A comparison of pentapy's solver when using np.array versus np.asarray

pentapy_solver_using_asarray.py

# -*- coding: utf-8 -*-
"""
Modified version of pentapy's 03_perform_simple.py example from
https://github.com/GeoStat-Framework/pentapy/blob/develop/examples/03_perform_simple.py

The code was modified to include a solve_new function that uses np.asarray rather than
np.array whereever the input data is not modified, and to compare the time required to
convert the matrix and array using np.array and np.asarray.

Modifications of pentapy's code was done in accordance with it's MIT license, which is
included below:

The MIT License (MIT)

Copyright (c) 2021 Sebastian Mueller

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

"""
from __future__ import division, absolute_import, print_function

import warnings

import numpy as np
from pentapy import solve
from pentapy import tools
import perfplot


# imports to simulate being in pentapy.core.py
from pentapy.tools import shift_banded, create_banded, _check_penta
from pentapy.solver import penta_solver1, penta_solver2


# solve_new uses np.asarray instead of np.array wherever the input would not be
# modified; otherwise, it is a direct copy of pentapy's solve function
def solve_new(mat, rhs, is_flat=False, index_row_wise=True, solver=1):
    """
    Solver for a pentadiagonal system.

    The matrix can be given as a full n x n matrix or as a flattend one.
    The flattend matrix can be given in a row-wise flattend form::

      [[Dup2[0]  Dup2[1]  Dup2[2]  ... Dup2[N-2]  0          0       ]
       [Dup1[0]  Dup1[1]  Dup1[2]  ... Dup1[N-2]  Dup1[N-1]  0       ]
       [Diag[0]  Diag[1]  Diag[2]  ... Diag[N-2]  Diag[N-1]  Diag[N] ]
       [0        Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] Dlow1[N]]
       [0        0        Dlow2[2] ... Dlow2[N-2] Dlow2[N-2] Dlow2[N]]]

    Or a column-wise flattend form::

      [[0        0        Dup2[2]  ... Dup2[N-2]  Dup2[N-1]  Dup2[N] ]
       [0        Dup1[1]  Dup1[2]  ... Dup1[N-2]  Dup1[N-1]  Dup1[N] ]
       [Diag[0]  Diag[1]  Diag[2]  ... Diag[N-2]  Diag[N-1]  Diag[N] ]
       [Dlow1[0] Dlow1[1] Dlow1[2] ... Dlow1[N-2] Dlow1[N-1] 0       ]
       [Dlow2[0] Dlow2[1] Dlow2[2] ... Dlow2[N-2] 0          0       ]]

    Dup1 and Dup2 are the first and second upper minor-diagonals
    and Dlow1 resp. Dlow2 are the lower ones.
    If you provide a column-wise flattend matrix, you have to set::

      index_row_wise=False


    Parameters
    ----------
    mat : :class:`numpy.ndarray`
        The Matrix or the flattened Version of the pentadiagonal matrix.
    rhs : :class:`numpy.ndarray`
        The right hand side of the equation system.
    is_flat : :class:`bool`, optional
        State if the matrix is already flattend. Default: ``False``
    index_row_wise : :class:`bool`, optional
        State if the flattend matrix is row-wise flattend. Default: ``True``
    solver : :class:`int` or :class:`str`, optional
        Which solver should be used. The following are provided:

            * ``[1, "1", "PTRANS-I"]`` : The PTRANS-I algorithm
            * ``[2, "2", "PTRANS-II"]`` : The PTRANS-II algorithm
            * ``[3, "3", "lapack", "solve_banded"]`` :
              scipy.linalg.solve_banded
            * ``[4, "4", "spsolve"]`` :
              The scipy sparse solver without umf_pack
            * ``[5, "5", "spsolve_umf", "umf", "umf_pack"]`` :
              The scipy sparse solver with umf_pack

        Default: ``1``

    Returns
    -------
    result : :class:`numpy.ndarray`
        Solution of the equation system
    """

