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import pytest
# combinations of na, nev, nblk to run all the tests with
parameter_list = [
(200, 20, 16),
(200, 200, 16),
(200, 20, 64),
(200, 200, 64),
(200, 20, 4),
(200, 200, 4),
(50, 20, 16),
(100, 20, 16),
]
def get_random_vector(size):
"""generate random vector with given size that is equal on all cores"""
import numpy as np
from mpi4py import MPI
comm = MPI.COMM_WORLD
am_i_root = comm.Get_rank() == 0
vector = np.empty(size)
if am_i_root:
vector[:] = np.random.rand(size)
comm.Bcast(vector)
return vector
def test_processor_layout():
from pyelpa import ProcessorLayout
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
assert(comm.Get_size() == layout_p.np_cols*layout_p.np_rows)
assert(layout_p.my_prow >= 0)
assert(layout_p.my_pcol >= 0)
assert(layout_p.my_prow <= comm.Get_size())
assert(layout_p.my_pcol <= comm.Get_size())
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_distributed_matrix_from_processor_layout(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.float32, np.complex64, np.complex128]:
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
assert(a.data.dtype == dtype)
assert(a.data.shape == (a.na_rows, a.na_cols))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_distributed_matrix_from_communicator(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
from mpi4py import MPI
comm = MPI.COMM_WORLD
for dtype in [np.float64, np.float32, np.complex64, np.complex128]:
a = DistributedMatrix.from_communicator(comm, na, nev, nblk,
dtype=dtype)
assert(a.data.dtype == dtype)
assert(a.data.shape == (a.na_rows, a.na_cols))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_distributed_matrix_from_world(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.float32, np.complex64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
assert(a.data.dtype == dtype)
assert(a.data.shape == (a.na_rows, a.na_cols))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_distributed_matrix_like_other_matrix(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.float32, np.complex64, np.complex128]:
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
b = DistributedMatrix.like(a)
assert(a.na == b.na)
assert(a.nev == b.nev)
assert(a.nblk == b.nblk)
assert(a.data.dtype == b.data.dtype)
assert(a.data.shape == b.data.shape)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_call_eigenvectors(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix, Elpa
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.complex128]:
# create arrays
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
a.data[:, :] = np.random.rand(a.na_rows, a.na_cols).astype(dtype)
q = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
ev = np.zeros(na, dtype=np.float64)
e = Elpa.from_distributed_matrix(a)
e.eigenvectors(a.data, ev, q.data)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_call_eigenvalues(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix, Elpa
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.complex128]:
# create arrays
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
a.data[:, :] = np.random.rand(a.na_rows, a.na_cols).astype(dtype)
ev = np.zeros(na, dtype=np.float64)
e = Elpa.from_distributed_matrix(a)
e.eigenvalues(a.data, ev)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_compare_eigenvalues_to_those_from_eigenvectors(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix, Elpa
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.complex128]:
# create arrays
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
random_matrix = np.random.rand(a.na_rows, a.na_cols).astype(dtype)
a.data[:, :] = random_matrix
q = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
ev = np.zeros(na, dtype=np.float64)
ev2 = np.zeros(na, dtype=np.float64)
e = Elpa.from_distributed_matrix(a)
e.eigenvectors(a.data, ev, q.data)
a.data[:, :] = random_matrix
e.eigenvalues(a.data, ev2)
assert(np.allclose(ev, ev2))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_compare_eigenvalues_to_those_from_eigenvectors_self_functions(
na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
# create arrays
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
random_matrix = np.random.rand(a.na_rows, a.na_cols).astype(dtype)
a.data[:, :] = random_matrix
data = a.compute_eigenvectors()
a.data[:, :] = random_matrix
eigenvalues = a.compute_eigenvalues()
assert(np.allclose(data['eigenvalues'], eigenvalues))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_distributed_matrix_global_index(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
for local_row in range(a.na_rows):
for local_col in range(a.na_cols):
global_row, global_col = a.get_global_index(local_row,
local_col)
l_row, l_col = a.get_local_index(global_row, global_col)
assert(global_row >= 0 and global_row < a.na)
assert(global_col >= 0 and global_col < a.na)
assert(local_row == l_row and local_col == l_col)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_distributed_matrix_local_index(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
for global_row in range(a.na):
for global_col in range(a.na):
if not a.is_local_index(global_row, global_col):
continue
local_row, local_col = a.get_local_index(global_row,
global_col)
g_row, g_col = a.get_global_index(local_row, local_col)
assert(local_row >= 0 and local_row < a.na_rows)
assert(local_col >= 0 and local_col < a.na_cols)
assert(global_row == g_row and global_col == g_col)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_distributed_matrix_indexing_loop(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
for local_row in range(a.na_rows):
