Add sample_package with linear algebra tools
- add sample_package: + __init__.py => high-level description and imports + matrix.py => define a Matrix class + vector.py => define a Vector class + utils.py => package-wide utilities - streamline the code snippets in the chapter 11 notebooks to align with the sample_package
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7 changed files with 770 additions and 40 deletions
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@ -272,7 +272,7 @@
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"class Vector:\n",
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"class Vector:\n",
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" \"\"\"A standard one-dimensional vector from linear algebra.\"\"\"\n",
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" \"\"\"A one-dimensional vector from linear algebra.\"\"\"\n",
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"\n",
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"\n",
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" dummy_variable = \"I am a vector\"\n",
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" dummy_variable = \"I am a vector\"\n",
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"\n",
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"\n",
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@ -403,7 +403,7 @@
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"data": {
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"data": {
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"text/plain": [
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"text/plain": [
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"\u001b[0;31mInit signature:\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mInit signature:\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mDocstring:\u001b[0m A standard one-dimensional vector from linear algebra.\n",
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"\u001b[0;31mDocstring:\u001b[0m A one-dimensional vector from linear algebra.\n",
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"\u001b[0;31mType:\u001b[0m type\n",
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"\u001b[0;31mType:\u001b[0m type\n",
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"\u001b[0;31mSubclasses:\u001b[0m \n"
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"\u001b[0;31mSubclasses:\u001b[0m \n"
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]
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]
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@ -432,7 +432,7 @@
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"Help on class Vector in module __main__:\n",
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"Help on class Vector in module __main__:\n",
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"\n",
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"\n",
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"class Vector(builtins.object)\n",
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"class Vector(builtins.object)\n",
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" | A standard one-dimensional vector from linear algebra.\n",
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" | A one-dimensional vector from linear algebra.\n",
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" | \n",
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" | \n",
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" | Methods defined here:\n",
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" | Methods defined here:\n",
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" | \n",
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" | \n",
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@ -484,7 +484,7 @@
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"data": {
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"data": {
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"text/plain": [
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"text/plain": [
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"mappingproxy({'__module__': '__main__',\n",
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"mappingproxy({'__module__': '__main__',\n",
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" '__doc__': 'A standard one-dimensional vector from linear algebra.',\n",
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" '__doc__': 'A one-dimensional vector from linear algebra.',\n",
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" 'dummy_variable': 'I am a vector',\n",
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" 'dummy_variable': 'I am a vector',\n",
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" 'dummy_method': <function __main__.Vector.dummy_method(self)>,\n",
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" 'dummy_method': <function __main__.Vector.dummy_method(self)>,\n",
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" '__dict__': <attribute '__dict__' of 'Vector' objects>,\n",
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" '__dict__': <attribute '__dict__' of 'Vector' objects>,\n",
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@ -687,7 +687,7 @@
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"class Vector:\n",
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"class Vector:\n",
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" \"\"\"A standard one-dimensional vector from linear algebra.\n",
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" \"\"\"A one-dimensional vector from linear algebra.\n",
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"\n",
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"\n",
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" All entries are converted to floats.\n",
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" All entries are converted to floats.\n",
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" \"\"\"\n",
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" \"\"\"\n",
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@ -1815,17 +1815,16 @@
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},
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},
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"def norm(vector_or_matrix):\n",
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"def norm(vec_or_mat):\n",
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" \"\"\"Calculate the Frobenius or Euclidean norm of a matrix or vector.\n",
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" \"\"\"Calculate the Frobenius or Euclidean norm of a matrix or vector.\n",
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"\n",
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"\n",
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" Args:\n",
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" Args:\n",
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" vector_or_matrix (Vector/Matrix): the entries whose squares\n",
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" vec_or_mat (Vector / Matrix): object whose entries are squared and summed up\n",
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" are summed up\n",
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"\n",
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"\n",
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" Returns:\n",
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" Returns:\n",
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" norm (float)\n",
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" norm (float)\n",
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" \"\"\"\n",
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" \"\"\"\n",
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" return math.sqrt(sum(x ** 2 for x in vector_or_matrix))"
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" return math.sqrt(sum(x ** 2 for x in vec_or_mat))"
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]
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]
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},
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},
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{
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{
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@ -694,7 +694,7 @@
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" def __add__(self, other):\n",
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" def __add__(self, other):\n",
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" if isinstance(other, self.__class__): # vector addition\n",
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" if isinstance(other, self.__class__): # vector addition\n",
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" if len(self) != len(other):\n",
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" if len(self) != len(other):\n",
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" raise ValueError(\"vectors need to be of the same length\")\n",
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" raise ValueError(\"vectors must be of the same length\")\n",
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" return Vector(x + y for (x, y) in zip(self, other))\n",
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" return Vector(x + y for (x, y) in zip(self, other))\n",
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" elif isinstance(other, numbers.Number): # broadcasting addition\n",
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" elif isinstance(other, numbers.Number): # broadcasting addition\n",
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" return Vector(x + other for x in self)\n",
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" return Vector(x + other for x in self)\n",
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@ -706,7 +706,7 @@
