data/tests/test_matrix.py

from visma.matrix.checks import isMatrix, dimCheck, multiplyCheck, isEqual
from visma.matrix.operations import simplifyMatrix, addMatrix, subMatrix, scalarAdd, scalarSub, scalarMult, scalarDiv, gauss_elim, row_echelon
from visma.matrix.structure import DiagMat, IdenMat
from visma.functions.constant import Constant
from tests.tester import getTokens
from visma.io.parser import tokensToString


####################
# matrix.structure #
####################


def test_strMatrix():

    mat = getTokens("[1+x, 2; \
                      3  , 4]")
    assert mat.__str__() == "[{1.0}+{x},{2.0};{3.0},{4.0}]"


def test_traceMat():

    mat = getTokens("[1, 2, 3; \
                      3, 4, 7; \
                      4, 6, 9]")
    mat.isSquare()
    trace = mat.traceMat()
    assert tokensToString(trace) == "14.0"

    mat = getTokens("[7, 5; \
                      2, 0]")
    mat.isSquare()
    trace = mat.traceMat()
    assert tokensToString(trace) == "7.0"


def test_isSquare():

    mat = getTokens("[1, 0, 3; \
                      2, 1, 2]")
    assert not mat.isSquare()

    mat = getTokens("[1, 2; \
                      x, z]")
    assert mat.isSquare()

    mat = getTokens("[1, 2; \
                      1, 3; \
                      1, 4]")
    assert not mat.isSquare()


def test_transposeMat():
    mat = getTokens("[1, 3; \
                      2, 6]")
    matTranspose = mat.transposeMat()
    assert matTranspose.__str__() == "[{1.0},{2.0};{3.0},{6.0}]"

    mat = getTokens("[5,8,2;\
                      12,30,9;\
                      4,17,7]")
    matTranspose = mat.transposeMat()
    assert matTranspose.__str__() == "[{5.0},{12.0},{4.0};{8.0},{30.0},{17.0};{2.0},{9.0},{7.0}]"

    mat = getTokens("[5,8,2;\
                      2,3,4]")
    matTranspose = mat.transposeMat()
    assert matTranspose.__str__() == "[{5.0},{2.0};{8.0},{3.0};{2.0},{4.0}]"

    mat = getTokens("[1, 2; \
                    3,  4]")
    matTranspose = mat.transposeMat()
    assert matTranspose.__str__() == "[{1.0},{3.0};{2.0},{4.0}]"


def test_isDiagonal():

    mat = getTokens("[1, 0; \
                      0, z]")
    assert mat.isDiagonal()

    mat = getTokens("[1+x, 0+y; \
                      0, z]")
    assert not mat.isDiagonal()

    mat = getTokens("[1, 2; \
                      1, 3; \
                      1, 4]")
    assert not mat.isDiagonal()

    mat = DiagMat([3, 3], [[Constant(1)], [Constant(5)], [Constant(2)]])
    assert mat.isDiagonal()

    mat = IdenMat([2, 2])
    assert mat.isDiagonal()


def test_isIdentity():

    mat = getTokens("[1, 0; \
                      0, 1]")
    assert mat.isIdentity()

    mat = getTokens("[1+x, 0+y; \
                      0, 1]")
    assert not mat.isIdentity()

    mat = getTokens("[1, 2; \
                      1, 3; \
                      1, 4]")
    assert not mat.isIdentity()


#################
# matrix.checks #
#################


def test_isMatrix():

    mat = getTokens("[1, 2, 3; \
                      x, z, 3]")
    assert isMatrix(mat)

    mat = getTokens("[1, 2; \
                      1, 3; \
                      1]")
    assert mat == []  # not a matrix; returns empty matrix


def test_dimCheck():

    matA = getTokens("[2, x; \
                       3, y]")
    matB = getTokens("[1, 2, x; \
                       2, 3, y]")
    assert not dimCheck(matA, matB)

    matA = getTokens("[2, x; \
                       3, y]")
    matB = getTokens("[1, 2; \
                       2, 3]")
    assert dimCheck(matA, matB)


def test_multiplyCheck():

    matA = getTokens("[2, x; \
                       3, y; \
                       3, y]")
    matB = getTokens("[2, x; \
                       3, y]")
    assert multiplyCheck(matA, matB)

    matA = getTokens("[2, x, 1; \
                       3, y, z]")
    matB = getTokens("[1, 2; 2, 3]")
    assert not multiplyCheck(matA, matB)


def test_isEqual():

    matA = getTokens("[1, 2; \
                      x, z]")
    matB = getTokens("[1, 2; \
                      x, z]")

    assert isEqual(matA, matB)

    matA = getTokens("[2, x, 1; \
                       3, y, z]")
    matB = getTokens("[1, 2; 2, 3]")
    assert not isEqual(matA, matB)


