Reworked math lib generation script

Script can now generate matrices up to 9x9

generate_math_lib.py

@@ -0,0 +1,946 @@
+#!/bin/python3
+"""
+A python script to generate a c++ vector and matrix library for mathematics.
+Should work with vectors/matrix up to a length of 9.
+
+The script generates a header (and source) for each container (vector/matrix).
+There are overloads for each container which allow convenient usage. 
+Eg multiplication with matrix rules is as easy as: (example)
+mat3x2 = mat3x3 * mat3x2
+n = rvec4 * vec4
+To be accurate, there is a differentiation between row and column vector, they are basically the same but each has a separate class which differ only for the matrix multiplication overloads.
+
+To help compile times, the templated definitions of most methods is in the source file (by default).
+That means that all templates must be explictly instantiated beforehand. The instantiations are in the tpp file included by the cpp files.
+Specify the needed types by adding them to templateInstantiationIntTypes and templateInstantiationFloatTypes respectively (the differentiation is needed for the modulo operator).
+
+All that makes the generated library is not memory efficient, but very fast and convenient.
+
+AS OF NOW, THIS SOFTWARE IS NEARLY UNTESTED AND BOUND TO CONTAIN LOTS OF BUGS.
+
+Copyright  ©  2022  Matthias  Quintern.
+This software comes with no warranty.
+This software is licensed under the GPL3
+"""
+
+from os import path, mkdir
+#
+# SETTINGS
+# 
+# generate up to MAX_N (-> vecN, matNxN)
+MAX_N = 4
+letters_ = {
+    2: [ "x", "y" ],
+    3: [ "x", "y", "z" ],
+    4: [ "x", "y", "z", "w"],
+}
+directory = "math"
+#
+# \t or x-spaces
+tab = "\t"
+# float, double, long double...
+float_type = "float"
+# string or None
+namespace = "gz"
+typeShorts = {
+    "float": "f",
+    "double": "d",
+    "int": "i",
+    "unsigned int": "u",
+}
+include_static_asserts = True
+include_template_instantiations = True
+templateInstantiationIntTypes = [  # these must be usable with %
+    # "uint8_t"
+    "uint8_t", "uint16_t", "uint32_t", "uint64_t",
+    "int8_t", "int16_t", "int32_t", "int64_t",
+]
+templateInstantiationFloatTypes = [
+    # "float",
+    "float", "double", "long double"
+]
+templateInstantiationTypes = templateInstantiationFloatTypes + templateInstantiationIntTypes
+
+
+headerIncludes = [ "\"concepts.hpp\"", "\"../container/iterator.hpp\"" ]
+sourceIncludes = ["<cmath>", "<algorithm>", "<cstdint>"]
+
+
+# shorthands
+Number_N = ("Number", "N")
+Class_T = [("Number", "T")]
+constexpr = "constexpr"
+inline = "inline"
+
+
+def template(t:list[tuple[str, str]]):
+    if len(t) == 0:
+        return ""
+    s = "template<"
+    for temp in t:
+        s += temp[0] + " " + temp[1] + ", "
+    return s.removesuffix(", ") + ">\n"
+
+
+class Member:
+    def __init__(self, class_:str, name:str, c_temp:list=[], m_temp:list=[], prefixes:list=[], ret_type:str="", args:str="", init:str="", const=False, body:list=[], comment:str=""):
+        """
+        :param class: class name
+        :param name: member name
+        :param c_temp: list of templates of the class
+        :param m_temp: list of templates of the member
+        :param prefixes:  things like constexpr, inline...
+        :param ret_type: return type of the member
+        :param args: arguments of the member
+        :param init: initializion of the member
+        :param const: True if the method does not change the object
+        :param body: method body
+        :param comment: a single-line docstring
+
+        template<c_temp>
+        class class {
+            comment
+            template<m_temp>
+            prefixes ret_type name(args) const : init {
+                body
+            }
+        }
+        """
+        self.class_ = class_
+        self.name = name
+        self.prefixes = prefixes
+        self.c_temp = c_temp
+        self.m_temp = m_temp
+        self.ret_type = ""
+        if ret_type: self.ret_type = ret_type + " "
+        self.args = args
+        self.init = ""
+        if init: self.init = f"\n{tab} : {init} "
+        self.const = ""
+        if const: self.const = " const"
+        self.body = body
+        self.comment = ""
+        if comment: self.comment = "/// " + comment + "\n"
+
+    def getArgsAsList(self):
+        args = []
+        const = False
+        arglist = self.args.split(", ")
+        for i in range(len(arglist)):
+            if "const" in arglist[i]:
+                arglist[i] = arglist[i].replace("const ", "")
+                const = True
+            args.append(arglist[i].split(" "))
+            if const:
+                args[-1][0] = "const " + args[-1][0]
+        return args
+
+    def defintionH(self, depth:int=0):
+        """
+        Return the defition to be used in a header
+        """
+        s = ""
+        s += self.comment
+        s += template(self.m_temp)
+        for p in self.prefixes:
+            s += p + " "
+        s += self.ret_type + self.name + f"({self.args}){self.const};\n"
+        return transformString(s, depth)
+
+    def source(self, depth:int=0):
+        """
+        Return the defition + declarations for a source file
+        """
+        s = ""
+        class_ = self.class_