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" def __sub__(self, other):\n",
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" def __sub__(self, other):\n",
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" if isinstance(other, self.__class__): # vector subtraction\n",
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" if isinstance(other, self.__class__): # vector subtraction\n",
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" if len(self) != len(other):\n",
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" if len(self) != len(other):\n",
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" raise ValueError(\"vectors need to be of the same length\")\n",
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" raise ValueError(\"vectors must be of the same length\")\n",
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" return Vector(x - y for (x, y) in zip(self, other))\n",
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" return Vector(x - y for (x, y) in zip(self, other))\n",
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" elif isinstance(other, numbers.Number): # broadcasting subtraction\n",
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" elif isinstance(other, numbers.Number): # broadcasting subtraction\n",
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" return Vector(x - other for x in self)\n",
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" return Vector(x - other for x in self)\n",
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@ -721,7 +721,7 @@
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" def __mul__(self, other):\n",
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" def __mul__(self, other):\n",
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" if isinstance(other, self.__class__): # dot product\n",
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" if isinstance(other, self.__class__): # dot product\n",
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" if len(self) != len(other):\n",
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" if len(self) != len(other):\n",
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" raise ValueError(\"vectors need to be of the same length\")\n",
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" raise ValueError(\"vectors must be of the same length\")\n",
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" return sum(x * y for (x, y) in zip(self, other))\n",
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" return sum(x * y for (x, y) in zip(self, other))\n",
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" elif isinstance(other, numbers.Number): # scalar multiplication\n",
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" elif isinstance(other, numbers.Number): # scalar multiplication\n",
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" return Vector(x * other for x in self)\n",
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" return Vector(x * other for x in self)\n",
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@ -872,14 +872,14 @@
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"outputs": [
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"outputs": [
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{
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{
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"ename": "ValueError",
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"ename": "ValueError",
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"evalue": "vectors need to be of the same length",
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"evalue": "vectors must be of the same length",
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"output_type": "error",
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"output_type": "error",
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"traceback": [
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-27-21fab2d5f12e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-27-21fab2d5f12e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-21-12852bd26164>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 45\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# dot product\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 46\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 47\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors need to be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 48\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 49\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# scalar multiplication\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m<ipython-input-21-e7b5dd8e219a>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 45\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# dot product\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 46\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 47\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors must be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 48\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 49\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# scalar multiplication\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mValueError\u001b[0m: vectors need to be of the same length"
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"\u001b[0;31mValueError\u001b[0m: vectors must be of the same length"
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]
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}
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],
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"outputs": [
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"outputs": [
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{
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{
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"ename": "ValueError",
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"ename": "ValueError",
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"evalue": "vectors need to be of the same length",
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"evalue": "vectors must be of the same length",
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"output_type": "error",
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"output_type": "error",
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"traceback": [
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-31-490ee3f2b9e8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-31-490ee3f2b9e8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-21-12852bd26164>\u001b[0m in \u001b[0;36m__add__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# vector addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors need to be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# broadcasting addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
"\u001b[0;32m<ipython-input-21-e7b5dd8e219a>\u001b[0m in \u001b[0;36m__add__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# vector addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors must be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# broadcasting addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||||
"\u001b[0;31mValueError\u001b[0m: vectors need to be of the same length"
|
"\u001b[0;31mValueError\u001b[0m: vectors must be of the same length"
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
|
|
@ -1171,7 +1171,7 @@
|
||||||
" def __add__(self, other):\n",
|
" def __add__(self, other):\n",
|
||||||
" if isinstance(other, self.__class__): # matrix addition\n",
|
" if isinstance(other, self.__class__): # matrix addition\n",
|
||||||
" if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):\n",
|
" if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):\n",
|
||||||
" raise ValueError(\"matrices need to be of the same dimensions\")\n",
|
" raise ValueError(\"matrices must have the same dimensions\")\n",
|
||||||
" return Matrix((s_col + o_col for (s_col, o_col) in zip(s_row, o_row))\n",
|
" return Matrix((s_col + o_col for (s_col, o_col) in zip(s_row, o_row))\n",
|
||||||
" for (s_row, o_row) in zip(self._entries, other._entries))\n",
|
" for (s_row, o_row) in zip(self._entries, other._entries))\n",
|
||||||
" elif isinstance(other, numbers.Number): # broadcasting addition\n",
|
" elif isinstance(other, numbers.Number): # broadcasting addition\n",
|
||||||
|
|
@ -1186,7 +1186,7 @@
|
||||||
" def __sub__(self, other):\n",
|
" def __sub__(self, other):\n",
|
||||||
" if isinstance(other, self.__class__): # matrix subtraction\n",
|
" if isinstance(other, self.__class__): # matrix subtraction\n",
|
||||||
" if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):\n",
|
" if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):\n",
|
||||||
" raise ValueError(\"matrices need to be of the same dimensions\")\n",
|
" raise ValueError(\"matrices must have the same dimensions\")\n",
|
||||||
" return Matrix((s_col - o_col for (s_col, o_col) in zip(s_row, o_row))\n",
|
" return Matrix((s_col - o_col for (s_col, o_col) in zip(s_row, o_row))\n",
|
||||||
" for (s_row, o_row) in zip(self._entries, other._entries))\n",
|
" for (s_row, o_row) in zip(self._entries, other._entries))\n",
|
||||||
" elif isinstance(other, numbers.Number): # broadcasting subtraction\n",
|
" elif isinstance(other, numbers.Number): # broadcasting subtraction\n",
|
||||||
|
|
@ -1203,7 +1203,7 @@
|
||||||
" \n",
|
" \n",
|
||||||
" def _matrix_multiply(self, other):\n",
|
" def _matrix_multiply(self, other):\n",
|
||||||
" if self.n_cols != other.n_rows:\n",
|
" if self.n_cols != other.n_rows:\n",
|
||||||
" raise ValueError(\"matrices need to have compatible dimensions\")\n",
|
" raise ValueError(\"matrices must have compatible dimensions\")\n",
|
||||||
" return Matrix((rv * cv for cv in other.cols()) for rv in self.rows())\n",
|
" return Matrix((rv * cv for cv in other.cols()) for rv in self.rows())\n",