for local_col in range(a.na_cols):
global_row, global_col = a.get_global_index(local_row,
local_col)
a.data[local_row, local_col] = global_row*10 + global_col
for global_row in range(a.na):
for global_col in range(a.na):
if not a.is_local_index(global_row, global_col):
continue
local_row, local_col = a.get_local_index(global_row,
global_col)
assert(a.data[local_row, local_col] ==
global_row*10 + global_col)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_setting_global_matrix(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix
from mpi4py import MPI
comm = MPI.COMM_WORLD
layout_p = ProcessorLayout(comm)
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix(layout_p, na, nev, nblk, dtype=dtype)
# get global matrix that is equal on all cores
matrix = get_random_vector(na*na).reshape(na, na).astype(dtype)
a.set_data_from_global_matrix(matrix)
# check data
for global_row in range(a.na):
for global_col in range(a.na):
if not a.is_local_index(global_row, global_col):
continue
local_row, local_col = a.get_local_index(global_row,
global_col)
assert(a.data[local_row, local_col] ==
matrix[global_row, global_col])
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_dot_product(na, nev, nblk):
import numpy as np
from pyelpa import ProcessorLayout, DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
# get global matrix and vector that is equal on all cores
matrix = get_random_vector(na*na).reshape(na, na).astype(dtype)
vector = get_random_vector(na).astype(dtype)
a.set_data_from_global_matrix(matrix)
product_distributed = a.dot(vector)
product_naive = a._dot_naive(vector)
product_serial = np.dot(matrix, vector)
assert(np.allclose(product_distributed, product_serial))
assert(np.allclose(product_distributed, product_naive))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_dot_product_incompatible_size(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
# get global matrix and vector that is equal on all cores
matrix = get_random_vector(na*na).reshape(na, na).astype(dtype)
vector = get_random_vector(na*2).astype(dtype)
a.set_data_from_global_matrix(matrix)
with pytest.raises(ValueError):
product_distributed = a.dot(vector)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_validate_eigenvectors(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
# get a symmetric/hermitian matrix
matrix = get_random_vector(na*na).reshape(na, na).astype(dtype)
matrix = 0.5*(matrix + np.conj(matrix.T))
a.set_data_from_global_matrix(matrix)
data = a.compute_eigenvectors()
eigenvalues = data['eigenvalues']
eigenvectors = data['eigenvectors']
# reset data of a
a.set_data_from_global_matrix(matrix)
for index in range(a.nev):
eigenvector = eigenvectors.get_column(index)
scaled_eigenvector = eigenvalues[index]*eigenvector
# test solution
assert(np.allclose(a.dot(eigenvector),
scaled_eigenvector))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_validate_eigenvectors_to_numpy(na, nev, nblk):
import numpy as np
from numpy import linalg
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
# get a symmetric/hermitian matrix
matrix = get_random_vector(na*na).reshape(na, na).astype(dtype)
matrix = 0.5*(matrix + np.conj(matrix.T))
a.set_data_from_global_matrix(matrix)
data = a.compute_eigenvectors()
eigenvalues = data['eigenvalues']
eigenvectors = data['eigenvectors']
# get numpy solution
eigenvalues_np, eigenvectors_np = linalg.eigh(matrix)
assert(np.allclose(eigenvalues, eigenvalues_np))
for index in range(a.nev):
eigenvector = eigenvectors.get_column(index)
assert(np.allclose(eigenvector, eigenvectors_np[:, index]) or
np.allclose(eigenvector, -eigenvectors_np[:, index]))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_accessing_matrix(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
matrix = get_random_vector(na*na).reshape(na, na).astype(dtype)
a.set_data_from_global_matrix(matrix)
for index in range(a.na):
column = a.get_column(index)
assert(np.allclose(column, matrix[:, index]))
row = a.get_row(index)
assert(np.allclose(row, matrix[index, :]))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_global_index_iterator(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
for i, j in a.global_indices():
assert(a.is_local_index(i, j))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_global_index_access(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
for i, j in a.global_indices():
x = dtype(i*j)
a.set_data_for_global_index(i, j, x)
for i, j in a.global_indices():
x = a.get_data_for_global_index(i, j)
assert(np.isclose(x, i*j))
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_global_block_iterator(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
for i, j, blk_i, blk_j in a.global_block_indices():
assert(a.is_local_index(i, j))
assert(blk_i <= nblk)
assert(blk_j <= nblk)
assert(i+blk_i <= na)
assert(j+blk_j <= na)
@pytest.mark.parametrize("na,nev,nblk", parameter_list)
def test_global_block_access(na, nev, nblk):
import numpy as np
from pyelpa import DistributedMatrix
for dtype in [np.float64, np.complex128]:
a = DistributedMatrix.from_comm_world(na, nev, nblk, dtype=dtype)
for i, j, blk_i, blk_j in a.global_block_indices():
x = np.arange(i, i+blk_i)[:, None] * np.arange(j, j+blk_j)[None, :]
a.set_block_for_global_index(i, j, blk_i, blk_j, x)
for i, j, blk_i, blk_j in a.global_block_indices():
original = np.arange(i, i+blk_i)[:, None] * np.arange(j, j+blk_j)[None, :]
x = a.get_block_for_global_index(i, j, blk_i, blk_j)
assert(np.allclose(x, original))
for i, j in a.global_indices():
x = a.get_data_for_global_index(i, j)
assert(np.isclose(x, i*j))
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