xref: /libCEED/python/tests/test-3-basis.py (revision c3a5a6094aa370d9b1d225615082a3e1f73f831f)

# Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
# the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
# reserved. See files LICENSE and NOTICE for details.
#
# This file is part of CEED, a collection of benchmarks, miniapps, software
# libraries and APIs for efficient high-order finite element and spectral
# element discretizations for exascale applications. For more information and
# source code availability see http://github.com/ceed.
#
# The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
# a collaborative effort of two U.S. Department of Energy organizations (Office
# of Science and the National Nuclear Security Administration) responsible for
# the planning and preparation of a capable exascale ecosystem, including
# software, applications, hardware, advanced system engineering and early
# testbed platforms, in support of the nation's exascale computing imperative.

# @file
# Test Ceed Basis functionality

import os
import math
import libceed
import numpy as np
import buildmats as bm
import check

TOL = np.finfo(float).eps * 256

# -------------------------------------------------------------------------------
# Utilities
# -------------------------------------------------------------------------------


def eval(dim, x):
    result, center = 1, 0.1
    for d in range(dim):
        result *= math.tanh(x[d] - center)
        center += 0.1
    return result


def feval(x1, x2):
    return x1 * x1 + x2 * x2 + x1 * x2 + 1


def dfeval(x1, x2):
    return 2 * x1 + x2

# -------------------------------------------------------------------------------
# Test creation and distruction of a H1Lagrange basis
# -------------------------------------------------------------------------------


def test_300(ceed_resource, capsys):
    ceed = libceed.Ceed(ceed_resource)

    b = ceed.BasisTensorH1Lagrange(1, 1, 4, 4, libceed.GAUSS_LOBATTO)
    print(b)
    del b

    b = ceed.BasisTensorH1Lagrange(1, 1, 4, 4, libceed.GAUSS)
    print(b)
    del b

    stdout, stderr, ref_stdout = check.output(capsys)
    assert not stderr
    assert stdout == ref_stdout

# -------------------------------------------------------------------------------
# Test QR factorization
# -------------------------------------------------------------------------------


def test_301(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    m = 4
    n = 3
    a = np.array([1, -1, 4, 1, 4, -2, 1, 4, 2, 1, -1, 0], dtype="float64")
    qr = np.array([1, -1, 4, 1, 4, -2, 1, 4, 2, 1, -1, 0], dtype="float64")
    tau = np.empty(3, dtype="float64")

    qr, tau = ceed.qr_factorization(qr, tau, m, n)
    np_qr, np_tau = np.linalg.qr(a.reshape(m, n), mode="raw")

    for i in range(n):
        assert tau[i] == np_tau[i]

    qr = qr.reshape(m, n)
    for i in range(m):
        for j in range(n):
            assert round(qr[i, j] - np_qr[j, i], 10) == 0

# -------------------------------------------------------------------------------
# Test Symmetric Schur Decomposition
# -------------------------------------------------------------------------------


def test_304(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    A = np.array([0.2, 0.0745355993, -0.0745355993, 0.0333333333,
                  0.0745355993, 1., 0.1666666667, -0.0745355993,
                  -0.0745355993, 0.1666666667, 1., 0.0745355993,
                  0.0333333333, -0.0745355993, 0.0745355993, 0.2], dtype="float64")

    Q = A.copy()

    lam = ceed.symmetric_schur_decomposition(Q, 4)
    Q = Q.reshape(4, 4)
    lam = np.diag(lam)

    Q_lambda_Qt = np.matmul(np.matmul(Q, lam), Q.T)
    assert np.max(Q_lambda_Qt - A.reshape(4, 4)) < 1E-14

# -------------------------------------------------------------------------------
# Test Simultaneous Diagonalization
# -------------------------------------------------------------------------------


def test_305(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    M = np.array([0.2, 0.0745355993, -0.0745355993, 0.0333333333,
                  0.0745355993, 1., 0.1666666667, -0.0745355993,
                  -0.0745355993, 0.1666666667, 1., 0.0745355993,
                  0.0333333333, -0.0745355993, 0.0745355993, 0.2], dtype="float64")
    K = np.array([3.0333333333, -3.4148928136, 0.4982261470, -0.1166666667,
                  -3.4148928136, 5.8333333333, -2.9166666667, 0.4982261470,
                  0.4982261470, -2.9166666667, 5.8333333333, -3.4148928136,
                  -0.1166666667, 0.4982261470, -3.4148928136, 3.0333333333], dtype="float64")

    X, lam = ceed.simultaneous_diagonalization(K, M, 4)
    X = X.reshape(4, 4)
    np.diag(lam)

    M = M.reshape(4, 4)
    K = K.reshape(4, 4)

