Source code for PyDynamic.misc.tools

# -*- coding: utf-8 -*-
"""
The :mod:`PyDynamic.misc.tools` module is a collection of miscellaneous helper
functions.

This module contains the following functions:

* :func:`print_vec`: Print vector (1D array) to the console or return as formatted
  string
* :func:`print_mat`: Print matrix (2D array) to the console or return as formatted
  string
* :func:`make_semiposdef`: Make quadratic matrix positive semi-definite
* :func:`FreqResp2RealImag`: Calculate real and imaginary parts from frequency
  response
* :func:`make_equidistant`: Interpolate non-equidistant time series to equidistant
* :func:`trimOrPad`: trim or pad (with zeros) a vector to desired length
* :func:`progress_bar`: A simple and reusable progress-bar
"""

import sys

import numpy as np
from scipy.sparse import eye, issparse
from scipy.sparse.linalg.eigen.arpack import eigs

__all__ = [
    "print_mat",
    "print_vec",
    "make_semiposdef",
    "FreqResp2RealImag",
    "make_equidistant",
    "trimOrPad",
    "progress_bar",
]


[docs]def trimOrPad(array, length, mode="constant"): """Trim or pad (with zeros) a vector to desired length""" if len(array) < length: # pad zeros to the right if too short return np.pad(array, (0, length - len(array)), mode=mode) else: # trim to given length otherwise return array[0:length]
[docs]def make_semiposdef(matrix, maxiter=10, tol=1e-12, verbose=False): """Make quadratic matrix positive semi-definite by increasing its eigenvalues Parameters ---------- matrix : (N,N) array_like the matrix to process maxiter : int the maximum number of iterations for increasing the eigenvalues tol : float tolerance for deciding if pos. semi-def. verbose : bool If `True` print smallest eigenvalue of the resulting matrix Returns ------- (N,N) array_like quadratic positive semi-definite matrix """ n, m = matrix.shape if n != m: raise ValueError("Matrix has to be quadratic") # use specialised functions for sparse matrices if issparse(matrix): # enforce symmetric matrix matrix = 0.5 * (matrix + matrix.T) # calculate smallest eigenvalue e = np.real(eigs(matrix, which="SR", return_eigenvectors=False)).min() count = 0 # increase the eigenvalues until matrix is positive semi-definite while e < tol and count < maxiter: matrix += (np.absolute(e) + tol) * eye(n, format=matrix.format) e = np.real(eigs(matrix, which="SR", return_eigenvectors=False)).min() count += 1 e = np.real(eigs(matrix, which="SR", return_eigenvectors=False)).min() # same procedure for non-sparse matrices else: matrix = 0.5 * (matrix + matrix.T) count = 0 e = np.real(np.linalg.eigvals(matrix)).min() while e < tol and count < maxiter: e = np.real(np.linalg.eigvals(matrix)).min() matrix += (np.absolute(e) + tol) * np.eye(n) e = np.real(np.linalg.eigvals(matrix)).min() if verbose: print("Final result of make_semiposdef: smallest eigenvalue is %e" % e) return matrix
[docs]def FreqResp2RealImag(Abs, Phase, Unc, MCruns=1e4): """ Calculate real and imaginary parts from frequency response Calculate real and imaginary parts from amplitude and phase with associated uncertainties. Parameters ---------- Abs: (N,) array_like amplitude values Phase: (N,) array_like phase values in rad Unc: (2N, 2N) or (2N,) array_like uncertainties MCruns: bool Iterations for Monte Carlo simulation Returns ------- Re, Im: (N,) array_like real and imaginary parts (best estimate) URI: (2N, 2N) array_like uncertainties assoc. with Re and Im """ if len(Abs) != len(Phase) or 2 * len(Abs) != len(Unc): raise ValueError("\nLength of inputs are inconsistent.") if len(Unc.shape) == 1: Unc = np.diag(Unc) Nf = len(Abs) AbsPhas = np.random.multivariate_normal( np.hstack((Abs, Phase)), Unc, int(MCruns) ) # draw MC inputs H = AbsPhas[:, :Nf] * np.exp( 1j * AbsPhas[:, Nf:] ) # calculate complex frequency response values RI = np.hstack((np.real(H), np.imag(H))) # transform to real, imag Re = np.mean(RI[:, :Nf]) Im = np.mean(RI[:, Nf:]) URI = np.cov(RI, rowvar=False) return Re, Im, URI
[docs]def make_equidistant(t, y, uy, dt=5e-2, kind="linear"): """ Interpolate non-equidistant time series to equidistant Interpolate measurement values and propagate uncertainties accordingly. Parameters ---------- t: (N,) array_like timestamps (or frequencies) y: (N,) array_like corresponding measurement values uy: (N,) array_like corresponding measurement values' standard uncertainties dt: float, optional desired interval length kind: str, optional Specifies the kind of interpolation for the measurement values as a string ('previous', 'next', 'nearest' or 'linear'). Returns ------- t_new : (M,) array_like interpolation timestamps (or frequencies) y_new : (M,) array_like interpolated measurement values uy_new : (M,) array_like interpolated measurement values' standard uncertainties References ---------- * White [White2017]_ """ from ..uncertainty.interpolation import interp1d_unc # Find t's maximum. t_max = np.max(t) # Setup new vector of timestamps. t_new = np.arange(np.min(t), t_max, dt) # Since np.arange in overflow situations results in the biggest values not # guaranteed to be smaller than t's maximum', we need to check for this and delete # these unexpected values. if t_new[-1] > t_max: t_new = t_new[t_new <= t_max] return interp1d_unc(t_new, t, y, uy, kind)
[docs]def progress_bar( count, count_max, width=30, prefix="", done_indicator="#", todo_indicator=".", fout=sys.stdout, ): """ A simple and reusable progress-bar Parameters ---------- count: int current status of iterations, assumed to be zero-based count_max: int total number of iterations width: int, optional width of the actual progressbar (actual printed line will be wider) prefix: str, optional some text that will be printed in front of the bar (i.e. "Progress of ABC:") done_indicator: str, optional what character is used as "already-done"-indicator todo_indicator: str, optional what character is used as "not-done-yet"-indicator fout: file-object, optional where the progress-bar should be written/printed to """ x = int(width * (count + 1) / count_max) progressString = "{PREFIX}[{DONE}{NOTDONE}] {COUNT}/{COUNTMAX}\r".format( PREFIX=prefix, DONE=x * done_indicator, NOTDONE=(width - x) * todo_indicator, COUNT=count + 1, COUNTMAX=count_max, ) fout.write(progressString)