+        s += template(self.c_temp)
+        if len(self.c_temp) > 0:
+            class_ = self.class_ + "<"
+            for t in self.c_temp:
+                class_ += f"{t[1]}, "
+            class_ = class_.removesuffix(", ") + ">"
+
+        s += template(self.m_temp)
+        for p in self.prefixes:
+            s += p + " "
+        s += f"{self.ret_type}{class_}::{self.name}({self.args}){self.const}{self.init}"
+        if self.body:
+            s += " {\n"
+            body = ""
+            for l in self.body: body += l + "\n"
+            s += transformString(body, depth)
+            s += "}\n"
+        else:
+            s += "{}"
+        return transformString(s, depth)
+
+    def header(self, depth:int=0):
+        """
+        Return the defition + declarations for a header file
+        """
+        s = ""
+        s += self.comment
+        s += template(self.m_temp)
+        for p in self.prefixes:
+            s += p + " "
+        s += f"{self.ret_type}{self.name}({self.args}){self.const}{self.init}"
+        if self.body:
+            s += " {\n"
+            body = ""
+            for l in self.body: body += l + "\n"
+            s += transformString(body, depth+1)
+            s += "}\n"
+        else:
+            s += "{}\n"
+        return transformString(s, depth)
+
+    def isConstructor(self):
+        return self.class_ == self.name
+
+    def templateInstantiations(self):
+        """
+        generate instantiations for all templates
+        right now only works with Number concepts
+        temp<Number T>
+        temp<Number N>
+        void Class<T>::operator+(class<N>) {
+        ->
+        temp<> void Class<float>::operator+(class<float>)
+        ...
+        """
+        if len(self.m_temp) == 0:
+            return ""
+        class_ = self.class_
+        if len(self.c_temp) > 0:
+            class_ = self.class_ + "<"
+            for t in self.c_temp:
+                class_ += f"{t[1]}, "
+            class_ = class_.removesuffix(", ") + ">"
+
+        arglist = self.getArgsAsList()
+        args = ""
+        for arg in arglist:
+            args += arg[0] + ", "
+        args = args.removesuffix(", ")
+        name = self.name.removesuffix(" ")
+        if len(self.m_temp) > 0:
+            name += " <"
+            for type_ in self.m_temp:
+                name += type_[1] + ", "
+            name = name.removesuffix(", ") + ">"
+
+        method = f"{self.ret_type}{class_}::{name}({args}){self.const}"
+        instantiations = []
+        if len(self.c_temp) > 0 or len(self.m_temp) > 0:
+            if "%" in method: types = templateInstantiationIntTypes
+            else: types = templateInstantiationTypes
+            getTemplateInsts(method, instantiations, self.c_temp + self.m_temp, types, 0)
+        s = ""
+        for spec in instantiations:
+            s += spec + "\n"
+        return s + "\n";
+
+
+#
+# HELPERS
+#
+def classname(row, col, template=""):
+    name = ""
+    if template and col == 1 and row == 1:
+        return template
+    elif col == 1:
+        name =  "vec" + str(row)
+    elif row == 1:
+        name = "rvec" + str(col)
+    else:
+        name = "mat" + str(row) + "x" + str(col);
+    if template:
+        name += "<" + template + ">"
+    return name
+
+
+def concept(row, col, template=""):
+    name = ""
+    if template and col == 1 and row == 1:
+        return template
+    elif col == 1:
+        name =  "ColumnVector" + str(row)
+    elif row == 1:
+        name = "RowVector" + str(col)
+    else:
+        name = "Mat" + str(row) + "x" + str(col);
+    if template:
+        name += "<" + template + ">"
+    return name
+
+
+def classnameFromConcept(concept:str):
+    name = ""
+    number = ""
+    if concept.startswith("ColumnVector"):
+        name = "vec"
+        number = concept.removeprefix("ColumnVector")
+    elif concept.startswith("RowVector"):
+        name = "rvec"
+        number = concept.removeprefix("RowVector")
+    elif concept.startswith("Mat"):
+        name = "mat"
+        number = concept.removeprefix("Mat")
+    return name + number
+
+
+def varname(r, c, rows, cols):
+    """Get the name of the variable in row r and column c"""
+    if rows == 1:
+        if cols in letters_.keys():
+            return letters_[cols][c]
+        else:
+            return f"x{r+1}"
+    elif cols == 1:
+        if rows in letters_.keys():
+            return letters_[rows][r]
+        else:
+            return f"x{c+1}"
+    else:
+        return f"x{r+1}_{c+1}"
+
+
+def varnameI(i, rows, cols):
+    """Get the name of the ith variable"""
+    if rows == 1:
+        if cols in letters_.keys():
+            return letters_[cols][i%cols]
+        else:
+            return f"x{i+1}"
+    elif cols == 1:
+        if rows in letters_.keys():
+            return letters_[rows][i%rows]
+        else:
+            return f"x{i+1}"
+    else:
+        return f"x{i%rows+1}_{i%cols+1}"
+
+
+
+def genstring(row: int, col: int, template: str, sep=", "):
+    """
+    Generate a string from a template for each vector component
+    eg genstring(3, "@ + ") -> x + y + z
+    @C -> varname(1, c, 1, col)
+    @R -> varname(r, 1, row, 1)
+    @ -> varname(r, c, row, col)
