmath.mnorm(mpmat_a, 'f'),
mpmath.mnorm(mpmat_b, 'f'))
print('mpfr = ', xd_norm_fro(mpfr_mat_a, row_dim, mid_dim, mpfr_zero),
xd_norm_fro(mpfr_mat_b, mid_dim, col_dim, mpfr_zero))
# double
start_time = time.time()
d_mat_c = xd_mymatmul(d_mat_a, row_dim, mid_dim, d_mat_b, mid_dim,
col_dim, d_zero)
end_time = time.time()
d_matmul_time = end_time - start_time
print('d(', 53, ')')
# cProfile.run('xd_mymatmul(d_mat_a, row_dim, mid_dim, d_mat_b, mid_dim, col_dim, d_zero)')
# mpmath
start_time = time.time()