#####################
# matrix.operations #
#####################


def test_simplifyMatrix():

    mat = getTokens("[x + y + x, x^2 + x^2; \
                      1 + 4/2  , z^3/z^2  ]")
    matRes = simplifyMatrix(mat)
    assert matRes.__str__() == "[2{x}+{y},2{x}^{2.0};{3.0},{z}]"

    mat = getTokens("[1 + x^2 + 2]")
    matRes = simplifyMatrix(mat)
    assert matRes.__str__() == "[{3.0}+{x}^{2.0}]"


def test_addMatrix():

    matA = getTokens("[2x + y, 2x]")
    matB = getTokens("[-x, -x]")
    matSum = addMatrix(matA, matB)
    # assert matSum.__str__() == "[2{x}+{y}]"  # BUG: Strange simplification for matSum

    matA = getTokens("[ x      , x^2; \
                        3 + x^2, xy ]")
    matB = getTokens("[ y + 1  , x^2; \
                        2 - x^2, xy - 1 ]")
    matSum = addMatrix(matA, matB)
    assert matSum.__str__() == "[{x}+{y}+{1.0},2{x}^{2.0};{5.0},2{x}{y}-{1.0}]"


def test_subMatrix():

    matA = getTokens("[y, 2x]")
    matB = getTokens("[-x, -x]")
    matSub = subMatrix(matA, matB)
    assert matSub.__str__() == "[{y}--1.0{x},3.0{x}]"


def test_scalarAddMatrix():

    mat = getTokens("[1, 2; \
                    2,  1]")
    const = 2
    matSum = scalarAdd(const, mat)
    assert matSum.__str__() == "[{3.0},{2.0};{2.0},{3.0}]"

    mat = getTokens("[1, 2, 3;\
                        4, 5, 6;\
                        7, 8, 9]")
    const = 3
    matSum = scalarAdd(const, mat)
    assert matSum.__str__() == "[{4.0},{2.0},{3.0};{4.0},{8.0},{6.0};{7.0},{8.0},{12.0}]"


def test_scalarSubMatrix():

    mat = getTokens("[8,6;\
                      1,9]")
    const = 2
    matSub = scalarSub(const, mat)
    assert matSub.__str__() == "[{6.0},{6.0};{1.0},{7.0}]"

    mat = getTokens("[5,8,2;\
                      12,30,9;\
                      4,17,7]")
    const = 10
    matSub = scalarSub(const, mat)
    assert matSub.__str__() == "[{-5.0},{8.0},{2.0};{12.0},{20.0},{9.0};{4.0},{17.0},{-3.0}]"


def test_scalarMultMatrix():

    mat = getTokens("[1, 2]")
    const = 2
    matSum = scalarMult(const, mat)
    assert matSum.__str__() == "[{2.0},{4.0}]"

    mat = getTokens("[2,4;\
                      -5,7]")
    const = 2
    matSum = scalarMult(const, mat)
    assert matSum.__str__() == "[{4.0},{8.0};{-10.0},{14.0}]"


def test_scalarDivMatrix():

    mat = getTokens("[4, 2]")
    const = 2
    matSum = scalarDiv(const, mat)
    assert matSum.__str__() == "[{2.0},{1.0}]"

    mat = getTokens("[48,36;\
                      24,-3]")
    const = 6
    matSum = scalarDiv(const, mat)
    assert matSum.__str__() == "[{8.0},{6.0};{4.0},{-0.5}]"


def test_multiplyMatrix():
    """
    # FIXME: Fixing addition fixes multiplication
    matA = getTokens("[1, 0; 0, 1]")
    matB = getTokens("[2; 3]")
    matPro = multiplyMatrix(matA, matB)
    # assert matPro.__str__() == ""

    matA = getTokens("[1, 2; x, 2; 3, y]")
    matB = getTokens("[2, x; 3, y]")
    matPro = multiplyMatrix(matA, matB)
    # assert matPro.__str__() == ""

    matA = getTokens("[2, x, 1; \
                       3, y, z]")
    matB = getTokens("[1, 2; 2, 3; 5, 6]")
    matPro = multiplyMatrix(matA, matB)
    # assert matPro.__str__() == ""
    """
    pass


def test_determinant():
    mat = getTokens('[1,2;3,4]')
    if mat.isSquare():
        a = ''
        for i in mat.determinant():
            a += i.__str__()
        assert a == "{-2.0}"
    mat = getTokens('[1,2,3;4,5,6;7,8,9]')
    if mat.isSquare():
        a = ''
        for i in mat.determinant():
            a += i.__str__()
        assert a == "{0}"
    mat = getTokens('[1]')
    if mat.isSquare():
        a = ''
        for i in mat.determinant():
            a += i.__str__()
        assert a == "{1.0}"


