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2020-11-25 07:46:46 -03:00
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# Seals - Numeric Calculus
This python namespace is made for applied Numeric Calculus of Linear Algebra. It is made with the following objectives in mind:
* Scan *csv* files to make a numpy matrix.
* Write a matrix into a *csv* file.
* Insert user input into a matrix or a vector.
* Calculate Eigenvalues and his Eigenvectors.
* Use methods to proccess the matrices.
* Identity Matrix
* Gauss Elimination
* Inverse Matrix
* Cholesky Decomposition
* LU Decomposition
* Cramer
## Syntax
To call the package *scan* use the syntax: `from Seals import scan`. The package also has a function for *Numpy* arrays and *Pandas* dataframes, and used the following syntax `scan.np(path)` for *Numpy* and `scan.pd(path)` for *Pandas*, where `path` is the path to your directory.
To call the package *write* use the syntax: `from Seals import write`. The package also has a function for *Numpy* arrays and *Pandas* dataframes, and uses the following syntax `write.np(array,path)` for *Numpy*, where `array` is the matrix that you desire to output and `path` is the path to your directory, and `write.pd(df,path)` for *Pandas*, where `df` is the matrix that you desire to output and `path` is the path to your directory.
To call the package *insert* use the syntax: `from Seals import insert`. The package also has a function for *matrix* and another for *vector*, and it has the following syntax `insert.function(array)`, where `insert` is the *Python Module* and `function` is either a `matrix` or a `vector` and `array` is either a *matrix* or a *vector*.
There is also a function that given a matrix it return all real eigenvalues and all real eigenvectors, this function uses the power method to find the eigenvalues and inverse power method for the eigenvector.
### Processes
To call the module `process` use the syntax: `from Seals import process as sl`, where `sl` is an instance and to use a function you have to append the desired function in front of the instance like: `sl.identity(array)`.
* The function *identity* returns a *numpy* identity matrix of the order of the matrix passed into to it, and it has the following syntax `sl.identity(array)`, which `array` is a square matrix.
* The function *gauss* returns a *numpy* vector containing the vector of variables from the augmented matrix. `sl.gauss(matrix)`, which `matrix` is the augmented matrix.
* The function *inverse* returns a *numpy* inverse matrix of the matrix passed into to it, and it has the following syntax `sl.inverse(matrix)`, which `matrix` is a square matrix.
* The function *cholesky* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector.
* The function *decomposition* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector.
* The function *cramer* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector.
## Installation
To install the package from source `cd` into the directory and run:
`pip install .`
or run
`pip install yoshi-seals`

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .eigen import eigen

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import numpy as np
def eigen(a):
k = 0
l = np.ones((a.shape[0]))
at = a #variavel temporaria para A
b = np.random.rand(a.shape[0],a.shape[1])
while (k < at.shape[0]):
u = np.random.rand(at.shape[0],1)
u = u/max(u.min(), u.max(), key=abs)
ctrl = 0
while (ctrl != l[k]):
ctrl = l[k]
u = at.dot(u)
l[k] = max(u.min(), u.max(), key=abs)
u = u/l[k]
alpha = 0.999*l[k]
t = np.random.rand(a.shape[0],1)
b[k] = b[k]/max(b[k].min(), b[k].max(), key=abs)
t = l/max(l.min(), l.max(), key=abs)
while not (np.allclose(b[k],t,atol=10**(-17))):
t = b[k].copy()
b[k] = np.linalg.solve((a - alpha*np.identity(a.shape[0])),((l[k]-alpha)*t))
b[k] = b[k]/max(b[k].min(), b[k].max(), key=abs)
i = 0
while (u[i] == 0):
i += 1
at = at - (1/u[i])*u*at[i]
k += 1
return l, b

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .insert import matrix
from .insert import vector

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
def matrix(matrix):
i = 0
while (i < matrix.shape[0]):
j = 0
while (j < matrix.shape[1]):
matrix[i][j] = float(input('Insira o elemento {}x{}: '.format((i+1),(j+1))))
j += 1
i += 1
return matrix
def vector(vector):
j=0
while (j < vector.shape[0]):
vector[j] = float(input('Insira o elemento b{}: '.format((j+1))))
j += 1
return vector

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .process import identity
from .process import gauss
from .process import inverse
from .process import cholesky
from .process import decomposition
from .process import cramer

