def apply(self, f_del, h, step_ratio=2.0):
"""
Apply finite difference rule along the first axis.
Return derivative estimates of fun at x0 for a sequence of stepsizes h
Parameters
----------
f_del: finite differences
h: steps
"""
fd_rule = self.rule(step_ratio)
ne = h.shape[0]
nr = fd_rule.size - 1
_assert(
nr < ne, 'num_steps ({0:d}) must be larger than '
'({1:d}) n + order - 1 = {2:d} + {3:d} -1'
' ({4:s})'.format(ne, nr + 1, self.n, self.order, self.method))
f_diff = convolve(f_del, fd_rule[::-1], axis=0, origin=nr // 2)
der_init = f_diff / (h**self.n)
ne = max(ne - nr, 1)
return der_init[:ne], h[:ne]
def _apply_fd_rule(self, step_ratio, sequence, steps):
"""
Return derivative estimates of fun at x0 for a sequence of stepsizes h
Member variables used
---------------------
n
"""
f_del, h, original_shape = self._vstack(sequence, steps)
fd_rule = self._get_finite_difference_rule(step_ratio)
ne = h.shape[0]
nr = fd_rule.size - 1
_assert(nr < ne, 'num_steps ({0:d}) must be larger than '
'({1:d}) n + order - 1 = {2:d} + {3:d} -1'
' ({4:s})'.format(ne, nr+1, self.n, self.order, self.method))
f_diff = convolve(f_del, fd_rule[::-1], axis=0, origin=nr // 2)
der_init = f_diff / (h ** self.n)
ne = max(ne - nr, 1)
return der_init[:ne], h[:ne], original_shape
def _apply_fd_rule(self, step_ratio, sequence, steps):
"""
Return derivative estimates of f at x0 for a sequence of stepsizes h
Member variables used
---------------------
n
"""
f_del, h, original_shape = self._vstack(sequence, steps)
fd_rule = self._get_finite_difference_rule(step_ratio)
ne = h.shape[0]
nr = fd_rule.size - 1
_assert(nr < ne, 'num_steps ({0:d}) must be larger than '
'({1:d}) n + order - 1 = {2:d} + {3:d} -1'
' ({4:s})'.format(ne, nr+1, self.n, self.order, self.method)
)
f_diff = convolve(f_del, fd_rule[::-1], axis=0, origin=nr // 2)
der_init = f_diff / (h ** self.n)
ne = max(ne - nr, 1)
return der_init[:ne], h[:ne], original_shape
def _apply_fd_rule(self, fd_rule, sequence, steps):
"""
Return derivative estimates of f at x0 for a sequence of stepsizes h
Member variables used
---------------------
n
"""
f_del, h, original_shape = self._vstack(sequence, steps)
ne = h.shape[0]
if ne < fd_rule.size:
raise ValueError('num_steps (%d) must be larger than '
'(%d) n + order - 1 = %d + %d -1'
' (%s)' % (ne, fd_rule.size, self.n, self.order,
self.method)
)
nr = (fd_rule.size-1)
f_diff = convolve(f_del, fd_rule[::-1], axis=0, origin=nr//2)
der_init = f_diff / (h ** self.n)
ne = max(ne - nr, 1)
return der_init[:ne], h[:ne], original_shape