




"""simple docstring"""


import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)


class _lowerCamelCase    (					unittest.TestCase						):






   def 	_lowerCAmelCase   (		self       :		Dict   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 2, 3]   )
         self.assertEqual(x.component(0   )   ,     1   )
         self.assertEqual(x.component(2   )   ,     3   )
         lowerCAmelCase__      :			Union[str, Any]   =	Vector()






   def 	_lowerCAmelCase   (		self       :		Union[str, Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			str   =	Vector([0, 0, 0, 0, 0, 1]   )
         self.assertEqual(str(UpperCamelCase   )   ,     """(0,0,0,0,0,1)"""   )






   def 	_lowerCAmelCase   (		self       :		Any   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			List[Any]   =	Vector([1, 2, 3, 4]   )
         self.assertEqual(len(UpperCamelCase   )   ,     4   )






   def 	_lowerCAmelCase   (		self       :		List[str]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			str   =	Vector([1, 2]   )
         lowerCAmelCase__      :			Optional[int]   =	Vector([1, 2, 3, 4, 5]   )
         lowerCAmelCase__      :			Union[str, Any]   =	Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]   )
         lowerCAmelCase__      :			List[Any]   =	Vector([1, -1, 1, -1, 2, -3, 4, -5]   )
         self.assertAlmostEqual(x.euclidean_length()   ,     2.236   ,     3   )
         self.assertAlmostEqual(y.euclidean_length()   ,     7.416   ,     3   )
         self.assertEqual(z.euclidean_length()   ,     0   )
         self.assertAlmostEqual(w.euclidean_length()   ,     7.616   ,     3   )






   def 	_lowerCAmelCase   (		self       :		Any   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			int   =	Vector([1, 2, 3]   )
         lowerCAmelCase__      :			Optional[Any]   =	Vector([1, 1, 1]   )
         self.assertEqual((x + y).component(0   )   ,     2   )
         self.assertEqual((x + y).component(1   )   ,     3   )
         self.assertEqual((x + y).component(2   )   ,     4   )






   def 	_lowerCAmelCase   (		self       :		Optional[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Union[str, Any]   =	Vector([1, 2, 3]   )
         lowerCAmelCase__      :			Dict   =	Vector([1, 1, 1]   )
         self.assertEqual((x - y).component(0   )   ,     0   )
         self.assertEqual((x - y).component(1   )   ,     1   )
         self.assertEqual((x - y).component(2   )   ,     2   )






   def 	_lowerCAmelCase   (		self       :		Optional[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Any   =	Vector([1, 2, 3]   )
         lowerCAmelCase__      :			Any   =	Vector([2, -1, 4]   )  # for test of dot product
         lowerCAmelCase__      :			Any   =	Vector([1, -2, -1]   )
         self.assertEqual(str(x * 3.0   )   ,     """(3.0,6.0,9.0)"""   )
         self.assertEqual((a * b)   ,     0   )






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

         """simple docstring"""
         self.assertEqual(str(zero_vector(10   )   ).count("""0"""   )   ,     10   )






   def 	_lowerCAmelCase   (		self       :		Tuple   )			->						None:

         """simple docstring"""
         self.assertEqual(str(unit_basis_vector(3   ,     1   )   )   ,     """(0,1,0)"""   )






   def 	_lowerCAmelCase   (		self       :		Optional[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 2, 3]   )
         lowerCAmelCase__      :			Optional[Any]   =	Vector([1, 0, 1]   )
         self.assertEqual(str(axpy(2   ,     UpperCamelCase   ,     UpperCamelCase   )   )   ,     """(3,4,7)"""   )






   def 	_lowerCAmelCase   (		self       :		Optional[int]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 0, 0, 0, 0, 0]   )
         lowerCAmelCase__      :			Any   =	x.copy()
         self.assertEqual(str(UpperCamelCase   )   ,     str(UpperCamelCase   )   )






   def 	_lowerCAmelCase   (		self       :		Optional[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Vector([1, 0, 0]   )
         x.change_component(0   ,     0   )
         x.change_component(1   ,     1   )
         self.assertEqual(str(UpperCamelCase   )   ,     """(0,1,0)"""   )






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Optional[int]   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         self.assertEqual("""|1,2,3|\n|2,4,5|\n|6,7,8|\n"""   ,     str(UpperCamelCase   )   )






   def 	_lowerCAmelCase   (		self       :		Union[str, Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         lowerCAmelCase__      :			Dict   =	[[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
         for x in range(a.height()   ):
               for y in range(a.width()   ):
                     self.assertEqual(minors[x][y]   ,     a.minor(UpperCamelCase   ,     UpperCamelCase   )   )






   def 	_lowerCAmelCase   (		self       :		List[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			str   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         lowerCAmelCase__      :			int   =	[[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
         for x in range(a.height()   ):
               for y in range(a.width()   ):
                     self.assertEqual(cofactors[x][y]   ,     a.cofactor(UpperCamelCase   ,     UpperCamelCase   )   )