+    @c -> c
+    @r -> r
+
+    """
+    s = ""
+    for r in range(row):
+        for c in range(col):
+            s += template.replace("@r", str(r)).replace("@c", str(c)).replace("@R", varname(r, c, row, 1)).replace("@C", varname(r, c, 1, col)).replace("@", varname(r, c, row, col)) + sep
+
+    s.removesuffix(sep)
+    return s[0:len(s)-len(sep)]
+
+
+def transformString(s: str, depth: int):
+    """Add tabs after all but the last line break and before the first char"""
+    return depth * tab + s.replace("\n", "\n" + depth * tab, s.count("\n") - 1)
+
+
+def getPossiblities(i, a, depth=0):
+    """
+    get all possibilites to get i by addition of numbers lower than i
+    eg i=3 -> 3, 2+1, 1+2, 1+1+1
+    """
+    if i == 0:
+        return
+    if i == 1:
+        a.append(str(1))
+        return
+    for j in range(1, i):
+        b = []
+        # print("\t" * depth + "gp: i="+str(i)+" j="+str(j))
+        getPossiblities(i-j, b, depth+1)
+
+        for poss in b:
+            # print("\t"*depth + f"{i}-{j} returned", b)
+            a.append(str(j) + poss)
+    a.append(str(i))
+
+
+
+#
+# GENERATORS
+#
+def genConstructors(row, col):
+    constructors = []
+    class_ = classname(row, col)
+
+    # default
+    constructors.append(Member(class_, class_, c_temp=Class_T, prefixes=[constexpr], init=genstring(row, col, "@(0)"), comment="Default constructor"))
+
+    # from single scalar
+    constructors.append(Member(class_, class_, c_temp=Class_T, prefixes=[constexpr], m_temp=[["Number", "N"]], args="const N n", init=genstring(row, col, "@(static_cast<T>(n))"), comment="Create from scalar, all components will have value n"))
+
+    # generate a constructor for every possible vector initialization
+    if row == 1 or col == 1:
+        rows_or_cols = max(row, col)  # vec and rvec share same variable names
+        size = max(row, col)
+        a = []
+        getPossiblities(size, a)
+        for possiblity in a:
+            n_count = 1  # counts how many numbers appear 
+            v_count = 1  # counts how many vectors appear
+            i = 0  # index the member variable to initialize
+            comment = "Create from "
+            templates = []
+            args = ""
+            init = ""
+
+            for nstr in possiblity:
+                n = int(nstr)
+                if n == 1:  # if number
+                    comment += "n "
+                    templates.append(("Number", f"N{n_count}"))
+                    args += f"N{n_count} n{n_count}, "
+                    init += varnameI(i, row, col) + f"(static_cast<T>(n{n_count})), "
+                    n_count += 1
+                    i += 1
+                else:  # if vector
+                    comment += f"vec{n} "
+                    args += f"const V{v_count}& v{v_count}, "
+                    templates.append((f"Vector{rows_or_cols}", f"V{v_count}"))
+                    for j in range(n):
+                        init += varnameI(i, rows_or_cols, 1) + "(static_cast<T>(v" + str(v_count) + "." + varnameI(j, rows_or_cols, 1) + ")), "
+                        i += 1
+                    v_count += 1
+            args = args.removesuffix(", ")
+            init = init.removesuffix(", ")
+            constructors.append(Member(class_, class_, c_temp=Class_T, m_temp=templates, prefixes=[constexpr], args=args, init=init, comment=comment))
+    # constructor for all matrices
+    else:
+        # from scalar
+        constructors.append(Member(class_, class_, c_temp=Class_T, m_temp=[ t.split(" ") for t in genstring(row, col, f"Number N@r_@c").split(", ")], prefixes=[constexpr],
+                                   args=genstring(row, col, "const N@r_@c @"), init=genstring(row, col, "@(static_cast<T>(@))"), comment="Create from scalars"))
+
+        # from row vec
+        constructors.append(Member(class_, class_, c_temp=Class_T, m_temp=[ t.split(" ") for t in genstring(row, 1, f"RowVector{col} V@r").split(", ")], prefixes=[constexpr],
+                                   args=genstring(row, 1, "const V@r& v@r"), init=genstring(row, col, "@(static_cast<T>(v@r.@C))"), comment="Create from row vectors"))
+
+        # from col vec
+        constructors.append(Member(class_, class_, c_temp=Class_T, m_temp=[ t. split(" ") for t in genstring(1, col, f"ColumnVector{row} V@c").split(", ")], prefixes=[constexpr],
+                                   args=genstring(1, col, "const V@c& v@c"), init=genstring(row, col, "@(static_cast<T>(v@c.@R))"), comment="Create from column vectors"))
+
+    return constructors
+
+
+def genValues(row, col):
+    s = genstring(row, col, "T @;\n", "")
+    return s
+
+def genAssignment(row, col):
+    # TODO opt idea: memcpy for component wise assignment when types have same size
+    members = []
+    members.append(Member(classname(row, col), "operator=", c_temp=Class_T, m_temp=[Number_N], prefixes=[constexpr], ret_type="void",
+                          args=f"const {classname(row, col, 'N')}& other", body=genstring(row, col, f"\t@ = static_cast<T>(other.@);\n", "").split("\n"), comment="Component-wise assignment"))
+
+    members.append(Member(classname(row, col), "operator=", c_temp=Class_T, m_temp=[Number_N], prefixes=[constexpr], ret_type="void",
