def getEquivalent(self):
left = []
right = []
for elem in self.elementary:
if(elem[0] == 'l'):
left.append(elem[1])
else:
right.append(elem[1])
leftWritable = reversed(left)
data = []
for mat in leftWritable:
data.append(Matrix(mat))
data.append(Matrix(self.states[0]))
for mat in right:
data.append(Matrix(mat))
return Math(data=data).dumps()
def getLatex(self):
data = []
for elem in self.states:
data.append(Matrix(elem))
data.append(Command('to'))
data.pop()
return Math(data=data).dumps()
def test_math():
Math(data=None, inline=False)
VectorName(name='')
# Numpy
m = np.matrix([[2, 3, 4], [0, 0, 1], [0, 0, 2]])
Matrix(matrix=m, name='', mtype='p', alignment=None)
def getEquivalentTruncated(self):
left = []
right = []
print(self.elementary)
for elem in self.elementary:
if(elem[0] == 'l'):
left.append(elem[1])
else:
right.append(elem[1])
leftWritable = reversed(left)
rows, cols = self.matrix.shape
leftMat = np.identity(rows)
rightMat = np.identity(cols)
for mat in leftWritable:
leftMat = np.matmul(leftMat, mat)
for mat in right:
rightMat = np.matmul(rightMat, mat)
data = [Matrix(leftMat), Matrix(self.states[0]), Matrix(rightMat)]
print(left)
return Math(data=data).dumps()
def test_math():
math = Math(data=None, inline=False)
repr(math)
vec = VectorName(name='')
repr(vec)
# Numpy
m = np.matrix([[2, 3, 4], [0, 0, 1], [0, 0, 2]])
matrix = Matrix(matrix=m, mtype='p', alignment=None)
repr(matrix)
def complexStuff(doc):
with doc.create(Section('The simple stuff')):
doc.append('Some regular text and some')
doc.append(italic('italic text. '))
doc.append('\nAlso some crazy characters: $&#{}')
with doc.create(Subsection('Math that is incorrect')):
doc.append(Math(data=['2*3', '=', 9]))
with doc.create(Subsection('Table of something')):
with doc.create(Tabular('rc|cl')) as table:
table.add_hline()
table.add_row((1, 2, 3, 4))
table.add_hline(1, 2)
table.add_empty_row()
table.add_row((4, 5, 6, 7))
a = np.array([[100, 10, 20]]).T
M = np.matrix([[2, 3, 4], [0, 0, 1], [0, 0, 2]])
with doc.create(Section('The fancy stuff')):
with doc.create(Subsection('Correct matrix equations')):
doc.append(Math(data=[Matrix(M), Matrix(a), '=', Matrix(M * a)]))
with doc.create(Subsection('Alignat math environment')):
with doc.create(Alignat(numbering=False, escape=False)) as agn:
agn.append(r'\frac{a}{b} &= 0 \\')
agn.extend([Matrix(M), Matrix(a), '&=', Matrix(M * a)])
with doc.create(Subsection('Beautiful graphs')):
with doc.create(TikZ()):
plot_options = 'height=4cm, width=6cm, grid=major'
with doc.create(Axis(options=plot_options)) as plot:
plot.append(Plot(name='model', func='-x^5 - 242'))
coordinates = [
(-4.77778, 2027.60977),
(-3.55556, 347.84069),
(-2.33333, 22.58953),
(-1.11111, -493.50066),
(0.11111, 46.66082),
(1.33333, -205.56286),
(2.55556, -341.40638),
(3.77778, -1169.24780),
(5.00000, -3269.56775),
]
plot.append(Plot(name='estimate', coordinates=coordinates))
# with doc.create(Subsection('Cute kitten pictures')):
# with doc.create(Figure(position='h!')) as kitten_pic:
# kitten_pic.add_image(image_filename, width='120px')
# kitten_pic.add_caption('Look it\'s on its back')
doc.generate_pdf('full', clean_tex=False)
def transitionMatrix(doc, tM):
with doc.create(Subsection('Transitions')):
data = ['\setcounter{MaxMatrixCols}{20}', '\Pi=']
with doc.create(Alignat(numbering=False, escape=False)) as agn:
agn.extend(data)
agn.append(Matrix(tM, mtype='b'))