|
||||||
"\n",
|
"\n",
|
||||||
" def __mul__(self, other):\n",
|
" def __mul__(self, other):\n",
|
||||||
|
|
@ -1387,15 +1387,15 @@
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"ename": "ValueError",
|
"ename": "ValueError",
|
||||||
"evalue": "matrices need to have compatible dimensions",
|
"evalue": "matrices must have compatible dimensions",
|
||||||
"output_type": "error",
|
"output_type": "error",
|
||||||
"traceback": [
|
"traceback": [
|
||||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||||
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
|
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
|
||||||
"\u001b[0;32m<ipython-input-41-b57a49d097c9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mm\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
"\u001b[0;32m<ipython-input-41-b57a49d097c9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mm\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
||||||
"\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 72\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 73\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 74\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 75\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 76\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
"\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 72\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 73\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 74\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 75\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 76\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||||
"\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 63\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices need to have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 66\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
"\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 63\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices must have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 66\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||||
"\u001b[0;31mValueError\u001b[0m: matrices need to have compatible dimensions"
|
"\u001b[0;31mValueError\u001b[0m: matrices must have compatible dimensions"
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
|
|
@ -1497,15 +1497,15 @@
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"ename": "ValueError",
|
"ename": "ValueError",
|
||||||
"evalue": "matrices need to have compatible dimensions",
|
"evalue": "matrices must have compatible dimensions",
|
||||||
"output_type": "error",
|
"output_type": "error",
|
||||||
"traceback": [
|
"traceback": [
|
||||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||||
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
|
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
|
||||||
"\u001b[0;32m<ipython-input-45-9faf2ee0ae54>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
"\u001b[0;32m<ipython-input-45-9faf2ee0ae54>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
||||||
"\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m__rmul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 79\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 80\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcolumn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 82\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
"\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m__rmul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 79\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 80\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcolumn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 82\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||||
"\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 63\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices need to have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 66\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
"\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 63\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices must have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 66\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||||
"\u001b[0;31mValueError\u001b[0m: matrices need to have compatible dimensions"
|
"\u001b[0;31mValueError\u001b[0m: matrices must have compatible dimensions"
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
|
|
@ -1736,7 +1736,7 @@
|
||||||
" def __eq__(self, other):\n",
|
" def __eq__(self, other):\n",
|
||||||
" if isinstance(other, self.__class__):\n",
|
" if isinstance(other, self.__class__):\n",
|
||||||
" if len(self) != len(other):\n",
|
" if len(self) != len(other):\n",
|
||||||
" raise ValueError(\"vectors need to be of the same length\")\n",
|
" raise ValueError(\"vectors must be of the same length\")\n",
|
||||||
" for x, y in zip(self, other):\n",
|
" for x, y in zip(self, other):\n",
|
||||||
" if abs(x - y) > self.zero_threshold:\n",
|
" if abs(x - y) > self.zero_threshold:\n",
|
||||||
" return False # exit early if two corresponding entries differ\n",
|
" return False # exit early if two corresponding entries differ\n",
|
||||||
|
|
@ -1972,12 +1972,9 @@
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [],
|
"outputs": [],
|
||||||
"source": [
|
"source": [
|
||||||
"def norm(vector_or_matrix):\n",
|
"def norm(vec_or_mat):\n",
|
||||||
" \"\"\"Calculate the Frobenius or Euclidean norm of a matrix or vector.\n",
|
" \"\"\"Calculate the Frobenius or Euclidean norm of a matrix or vector.\"\"\"\n",
|
||||||
" \n",
|
" return math.sqrt(sum(x ** 2 for x in vec_or_mat))"
|
||||||
" ...\n",
|
|
||||||
" \"\"\"\n",
|
|
||||||
" return math.sqrt(sum(x ** 2 for x in vector_or_matrix))"
|
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
|
|
@ -2020,7 +2017,7 @@
|
||||||
"\n",
|
"\n",
|
||||||
" def __float__(self):\n",
|
" def __float__(self):\n",
|
||||||
" if len(self) != 1:\n",
|
" if len(self) != 1:\n",
|
||||||
" raise RuntimeError(\"vector must have one entry to become a scalar\")\n",
|
" raise RuntimeError(\"vector must have exactly one entry to become a scalar\")\n",
|
||||||
" return self._entries[0]"
|
" return self._entries[0]"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
|
|
@ -2303,14 +2300,14 @@
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"ename": "RuntimeError",
|
"ename": "RuntimeError",
|
||||||
"evalue": "vector must have one entry to become a scalar",
|
"evalue": "vector must have exactly one entry to become a scalar",
|
||||||
"output_type": "error",
|
"output_type": "error",
|
||||||
"traceback": [
|
"traceback": [
|
||||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||||
"\u001b[0;31mRuntimeError\u001b[0m Traceback (most recent call last)",
|
"\u001b[0;31mRuntimeError\u001b[0m Traceback (most recent call last)",
|
||||||
"\u001b[0;32m<ipython-input-75-8369cec552f3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
"\u001b[0;32m<ipython-input-75-8369cec552f3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
||||||
"\u001b[0;32m<ipython-input-63-01438fec4aa0>\u001b[0m in \u001b[0;36m__float__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__float__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vector must have one entry to become a scalar\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 32\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_entries\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
"\u001b[0;32m<ipython-input-63-67b90fc89e7c>\u001b[0m in \u001b[0;36m__float__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__float__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vector must have exactly one entry to become a scalar\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 32\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_entries\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||||
"\u001b[0;31mRuntimeError\u001b[0m: vector must have one entry to become a scalar"
|
"\u001b[0;31mRuntimeError\u001b[0m: vector must have exactly one entry to become a scalar"
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
|
|
|
||||||
30
11_classes/sample_package/__init__.py
Normal file
30
11_classes/sample_package/__init__.py
Normal file
|
|
@ -0,0 +1,30 @@
|
||||||
|
"""This package provides linear algebra functionalities.
|
||||||
|
|
||||||
|
The package is split into three modules:
|
||||||
|
- matrix: defines the Matrix class
|
||||||
|
- vector: defines the Vector class
|
||||||
|
- utils: defines the norm() function that is shared by Matrix and Vector
|
||||||
|
and package-wide constants
|
||||||
|
|
||||||
|
The classes implement arithmetic operations involving vectors and matrices.
|
||||||
|
|
||||||
|
See the docstrings in the modules and classes for further info.
|
||||||
|
"""
|
||||||
|
|
||||||
|
# Import the classes here so that they are available
|
||||||
|
# from the package's top level. That means that a user
|
||||||
|
# who imports this package with `import sample_package`
|
||||||
|
# may then refer to, for example, the Matrix class with
|
||||||
|
# simply `sample_package.Matrix` instead of the longer
|
||||||
|
# `sample_package.matrix.Matrix`.
|
||||||
|
from sample_package.matrix import Matrix
|
||||||
|
from sample_package.vector import Vector
|
||||||
|
|
||||||
|
|
||||||
|
# Define meta information for the package.
|
||||||
|
# There are other (and more modern) ways of
|
||||||
|
# doing this, but specifying the following
|
||||||
|
# dunder variables here is the traditional way.
|
||||||
|
__name__ = "linear_algebra_tools"
|
||||||
|
__version__ = "0.1.0" # see https://semver.org/ for how the format works
|
||||||
|
__author__ = "Alexander Hess"
|
||||||
416
11_classes/sample_package/matrix.py
Normal file
416
11_classes/sample_package/matrix.py
Normal file
|
|
@ -0,0 +1,416 @@
|
||||||
|
"""This module defines a Matrix class."""