    if solver in [1, "1", "PTRANS-I"]:
        if is_flat and index_row_wise:
            mat_flat = np.asarray(mat, dtype=np.double)
            _check_penta(mat_flat)
        elif is_flat:
            mat_flat = np.array(mat, dtype=np.double)
            _check_penta(mat_flat)
            shift_banded(mat_flat, copy=False)
        else:
            mat_flat = create_banded(mat, col_wise=False, dtype=np.double)
        rhs = np.asarray(rhs, dtype=np.double)
        try:
            return penta_solver1(mat_flat, rhs)
        except ZeroDivisionError:
            warnings.warn("pentapy: PTRANS-I not suitable for input-matrix.")
            return np.full_like(rhs, np.nan)
    elif solver in [2, "2", "PTRANS-II"]:
        if is_flat and index_row_wise:
            mat_flat = np.asarray(mat, dtype=np.double)
            _check_penta(mat_flat)
        elif is_flat:
            mat_flat = np.array(mat, dtype=np.double)
            _check_penta(mat_flat)
            shift_banded(mat_flat, copy=False)
        else:
            mat_flat = create_banded(mat, col_wise=False, dtype=np.double)
        rhs = np.asarray(rhs, dtype=np.double)
        try:
            return penta_solver2(mat_flat, rhs)
        except ZeroDivisionError:
            warnings.warn("pentapy: PTRANS-II not suitable for input-matrix.")
            return np.full_like(rhs, np.nan)
    elif solver in [3, "3", "lapack", "solve_banded"]:  # pragma: no cover
        try:
            from scipy.linalg import solve_banded
        except ImportError:  # pragma: no cover
            raise ValueError(
                "pentapy.solve: "
                + "scipy.linalg.solve_banded could not be imported"
            )
        if is_flat and index_row_wise:
            mat_flat = np.array(mat)
            _check_penta(mat_flat)
            shift_banded(mat_flat, col_to_row=False, copy=False)
        elif is_flat:
            mat_flat = np.asarray(mat)
        else:
            mat_flat = create_banded(mat)
        return solve_banded((2, 2), mat_flat, rhs)
    elif solver in [4, "4", "spsolve"]:  # pragma: no cover
        try:
            from scipy import sparse as sps
            from scipy.sparse.linalg import spsolve
        except ImportError:
            raise ValueError(
                "pentapy.solve: scipy.sparse could not be imported"
            )
        if is_flat and index_row_wise:
            mat_flat = np.array(mat)
            _check_penta(mat_flat)
            shift_banded(mat_flat, col_to_row=False, copy=False)
        elif is_flat:
            mat_flat = np.asarray(mat)
        else:
            mat_flat = create_banded(mat)
        size = mat_flat.shape[1]
        M = sps.spdiags(mat_flat, [2, 1, 0, -1, -2], size, size, format="csc")
        return spsolve(M, rhs, use_umfpack=False)
    elif solver in [
        5,
        "5",
        "spsolve_umf",
        "umf",
        "umf_pack",
    ]:  # pragma: no cover
        try:
            from scipy import sparse as sps
            from scipy.sparse.linalg import spsolve
        except ImportError:
            raise ValueError(
                "pentapy.solve: scipy.sparse could not be imported"
            )
        if is_flat and index_row_wise:
            mat_flat = np.array(mat)
            _check_penta(mat_flat)
            shift_banded(mat_flat, col_to_row=False, copy=False)
        elif is_flat:
            mat_flat = np.asarray(mat)
        else:
            mat_flat = create_banded(mat)
        size = mat_flat.shape[1]
        M = sps.spdiags(mat_flat, [2, 1, 0, -1, -2], size, size, format="csc")
        return spsolve(M, rhs, use_umfpack=True)
    else:  # pragma: no cover
        raise ValueError("pentapy.solve: unknown solver (" + str(solver) + ")")


def get_les(size):
    """Create the matrix and array for fitting."""
    mat = (np.random.random((5, size)) - 0.5) * 1e-5
    # create index-row-wise matrix so that solver can be called with index_row_wise=True
    tools.shift_banded(mat, copy=False)
    V = np.array(np.random.random(size) * 1e5)
    return mat, V


def solve_1(in_val):
    """PTRANS-I"""
    mat, V = in_val
    return solve(mat, V, is_flat=True, solver=1)


def solve_2(in_val):
    """PTRANS-II"""
    mat, V = in_val
    return solve(mat, V, is_flat=True, solver=2)


def solve_1_new(in_val):
    """PTRANS-I with new solver."""
    mat, V = in_val
    return solve_new(mat, V, is_flat=True, solver=1)


def solve_2_new(in_val):
    """PTRANS-II with new solver."""
    mat, V = in_val
    return solve_new(mat, V, is_flat=True, solver=2)


def use_np_array(in_val):
    """Used to see the time required just calling np.array on the matrix and rhs."""
    mat, V = in_val
    new_mat = np.array(mat, dtype=np.double)
    new_V = np.array(V, dtype=np.double)


def use_np_asarray(in_val):
    """Used to see the time required just calling np.asarray on the matrix and rhs."""
    mat, V = in_val
    new_mat = np.asarray(mat, dtype=np.double)
    new_V = np.asarray(V, dtype=np.double)


perfplot.show(
    setup=get_les,
    kernels=[
        solve_1,
        solve_2,
        solve_1_new,
        solve_2_new,
        use_np_array,
        use_np_asarray
    ],
    labels=[
        "PTRANS-I",
        "PTRANS-II",
        "new-I",
        "new-II",
        "np.array",
        "np.asarray"
    ],
    n_range=[int(2 ** k) for k in np.arange(6, 18.5, 0.5)],
    xlabel="Size [n]",
    logy=True,
    logx=True,
    equality_check=None  # don't check output since use_np_(as)array output is different than solvers
)