log vector programming

log vector tasks programming

Math/linear_algebra/lecture1.py

@@ -0,0 +1,72 @@
+"""Vectors.
+
+Python programming.
+"""
+
+# mypy: allow-untyped-defs
+# mypy: allow-untyped-calls
+import numpy as np
+
+# ![image.png](attachment:image.png)
+
+# L2 norm
+# Euclidean distance
+#
+#
+# ![image.png](attachment:image.png)
+
+vc = np.array([1, 2, 3, 7, 8, 9])
+VC_DIM = len(vc)
+vc_mag = np.linalg.norm(vc)
+
+
+def norm_of_vector(vt):
+    """Return a norm of a vector."""
+    return np.sqrt(np.sum(vt**2))
+
+
+norm_of_vector(vc)
+
+vc_mag  # для сравнения с norm_of_vector
+
+# ![image.png](attachment:image.png)
+
+# ![image.png](attachment:image.png)
+
+# w_unit = np.array([0, 1, 0])
+wt = np.array([1, 3, 0])
+
+
+def vector_to_unit_vector(vt):
+    """Return a vector to unit vector."""
+    norm_of_vector2 = np.linalg.norm(vt)
+    return vt / norm_of_vector2
+
+
+vector_to_unit_vector(wt)
+
+vector_to_unit_vector(np.zeros((4, 1)))  # error
+
+
+# ![image.png](attachment:image.png)
+
+
+def mag_vector(vct, mag):
+    """Return a vector in the same direction with a magnitude."""
+    norm = norm_of_vector(vct)
+    return mag * vct / norm
+
+
+wt = np.array([1, 0, 0])
+mag_vector(wt, 2)
+
+data = [1.72, 54, 36.2]
+# type(data)
+
+data_numpy = np.array(data)
+
+data_matrix = np.array([[1.72, 54, 36.2], [1.74, 58, 36.3], [1.68, 52, 32.9]])
+
+data_matrix  # визуализация матрицы
+
+data_matrix.shape

log.ipynb

@@ -9,6 +9,27 @@
     "\"\"\"Логирование уроков.\"\"\""
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<font size=\"5\">\n",
+    "22/12/2024 Linear algebra\n",
+    "</font>\n",
+    "\n",
+    "Python programming:\n",
+    "\n",
+    "1. The norm of vector\n",
+    "\n",
+    "2. A vector to unit vector transformation\n",
+    "\n",
+    "3. Zeros vector to unit vector transformation impossibility\n",
+    "\n",
+    "4. Creation of a vector of any arbitrary magnitude\n",
+    "\n",
+    "Dot product as optimization task"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -51,7 +72,8 @@
     "\n",
     "4. Attribute and method in Python class\n",
     "\n",
-    "5. Vector addition and subtraction peculiarities (including -1 multiplication)\n",
+    "5. Vector addition and subtraction peculiarities (including -1\n",
+    "multiplication)\n",
     "\n",
     "6. Algebraic and geometric vector interpretation\n",
     "\n",
@@ -153,8 +175,8 @@
     "\n",
     "12. Отношение функций и их степеней в пределе (бесконечность, 0, k, 1)\n",
     "\n",
-    "13. Методы избавления от неопределенностей разного вида. Непрерывность функции\n",
-    "и ее доказательство\n",
+    "13. Методы избавления от неопределенностей разного вида. Непрерывность\n",
+    "функции и ее доказательство\n",
     "\n",
     "14. Точки разрыва (род и тип)\n",
     "\n",

log.py

@@ -1,5 +1,21 @@
 """Логирование уроков."""
 
+# <font size="5">
+# 22/12/2024 Linear algebra
+# </font>
+#
+# Python programming:
+#
+# 1. The norm of vector
+#
+# 2. A vector to unit vector transformation
+#
+# 3. Zeros vector to unit vector transformation impossibility
+#
+# 4. Creation of a vector of any arbitrary magnitude
+#
+# Dot product as optimization task
+
 # <font size="5">
 # 17/12/2024 Linear algebra
 # </font>
@@ -33,7 +49,8 @@
 #
 # 4. Attribute and method in Python class
 #
-# 5. Vector addition and subtraction peculiarities (including -1 multiplication)
+# 5. Vector addition and subtraction peculiarities (including -1
+# multiplication)
 #
 # 6. Algebraic and geometric vector interpretation
 #
@@ -120,8 +137,8 @@
 #
 # 12. Отношение функций и их степеней в пределе (бесконечность, 0, k, 1)
 #
-# 13. Методы избавления от неопределенностей разного вида. Непрерывность функции
-# и ее доказательство
+# 13. Методы избавления от неопределенностей разного вида. Непрерывность
+# функции и ее доказательство
 #
 # 14. Точки разрыва (род и тип)
 #