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import numpy as np
import math
def identity(matrix):
i = 0
while (i < matrix.shape[0]):
j = 0
while (j < matrix.shape[0]):
if (i == j):
matrix[i][j] = 1
elif (i != j):
matrix[i][j] = 0
j += 1
i += 1
return matrix
def gauss(a):
for i in range(a.shape[0]):
k = i + 1
while (k<a.shape[0]):
l = 1
while (a[i][i] == 0 and l < a.shape[0]):
temp = a[i].copy()
a[i] = a[i+l]
a[i+l] = temp
l += 1
if (a[k][i] == 0):
while (k < a.shape[0]):
k += 1
else:
a[k] = a[k] - (a[k][i]/a[i][i])*a[i]
k += 1
i += 1
x = np.zeros(a.shape[0])
for j in reversed(range(x.shape[0])):
suma = 0
for k in range (j,a.shape[0]):
suma += a[j][k]*x[k]
x[j] = (a[j][a.shape[0]] - suma)/a[j][j]
return x
def inverse(matrix):
matrix = np.hstack(matrix,np.identity(matrix.shape[0]))
i = 0
k = 0
while (i < matrix.shape[0]):
if (matrix[i][i] == 0):
n = i
while (matrix[i][i] == 0) and (n < matrix.shape[0]):
temp = matrix[i].copy()
matrix[i] = matrix[n]
matrix[n] = temp
n += 1
while (k < matrix.shape[0]):
if (k == i) or (matrix[k][i] == 0) or (matrix[i][i] == 0):
k += 1
else:
mult = matrix[k][i]/matrix[i][i]
matrix[k] = matrix[k] - mult*matrix[i]
k += 1
i += 1
k = 0
i = 0
while ((i) < matrix.shape[0]) and (matrix[i][i] != 0):
matrix[i] = matrix[i]/matrix[i][i]
i += 1
return matrix[:,(matrix.shape[0]):]
def cholesky(A, b):
g = np.zeros((A.shape))
i = 0
j = 0
while j < A.shape[1]:
while i < A.shape[0]:
if i == 0 and j == 0:
g[i][j] = math.sqrt(A[0][0])
elif j == 0:
g[i][j] = A[i][0]/g[0][0]
elif i == j:
k = 0
theta = 0
while k < i:
theta += g[i][k]**2
k += 1
g[i][j] = math.sqrt(A[i][i] - theta)
else:
k = 0
theta = 0
while k < j:
theta += g[i][k]*g[j][k]
k += 1
g[i][j] = (A[i][j] - theta)/g[j][j]
i += 1
j += 1
i = j
y = (inverse(g)).dot(b)
x = (inverse(g.T)).dot(y)
return x
def decomposition(U, b):
L = identity(np.zeros(U.shape))
i = 0
k = 0
while (i < U.shape[0]):
k = 0
if (U[i][i] == 0):
n = i
while (U[i][i] == 0) and (n < U.shape[0]):
temp = U[i].copy()
U[i] = U[n]
U[n] = temp
n += 1
while (k < U.shape[0]):
if (k <= i) or (U[i][i] == 0):
k += 1
else:
L[k][i] = U[k][i]/U[i][i]
U[k] = U[k] - L[k][i]*U[i]
k += 1
i += 1
y = (inverse(L)).dot(b)
x = (inverse(U)).dot(y)
return x
def cramer(A, b):
x = np.vstack(np.zeros(b.shape))
k = 0
while (k < A.shape[0]):
temp = A.copy()
temp[:,k] = b
x[k] = np.linalg.det(temp)/np.linalg.det(A)
k += 1
return x

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .scan import numpy as np
from .scan import pandas as pd

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import numpy as np
import pandas as pd
def numpy(path, sep=None, decimal=None):
if sep is None:
sep = ","
if decimal is None:
decimal = "."
df=pd.read_csv(path, sep=sep, decimal=decimal, header=None)
array = df.to_numpy()
return array
def pandas(path, sep=None, decimal=None):
if sep is None:
sep = ","
if decimal is None:
decimal = "."
return pd.read_csv(path, sep=sep, decimal=decimal)

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .write import numpy as np
from .write import pandas as pd

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import csv
def numpy(array, path):
with open(path, mode='w') as sistema_linear:
solution_writer = csv.writer(sistema_linear, delimiter=',', quotechar='"', quoting=csv.QUOTE_MINIMAL)
solution_writer.writerows(array)
return array
def pandas(df, path):
df.to_csv(path)

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .eigen import eigen

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import numpy as np
def eigen(a):
k = 0
l = np.ones((a.shape[0]))
at = a #variavel temporaria para A
b = np.random.rand(a.shape[0],a.shape[1])
while (k < at.shape[0]):
u = np.random.rand(at.shape[0],1)
u = u/max(u.min(), u.max(), key=abs)
ctrl = 0
while (ctrl != l[k]):
ctrl = l[k]
u = at.dot(u)
l[k] = max(u.min(), u.max(), key=abs)
u = u/l[k]
alpha = 0.999*l[k]
t = np.random.rand(a.shape[0],1)
b[k] = b[k]/max(b[k].min(), b[k].max(), key=abs)
t = l/max(l.min(), l.max(), key=abs)
while not (np.allclose(b[k],t,atol=10**(-17))):
t = b[k].copy()
b[k] = np.linalg.solve((a - alpha*np.identity(a.shape[0])),((l[k]-alpha)*t))
b[k] = b[k]/max(b[k].min(), b[k].max(), key=abs)
i = 0
while (u[i] == 0):
i += 1
at = at - (1/u[i])*u*at[i]
k += 1
return l, b