|
||||||
|
|
||||||
|
import numbers
|
||||||
|
|
||||||
|
# Note the import at the bottom of this file, and
|
||||||
|
# see the comments about imports in the matrix module.
|
||||||
|
from sample_package import utils
|
||||||
|
|
||||||
|
|
||||||
|
class Matrix:
|
||||||
|
"""An m-by-n-dimensional matrix from linear algebra.
|
||||||
|
|
||||||
|
All entries are converted to floats, or whatever is set in the typing attribute.
|
||||||
|
|
||||||
|
Attributes:
|
||||||
|
storage (callable): data type used to store the entries internally;
|
||||||
|
defaults to tuple
|
||||||
|
typing (callable): type casting applied to all entries upon creation;
|
||||||
|
defaults to float
|
||||||
|
zero_threshold (float): max. tolerance when comparing an entry to zero;
|
||||||
|
defaults to 1e-12
|
||||||
|
"""
|
||||||
|
|
||||||
|
storage = utils.DEFAULT_ENTRIES_STORAGE
|
||||||
|
typing = utils.DEFAULT_ENTRY_TYPE
|
||||||
|
zero_threshold = utils.ZERO_THRESHOLD
|
||||||
|
|
||||||
|
def __init__(self, data):
|
||||||
|
"""Create a new matrix.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
data (sequence of sequences): the matrix's entries;
|
||||||
|
viewed as a sequence of the matrix's rows (i.e., row-major order);
|
||||||
|
use the .from_columns() class method if the data come as a sequence
|
||||||
|
of the matrix's columns (i.e., column-major order)
|
||||||
|
|
||||||
|
Raises:
|
||||||
|
ValueError:
|
||||||
|
- if no entries are provided
|
||||||
|
- if the number of columns is inconsistent across the rows
|
||||||
|
"""
|
||||||
|
self._entries = self.storage(
|
||||||
|
self.storage(self.typing(x) for x in r) for r in data
|
||||||
|
)
|
||||||
|
for row in self._entries[1:]:
|
||||||
|
if len(row) != self.n_cols:
|
||||||
|
raise ValueError("rows must have the same number of entries")
|
||||||
|
if len(self) == 0:
|
||||||
|
raise ValueError("a matrix must have at least one entry")
|
||||||
|
|
||||||
|
@classmethod
|
||||||
|
def from_columns(cls, data):
|
||||||
|
"""Create a new matrix.
|
||||||
|
|
||||||
|
This is an alternative constructor for data provided in column-major order.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
data (sequence of sequences): the matrix's entries;
|
||||||
|
viewed as a sequence of the matrix's columns (i.e., column-major order);
|
||||||
|
use the normal constructor method if the data come as a sequence
|
||||||
|
of the matrix's rows (i.e., row-major order)
|
||||||
|
|
||||||
|
Raises:
|
||||||
|
ValueError:
|
||||||
|
- if no entries are provided
|
||||||
|
- if the number of rows is inconsistent across the columns
|
||||||
|
"""
|
||||||
|
return cls(data).transpose()
|
||||||
|
|
||||||
|
@classmethod
|
||||||
|
def from_rows(cls, data):
|
||||||
|
"""See docstring for .__init__()."""
|
||||||
|
# Some users may want to use this .from_rows() constructor
|
||||||
|
# to explicitly communicate that the data are in row-major order.
|
||||||
|
# Otherwise, this method is redundant.
|
||||||
|
return cls(data)
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
"""Text representation of a Matrix."""
|
||||||
|
name = self.__class__.__name__
|
||||||
|
args = ", ".join(
|
||||||
|
"(" + ", ".join(f"{c:.3f}" for c in r) + ",)" for r in self._entries
|
||||||
|
)
|
||||||
|
return f"{name}(({args}))"
|
||||||
|
|
||||||
|
def __str__(self):
|
||||||
|
"""Human-readable text representation of a Matrix."""
|
||||||
|
name = self.__class__.__name__
|
||||||
|
first, last, m, n = self[0], self[-1], self.n_rows, self.n_cols
|
||||||
|
return f"{name}(({first:.1f}, ...), ..., (..., {last:.1f}))[{m:d}x{n:d}]"
|
||||||
|
|
||||||
|
@property
|
||||||
|
def n_rows(self):
|
||||||
|
"""Number of rows in a Matrix."""
|
||||||
|
return len(self._entries)
|
||||||
|
|
||||||
|
@property
|
||||||
|
def n_cols(self):
|
||||||
|
"""Number of columns in a Matrix."""
|
||||||
|
return len(self._entries[0])
|
||||||
|
|
||||||
|
def __len__(self):
|
||||||
|
"""Number of entries in a Matrix."""