def communicationMatrix(doc, cM):
with doc.create(Subsection('Communication Matrix')):
data = ['\setcounter{MaxMatrixCols}{20}', 'C=']
with doc.create(Alignat(numbering=False, escape=False)) as agn:
agn.extend(data)
agn.append(Matrix(cM, mtype='b'))
import numpy as np
from pylatex import Document, Section, Subsection, Math, Matrix, VectorName
if __name__ == '__main__':
a = np.array([[100, 10, 20]]).T
doc = Document()
section = Section('Numpy tests')
subsection = Subsection('Array')
vec = Matrix(a)
vec_name = VectorName('a')
math = Math(data=[vec_name, '=', vec])
subsection.append(math)
section.append(subsection)
subsection = Subsection('Matrix')
M = np.matrix([[2, 3, 4], [0, 0, 1], [0, 0, 2]])
matrix = Matrix(M, mtype='b')
math = Math(data=['M=', matrix])
subsection.append(math)
section.append(subsection)
subsection = Subsection('Product')
math = Math(data=['M', vec_name, '=', Matrix(M * a)])
subsection.append(math)
def draw_inverse_matrix(data):
M = np.matrix(data['vals']).reshape([data['first_dim'], data['second_dim']])
return Math(data=['inv', Matrix(M), '=', Matrix(np.linalg.pinv(M))])
def draw_matrix(data):
M = np.matrix(data['vals']).reshape([data['first_dim'], data['second_dim']])
return Math(data=[Matrix(M)])
def array(lis, **kwargs):
return Matrix(np.array(lis), **kwargs)
def generateLatex(phrases, key, result, flag):
geometry_options = {"tmargin": "1cm", "lmargin": "3cm", "rmargin": "3cm"}
doc = Document(geometry_options=geometry_options)
if(flag == "E"):
with doc.create(Section('Encyption Input')):
doc.append('Text: ' + "".join(phrases) + "\n")
doc.append('Key: ' +key)
with doc.create(Section("Matrix Mltiplications")):
for phrase in phrases:
M = createEncryptMatrix(key)
messageMatrix = np.array([[getCapitalAlphaMod(phrase[0]),getCapitalAlphaMod(phrase[1]),getCapitalAlphaMod(phrase[2])]]).astype("float64").T
doc.append(Math(data=[r'1/' + str(26), Matrix(M), Matrix(messageMatrix), '=', Matrix(getModMatrix(M @ messageMatrix))]))
doc.append("\n")
doc.append("Encrypted chunk: " + getStringFromMatrix(getModMatrix(M @ messageMatrix)))
with doc.create(Section('Encyption Result')):
doc.append('Cipher: ' + result)
elif(flag == "D"):
image_filename = './LookupHill.png'
with doc.create(Section('Introduction')):
doc.append('In this project, I implement a 3 × 3 Hill Cipher Machine in Python. This machine automatically generates LaTex reports to decipher user-input step by step. \n')
doc.append('We will be deciphering: ' + "".join(phrases) + ' using the key: ' + key + '. \n')
with doc.create(Section("Enryption Matrix")):
with doc.create(Figure(position='h!')) as lookup_hill:
lookup_hill.add_image(image_filename, width='120px')
lookup_hill.add_caption('Lookup Table of Hill Cipher')
doc.append('We use the Lookup Table above to create the Encryption Matrix below. \n')
M = createEncryptMatrix(key)
doc.append(Math(data=[Matrix(M)]))
with doc.create(Section("Encryption Matrix Mod 26 Inverse")):
'''iM = np.array([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
E21E31 = iM.copy()
E21E31[(1,0)] = -1 * (augM[(1,0)]/augM[(0,0)])
E21E31[(2,0)] = -1 * (augM[(2,0)]/augM[(0,0)])
augM = E21E31.dot(augM)
E32 = iM.copy()
E32[(2,1)] = -1 * (augM[(2,1)]/augM[(1,1)])
augM = E32.dot(augM)
E23E13 = iM.copy()
E23E13[(1,2)] = -1 * (augM[(1,2)]/augM[(2,2)])
E23E13[(0,2)] = -1 * (augM[(0,2)]/augM[(2,2)])
augM = E23E13.dot(augM)