+                          args="const N& other", body=genstring(row, col, f"\t@ = static_cast<T>(other);\n", "").split("\n"), comment="Assignment from scalar"))
+
+    return members
+
+
+
+ops = {
+    "+": "operator+",
+    "-": "operator-",
+    "%": "operator%",
+    "*": "compWiseMult",
+    "/": "compWiseDiv",
+}
+as_ops = {
+    "+=": "operator+=",
+    "-=": "operator-=",
+    "%=": "operator%=",
+    "*=": "compWiseAssMult",
+    "/=": "compWiseAssDiv",
+}
+def genArithmeticVectorial(row, col):
+    operators = []
+    for op, opname in ops.items():
+        body = "return " + classname(row, col, "T") + "(" + genstring(row, col, f"@ {op} static_cast<T>(other.@)") + ");"
+        operators.append(Member(classname(row, col), opname, c_temp=Class_T, m_temp=[(concept(row, col), concept(row, col)[0])], prefixes=[constexpr], ret_type=classname(row, col, "T"),
+                                args=f"const {concept(row, col)[0]}& other", const=True, body=[body], comment=f"Component-wise {op}"))
+
+    for op, opname in as_ops.items():
+        body = genstring(row, col, f"\t@ {op} static_cast<T>(other.@);", "\n")
+        operators.append(Member(classname(row, col), opname, c_temp=Class_T, m_temp=[(concept(row, col), concept(row, col)[0])], prefixes=[constexpr], ret_type="void",
+                                args=f"const {concept(row, col)[0]}& other", body=body.split("\n"), comment=f"Component-wise assignment {op}"))
+    return operators
+
+def genArithmeticScalar(row, col):
+    operators = []
+    for op, opname in ops.items():
+        body = "return " + classname(row, col, "T") + "(" + genstring(row, col, f"@ {op} static_cast<T>(other)") + ");"
+        operators.append(Member(classname(row, col), opname, c_temp=Class_T, m_temp=[Number_N], prefixes=[constexpr], ret_type=classname(row, col, "T"),
+                                args=f"const N& other", const=True, body=[body], comment=f"Component-wise {op} with scalar"))
+    for op, opname in as_ops.items():
+        body = genstring(row, col, f"\t@ {op} static_cast<T>(other);", "\n")
+        operators.append(Member(classname(row, col), opname, c_temp=Class_T, m_temp=[Number_N], prefixes=[constexpr], ret_type="void",
+                                args=f"const N& other", body=body.split("\n"), comment=f"Component-wise assignment {op} from scalar"))
+    return operators
+
+
+def genComparisonVectorial(row, col):
+    operators = []
+    for op in ["==", "<", ">"]:
+        body = "return " + genstring(row, col, f"@ {op} other.@", " and ") + ";"
+        operators.append(Member(classname(row, col), f"operator{op}", c_temp=Class_T, m_temp=[(concept(row, col), concept(row, col)[0])], prefixes=[constexpr], ret_type="bool",
+                                args=f"const {concept(row, col)[0]}& other", const=True, body=[body], comment=f"Component-wise comparison {op} (and)"))
+    for op, antiop in { "!=": "==", "<=": ">", ">=": "<" }.items():
+        body = "return " + genstring(row, col, f"@ {antiop} other.@", " and ") + ";"
+        operators.append(Member(classname(row, col), f"operator{op}", c_temp=Class_T, m_temp=[(concept(row, col), concept(row, col)[0])], prefixes=[constexpr], ret_type="bool",
+                                args=f"const {concept(row, col)[0]}& other", const=True, body=[body], comment=f"Component-wise comparison {op} (and)"))
+    return operators
+
+def genComparisonScalar(row, col):
+    operators = []
+    for op in ["==", "<", ">"]:
+        body = "return " + genstring(row, col, f"@ {op} other", " and ") + ";"
+        operators.append(Member(classname(row, col), f"operator{op}", c_temp=Class_T, m_temp=[Number_N], prefixes=[constexpr], ret_type="bool",
+                                args=f"const N& other", const=True, body=[body], comment=f"Component-wise comparison {op} (and)"))
+    for op, antiop in { "!=": "==", "<=": ">", ">=": "<" }.items():
+        body = "return " + genstring(row, col, f"@ {antiop} other", " and ") + ";"
+        operators.append(Member(classname(row, col), f"operator{op}", c_temp=Class_T, m_temp=[Number_N], prefixes=[constexpr], ret_type="bool",
+                                args=f"const N& other", const=True, body=[body], comment=f"Component-wise comparison {op} (and)"))
+    return operators
+
+
+
+def getDependecyClasses(row, col):
+    """
+    Get all class names that row,col class depends on for matrix multplication and the .row() and .column() methods
+    The dependencies will be forward declared in the header and included in the source
+    """
+    deps = []
+    # for .row(), .column()
+    if row > 1 and col > 1:
+        deps.append(classname(row, 1))
+        deps.append(classname(1, col))
+
+    # for matrix mult
+    for i in range(1, MAX_N + 1):
+        # results from matrix calculations
+        deps.append(classname(row, i))
+
+        # operands from matrix calculations
+        deps.append(classname(col, i))
+
+    deps = list(dict.fromkeys(deps))
+    # remove vec1
+    if classname(1, 1) in deps:
+        deps.remove(classname(1, 1))
+    if classname(row, col) in deps:
+        deps.remove(classname(row, col))
+    deps.sort()
+    return deps
+
+
+def genArithmeticMatrix(row, col):
+    """
+    Generate all matrix multiplications.