    Xt_M_X = np.matmul(X.T, np.matmul(M, X))
    assert np.max(Xt_M_X - np.identity(4)) < 1E-14

    Xt_K_X = np.matmul(X.T, np.matmul(K, X))
    assert np.max(Xt_K_X - lam) < 1E-14

# -------------------------------------------------------------------------------
# Test GetNumNodes and GetNumQuadraturePoints for basis
# -------------------------------------------------------------------------------


def test_306(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    b = ceed.BasisTensorH1Lagrange(3, 1, 4, 5, libceed.GAUSS_LOBATTO)

    p = b.get_num_nodes()
    q = b.get_num_quadrature_points()

    assert p == 64
    assert q == 125

# -------------------------------------------------------------------------------
# Test interpolation in multiple dimensions
# -------------------------------------------------------------------------------


def test_313(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    for dim in range(1, 4):
        Q = 10
        Qdim = Q**dim
        Xdim = 2**dim
        x = np.empty(Xdim * dim, dtype="float64")
        uq = np.empty(Qdim, dtype="float64")

        for d in range(dim):
            for i in range(Xdim):
                x[d * Xdim + i] = 1 if (i %
                                        (2**(dim - d))) // (2**(dim - d - 1)) else -1

        X = ceed.Vector(Xdim * dim)
        X.set_array(x, cmode=libceed.USE_POINTER)
        Xq = ceed.Vector(Qdim * dim)
        Xq.set_value(0)
        U = ceed.Vector(Qdim)
        U.set_value(0)
        Uq = ceed.Vector(Qdim)

        bxl = ceed.BasisTensorH1Lagrange(dim, dim, 2, Q, libceed.GAUSS_LOBATTO)
        bul = ceed.BasisTensorH1Lagrange(dim, 1, Q, Q, libceed.GAUSS_LOBATTO)

        bxl.apply(1, libceed.EVAL_INTERP, X, Xq)

        with Xq.array_read() as xq:
            for i in range(Qdim):
                xx = np.empty(dim, dtype="float64")
                for d in range(dim):
                    xx[d] = xq[d * Qdim + i]
                uq[i] = eval(dim, xx)

        Uq.set_array(uq, cmode=libceed.USE_POINTER)

        # This operation is the identity because the quadrature is collocated
        bul.T.apply(1, libceed.EVAL_INTERP, Uq, U)

        bxg = ceed.BasisTensorH1Lagrange(dim, dim, 2, Q, libceed.GAUSS)
        bug = ceed.BasisTensorH1Lagrange(dim, 1, Q, Q, libceed.GAUSS)

        bxg.apply(1, libceed.EVAL_INTERP, X, Xq)
        bug.apply(1, libceed.EVAL_INTERP, U, Uq)

        with Xq.array_read() as xq, Uq.array_read() as u:
            for i in range(Qdim):
                xx = np.empty(dim, dtype="float64")
                for d in range(dim):
                    xx[d] = xq[d * Qdim + i]
                fx = eval(dim, xx)
                assert math.fabs(u[i] - fx) < 1E-4

# -------------------------------------------------------------------------------
# Test grad in multiple dimensions
# -------------------------------------------------------------------------------


def test_314(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    for dim in range(1, 4):
        P, Q = 8, 10
        Pdim = P**dim
        Qdim = Q**dim
        Xdim = 2**dim
        sum1 = sum2 = 0
        x = np.empty(Xdim * dim, dtype="float64")
        u = np.empty(Pdim, dtype="float64")

        for d in range(dim):
            for i in range(Xdim):
                x[d * Xdim + i] = 1 if (i %
                                        (2**(dim - d))) // (2**(dim - d - 1)) else -1

        X = ceed.Vector(Xdim * dim)
        X.set_array(x, cmode=libceed.USE_POINTER)
        Xq = ceed.Vector(Pdim * dim)
        Xq.set_value(0)
        U = ceed.Vector(Pdim)
        Uq = ceed.Vector(Qdim * dim)
        Uq.set_value(0)
        Ones = ceed.Vector(Qdim * dim)
        Ones.set_value(1)
        Gtposeones = ceed.Vector(Pdim)
        Gtposeones.set_value(0)

        # Get function values at quadrature points
        bxl = ceed.BasisTensorH1Lagrange(dim, dim, 2, P, libceed.GAUSS_LOBATTO)
        bxl.apply(1, libceed.EVAL_INTERP, X, Xq)

        with Xq.array_read() as xq:
            for i in range(Pdim):
                xx = np.empty(dim, dtype="float64")
                for d in range(dim):
                    xx[d] = xq[d * Pdim + i]
                u[i] = eval(dim, xx)

        U.set_array(u, cmode=libceed.USE_POINTER)