E12 = iM.copy()
E12[(0,1)] = -1 * (augM[(0,1)]/augM[(1,1)])
augM = E12.dot(augM)
det = augM[(0,0)] * augM[(1,1)] * augM[(2,2)]
if(det == 0 or math.isnan(det)):
raise ValueError("Matrix Non-Invertible")
#print("Det: " + str(det))
if(egcd(int(round(det)), 26)[0] != 1):
raise ValueError("Key Matrix determinent not co-prime with 26")
#print("Mod inv of det: " + str(modinv(det, 26)))
D = iM.copy()
D[(0,0)] = 1/augM[(0,0)]
D[(1,1)] = 1/augM[(1,1)]
D[(2,2)] = 1/augM[(2,2)]
augM = D.dot(augM)
#Here are the additional steps needed to find the modular inverse of a matrix
augM = augM * det
augM = augM * modinv(int(round(det)), 26)
modAugM = getModMatrix(augM[0:, 3:])
return modAugM'''
invMat = gaussianInverseMod26(createEncryptMatrixAug(key))
doc.append(Math(data=[Matrix(invMat)]))
doc.append("\n")
with doc.create(Section("Matrix Multiplications")):
for phrase in phrases:
M = invMat
#print(M)
messageMatrix = np.array([[getCapitalAlphaMod(phrase[0]),getCapitalAlphaMod(phrase[1]),getCapitalAlphaMod(phrase[2])]]).astype("float64").T
doc.append(Math(data=[Matrix(M), Matrix(messageMatrix), '=', Matrix(getModMatrix(M @ messageMatrix))]))
doc.append("\n")
doc.append("Decrypted chunk: " + getStringFromMatrix(getModMatrix(M @ messageMatrix)))
with doc.create(Section('Decryption Result')):
doc.append('Plaintext: ' + result)
doc.generate_pdf('full', clean_tex=False)
subprocess.call(['open', 'full.pdf'])
def details():
if __name__ == '__main__':
image_filename = os.path.join(os.path.dirname(__file__), 'kitten.jpg')
logo_file = os.path.join(os.path.dirname(__file__),'sample-logo.png')
geometry_options = {"tmargin": "1cm", "lmargin": "3cm"}
doc = Document(geometry_options=geometry_options)
header = PageStyle("header")
with header.create(Head("R")):
header.append(simple_page_number())
with header.create(Foot("C")):
header.append("Center Footer")
first_page = PageStyle("firstpage")
with first_page.create(Head("L")) as header_left:
with header_left.create(MiniPage(width=NoEscape(r"0.49\textwidth"),pos='c')) as logo_wrapper
with doc.create(MiniPage(align='l')):
doc.append(LargeText(bold("INVESTMENT PROPERTY - BUY & HOLD")))
doc.append(LineBreak())
doc.append(MediumText(bold(" ")))
logo_wrapper.append(StandAloneGraphic(image_options="width=120px",
filename=logo_file))
with doc.create(Section('Home Adress')):
doc.append('Some regular text and some')
doc.append(italic('italic text. '))
doc.append('\nAlso some crazy characters: $&#{}')
with doc.create(Subsection('Math that is incorrect')):
doc.append(Math(data=['2*3', '=', 9]))
with doc.create(Subsection('Table of something')):
with doc.create(Tabular('rc|cl')) as table:
table.add_hline()
table.add_row((1, 2, 3, 4))
table.add_hline(1, 2)
table.add_empty_row()
table.add_row((4, 5, 6, 7))
a = np.array([[100, 10, 20]]).T
M = np.matrix([[2, 3, 4],
[0, 0, 1],
[0, 0, 2]])
with doc.create(Section('The fancy stuff')):
with doc.create(Subsection('Correct matrix equations')):
doc.append(Math(data=[Matrix(M), Matrix(a), '=', Matrix(M * a)]))
with doc.create(Subsection('Alignat math environment')):
with doc.create(Alignat(numbering=False, escape=False)) as agn:
agn.append(r'\frac{a}{b} &= 0 \\')
agn.extend([Matrix(M), Matrix(a), '&=', Matrix(M * a)])
with doc.create(Subsection('Beautiful graphs')):
with doc.create(TikZ()):
plot_options = 'height=4cm, width=6cm, grid=major'
with doc.create(Axis(options=plot_options)) as plot:
plot.append(Plot(name='model', func='-x^5 - 242'))
coordinates = [
(-4.77778, 2027.60977),
(-3.55556, 347.84069),
(-2.33333, 22.58953),
(-1.11111, -493.50066),
(0.11111, 46.66082),
(1.33333, -205.56286),
(2.55556, -341.40638),
(3.77778, -1169.24780),
(5.00000, -3269.56775),
]
plot.append(Plot(name='estimate', coordinates=coordinates))
with doc.create(Subsection('Cute kitten pictures')):
with doc.create(Figure(position='h!')) as kitten_pic:
kitten_pic.add_image(image_filename, width='120px')
kitten_pic.add_caption('Look it\'s on its back')
doc.generate_pdf('full', clean_tex=False)
def draw_random_matrix(data):
M = np.random.randint(1, 99, size=(data.get('first_dim'), data.get('second_dim')))
return Math(data=[Matrix(M)])
with doc.create(Subsection('Table of something')):
with doc.create(Tabular('rc|cl')) as table:
table.add_hline()
table.add_row((1, 2, 3, 4))
table.add_hline(1, 2)
table.add_empty_row()
table.add_row((4, 5, 6, 7))
a = np.array([[100, 10, 20]]).T
M = np.matrix([[2, 3, 4],
[0, 0, 1],
[0, 0, 2]])
with doc.create(Section('The fancy stuff')):
with doc.create(Subsection('Correct matrix equations')):
doc.append(Math(data=[Matrix(M), Matrix(a), '=', Matrix(M * a)]))
with doc.create(Subsection('Beautiful graphs')):
with doc.create(TikZ()):
plot_options = 'height=6cm, width=6cm, grid=major'
with doc.create(Axis(options=plot_options)) as plot:
plot.append(Plot(name='model', func='-x^5 - 242'))
coordinates = [
(-4.77778, 2027.60977),
(-3.55556, 347.84069),
(-2.33333, 22.58953),
(-1.11111, -493.50066),
(0.11111, 46.66082),
(1.33333, -205.56286),
(2.55556, -341.40638),
def draw_random_multiply_matrix(data):
M1 = np.random.randint(1, 99, size=(data.get('first_dim'), data.get('second_dim')))
M2 = np.random.randint(1, 99, size=(data.get('second_dim'), data.get('third_dim')))
return Math(data=[Matrix(M1), Matrix(M2), '=', Matrix(M1.dot(M2))])
doc.append(Math(data=['2*3', '=', 9]))
with doc.create(Subsection('Table of something')):
with doc.create(Tabular('rc|cl')) as table:
table.add_hline()
table.add_row((1, 2, 3, 4))
table.add_hline(1, 2)
table.add_empty_row()
table.add_row((4, 5, 6, 7))
a = np.array([[100, 10, 20]]).T
M = np.matrix([[2, 3, 4], [0, 0, 1], [0, 0, 2]])
with doc.create(Section('The fancy stuff')):
with doc.create(Subsection('Correct matrix equations')):
doc.append(Math(data=[Matrix(M), Matrix(a), '=', Matrix(M * a)]))
with doc.create(Subsection('Alignat math environment')):
with doc.create(Alignat(numbering=False, escape=False)) as agn:
agn.append(r'\frac{a}{b} &= 0 \\')
agn.extend([Matrix(M), Matrix(a), '&=', Matrix(M * a)])
with doc.create(Subsection('Beautiful graphs')):
with doc.create(TikZ()):
plot_options = 'height=4cm, width=6cm, grid=major'
with doc.create(Axis(options=plot_options)) as plot:
plot.append(Plot(name='model', func='-x^5 - 242'))
coordinates = [
(-4.77778, 2027.60977),
(-3.55556, 347.84069),
def update(self, i):
i = int(i)
self.parent.matrix = np.array(
(self.parent.i_vector, self.parent.j_vector,
self.parent.k_vector)).T
self.parent.plus_matrix = np.array(
(self.parent.i_plus_vector, self.parent.j_plus_vector,
self.parent.k_plus_vector)).T
if self.canvasFigure != None:
try:
self.parent.quiver.remove()
self.parent.plus_quiver.remove()
except:
print("do nothing")
self.parent.matrix = (1 - self.parent.sigmoid(i)) * np.array(
(self.parent.i_origin, self.parent.j_origin, self.parent.