+    dimensions of result = mat(row, other.col) where col = other.row
+    """
+    operators = []
+    other_row = col
+    other_cols = [ i for i in range(1, MAX_N + 1) ]
+    for other_col in other_cols:
+        if (row == 1 and other_col == 1) or (other_row == 1 and other_col == 1):  # if ret_type or arg is a scalar
+            continue
+        body = classname(row, other_col, "T") + " new_;\n"
+        for r in range(row):
+            for o_c in range(other_col):
+                body += "new_." + varname(r, o_c, row, other_col) + " = "
+                for i in range(col):
+                    # print(f"genArithmeticMatrix: {row}x{col} * {other_row}x{other_col}", r, o_c, "->", c)
+                    body += varname(r, i, row, col) + " * other." + varname(i, o_c, other_row, other_col) + " + "
+                body = body.removesuffix(" + ") + ";\n"
+        # if scalar, put ret_type creation and assignment in same line
+        body = body.replace("new_;\nnew_." + varname(0, 0, 1, 1) + " =", "new_ =") + "return new_;"
+        arg_concept = concept(other_row, other_col)
+        operators.append(Member(classname(row, col), "operator*", c_temp=Class_T, m_temp=[(arg_concept, arg_concept[0])], prefixes=[constexpr], ret_type=classname(row, other_col, "T"), const=True,
+                                args=f"const {arg_concept[0]}& other", body=body.split("\n"), comment=f"Matrix multiplication with {classname(other_row, other_col)} -> {classname(row, other_col)}"))
+
+    return operators
+
+
+def genSubscription(row, col):
+    operators = []
+    # [i]
+    operators.append(Member(classname(row, col), "operator[]", c_temp=Class_T, prefixes=[constexpr], ret_type="T",
+                            args="std::size_t i", const=True, body=[f"return *(&{varname(0, 0, row, col)} + sizeof(T) * i);"], comment="Get the ith element. i starts at 0"))
+
+    if row > 1 and col > 1:
+        # at(row, col)
+        body = f"return *(&{varname(0, 0, row, col)} + (row * {row} + col * {col}) * sizeof(T));"
+        operators.append(Member(classname(row, col), "at", c_temp=Class_T, prefixes=[constexpr], ret_type="T",
+                                args="std::size_t row, std::size_t col", const=True, body=[body], comment="Get the element at row and col. row and col start at 0"))
+
+        # row()
+        body = f"return {classname(1, col, 'T')}(" + genstring(1, col, f"*(&{varname(0, 0, row, col)} + ({row} * @c + i) * sizeof(T))") + ");"
+        operators.append(Member(classname(row, col), "row", c_temp=Class_T, prefixes=[constexpr], ret_type=classname(1, col, 'T'),
+                                args="std::size_t i", const=True, body=[body], comment="Get the ith row as column vector. i starts at 0"))
+
+        # column()
+        body = f"return {classname(row, 1, 'T')}(" + genstring(row, 1, f"*(&{varname(0, 0, row, col)} + ({col} * @r + i) * sizeof(T))") + ");"
+        operators.append(Member(classname(row, col), "column", c_temp=Class_T, prefixes=[constexpr], ret_type=classname(row, 1, 'T'),
+                                args="std::size_t i", const=True, body=[body], comment="Get the ith column as row vector. i starts at 0"))
+
+    return operators
+
+
+def genIterator(row, col):
+    members = []
+    its = [
+        ("cbegin", "return Iterator(const_cast<T*>(&" + varname(0, 0, row, col) + "));", "Return an Iterator to the first element"),
+        ("cend", "return Iterator(const_cast<T*>(&" + varname(row-1, col-1, row, col) + " + sizeof(T)));", "Return an Iterator past the last element"),
+        ("begin", "return Iterator(const_cast<T*>(&" + varname(0, 0, row, col) + "));", "Return an Iterator to the first element"),
+        ("end", "return Iterator(const_cast<T*>(&" + varname(row-1, col-1, row, col) + " + sizeof(T)));", "Return an Iterator past the last element"),
+    ]
+    for name, body, comment in its:
+        members.append(Member(classname(row, col), name, c_temp=Class_T, prefixes=[constexpr], ret_type="Iterator<T>", const=True, body=[body], comment=comment))
+    return members
+
+
+def genFunctional(row, col):
+    members = []
+    # abs
+    members.append(Member(classname(row, col), "abs", c_temp=Class_T, prefixes=[constexpr, inline], ret_type=float_type,