|
||||||
|
return self.n_rows * self.n_cols
|
||||||
|
|
||||||
|
def __getitem__(self, index):
|
||||||
|
"""Obtain an individual entry of a Matrix.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
index (int / tuple of int's): if index is an integer,
|
||||||
|
the Matrix is viewed as a sequence in row-major order;
|
||||||
|
if index is a tuple of integers, the first one refers to
|
||||||
|
the row and the second one to the column of the entry
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
entry (Matrix.typing)
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> m = Matrix([(1, 2), (3, 4)])
|
||||||
|
>>> m[0]
|
||||||
|
1.0
|
||||||
|
>>> m[-1]
|
||||||
|
4.0
|
||||||
|
>>> m[0, 1]
|
||||||
|
3.0
|
||||||
|
"""
|
||||||
|
# Sequence-like indexing (one-dimensional)
|
||||||
|
if isinstance(index, int):
|
||||||
|
if index < 0:
|
||||||
|
index += len(self)
|
||||||
|
if not (0 <= index < len(self)):
|
||||||
|
raise IndexError("integer index out of range")
|
||||||
|
row, col = divmod(index, self.n_cols)
|
||||||
|
return self._entries[row][col]
|
||||||
|
# Mathematical-like indexing (two-dimensional)
|
||||||
|
elif (
|
||||||
|
isinstance(index, tuple)
|
||||||
|
and len(index) == 2
|
||||||
|
and isinstance(index[0], int)
|
||||||
|
and isinstance(index[1], int)
|
||||||
|
):
|
||||||
|
return self._entries[index[0]][index[1]]
|
||||||
|
raise TypeError("index must be either an int or a tuple of two int's")
|
||||||
|
|
||||||
|
def rows(self):
|
||||||
|
"""Loop over a Matrix's rows.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
rows (generator): produces a Matrix's rows as Vectors
|
||||||
|
"""
|
||||||
|
return (Vector(r) for r in self._entries)
|
||||||
|
|
||||||
|
def cols(self):
|
||||||
|
"""Loop over a Matrix's columns.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
columns (generator): produces a Matrix's columns as Vectors
|
||||||
|
"""
|
||||||
|
return (
|
||||||
|
Vector(self._entries[r][c] for r in range(self.n_rows))
|
||||||
|
for c in range(self.n_cols)
|
||||||
|
)
|
||||||
|
|
||||||
|
def entries(self, *, reverse=False, row_major=True):
|
||||||
|
"""Loop over a Matrix's entries.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
reverse (bool): flag to loop backwards; defaults to False
|
||||||
|
row_major (bool): flag to loop in row-major order; defaults to True
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
entries (generator): produces a Matrix's entries
|
||||||
|
"""
|
||||||
|
if reverse:
|
||||||
|
rows = range(self.n_rows - 1, -1, -1)
|
||||||
|
cols = range(self.n_cols - 1, -1, -1)
|
||||||
|
else:
|
||||||
|
rows, cols = range(self.n_rows), range(self.n_cols)
|
||||||
|
if row_major:
|
||||||
|
return (self._entries[r][c] for r in rows for c in cols)
|
||||||
|
return (self._entries[r][c] for c in cols for r in rows)
|
||||||
|
|
||||||
|
def __iter__(self):
|
||||||
|
"""Loop over a Matrix's entries.
|
||||||
|
|
||||||
|
See .entries() for more customization options.
|
||||||
|
"""
|
||||||
|
return self.entries()
|
||||||
|
|
||||||
|
def __reversed__(self):
|
||||||
|
"""Loop over a Matrix's entries in reverse order.
|
||||||
|
|
||||||
|
See .entries() for more customization options.
|
||||||
|
"""
|
||||||
|
return self.entries(reverse=True)
|
||||||
|
|
||||||
|
def __add__(self, other):
|
||||||
|
"""Handle `self + other` and `other + self`.
|
||||||
|
|
||||||
|
This may be either matrix addition or broadcasting addition.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) + Matrix([(2, 3), (4, 5)])
|
||||||
|
Matrix(((3.0, 5.0), (7.0, 9.0)))
|
||||||
|
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) + 5
|
||||||
|
Matrix(((6.0, 7.0), (8.0, 9.0)))
|
||||||
|
|
||||||
|
>>> 10 + Matrix([(1, 2), (3, 4)])
|
||||||
|
Matrix(((11.0, 12.0), (13.0, 14.0)))
|
||||||
|
"""
|
||||||
|
# Matrix addition
|
||||||
|
if isinstance(other, self.__class__):
|
||||||
|
if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):
|
||||||
|
raise ValueError("matrices must have the same dimensions")
|
||||||
|
return self.__class__(
|
||||||
|
(s_col + o_col for (s_col, o_col) in zip(s_row, o_row))
|
||||||
|
for (s_row, o_row) in zip(self._entries, other._entries)
|
||||||
|
)
|
||||||
|
# Broadcasting addition
|
||||||
|
elif isinstance(other, numbers.Number):
|
||||||
|
return self.__class__((c + other for c in r) for r in self._entries)
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __radd__(self, other):
|
||||||
|
"""See docstring for .__add__()."""
|
||||||
|
if isinstance(other, Vector):
|
||||||
|
raise TypeError("vectors and matrices cannot be added")
|
||||||
|
# As both matrix and broadcasting addition are commutative,
|
||||||
|
# we dispatch to .__add__().
|
||||||
|
return self + other
|
||||||
|
|
||||||
|
def __sub__(self, other):
|
||||||
|
"""Handle `self - other` and `other - self`.
|
||||||
|
|
||||||
|
This may be either matrix subtraction or broadcasting subtraction.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Matrix([(2, 3), (4, 5)]) - Matrix([(1, 2), (3, 4)])
|
||||||
|
Matrix(((1.0, 1.0), (1.0, 1.0)))
|
||||||
|
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) - 1
|
||||||
|
Matrix(((0.0, 1.0), (2.0, 3.0)))
|
||||||
|
|
||||||
|
>>> 10 - Matrix([(1, 2), (3, 4)])
|
||||||
|
Matrix(((9.0, 8.0), (7.0, 6.0)))
|
||||||
|
"""
|
||||||
|
# As subtraction is the inverse of addition,
|
||||||
|
# we first dispatch to .__neg__() to invert the signs of
|
||||||
|
# all entries in other and then dispatch to .__add__().
|
||||||
|
return self + (-other)
|
||||||
|
|
||||||
|
def __rsub__(self, other):
|
||||||
|
"""See docstring for .__sub__()."""
|
||||||
|
if isinstance(other, Vector):
|
||||||
|
raise TypeError("vectors and matrices cannot be subtracted")
|
||||||
|
# Same comments as in .__sub__() apply
|
||||||
|
# with the roles of self and other swapped.
|
||||||
|
return (-self) + other
|
||||||
|
|
||||||
|
def _matrix_multiply(self, other):
|
||||||
|
"""Internal utility method to multiply to Matrix instances."""
|
||||||
|
if self.n_cols != other.n_rows:
|
||||||
|
raise ValueError("matrices must have compatible dimensions")
|
||||||
|
# Matrix-matrix multiplication means that each entry of the resulting
|
||||||
|
# Matrix is the dot product of the respective row of the "left" Matrix
|
||||||
|
# and column of the "right" Matrix. So, the rows/columns are represented
|
||||||
|
# by the Vector instances provided by the .cols() and .rows() methods.
|
||||||
|
return self.__class__((rv * cv for cv in other.cols()) for rv in self.rows())
|
||||||
|
|
||||||
|
def __mul__(self, other):
|
||||||
|
"""Handle `self * other` and `other * self`.