k_origin)) + self.parent.sigmoid(i) * self.parent.matrix
self.parent.plus_matrix = (1 - self.parent.sigmoid(i)) * np.array(
(self.parent.i_origin, self.parent.j_origin, self.parent.
k_origin)) + self.parent.sigmoid(i) * self.parent.plus_matrix
else:
self.parent.matrix = np.array(
(self.parent.i_origin, self.parent.j_origin,
self.parent.k_origin)) + self.parent.matrix
self.parent.plus_matrix = np.array(
(self.parent.i_origin, self.parent.j_origin,
self.parent.k_origin)) + self.parent.plus_matrix
# Compute a matrix that is in the middle between the full transformation matrix and the identity
self.parent.vector_location = np.array(
(self.parent.matrix.dot(self.parent.i_origin),
self.parent.matrix.dot(self.parent.j_origin),
self.parent.matrix.dot(self.parent.k_origin))).T
self.parent.quiver = self.parent.ax.quiver(
0,
0,
0,
self.parent.vector_location[0],
self.parent.vector_location[1],
self.parent.vector_location[2],
length=1,
color='r',
arrow_length_ratio=0.1)
self.parent.plus_vector_location = np.array(
(self.parent.plus_matrix.dot(self.parent.i_origin),
self.parent.plus_matrix.dot(self.parent.j_origin),
self.parent.plus_matrix.dot(self.parent.k_origin))).T
self.parent.plus_quiver = self.parent.ax.quiver(
0,
0,
0,
self.parent.plus_vector_location[0],
self.parent.plus_vector_location[1],
self.parent.plus_vector_location[2],
length=1,
color='y',
arrow_length_ratio=0.1)
# Set vector location - must transpose since we need U and V representing x and y components
# of each vector respectively (without transposing, e ach column represents each unit vector)
self.parent.transform = np.array(
[self.parent.matrix.dot(k) for k in self.parent.x])
#ax.view_init((1 - self.parent.sigmoid(i)) * elevation, (1 - self.parent.sigmoid(i)) * angle)
if self.canvasFigure != None:
self.parent.scat._offsets3d = [
self.parent.transform[:, 0], self.parent.transform[:, 1],
self.parent.transform[:, 2]
]
self.canvasFigure.draw()
a = self.parent.plus_vector_location
#with pylatex.config.active.change(indent=False):
doc = Document()
doc.packages.append(
Package('geometry',
options=['paperwidth=6in', 'paperheight=2.5in']))
section = Section('Linear Combination')
subsection = Subsection('Using the dot product')
V1 = np.transpose(np.array([[1, 1]]))
M1 = np.array((self.parent.i_vector, self.parent.j_vector)).T
math = Math(data=[
Matrix(M1), 'dot',
Matrix(V1), '=',
Matrix(np.dot(M1, V1))
])
subsection.append(math)
section.append(subsection)
subsection = Subsection('Using vector addition')
V1 = np.array([self.parent.i_vector])
V2 = np.array([self.parent.j_vector])
math = Math(
data=[Matrix(V1), '+',
Matrix(V2), '=',
Matrix(V1 + V2)])
subsection.append(math)
section.append(subsection)
#doc.append(section)
'''
subsection = Subsection('Product')
math = Math(data=['M', vec_name, '=', Matrix(M * a)])
subsection.append(math)
section.append(subsection)
doc.append(section)
'''
doc.append(section)
latex = doc.dumps_as_content()
print(latex)
self.strvar.set(latex)
#self.strvar.set("\prod_{p\,\mathrm{prime}}\\frac1{1-p^{-s}} = \sum_{n=1}^\infty \\frac1{n^s}")
self.on_latex()
