Source code for pymatgen.util.num

# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.


"""
This module provides utilities for basic math operations.
"""

import collections

import numpy as np


def abs_cap(val, max_abs_val=1):
    """
    Returns the value with its absolute value capped at max_abs_val.
    Particularly useful in passing values to trignometric functions where
    numerical errors may result in an argument > 1 being passed in.

    Args:
        val (float): Input value.
        max_abs_val (float): The maximum absolute value for val. Defaults to 1.

    Returns:
        val if abs(val) < 1 else sign of val * max_abs_val.
    """
    return max(min(val, max_abs_val), -max_abs_val)


def sort_dict(d, key=None, reverse=False):
    """
    Sorts a dict by value.

    Args:
        d: Input dictionary
        key: Function which takes an tuple (key, object) and returns a value to
            compare and sort by. By default, the function compares the values
            of the dict i.e. key = lambda t : t[1]
        reverse: Allows to reverse sort order.

    Returns:
        OrderedDict object whose keys are ordered according to their value.
    """
    kv_items = [kv for kv in d.items()]

    # Sort kv_items according to key.
    if key is None:
        kv_items.sort(key=lambda t: t[1], reverse=reverse)
    else:
        kv_items.sort(key=key, reverse=reverse)

    # Build ordered dict.
    return collections.OrderedDict(kv_items)


def minloc(seq):
    """
    Return the index of the (first) minimum in seq

    >>> assert minloc(range(3)) == 0
    """
    return min(enumerate(seq), key=lambda s: s[1])[0]


def maxloc(seq):
    """
    Return the index of the (first) maximum in seq

    >>> assert maxloc([1,3,2,3]) == 1
    """
    return max(enumerate(seq), key=lambda s: s[1])[0]


def min_max_indexes(seq):
    """
    Uses enumerate, max, and min to return the indices of the values
    in a list with the maximum and minimum value:
    """
    l = sorted(enumerate(seq), key=lambda s: s[1])
    return l[0][0], l[-1][0]


def strictly_increasing(values):
    """True if values are stricly increasing."""
    return all(x < y for x, y in zip(values, values[1:]))


def strictly_decreasing(values):
    """True if values are stricly decreasing."""
    return all(x > y for x, y in zip(values, values[1:]))


def non_increasing(values):
    """True if values are not increasing."""
    return all(x >= y for x, y in zip(values, values[1:]))


def non_decreasing(values):
    """True if values are not decreasing."""
    return all(x <= y for x, y in zip(values, values[1:]))


def monotonic(values, mode="<", atol=1.e-8):
    """
    Returns False if values are not monotonic (decreasing|increasing).
    mode is "<" for a decreasing sequence, ">" for an increasing sequence.
    Two numbers are considered equal if they differ less that atol.

    .. warning:
        Not very efficient for large data sets.

    >>> values = [1.2, 1.3, 1.4]
    >>> monotonic(values, mode="<")
    False
    >>> monotonic(values, mode=">")
    True
    """
    if len(values) == 1:
        return True

    if mode == ">":
        for i in range(len(values) - 1):
            v, vp = values[i], values[i + 1]
            if abs(vp - v) > atol and vp <= v:
                return False

    elif mode == "<":
        for i in range(len(values) - 1):
            v, vp = values[i], values[i + 1]
            if abs(vp - v) > atol and vp >= v:
                return False

    else:
        raise ValueError("Wrong mode %s" % str(mode))

    return True


def round_to_sigfigs(num, sigfigs):
    """
    Rounds a number rounded to a specific number of significant
    figures instead of to a specific precision.
    """
    if type(sigfigs) != int:
        raise TypeError("Number of significant figures must be integer.")
    elif sigfigs < 1:
        raise ValueError("Number of significant figures "
                         "must be larger than zero.")
    elif num == 0:
        return num
    else:
        prec = int(sigfigs - np.ceil(np.log10(np.absolute(num))))
        return round(num, prec)


def make_symmetric_matrix_from_upper_tri(val):
    """
    Given a symmetric matrix in upper triangular matrix form as flat array indexes as:
    [A_xx,A_yy,A_zz,A_xy,A_xz,A_yz]
    This will generate the full matrix:
    [[A_xx,A_xy,A_xz],[A_xy,A_yy,A_yz],[A_xz,A_yz,A_zz]
    """
    idx = [0, 3, 4, 1, 5, 2]
    val = np.array(val)[idx]
    mask = ~np.tri(3, k=-1, dtype=bool)
    out = np.zeros((3, 3), dtype=val.dtype)
    out[mask] = val
    out.T[mask] = val
    return out


if __name__ == "__main__":
    import doctest

    doctest.testmod()