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_getVariables():
varA = getTokens("x")
assert getVariables([varA]) == ['x']
varB = getTokens("xy+ xy^2 +yz^3")
assert getVariables(varB) == ['x', 'y', 'z']
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_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_tokensToString():
# Matrix token to string
mat = getTokens("[1+x, 2; \
3 , 4]")
assert tokensToString([mat]) == "[1.0 + x,2.0;3.0,4.0]"
mat = getTokens("[1+x, 2] + [1, y + z^2]")
assert tokensToString(mat) == "[1.0 + x,2.0] + [1.0,y + z^(2.0)]"
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_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_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}]"
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_areTokensEqual():
varA = getTokens("3xy")
varB = getTokens("3yx")
varC = getTokens("3yz")
assert areTokensEqual(varA, varB)
assert not areTokensEqual(varA, varC)
opA = Operator()
opA.value = '+'
opB = Plus()
assert areTokensEqual(opA, opB)
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_tokensToLatex():
# Matrix token to latex
mat = getTokens("[1+x, 2; \
3 , 4]")
assert tokensToLatex([
mat
]) == "\\begin{bmatrix}{1.0}+{x}&{2.0}\\\\{3.0}&{4.0}\\end{bmatrix}"
mat = getTokens("[1+x, 2] + [1, y + z^2]")
assert tokensToLatex(
mat
) == "\\begin{bmatrix}{1.0}+{x}&{2.0}\\end{bmatrix}+\\begin{bmatrix}{1.0}&{y}+{z}^{2.0}\\end{bmatrix}"
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)
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_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_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_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_getVariables():
varA = getTokens("x")
assert getVariables([varA]) == ['x']
varB = getTokens("xy+ xy^2 +yz^3")
assert getVariables(varB) == ['x', 'y', 'z']
varC = getTokens("x + sin(x) + cos(y) + tan(2*z)*2 + tanh(z) + e^2")
# FIXME: getVariables() in visma.io.checks
# varC = getTokens("x + sin(x) + cos(y) + tan(2*z)*2 + tanh(z) + e^2")
# assert getVariables(varC) == ['x', 'y', 'z']
assert getVariables(varC) == ['x']
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_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()
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_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_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_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}]"
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_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_isTokenInToken():
varA = getTokens("x^3")
varB = getTokens("xy^2")
varC = Expression(getTokens("1 + w + x"))
varD = Expression(getTokens("w + y"))
assert isTokenInToken(varA, varB)
assert isTokenInToken(varA, varC)
assert not isTokenInToken(varA, varD)
varA = getTokens("xy^2")
varB = getTokens("x^(2)y^(4)z")
varC = getTokens("yx^0.5")
varD = getTokens("xy^(3)z")
varE = getTokens("2")
assert isTokenInToken(varA, varB)
assert isTokenInToken(varA, varC)
assert not isTokenInToken(varA, varD)
assert not isTokenInToken(varA, varE)
def test_suboverload():
matA = getTokens("[y, 2x]")
matB = getTokens("[-x, -x]")
matSub = matA - matB
assert matSub.__str__() == "[{y}--1.0{x},3.0{x}]"
def test_strMatrix():
mat = getTokens("[1+x, 2; \
3 , 4]")
assert mat.__str__() == "[{1.0}+{x},{2.0};{3.0},{4.0}]"
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}]"