+                          const=True, body=["return std::sqrt(" + genstring(row, col, f"static_cast<{float_type}>(@ * @)", " + ") + ");"], comment="Returns the absolute value of the vector (sqrt of scalar product with itself)"))
+
+    if (row == 2 and col == 1) or (col == 2 and row == 1):
+        # ratio
+        members.append(Member(classname(row, col), "ratio", c_temp=Class_T, prefixes=[constexpr, inline], ret_type=float_type,
+                              const=True, body=["return static_cast<" + float_type + f">({varnameI(0, row, col)}) / {varnameI(1, row, col)};"], comment=f"Returns x/y"))
+
+        # inverse ratio
+        members.append(Member(classname(row, col), "invereseRatio", c_temp=Class_T, prefixes=[constexpr, inline], ret_type=float_type,
+                              const=True, body=["return static_cast<" + float_type + f">({varnameI(1, row, col)}) / {varnameI(0, row, col)};"], comment=f"Returns y/x"))
+
+
+    # min
+    members.append(Member(classname(row, col), "min", c_temp=Class_T, prefixes=[constexpr, inline], ret_type="T", const=True,
+                          body=["return *std::min_element(cbegin(), cend());"], comment="Returns the min of the components"))
+
+    # max
+    members.append(Member(classname(row, col), "max", c_temp=Class_T, prefixes=[constexpr, inline], ret_type="T", const=True,
+                          body=["return *std::max_element(cbegin(), cend());"], comment="Returns the max of the components"))
+
+    # dot
+    body = f"return " + genstring(row, col, "@ * static_cast<T>(other.@)", " + ") + ";"
+    members.append(Member(classname(row, col), "dot", c_temp=Class_T, m_temp=[Number_N], prefixes=[constexpr, inline], ret_type="T", const=True,
+                          args=f"const {classname(row, col, 'N')}& other", body=[body], comment="Scalar product (x1 * other.x1 +  x2 * other.x2 ...)"))
+    return members
+
+
+def genUtility(row, col):
+    s = "\n"
+    # s = "std::string to_string() const { return \"(\" + " + genstring(row, col, "std::to_string(@)", " + \", \" + ") + " + \")\"; };\n"
+    return s
+
+
+def genUsing(row, col):
+    global typeShorts
+    s = ""
+    for t, c in typeShorts.items():
+        s += f"using {classname(row, col)}{c} = {classname(row, col)}<{t}>;\n"
+    return s
+
+
+
+#
+# TEMPLATE INSTANTIATION
+#
+def getTemplateInsts(method_name, instantiations, templates, types, depth=0):
+    """ method name must be like this:
+    constexpr ret_type Class<T>::name<U>(int, U) const;"""
+    if depth < len(templates):
+        if templates[depth][0] == "Number":
+            for n in types:
+                newmethod = method_name.replace(
+                    f"<{templates[depth][1]}>", f"<{n}>").replace(
+                    f"{templates[depth][1]} ", f"{n} ").replace(
+                    f"{templates[depth][1]})", f"{n})").replace(
+                    f"{templates[depth][1]},", f"{n},").replace(
+                    f"{templates[depth][1]}& ", f"{n}& ").replace(
+                    f"{templates[depth][1]}&)", f"{n}&)").replace(
+                    f"{templates[depth][1]}&,", f"{n}&,")
+                getTemplateInsts(newmethod, instantiations, templates, types, depth+1)
+        else:
+            for n in types:
+                newmethod = method_name.replace(
+                    f"<{templates[depth][1]}>", f"<{classnameFromConcept(templates[depth][0])}<{n}>>").replace(
+                    f"{templates[depth][1]} ", f"{classnameFromConcept(templates[depth][0])}<{n}> ").replace(
+                    f"{templates[depth][1]})", f"{classnameFromConcept(templates[depth][0])}<{n}> ").replace(
+                    f"{templates[depth][1]},", f"{classnameFromConcept(templates[depth][0])}<{n}> ").replace(
+                    f"{templates[depth][1]}& ", f"{classnameFromConcept(templates[depth][0])}<{n}>& ").replace(
+                    f"{templates[depth][1]}&)", f"{classnameFromConcept(templates[depth][0])}<{n}>&)").replace(
+                    f"{templates[depth][1]}&,", f"{classnameFromConcept(templates[depth][0])}<{n}>&,")
+                getTemplateInsts(newmethod, instantiations, templates, types, depth+1)
+    elif depth == len(templates) and len(templates)> 0:
+        instantiations.append("template " + method_name + ";")
+
+
+#
+# GENERATION
+#
+def generateFiles(row, col):
+    hd = 0  # header depth
+    sd = 0  # source and template depth
+
+    # header
+    h = "#pragma once\n\n"