|
||||||
|
|
||||||
|
This may be either scalar multiplication, matrix-vector multiplication,
|
||||||
|
vector-matrix multiplication, or matrix-matrix multiplication.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) * Matrix([(1, 2), (3, 4)])
|
||||||
|
Matrix(((7.0, 10.0), (15.0, 22.0)))
|
||||||
|
|
||||||
|
>>> 2 * Matrix([(1, 2), (3, 4)])
|
||||||
|
Matrix(((2.0, 4.0), (6.0, 8.0)))
|
||||||
|
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) * 3
|
||||||
|
Matrix(((3.0, 6.0), (9.0, 12.0)))
|
||||||
|
|
||||||
|
Matrix-vector and vector-matrix multiplication are not commutative.
|
||||||
|
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) * Vector([5, 6])
|
||||||
|
Vector((17.0, 39.0))
|
||||||
|
|
||||||
|
>>> Vector([5, 6]) * Matrix([(1, 2), (3, 4)])
|
||||||
|
Vector((23.0, 34.0))
|
||||||
|
"""
|
||||||
|
# Scalar multiplication
|
||||||
|
if isinstance(other, numbers.Number):
|
||||||
|
return self.__class__((x * other for x in r) for r in self._entries)
|
||||||
|
# Matrix-vector multiplication: Vector is a column Vector
|
||||||
|
elif isinstance(other, Vector):
|
||||||
|
# First, cast the other Vector as a Matrix, then do matrix-matrix
|
||||||
|
# multiplication, and lastly return the result as a Vector again.
|
||||||
|
return self._matrix_multiply(other.as_matrix()).as_vector()
|
||||||
|
# Matrix-matrix multiplication
|
||||||
|
elif isinstance(other, self.__class__):
|
||||||
|
return self._matrix_multiply(other)
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __rmul__(self, other):
|
||||||
|
"""See docstring for .__mul__()."""
|
||||||
|
# As scalar multiplication is commutative, we dispatch to .__mul__().
|
||||||
|
if isinstance(other, numbers.Number):
|
||||||
|
return self * other
|
||||||
|
# Vector-matrix multiplication: Vector is a row Vector
|
||||||
|
elif isinstance(other, Vector):
|
||||||
|
return other.as_matrix(column=False)._matrix_multiply(self).as_vector()
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __truediv__(self, other):
|
||||||
|
"""Handle `self / other`.
|
||||||
|
|
||||||
|
Divide a Matrix by a scalar.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) / 4
|
||||||
|
Matrix([(0.25, 0.5), (0.75, 1.0)])
|
||||||
|
"""
|
||||||
|
# As scalar division division is the same as multiplication
|
||||||
|
# with the inverse, we dispatch to .__mul__().
|
||||||
|
if isinstance(other, numbers.Number):
|
||||||
|
return self * (1 / other)
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __eq__(self, other):
|
||||||
|
"""Handle `self == other`.
|
||||||
|
|
||||||
|
Compare two Matrix instances for equality.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) == Matrix([(1, 2), (3, 4)])
|
||||||
|
True
|
||||||
|
|
||||||
|
>>> Matrix([(1, 2), (3, 4)]) == Matrix([(5, 6), (7, 8)])
|
||||||
|
False
|
||||||
|
"""
|
||||||
|
if isinstance(other, self.__class__):
|
||||||
|
if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):
|
||||||
|
raise ValueError("matrices must have the same dimensions")
|
||||||
|
for x, y in zip(self, other):
|
||||||
|
if abs(x - y) > self.zero_threshold:
|
||||||
|
return False # exit early if two corresponding entries differ
|
||||||
|
return True
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __pos__(self):
|
||||||
|
"""Handle `+self`.
|
||||||
|
|
||||||
|
This is simply an identity operator returning the Matrix itself.
|
||||||
|
"""
|
||||||
|
return self
|
||||||
|
|
||||||
|
def __neg__(self):
|
||||||
|
"""Handle `-self`.
|
||||||
|
|
||||||
|
Negate all entries of a Matrix.
|
||||||
|
"""
|
||||||
|
return self.__class__((-x for x in r) for r in self._entries)
|
||||||
|
|
||||||
|
def __abs__(self):
|
||||||
|
"""The Frobenius norm of a Matrix."""
|
||||||
|
return utils.norm(self) # use the norm() function shared with the Vector class
|
||||||
|
|
||||||
|
def __bool__(self):
|
||||||
|
"""A Matrix is truthy if its Frobenius norm is strictly positive."""
|
||||||
|
return bool(abs(self))
|
||||||
|
|
||||||
|
def __float__(self):
|
||||||
|
"""Cast a Matrix as a scalar.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
scalar (float)
|
||||||
|
|
||||||
|
Raises:
|
||||||
|
RuntimeError: if the Matrix has more than one entry
|
||||||
|
"""
|
||||||
|
if not (self.n_rows == 1 and self.n_cols == 1):
|
||||||
|
raise RuntimeError("matrix must have exactly one entry to become a scalar")
|
||||||
|
return self[0]
|
||||||
|
|
||||||
|
def as_vector(self):
|
||||||
|
"""Get a Vector representation of a Matrix.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
vector (Vector)
|
||||||
|
|
||||||
|
Raises:
|
||||||
|
RuntimeError: if one of the two dimensions, .n_rows or .n_cols, is not 1
|
||||||
|
"""
|
||||||
|
if not (self.n_rows == 1 or self.n_cols == 1):
|
||||||
|
raise RuntimeError("one dimension (m or n) must be 1")
|
||||||
|
return Vector(x for x in self)
|
||||||
|
|
||||||
|
def transpose(self):
|
||||||
|
"""Switch the rows and columns of a Matrix.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
matrix (Matrix)
|
||||||
|
"""
|
||||||
|
return self.__class__(zip(*self._entries))
|
||||||
|
|
||||||
|
|
||||||
|
# This import needs to be made here as otherwise an ImportError is raised.
|
||||||
|
# That is so as both the matrix and vector modules import a class from each other.
|
||||||
|
# We call that a circular import. Whereas Python handles "circular" references
|
||||||
|
# (e.g., both the Matrix and Vector classes have methods that reference the
|
||||||
|
# respective other class), that is forbidden for imports.
|
||||||
|
from sample_package.vector import Vector
|
||||||
35
11_classes/sample_package/utils.py
Normal file
35
11_classes/sample_package/utils.py
Normal file
|
|
@ -0,0 +1,35 @@
|
||||||
|
"""This module provides utilities for the whole package.