def test_inverse():
    mat = getTokens("[5, 7, 9;\
                    4, 3, 8;\
                    7, 5, 6]")
    if mat.isSquare():
        assert mat.inverse().__str__() == "[{-0.20977011494252873},{0.028735632183908046},{0.27586206896551724};{0.3023255813953489},{-0.3139534883720931},{-0.03779069767441861};{-0.009111617312072894},{0.22779043280182235},{-0.12300683371298407}]"

    mat = getTokens("[4, 5;\
                    7, 3]")
    if mat.isSquare():
        assert mat.inverse().__str__() == "[{-0.1301859799713877},{0.21745350500715305};{0.303951367781155},{-0.17325227963525833}]"

    mat = getTokens("[4, 5, 6, 8;\
                    3, 25, 4, 6;\
                    5, 1, 8, 4;\
                    1, 3, 5, 8]")
    if mat.isSquare():
        assert mat.inverse().__str__() == "[{0.49400000000000005},{-0.044000000000000004},{-0.08600000000000001},{-0.42400000000000004};{-0.057142857142857134},{0.049999999999999996},{0.014285714285714284},{0.0047619047619047615};{-0.40131578947368424},{0.03947368421052632},{0.25},{0.2565789473684211};{0.21321177223288548},{-0.03854766474728087},{-0.15067178502879078},{0.01599488163787588}]"

    mat = getTokens("[1,1;1,1]")
    if mat.isSquare():
        assert mat.inverse().__str__() == "-1"


def test_cofactor():
    mat = getTokens('[1,2;3,4]')
    if mat.isSquare():
        assert str(mat.cofactor()) == '[{4.0},{-3.0};{-2.0},{1.0}]'
    mat = getTokens('[1,2,3;0,4,5;1,0,6]')
    if mat.isSquare():
        assert str(mat.cofactor()) == '[{24.0},{5.0},{-4.0};{-12.0},{3.0},{2.0};{-2.0},{-5.0},{4.0}]'
    mat = getTokens('[1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16]')
    if mat.isSquare():
        assert str(mat.cofactor()) == '[{0},{0},{0},{0};{0},{0},{0},{0};{0},{0},{0},{0};{0},{0},{0},{0}]'


def test_echelon():
    mat = getTokens("[1, 4, 2;\
                      5, 7, 6;\
                      2, 4, 9]")
    assert row_echelon(mat).__str__() == "[{1.0},{4.0},{2.0};{0.0},{-13.0},{-4.0};{0.0},{0.0},{6.24}]"

    mat = getTokens("[1, 2, 3, 1;\
                      4, 5, 6, 1;\
                      7, 8, 9, 2]")
    assert row_echelon(mat).__str__() == "[{1.0},{2.0},{3.0},{1.0};{0.0},{-3.0},{-6.0},{-3.0};{0.0},{0.0},{0.0},{1.0}]"

    mat = getTokens("[1, 2, 3, 1;\
                      4, 5, 6, 1;\
                      7, 8, 9, 1;\
                      2, 3 ,1 ,4]")
    assert row_echelon(mat).__str__() == "[{1.0},{2.0},{3.0},{1.0};{0.0},{-3.0},{-6.0},{-3.0};{0.0},{0.0},{-3.02},{2.99};{0.0},{0.0},{0.0},{0.0}]"

    mat = getTokens("[6,2,8,26;\
                      3,5,2,8;\
                      0,8,2,-7]")
    assert row_echelon(mat).__str__() == "[{6.0},{2.0},{8.0},{26.0};{0.0},{4.0},{-2.0},{-5.0};{0.0},{0.0},{6.0},{3.0}]"


def test_multi_variable_solve():
    mat = getTokens("[1, 2, 3, 1;\
                      4, 5, 6, 1;\
                      7, 8, 2, 2]")
    assert gauss_elim(mat).__str__() == "[{-1.14};{1.2799999999999998};{-0.14285714285714285}]"

    mat = getTokens("[6,2,8,26;\
                      3,5,2,8;\
                      0,8,2,-7]")
    assert gauss_elim(mat).__str__() == "[{4.0};{-1.0};{0.5}]"

#######################
# Operator Overloading
#######################


def test_addoverload():

    matA = getTokens("[ x      , x^2; \
                        3 + x^2, xy ]")
    matB = getTokens("[ y + 1  , x^2; \
                        2 - x^2, xy - 1 ]")
    matSum = matA + matB
    assert matSum.__str__() == "[{x}+{y}+{1.0},2{x}^{2.0};{5.0},2{x}{y}-{1.0}]"


def test_suboverload():

    matA = getTokens("[y, 2x]")
    matB = getTokens("[-x, -x]")
    matSub = matA - matB
    assert matSub.__str__() == "[{y}--1.0{x},3.0{x}]"