def test_mul():
X = Matrix(
[
[12, 7, 3],
[4, 5, 6],
[7, 8, 9],
]
)
Y = Matrix(
[
[5, 8, 1, 2],
[6, 7, 3, 0],
[4, 5, 9, 1],
]
)
R = Matrix(
[
[114, 160, 60, 27],
[74, 97, 73, 14],
[119, 157, 112, 23],
]
)
assert X * Y == R
def tridiag():
m = Matrix(TRI_DIAGONAL)
a = [0] # a0 is not used but must be present
a.extend(m.diag(-1))
b = m.diag(0)
c = m.diag(+1)
return a, b, c
def test_iadd(X):
Y = X
Y += Y
assert Y == Matrix([[24, 14], [8, 10], [6, 16]])
assert Y[0, 0] != X[0, 0]
Z = Y
Z += 10
assert Z == Matrix([[34, 24], [18, 20], [16, 26]])
assert Y[0, 0] != Z[0, 0]
def test_detect_banded_matrix():
m1, m2 = detect_banded_matrix(BANDED_MATRIX)
assert (m1, m2) == (2, 1)
m1, m2 = detect_banded_matrix(TRICKY, check_all=False)
assert (m1, m2) == (2, 1)
m1, m2 = detect_banded_matrix(TRICKY, check_all=True)
assert (m1, m2) == (5, 6)
assert detect_banded_matrix(Matrix(shape=(10, 10))) == (0, 0)
identity = Matrix.identity(shape=(10, 10))
assert detect_banded_matrix(identity) == (0, 0)
def test_imul():
X = Matrix([
[12, 7, 3],
[4, 5, 6],
[7, 8, 9],
])
Y = X
Y *= 10
assert Y == Matrix([
[120, 70, 30],
[40, 50, 60],
[70, 80, 90],
])
assert X[0, 0] != Y[0, 0]
def matrix_init(X):
Y = Matrix([12, 7, 4, 5, 3, 8], shape=(3, 2))
assert X.shape == X.nrows, X.ncols
assert Y.shape == (3, 2)
assert X == Y
Y = Matrix(shape=(3, 3))
assert Y == Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
Y = Matrix(X)
assert Y == X
Y[0, 0] = -1
assert Y != X, "should not share the same list objects"
Y = Matrix(X, shape=(2, 3))
assert Y.rows() == [[12, 7, 4], [5, 3, 8]]
def test_transpose(X):
R = Matrix([
(12, 4, 3),
(7, 5, 8),
])
T = X.transpose()
assert T == R
# is T mutable?
T[0, 0] = 99
assert T[0, 0] == 99
def test_diag():
m = Matrix(DIAG)
assert m.diag(0) == [1, 2, 3, 4]
assert m.diag(1) == [2, 3, 4]
assert m.diag(2) == [5, 6]
assert m.diag(3) == [7]
assert m.diag(4) == []
assert m.diag(-1) == [5, 4, 3]
assert m.diag(-2) == [7, 6]
assert m.diag(-3) == [8]
assert m.diag(-4) == []
import pytest
import math
from ezdxf.math import (
Matrix,
detect_banded_matrix,
compact_banded_matrix,
BandedMatrixLU,
gauss_vector_solver,
banded_matrix,
)
BANDED_MATRIX = Matrix(matrix=[
[3, 1, 0, 0, 0, 0, 0],
[4, 1, 5, 0, 0, 0, 0],
[9, 2, 6, 5, 0, 0, 0],
[0, 3, 5, 8, 9, 0, 0],
[0, 0, 7, 9, 3, 2, 0],
[0, 0, 0, 3, 8, 4, 6],
[0, 0, 0, 0, 2, 4, 4],
])
TRICKY = Matrix(matrix=[
[3, 1, 0, 0, 0, 0, 1],
[4, 1, 5, 0, 0, 0, 0],
[9, 2, 6, 5, 0, 0, 0],
[0, 3, 5, 8, 9, 0, 0],
[0, 0, 7, 9, 3, 2, 0],
[0, 0, 0, 3, 8, 4, 6],
[0, 1, 0, 0, 2, 4, 4],
])
def test_LU_decomposition_inverse():
m = Matrix(matrix=EXPECTED_INVERSE)
assert LUDecomposition(A).inverse() == m
def test_gauss_jordan_inverse():
result = gauss_jordan_inverse(A)
assert result.nrows == len(A)
assert result.ncols == len(A[0])
m = Matrix(matrix=EXPECTED_INVERSE)
assert result == m
def test_gauss_jordan_vector_solver():
B = Matrix(items=B1, shape=(5, 1))
result_A, result_B = gauss_jordan_solver(A, B)
are_close_vectors(result_B.col(0), SOLUTION_B1)
def test_identity():
m = Matrix.identity((3, 4))
for i in range(3):
assert m[i, i] == 1.0
def test_set_diag_iterable():
m = Matrix(shape=(4, 4))
m.set_diag(0, range(5))
for i in range(4):
assert m[i, i] == i
def test_set_diag_below():
m = Matrix(shape=(4, 4))
m.set_diag(-1, 2)
for i in range(3):
assert m[i + 1, i] == 2.0
def test_set_diag_above():
m = Matrix(shape=(4, 4))
m.set_diag(1, 2)
for i in range(3):
assert m[i, i + 1] == 2.0
def test_set_diag_float():
m = Matrix(shape=(4, 4))
m.set_diag(0, 2)
for i in range(4):
assert m[i, i] == 2.0
def test_build_matrix_by_cols():
m = Matrix()
m.append_col([1, 2, 3])
assert m.nrows == 3
assert m.ncols == 1
def test_sub(X):
R = X - X
assert R == Matrix([[0, 0], [0, 0], [0, 0]])
R = X - 10
assert R == Matrix([[2, -3], [-6, -5], [-7, -2]])
def X():
return Matrix([[12, 7], [4, 5], [3, 8]])
def test_add(X):
R = X + X
assert R == Matrix([[24, 14], [8, 10], [6, 16]])
R = R + 10
assert R == Matrix([[34, 24], [18, 20], [16, 26]])
