Source code for openmdao.utils.cs_safe

"""
collection of complex-step safe functions to replace standard numpy operations.
"""

import numpy as np

if np.__version__[0] == '2':
    NumPy2 = True
else:
    NumPy2 = False


[docs]def abs(x): """ Complex-step safe version of numpy.abs function. Parameters ---------- x : ndarray Array value to be computed on. Returns ------- ndarray Absolute value. """ if isinstance(x, np.ndarray): # Changed in NumPy 2.0: Definition of complex sign changed to follow the Array API standard. # 1.x: For complex inputs, the sign function returns sign(x.real) + 0j if x.real != 0 # else sign(x.imag) + 0j. # 2.0: For complex inputs, the sign function returns x / abs(x), and 0 if x==0. if NumPy2 and np.any(np.iscomplex(x)): # replicate NumPy 1.x behavior for complex arrays z0_idx = x.real == 0 nz_idx = x.real != 0 signs = np.zeros(x.shape, dtype=complex) signs[nz_idx] = np.sign(x[nz_idx]).real + 0j signs[z0_idx] = np.sign(x[z0_idx].imag) + 0j return x * signs else: return x * np.sign(x) elif x.real < 0.0: return -x return x
[docs]def norm(x, axis=None): """ Complex-step safe version of numpy.linalg.norm function. Parameters ---------- x : ndarray Array value to be computed on. axis : None or int Axis to perform the norm up to. Returns ------- ndarray Matrix or vector norm. """ return np.sqrt(np.sum(x**2, axis=axis))
[docs]def arctan2(y, x): """ Numpy-compatible, complex-compatible arctan2 function for use with complex-step. Parameters ---------- y : float or complex The length of the side opposite the angle being determined. x : float or complex The length of the side adjacent to the angle being determined. Returns ------- ndarray The angle whose opposite side has length y and whose adjacent side has length x. """ if np.iscomplexobj(x) or np.iscomplexobj(y): a = np.real(y) b = np.imag(y) c = np.real(x) d = np.imag(x) return np.arctan2(a, c) + 1j * (c * b - a * d) / (a**2 + c**2) else: return np.arctan2(y, x)