|
||||||
|
|
||||||
|
The defined constants are used as defaults in the Vector and Matrix classes.
|
||||||
|
|
||||||
|
The norm() function is shared by Vector.__abs__() and Matrix.__abs__().
|
||||||
|
"""
|
||||||
|
|
||||||
|
import math
|
||||||
|
|
||||||
|
|
||||||
|
# Define constants (i.e., normal variables that are, by convention, named in UPPERCASE)
|
||||||
|
# that are used as the defaults for class attributes within Vector and Matrix.
|
||||||
|
DEFAULT_ENTRIES_STORAGE = tuple
|
||||||
|
DEFAULT_ENTRY_TYPE = float
|
||||||
|
ZERO_THRESHOLD = 1e-12
|
||||||
|
|
||||||
|
|
||||||
|
def norm(vec_or_mat):
|
||||||
|
"""Calculate the Frobenius or Euclidean norm of a matrix or vector.
|
||||||
|
|
||||||
|
Find more infos here: https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
|
||||||
|
|
||||||
|
Args:
|
||||||
|
vec_or_mat (Vector / Matrix): object whose entries are squared and summed up
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
norm (float)
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
As Vector and Matrix objects are by design non-empty sequences,
|
||||||
|
norm() may be called, for example, with `[3, 4]` as the argument:
|
||||||
|
>>> norm([3, 4])
|
||||||
|
5.0
|
||||||
|
"""
|
||||||
|
return math.sqrt(sum(x ** 2 for x in vec_or_mat))
|
||||||
253
11_classes/sample_package/vector.py
Normal file
253
11_classes/sample_package/vector.py
Normal file
|
|
@ -0,0 +1,253 @@
|
||||||
|
"""This module defines a Vector class."""
|
||||||
|
|
||||||
|
# Imports from the standard library go first ...
|
||||||
|
import numbers
|
||||||
|
|
||||||
|
# ... and are followed by project-internal ones.
|
||||||
|
# If third-party libraries are needed, they are
|
||||||
|
# put into a group on their own in between.
|
||||||
|
# Within a group, imports are sorted lexicographically.
|
||||||
|
from sample_package import utils
|
||||||
|
from sample_package.matrix import Matrix
|
||||||
|
|
||||||
|
|
||||||
|
class Vector:
|
||||||
|
"""A one-dimensional vector from linear algebra.
|
||||||
|
|
||||||
|
All entries are converted to floats, or whatever is set in the typing attribute.
|
||||||
|
|
||||||
|
Attributes:
|
||||||
|
storage (callable): data type used to store the entries internally;
|
||||||
|
defaults to tuple
|
||||||
|
typing (callable): type casting applied to all entries upon creation;
|
||||||
|
defaults to float
|
||||||
|
zero_threshold (float): max. tolerance when comparing an entry to zero;
|
||||||
|
defaults to 1e-12
|
||||||
|
"""
|
||||||
|
|
||||||
|
storage = utils.DEFAULT_ENTRIES_STORAGE
|
||||||
|
typing = utils.DEFAULT_ENTRY_TYPE
|
||||||
|
zero_threshold = utils.ZERO_THRESHOLD
|
||||||
|
|
||||||
|
def __init__(self, data):
|
||||||
|
"""Create a new vector.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
data (sequence): the vector's entries
|
||||||
|
|
||||||
|
Raises:
|
||||||
|
ValueError: if no entries are provided
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Vector([1, 2, 3])
|
||||||
|
Vector((1.0, 2.0, 3.0))
|
||||||
|
|
||||||
|
>>> Vector(range(3))
|
||||||
|
Vector((0.0, 1.0, 2.0))
|
||||||
|
"""
|
||||||
|
self._entries = self.storage(self.typing(x) for x in data)
|
||||||
|
if len(self) == 0:
|
||||||
|
raise ValueError("a vector must have at least one entry")
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
"""Text representation of a Vector."""
|
||||||
|
name = self.__class__.__name__
|
||||||
|
args = ", ".join(f"{x:.3f}" for x in self)
|
||||||
|
return f"{name}(({args}))"
|
||||||
|
|
||||||
|
def __str__(self):
|
||||||
|
"""Human-readable text representation of a Vector."""
|
||||||
|
name = self.__class__.__name__
|
||||||
|
first, last, n_entries = self[0], self[-1], len(self)
|
||||||
|
return f"{name}({first:.1f}, ..., {last:.1f})[{n_entries:d}]"
|
||||||
|
|
||||||
|
def __len__(self):
|
||||||
|
"""Number of entries in a Vector."""
|
||||||
|
return len(self._entries)
|
||||||
|
|
||||||
|
def __getitem__(self, index):
|
||||||
|
"""Obtain an individual entry of a Vector."""
|
||||||
|
if not isinstance(index, int):
|
||||||
|
raise TypeError("index must be an integer")
|
||||||
|
return self._entries[index]
|
||||||
|
|
||||||
|
def __iter__(self):
|
||||||
|
"""Loop over a Vector's entries."""
|
||||||
|
return iter(self._entries)
|
||||||
|
|
||||||
|
def __reversed__(self):
|
||||||
|
"""Loop over a Vector's entries in reverse order."""
|
||||||
|
return reversed(self._entries)
|
||||||
|
|
||||||
|
def __add__(self, other):
|
||||||
|
"""Handle `self + other` and `other + self`.
|
||||||
|
|
||||||
|
This may be either vector addition or broadcasting addition.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Vector([1, 2, 3]) + Vector([2, 3, 4])
|
||||||
|
Vector((3, 5, 7))
|
||||||
|
|
||||||
|
>>> Vector([1, 2, 3]) + 4
|
||||||
|
Vector((5, 6, 7))
|
||||||
|
|
||||||
|
>>> 10 + Vector([1, 2, 3])
|
||||||
|
Vector((11, 12, 13))
|
||||||
|
"""
|
||||||
|
# Vector addition
|
||||||
|
if isinstance(other, self.__class__):
|
||||||
|
if len(self) != len(other):
|
||||||
|
raise ValueError("vectors must be of the same length")
|
||||||
|
return self.__class__(x + y for (x, y) in zip(self, other))
|
||||||
|
# Broadcasting addition
|
||||||
|
elif isinstance(other, numbers.Number):
|
||||||
|
return self.__class__(x + other for x in self)
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __radd__(self, other):
|
||||||
|
"""See docstring for .__add__()."""
