# Matrix Multiplying Problem Generator 3
# Author: Aidan Murphy
# Last Modified: 3/9/17



# This code will generate a TeX file with a variable number of matrix multiplication practice problems

# These are the variables which you may change the values of for different results:
numberExamples = 20  # the number of examples that this program will generate
minSizeDimension = 2  # the minimum dimension of each matrix (must be >0)
maxSizeDimension = 5  # the maximum dimension of each matrix (must be >0)
probOfResize = 0.8  # the minimum proportion of products that will exist
minNum = -5  # the minimum cell entry in the matrices
maxNum = 5  # the maximum cell entry in the matrices

# Abandon all hope, ye who enter here
#####################################################################################################
# Here there be dragons

import numpy as np  # import package for matrices

# opens the text document to edit
text_file = open("M233-MMG-Exercises.tex", "w")

# starting the inserting of the prelude
preludeList = ["\documentclass[12pt]{article}",
               "\ usepackage[english]{babel}",
               "\ usepackage[utf8]{inputenc}",
               "\ usepackage[autostyle, english = american]{csquotes}",
               "\ usepackage{listings}",
               "\ usepackage{keyval}",
               "\ usepackage{xcolor}",
               "\ usepackage{textcomp}",
               "\ usepackage{fullpage}",
               "\ usepackage{setspace}",
               "\ usepackage{graphicx}",
               "\ usepackage{hyperref}",
               "\ usepackage{verbatim}",
               "\ usepackage{multicol}",
               "\ usepackage{float}",
               "\ usepackage{framed}",
               "\ usepackage[fleqn]{amsmath}",
               "\ usepackage{amssymb}",
               "\ usepackage{amsfonts}",
               "\ usepackage{amsthm}",
               "\ usepackage{marvosym}",
               "\ usepackage{wasysym}",
               "\ usepackage{tikz}",
               "\ usetikzlibrary{arrows}",
               "\ newtheorem{theorem}{Theorem}",
               "\ newtheorem{lemma}{Lemma}",
               "\ renewcommand\qedsymbol{$\blacksquare$}"]  # vector containing the prelude commands and packages

listLength = len(preludeList)
for i in range(0, listLength):
    text_file.write(preludeList[i].replace(" ", ""))  # get rid of strings

# declare the beginning of the document
prelim = "\ begin{document}"
text_file.write(prelim.replace(" ", ""))

# Build the title of the document
prelim = "\ noindent"
text_file.write(prelim.replace(" ", ""))
text_file.write(" Math 233 Matrix Multiplication Example Generator")
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
text_file.write(" Author: Aidan Murphy")
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
text_file.write(" Last Modified: 3/9/17")
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")

# input the description
prelim = "\ indent"
text_file.write(prelim.replace(" ", ""))
text_file.write(
    " This document was generated as a .txt file by Python, and then compiled with TeXMaker. The purpose of this document is to generate pairs of matrices, as well as their products if they exist, for the purpose of practicing matrix multiplication.")
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")
prelim = "\ indent"
text_file.write(prelim.replace(" ", ""))
text_file.write(" Practice Problems: ")
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")

# generating matrix examples
firstMatrixList = [None for x in range(numberExamples)]
secondMatrixList = [None for y in range(numberExamples)]
answers = [None for z in range(numberExamples)]
for i in range(0, numberExamples):
    # generating the matrices with Python
    m1 = np.random.randint(low=minSizeDimension, high=maxSizeDimension)
    n1 = np.random.randint(low=minSizeDimension, high=maxSizeDimension)
    m2 = np.random.randint(low=minSizeDimension, high=maxSizeDimension)
    n2 = np.random.randint(low=minSizeDimension, high=maxSizeDimension)
    if np.random.rand(1) < probOfResize:
        n1 = m2  # so that a higher proportion of products exist
    M1 = np.random.randint(low=minNum, high=maxNum, size=(m1, n1))
    M2 = np.random.randint(low=minNum, high=maxNum, size=(m2, n2))
    if n1 == m2:
        answers[i] = np.matmul(M1, M2)
    else:
        answers[i] = "Product does not exist."

    # start printing these results to the TeX file
    prelim = "\ indent"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" Problem %i " % (i + 1))
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")

    # trying to extend to general sized matrices
    prelim = "$\ begin{bmatrix}"
    text_file.write(prelim.replace(" ", ""))
    for j in range(m1):
        for k in range(n1):
            text_file.write("{}".format(M1.item((j, k))))
            if k < n1:
                text_file.write(" & ")
        prelim = "\ \ "
        text_file.write(prelim.replace(" ", ""))
    prelim = "\ end{bmatrix}$"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")

    # generating the second matrix
    prelim = "$\ begin{bmatrix}"
    text_file.write(prelim.replace(" ", ""))
    for j in range(m2):
        for k in range(n2):
            text_file.write("{}".format(M2.item((j, k))))
            if k < n2:
                text_file.write(" & ")
        prelim = "\ \ "
        text_file.write(prelim.replace(" ", ""))
    prelim = "\ end{bmatrix}$"
    text_file.write(" ")
    text_file.write(prelim.replace(" ", ""))

    # indent to a new line
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")

# skipping a page before printing the solutions
prelim = "\ newpage"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")
prelim = "\ hspace{0 mm}"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")
prelim = "\ indent"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")
prelim = "\ newpage"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")

# begin the page with the solutions
prelim = "\ indent"
text_file.write(prelim.replace(" ", ""))
text_file.write(" Solutions: ")
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
prelim = "\ newline"
text_file.write(prelim.replace(" ", ""))
text_file.write(" ")
for i in range(0, numberExamples):
    # start printing these results to the TeX file
    prelim = "\ indent"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" Problem %i " % (i + 1))
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")

    # print out answer matrices
    thisAnswer = answers[i]
    if isinstance(thisAnswer, str) == 0:
        m = len(thisAnswer[:, 1])
        n = len(thisAnswer[1, :])
        prelim = "$\ begin{bmatrix}"
        text_file.write(prelim.replace(" ", ""))
        for j in range(m):
            for k in range(n):
                text_file.write("{}".format(answers[i].item((j, k))))
                if k < n:
                    text_file.write(" & ")
            prelim = "\ \ "
            text_file.write(prelim.replace(" ", ""))
        prelim = "\ end{bmatrix}$"
        text_file.write(prelim.replace(" ", ""))
        text_file.write(" ")
    else:
        text_file.write("{}".format(thisAnswer))

    # indent to a new line
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")
    prelim = "\ newline"
    text_file.write(prelim.replace(" ", ""))
    text_file.write(" ")

# declare the end of the document
prelim = "\ end{document}"
text_file.write(prelim.replace(" ", ""))
text_file.close()