        # Calculate G u at quadrature points, G' * 1 at dofs
        bug = ceed.BasisTensorH1Lagrange(dim, 1, P, Q, libceed.GAUSS)
        bug.apply(1, libceed.EVAL_GRAD, U, Uq)
        bug.T.apply(1, libceed.EVAL_GRAD, Ones, Gtposeones)

        # Check if 1' * G * u = u' * (G' * 1)
        with Gtposeones.array_read() as gtposeones, Uq.array_read() as uq:
            for i in range(Pdim):
                sum1 += gtposeones[i] * u[i]
            for i in range(dim * Qdim):
                sum2 += uq[i]

        assert math.fabs(sum1 - sum2) < 1E-10

# -------------------------------------------------------------------------------
# Test creation and destruction of a 2D Simplex non-tensor H1 basis
# -------------------------------------------------------------------------------


def test_320(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    P, Q, dim = 6, 4, 2

    in_array = np.empty(P, dtype="float64")
    qref = np.empty(dim * Q, dtype="float64")
    qweight = np.empty(Q, dtype="float64")

    interp, grad = bm.buildmats(qref, qweight)

    b = ceed.BasisH1(libceed.TRIANGLE, 1, P, Q, interp, grad, qref, qweight)

    print(b)
    del b

# -------------------------------------------------------------------------------
# Test integration with a 2D Simplex non-tensor H1 basis
# -------------------------------------------------------------------------------


def test_322(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    P, Q, dim = 6, 4, 2

    xr = np.array([0., 0.5, 1., 0., 0.5, 0., 0., 0.,
                   0., 0.5, 0.5, 1.], dtype="float64")
    in_array = np.empty(P, dtype="float64")
    qref = np.empty(dim * Q, dtype="float64")
    qweight = np.empty(Q, dtype="float64")

    interp, grad = bm.buildmats(qref, qweight)

    b = ceed.BasisH1(libceed.TRIANGLE, 1, P, Q, interp, grad, qref, qweight)

    # Interpolate function to quadrature points
    for i in range(P):
        in_array[i] = feval(xr[0 * P + i], xr[1 * P + i])

    in_vec = ceed.Vector(P)
    in_vec.set_array(in_array, cmode=libceed.USE_POINTER)
    out_vec = ceed.Vector(Q)
    out_vec.set_value(0)
    weights_vec = ceed.Vector(Q)
    weights_vec.set_value(0)

    b.apply(1, libceed.EVAL_INTERP, in_vec, out_vec)
    b.apply(1, libceed.EVAL_WEIGHT, libceed.VECTOR_NONE, weights_vec)

    # Check values at quadrature points
    with out_vec.array_read() as out_array, weights_vec.array_read() as weights_array:
        sum = 0
        for i in range(Q):
            sum += out_array[i] * weights_array[i]
        assert math.fabs(sum - 17. / 24.) < 1E-10

# -------------------------------------------------------------------------------
# Test grad with a 2D Simplex non-tensor H1 basis
# -------------------------------------------------------------------------------


def test_323(ceed_resource):
    ceed = libceed.Ceed(ceed_resource)

    P, Q, dim = 6, 4, 2

    xq = np.array([0.2, 0.6, 1. / 3., 0.2, 0.2, 0.2,
                   1. / 3., 0.6], dtype="float64")
    xr = np.array([0., 0.5, 1., 0., 0.5, 0., 0., 0.,
                   0., 0.5, 0.5, 1.], dtype="float64")
    in_array = np.empty(P, dtype="float64")
    qref = np.empty(dim * Q, dtype="float64")
    qweight = np.empty(Q, dtype="float64")

    interp, grad = bm.buildmats(qref, qweight)

    b = ceed.BasisH1(libceed.TRIANGLE, 1, P, Q, interp, grad, qref, qweight)

    # Interpolate function to quadrature points
    for i in range(P):
        in_array[i] = feval(xr[0 * P + i], xr[1 * P + i])

    in_vec = ceed.Vector(P)
    in_vec.set_array(in_array, cmode=libceed.USE_POINTER)
    out_vec = ceed.Vector(Q * dim)
    out_vec.set_value(0)

    b.apply(1, libceed.EVAL_GRAD, in_vec, out_vec)

    # Check values at quadrature points
    with out_vec.array_read() as out_array:
        for i in range(Q):
            value = dfeval(xq[0 * Q + i], xq[1 * Q + i])
            assert math.fabs(out_array[0 * Q + i] - value) < 1E-10

            value = dfeval(xq[1 * Q + i], xq[0 * Q + i])
            assert math.fabs(out_array[1 * Q + i] - value) < 1E-10

# -------------------------------------------------------------------------------