|
||||||
|
# As both vector and broadcasting addition are commutative,
|
||||||
|
# we dispatch to .__add__().
|
||||||
|
return self + other
|
||||||
|
|
||||||
|
def __sub__(self, other):
|
||||||
|
"""Handle `self - other` and `other - self`.
|
||||||
|
|
||||||
|
This may be either vector subtraction or broadcasting subtraction.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Vector([7, 8, 9]) - Vector([1, 2, 3])
|
||||||
|
Vector((6, 6, 6))
|
||||||
|
|
||||||
|
>>> Vector([1, 2, 3]) - 1
|
||||||
|
Vector((0, 1, 2))
|
||||||
|
|
||||||
|
>>> 10 - Vector([1, 2, 3])
|
||||||
|
Vector((9, 8, 7))
|
||||||
|
"""
|
||||||
|
# As subtraction is the inverse of addition,
|
||||||
|
# we first dispatch to .__neg__() to invert the signs of
|
||||||
|
# all entries in other and then dispatch to .__add__().
|
||||||
|
return self + (-other)
|
||||||
|
|
||||||
|
def __rsub__(self, other):
|
||||||
|
"""See docstring for .__sub__()."""
|
||||||
|
# Same comments as in .__sub__() apply
|
||||||
|
# with the roles of self and other swapped.
|
||||||
|
return (-self) + other
|
||||||
|
|
||||||
|
def __mul__(self, other):
|
||||||
|
"""Handle `self * other` and `other * self`.
|
||||||
|
|
||||||
|
This may be either the dot product of two vectors or scalar multiplication.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Vector([1, 2, 3]) * Vector([2, 3, 4])
|
||||||
|
14
|
||||||
|
|
||||||
|
>>> 2 * Vector([1, 2, 3])
|
||||||
|
Vector((2.0, 4.0, 6.0))
|
||||||
|
|
||||||
|
>>> Vector([1, 2, 3]) * 3
|
||||||
|
Vector((3.0, 6.0, 9.0))
|
||||||
|
"""
|
||||||
|
# Dot product
|
||||||
|
if isinstance(other, self.__class__):
|
||||||
|
if len(self) != len(other):
|
||||||
|
raise ValueError("vectors must be of the same length")
|
||||||
|
return sum(x * y for (x, y) in zip(self, other))
|
||||||
|
# Scalar multiplication
|
||||||
|
elif isinstance(other, numbers.Number):
|
||||||
|
return self.__class__(x * other for x in self)
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __rmul__(self, other):
|
||||||
|
"""See docstring for .__mul__()."""
|
||||||
|
# As both dot product and scalar multiplication are commutative,
|
||||||
|
# we dispatch to .__mul__().
|
||||||
|
return self * other
|
||||||
|
|
||||||
|
def __truediv__(self, other):
|
||||||
|
"""Handle `self / other`.
|
||||||
|
|
||||||
|
Divide a Vector by a scalar.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Vector([9, 6, 12]) / 3
|
||||||
|
Vector((3.0, 2.0, 4.0))
|
||||||
|
"""
|
||||||
|
# As scalar division division is the same as multiplication
|
||||||
|
# with the inverse, we dispatch to .__mul__().
|
||||||
|
if isinstance(other, numbers.Number):
|
||||||
|
return self * (1 / other)
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __eq__(self, other):
|
||||||
|
"""Handle `self == other`.
|
||||||
|
|
||||||
|
Compare two Vectors for equality.
|
||||||
|
|
||||||
|
Example Usage:
|
||||||
|
>>> Vector([1, 2, 3]) == Vector([1, 2, 3])
|
||||||
|
True
|
||||||
|
|
||||||
|
>>> Vector([1, 2, 3]) == Vector([4, 5, 6])
|
||||||
|
False
|
||||||
|
"""
|
||||||
|
if isinstance(other, self.__class__):
|
||||||
|
if len(self) != len(other):
|
||||||
|
raise ValueError("vectors must be of the same length")
|
||||||
|
for x, y in zip(self, other):
|
||||||
|
if abs(x - y) > self.zero_threshold:
|
||||||
|
return False # exit early if two corresponding entries differ
|
||||||
|
return True
|
||||||
|
return NotImplemented
|
||||||
|
|
||||||
|
def __pos__(self):
|
||||||
|
"""Handle `+self`.
|
||||||
|
|
||||||
|
This is simply an identity operator returning the Vector itself.
|
||||||
|
"""
|
||||||
|
return self
|
||||||
|
|
||||||
|
def __neg__(self):
|
||||||
|
"""Handle `-self`.
|
||||||
|
|
||||||
|
Negate all entries of a Vector.
|
||||||
|
"""
|
||||||
|
return self.__class__(-x for x in self)
|
||||||
|
|
||||||
|
def __abs__(self):
|
||||||
|
"""The Euclidean norm of a vector."""
|
||||||
|
return utils.norm(self) # use the norm() function shared with the Matrix class
|
||||||
|
|
||||||
|
def __bool__(self):
|
||||||
|
"""A Vector is truthy if its Euclidean norm is strictly positive."""
|
||||||
|
return bool(abs(self))
|
||||||
|
|
||||||
|
def __float__(self):
|
||||||
|
"""Cast a Vector as a scalar.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
scalar (float)
|
||||||
|
|
||||||
|
Raises:
|
||||||
|
RuntimeError: if the Vector has more than one entry
|
||||||
|
"""
|
||||||
|
if len(self) != 1:
|
||||||
|
raise RuntimeError("vector must have exactly one entry to become a scalar")
|
||||||
|
return self[0]
|
||||||
|
|
||||||
|
def as_matrix(self, *, column=True):
|
||||||
|
"""Get a Matrix representation of a Vector.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
column (bool): if the vector is interpreted as a
|
||||||
|
column vector or a row vector; defaults to True
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
matrix (Matrix)
|
||||||
|
"""
|
||||||
|
if column:
|
||||||
|
return Matrix([x] for x in self)
|
||||||
|
return Matrix([(x for x in self)])
|
||||||
Loading…
Reference in a new issue