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Union[str, Any]   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         self.assertEqual(-5   ,     a.determinant()   )






   def 	_lowerCAmelCase   (		self       :		int   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Optional[Any]   =	Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]   ,     3   ,     3   )
         lowerCAmelCase__      :			Tuple   =	Vector([1, 2, 3]   )
         self.assertEqual("""(14,32,50)"""   ,     str(a * x   )   )
         self.assertEqual("""|2,4,6|\n|8,10,12|\n|14,16,18|\n"""   ,     str(a * 2   )   )






   def 	_lowerCAmelCase   (		self       :		str   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Dict   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         a.change_component(0   ,     2   ,     5   )
         self.assertEqual("""|1,2,5|\n|2,4,5|\n|6,7,8|\n"""   ,     str(UpperCamelCase   )   )






   def 	_lowerCAmelCase   (		self       :		Tuple   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         self.assertEqual(7   ,     a.component(2   ,     1   )   ,     0.01   )






   def 	_lowerCAmelCase   (		self       :		Any   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Tuple   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         lowerCAmelCase__      :			List[Any]   =	Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]   ,     3   ,     3   )
         self.assertEqual("""|2,4,10|\n|4,8,10|\n|12,14,18|\n"""   ,     str(a + b   )   )






   def 	_lowerCAmelCase   (		self       :		List[Any]   )			->						None:

         """simple docstring"""
         lowerCAmelCase__      :			Optional[Any]   =	Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]   ,     3   ,     3   )
         lowerCAmelCase__      :			Dict   =	Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]   ,     3   ,     3   )
         self.assertEqual("""|0,0,-4|\n|0,0,0|\n|0,0,-2|\n"""   ,     str(a - b   )   )






   def 	_lowerCAmelCase   (		self       :		Union[str, Any]   )			->						None:

         """simple docstring"""
         self.assertEqual(
             """|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n"""   ,     str(square_zero_matrix(5   )   )   ,     )


if __name__ == "__main__":
  unittest.main()











"""simple docstring"""


from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase



def 	lowercase_				(			__UpperCAmelCase				)						->    None:
      lowerCAmelCase__ ,   lowerCAmelCase__      :			int   =	analyze_text(__UpperCAmelCase				)
      lowerCAmelCase__      :			Optional[Any]   =	list(""" """ + ascii_lowercase				)
      # what is our total sum of probabilities.
      lowerCAmelCase__      :			List[str]   =	sum(single_char_strings.values()				)

      # one length string
      lowerCAmelCase__      :			List[str]   =	0
      # for each alpha we go in our dict and if it is in it we calculate entropy
      for ch in my_alphas:
            if ch in single_char_strings:
                  lowerCAmelCase__      :			List[Any]   =	single_char_strings[ch]
                  lowerCAmelCase__      :			int   =	my_str / all_sum
                  my_fir_sum += prob * math.loga(__UpperCAmelCase				)  # entropy formula.

    # print entropy
      print(f"""{round(-1 * my_fir_sum				):.1f}"""				)

      # two len string
      lowerCAmelCase__      :			Tuple   =	sum(two_char_strings.values()				)
      lowerCAmelCase__      :			str   =	0
      # for each alpha (two in size) calculate entropy.
      for cha in my_alphas:
            for cha in my_alphas:
                  lowerCAmelCase__      :			Optional[int]   =	cha + cha
                  if sequence in two_char_strings:
                        lowerCAmelCase__      :			int   =	two_char_strings[sequence]
                        lowerCAmelCase__      :			str   =	int(__UpperCAmelCase				) / all_sum
                        my_sec_sum += prob * math.loga(__UpperCAmelCase				)

    # print second entropy
      print(f"""{round(-1 * my_sec_sum				):.1f}"""				)

      # print the difference between them
      print(f"""{round((-1 * my_sec_sum) - (-1 * my_fir_sum)				):.1f}"""				)



def 	lowercase_				(			__UpperCAmelCase				)						->    tuple[dict, dict]:
      lowerCAmelCase__      :			Any   =	Counter()  # type: ignore
      lowerCAmelCase__      :			Tuple   =	Counter()  # type: ignore
      single_char_strings[text[-1]] += 1

      # first case when we have space at start.
      two_char_strings[" " + text[0]] += 1
      for i in range(0    ,		len(__UpperCAmelCase				) - 1				):
            single_char_strings[text[i]] += 1
            two_char_strings[text[i : i + 2]] += 1
      return single_char_strings, two_char_strings



def 	lowercase_				(			)						->    Any:
      import doctest

      doctest.testmod()
      # text = (
      #     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
      #     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
      #     "jointure saw horrible. He private he on be imagine suppose. Fertile "
      #     "beloved evident through no service elderly is. Blind there if every no so "
      #     "at. Own neglected you preferred way sincerity delivered his attempted. To "
      #     "of message cottage windows do besides against uncivil.  Delightful "
      #     "unreserved impossible few estimating men favourable see entreaties. She "
      #     "propriety immediate was improving. He or entrance humoured likewise "
      #     "moderate. Much nor game son say feel. Fat make met can must form into "
      #     "gate. Me we offending prevailed discovery. "
      # )

      # calculate_prob(text)


if __name__ == "__main__":
  main()