+    # source
+    s = "#include \"" + classname(row, col) + ".hpp\"\n\n"
+    # template instantiations
+    t = f"// template instantiations for {classname(row, col)}\n\n"
+
+    dependencies = getDependecyClasses(row, col)
+    for dep in dependencies:
+        s += "#include \"" + dep + ".hpp\"\n"
+    s += "\n"
+    for i in headerIncludes:
+        h += "#include " + i + "\n"
+    h += "\n"
+    for i in sourceIncludes:
+        s += "#include " + i + "\n"
+    s += "\n"
+    if namespace:
+        h += "namespace " + namespace + " {\n\n"
+        s += "namespace " + namespace + " {\n\n"
+        t += "namespace " + namespace + " {\n\n"
+        hd += 1
+        sd += 1
+
+    # template instantiations
+    if include_template_instantiations:
+        for typ in templateInstantiationTypes:
+            t += transformString("template class " + classname(row, col, typ) + ";\n", 0)
+            t += "\n"
+
+    # forward declarations
+    h += transformString("// Forward declarations\n", hd)
+    for dep in dependencies:
+        h += transformString("template<Number T>\nclass " + dep + ";\n", hd)
+    h += "\n"
+
+    header, source, templates = generateMatrix(row, col, hd, sd)
+    h += header + "\n"
+    s += source + "\n"
+    t += templates + "\n"
+
+    if include_static_asserts:
+        h += transformString("static_assert(" + concept(row, col, classname(row, col, "int")) +", \"" + classname(row, col, "int") + " does not satisfy the concept " + concept(row, col) + "\");\n", hd)
+
+    if namespace:
+        hd -= 1
+        sd -= 1
+        h += transformString("} // namespace " + namespace + "\n", hd)
+        s += transformString("} // namespace " + namespace + "\n", hd)
+        t += transformString("} // namespace " + namespace + "\n", hd)
+
+    for i in range(1, 5):
+        h = h.replace("\n" + i * tab + "\n", "\n\n")
+        s = s.replace("\n" + i * tab + "\n", "\n\n")
+
+    return h, s, t
+
+
+def append(header:str, source:str, templates:str, members:list[Member], hdepth:int, sdepth:int):
+    for m in members:
+        split = True
+        if m.isConstructor() or (len(m.body) < 2 and len(m.m_temp) > 1):
+            split = False
+
+        if split:
+            header += m.defintionH(hdepth)
+            source += m.source(sdepth)
+            templates += m.templateInstantiations()
+        else:
+            header += m.header(hdepth)
+    return header, source, templates
+
+
+
+
+def generateMatrix(r, c, hd, sd):
+    h = transformString(
+"""/**
+ * @brief Class containing $ numbers
+ */
+ """.replace("$", str(r*c)), hd)
+    h += transformString("""template<Number T>
+class $ {
+    public:
+""".replace("$", classname(r, c)), hd)
+
+    s = transformString("""//
+// CLASS $
+//
+""".replace("$", classname(r, c)), sd)
+
+
+    t = ""
+
+    hd += 1  # header depth
+    # sd += 1  # source depth
+
+    if classname(r, c).startswith("vec"):
+        h += transformString("/// just to satisfy concept ColumnVector\nusing isColumnVector = T;\n", hd + 1)
+    elif classname(r, c).startswith("rvec"):
+        h += transformString("/// just to satisfy concept RowVector\nusing isRowVector = T;\n", hd + 1)
+
+    h += transformString("// Constructors\n", hd)
+    h, s, t = append(h, s, t, genConstructors(r, c), hd+1, sd)
+
+    h += transformString("// Values\n", hd)
+    h += transformString(genValues(r, c), hd+1)
+
+    h += transformString("// Assignment\n", hd)
+    h, s, t = append(h, s, t, genAssignment(r, c), hd+1, sd)
+
+    h += transformString("// Arithmetic\n", hd-1)
+    h += transformString("// Vectorial\n", hd)
+    h, s, t = append(h, s, t, genArithmeticVectorial(r, c), hd+1, sd)
+    h += transformString("// Scalar\n", hd)
+    h, s, t = append(h, s, t, genArithmeticScalar(r, c),hd+1, sd)
+    h += transformString("// Matrix Multiplication\n", hd)
+    h, s, t = append(h, s, t, genArithmeticMatrix(r, c), hd+1, sd)
+
+    h += transformString("// Comparison\n", hd-1)
+    h += transformString("// Vectorial\n", hd)
+    h, s, t = append(h, s, t, genComparisonVectorial(r, c),hd+1, sd)
+    h += transformString("// Scalar\n", hd)
+    h, s, t = append(h, s, t, genComparisonScalar(r, c), hd+1, sd)
+
+
+    h += transformString("// Functional\n", hd - 1)
+    h, s, t = append(h, s, t, genFunctional(r, c), hd+1, sd)
+
+    h += transformString("// Utility\n", hd-1)
