def Jacobian(func, inputs, step_size=1e-7, fdtype='c'):
"""Calculate the Jacobian of a function.
INPUTS:
func: Function handle to use for Jacobian
inputs: Input values to function
step_size: Step size
fdtype: finite difference type ('c'entered, 'f'orward, 'b'ackward)
RETURNS:
jacobian: An mxn array as specified by the tuple dim.
"""
#test our return
#try to find dimensions by being smart
try:
ndim = len(func(*inputs)), len(inputs)
except TypeError:
ndim = 1, len(inputs)
jacobian = sp.zeros(ndim)
if fdtype is 'c':
for j in range(ndim[1]):
jacobian[:,j] = FD.cdiff(func, inputs, vary=[j], accur=6, degree=1, tol=step_size)
elif fdtype in ['f', 'b']:
for j in range(ndim[1]):
jacobian[:,j] = FD.fbdiff(func, inputs, vary=[j], accur=3, degree=1, direction=fdtype, tol=step_size)
return jacobian
def convergence():
"""Plot the convergence of the derivative approximation."""
f = np.cos
actual = -np.sin(3.0)
hvals = np.linspace(1e-5, 1e-1)
err1 = np.zeros(hvals.shape)
err2 = np.zeros(hvals.shape)
for i in xrange(len(hvals)):
err1[i] = np.abs(actual - FiniteDiff.der(f, np.array([3.0]), mode='forward', h=hvals[i], degree=1))
err2[i] = np.abs(actual - FiniteDiff.der(f, np.array([3.0]), mode='forward', h=hvals[i], degree=2))
plt.subplot(121)
plt.loglog(hvals, err1)
plt.ylim((1e-11, 1e-1))
plt.subplot(122)
plt.loglog(hvals, err2)
plt.ylim((1e-11, 1e-1))
plt.savefig('figures/convergence.pdf')
plt.clf()
def convergence():
"""Plot the convergence of the derivative approximation."""
f = np.cos
actual = -np.sin(3.0)
hvals = np.linspace(1e-5, 1e-1)
err1 = np.zeros(hvals.shape)
err2 = np.zeros(hvals.shape)
for i in xrange(len(hvals)):
err1[i] = np.abs(actual - FiniteDiff.der(
f, np.array([3.0]), mode='forward', h=hvals[i], degree=1))
err2[i] = np.abs(actual - FiniteDiff.der(
f, np.array([3.0]), mode='forward', h=hvals[i], degree=2))
plt.subplot(121)
plt.loglog(hvals, err1)
plt.ylim((1e-11, 1e-1))
plt.subplot(122)
plt.loglog(hvals, err2)
plt.ylim((1e-11, 1e-1))
plt.savefig('figures/convergence.pdf')
plt.clf()
"""
EPS = 1e-6
H = 1e-2
Y0 = 2
Y1 = 1.3
ALPHA0 = 0
ALPHA1 = 45
A = 0.7
B = 1
if __name__ == '__main__':
shoot = Shoot(A, B, Y0, Y1, H, EPS, ALPHA0, ALPHA1)
result = shoot.getAns()
x = list(np.arange(A, B, (B - A) / len(result)))
plt.plot(x, result)
plt.title("Методо пристрілки")
plt.show()
print("Shoot method")
k = 0
for i in result:
print('y%d' % k, i)
k += 1
finite = FiniteDiff(A, B, Y0, Y1, H, EPS)
print("\nFinite difference method")
rеsult = finite.getAns()
finite.print(result)
plt.plot(x, result)
plt.title("Методо скінчених різниць з використання метода прогонки")
plt.show()