+    h, s, t = append(h, s, t, genSubscription(r, c), hd+1, sd)
+    h, s, t = append(h, s, t, genIterator(r, c), hd + 1, sd)
+
+    h += transformString("}; // " + classname(r, c) + "\n\n", hd - 1)
+    h += transformString(genUsing(r, c), hd - 1)
+    h += "\n"
+    s += "\n"
+    t += "\n"
+
+    return h, s, t
+
+
+#
+# CONCEPTS
+#
+def generateConceptsFile(row, col):
+    # Number
+    s = "#pragma once\n\n"
+    s += "#include <concepts>\n\n"
+    s += "// Number\n"
+    s += "template<typename T>\n"
+    s += "concept Number = std::integral<T> or std::floating_point<T>;\n\n"
+
+    s += "// VectorX\n"
+    for i in range(2, max(row, col)):
+        s += "template<typename T>\n"
+        # s += "concept Vector" + str(i) + " = requires(T t) { " + genstring(i, 1, "{ t.@ } -> Number; ", "") + "};\n\n"
+        s += "concept Vector" + str(i) + " = requires(T t) {\n" + genstring(i, 1, tab + "requires Number<decltype(t.@)>;\n", "") + "} and requires(T t) { sizeof(t." + varname(0, 0, i, 1) + ") == (sizeof(T) * " + str(i) + "); };\n\n"
+    s += "// RowVectorX\n"
+    for i in range(2, max(row, col)):
+        s += "template<typename T>\n"
+        s += "concept RowVector" + str(i) + " = Vector" + str(i) + "<T> and Number<typename T::isRowVector>;\n\n"
+    s += "// ColumnVectorX\n"
+    for i in range(2, max(row, col)):
+        s += "template<typename T>\n"
+        s += "concept ColumnVector" + str(i) + " = Vector" + str(i) + "<T> and Number<typename T::isColumnVector>;\n\n"
+    s += "// Matrices\n"
+    for r in range(2, row):
+        for c in range(2, col):
+            s += "template<typename T>\n"
+            # s += "concept " + concept(r, c) + " = requires(T t) { t -> template " + classname(r, c) + "; };\n"
+            s += "concept " + concept(r, c) + " = requires(T t) {\n" + genstring(r, c, tab + "requires Number<decltype(t.@)>;\n", "") + "};\n" # and requires(T t) { sizeof(t." + varname(0, 0, r, c) + ") == (sizeof(T) * " + str(r*c) + "); };\n\n"
+    return s
+
+
+##
+## ITERATORS
+##
+#def generateIteratorFile():
+#    i = "#pragma once\n"
+#    if namespace:
+#        i += f"namespace {namespace} " + "{\n"
+
+#    i += """
+
+#template<typename T>
+#struct Iterator {
+#    public:
+#        using value_type = T;
+#        Iterator() : ptr(nullptr) {};
+#        Iterator(T* ptr) : ptr(ptr) {};
+#        T& operator*() const { return *ptr; };
+#        Iterator& operator=(const Iterator& other) {
+#            ptr = other.ptr;
+#            return *this;
+#        };
+#        Iterator& operator++() { ptr += sizeof(T); return *this; };
+#        Iterator operator++(int) { auto copy = *this; ptr += sizeof(T); return copy; };
+#        friend int operator-(Iterator lhs, Iterator rhs) {
+#            return lhs.ptr - rhs.ptr;
+#        };
+#        bool operator==(const Iterator& other) const { return ptr == other.ptr; };
+#        // bool operator!=(const Iterator& other) const { return ptr != other.ptr; };
+#    private:
+#        T* ptr;
+#}; // Iterator
+#"""
+
+#    if include_static_asserts:
+#        i += 'static_assert(std::forward_iterator<Iterator<int>>, "Iterator not a forward range.");'
+#    if namespace:
+#        i += "} // namespace " + namespace + "\n"
+#    return i
+
+
+
+#
+# MAIN
+#
+def write_file(s, filename):
+    if path.exists(filename):
+        answer = "y"
+        # answer = input("File " + filename + "already exists. Overwrite? (y/n): ")
+        if answer not in "yY":
+            return
+
+    with open(filename, "w") as file:
+        file.write(s)
+
+
+if __name__ == "__main__":
+    if not path.isdir(directory):
+        mkdir(directory)
+    todo = [ [i, j] for i in range(1, MAX_N + 1) for j in range(1, MAX_N + 1)]
+    todo.remove([1, 1])  # remove [1, 1]
+    for r, c in todo:
+        filename = directory + "/" + classname(r, c)
+        header, source, templates = generateFiles(r, c)
+        if include_template_instantiations:
+            write_file(templates, filename + ".tpp")
+            source += "\n#include \"" + classname(r, c) + ".tpp\""
+        write_file(header, filename + ".hpp")
+        write_file(source, filename + ".cpp")
+
+    write_file(generateConceptsFile(MAX_N + 1, MAX_N + 1), directory + "/" + "concepts.hpp")
+    # write_file(generateIteratorFile(), directory + "/" + "iterator.hpp")