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .insert import matrix
from .insert import vector

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
def matrix(matrix):
i = 0
while (i < matrix.shape[0]):
j = 0
while (j < matrix.shape[1]):
matrix[i][j] = float(input('Insira o elemento {}x{}: '.format((i+1),(j+1))))
j += 1
i += 1
return matrix
def vector(vector):
j=0
while (j < vector.shape[0]):
vector[j] = float(input('Insira o elemento b{}: '.format((j+1))))
j += 1
return vector

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .process import identity
from .process import gauss
from .process import inverse
from .process import cholesky
from .process import decomposition
from .process import cramer

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import numpy as np
import math
def identity(matrix):
i = 0
while (i < matrix.shape[0]):
j = 0
while (j < matrix.shape[0]):
if (i == j):
matrix[i][j] = 1
elif (i != j):
matrix[i][j] = 0
j += 1
i += 1
return matrix
def gauss(a):
for i in range(a.shape[0]):
k = i + 1
while (k<a.shape[0]):
l = 1
while (a[i][i] == 0 and l < a.shape[0]):
temp = a[i].copy()
a[i] = a[i+l]
a[i+l] = temp
l += 1
if (a[k][i] == 0):
while (k < a.shape[0]):
k += 1
else:
a[k] = a[k] - (a[k][i]/a[i][i])*a[i]
k += 1
i += 1
x = np.zeros(a.shape[0])
for j in reversed(range(x.shape[0])):
suma = 0
for k in range (j,a.shape[0]):
suma += a[j][k]*x[k]
x[j] = (a[j][a.shape[0]] - suma)/a[j][j]
return x
def inverse(matrix):
matrix = np.hstack(matrix,np.identity(matrix.shape[0]))
i = 0
k = 0
while (i < matrix.shape[0]):
if (matrix[i][i] == 0):
n = i
while (matrix[i][i] == 0) and (n < matrix.shape[0]):
temp = matrix[i].copy()
matrix[i] = matrix[n]
matrix[n] = temp
n += 1
while (k < matrix.shape[0]):
if (k == i) or (matrix[k][i] == 0) or (matrix[i][i] == 0):
k += 1
else:
mult = matrix[k][i]/matrix[i][i]
matrix[k] = matrix[k] - mult*matrix[i]
k += 1
i += 1
k = 0
i = 0
while ((i) < matrix.shape[0]) and (matrix[i][i] != 0):
matrix[i] = matrix[i]/matrix[i][i]
i += 1
return matrix[:,(matrix.shape[0]):]
def cholesky(A, b):
g = np.zeros((A.shape))
i = 0
j = 0
while j < A.shape[1]:
while i < A.shape[0]:
if i == 0 and j == 0:
g[i][j] = math.sqrt(A[0][0])
elif j == 0:
g[i][j] = A[i][0]/g[0][0]
elif i == j:
k = 0
theta = 0
while k < i:
theta += g[i][k]**2
k += 1
g[i][j] = math.sqrt(A[i][i] - theta)
else:
k = 0
theta = 0
while k < j:
theta += g[i][k]*g[j][k]
k += 1
g[i][j] = (A[i][j] - theta)/g[j][j]
i += 1
j += 1
i = j
y = (inverse(g)).dot(b)
x = (inverse(g.T)).dot(y)
return x
def decomposition(U, b):
L = identity(np.zeros(U.shape))
i = 0
k = 0
while (i < U.shape[0]):
k = 0
if (U[i][i] == 0):
n = i
while (U[i][i] == 0) and (n < U.shape[0]):
temp = U[i].copy()
U[i] = U[n]
U[n] = temp
n += 1
while (k < U.shape[0]):
if (k <= i) or (U[i][i] == 0):
k += 1
else:
L[k][i] = U[k][i]/U[i][i]
U[k] = U[k] - L[k][i]*U[i]
k += 1
i += 1
y = (inverse(L)).dot(b)
x = (inverse(U)).dot(y)
return x
def cramer(A, b):
x = np.vstack(np.zeros(b.shape))
k = 0
while (k < A.shape[0]):
temp = A.copy()
temp[:,k] = b
x[k] = np.linalg.det(temp)/np.linalg.det(A)
k += 1
return x

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .scan import numpy as np
from .scan import pandas as pd

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import numpy as np
import pandas as pd
def numpy(path, sep=None, decimal=None):
if sep is None:
sep = ","
if decimal is None:
decimal = "."
df=pd.read_csv(path, sep=sep, decimal=decimal, header=None)
array = df.to_numpy()
return array
def pandas(path, sep=None, decimal=None):
if sep is None:
sep = ","
if decimal is None:
decimal = "."
return pd.read_csv(path, sep=sep, decimal=decimal)

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
from .write import numpy as np
from .write import pandas as pd

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# Seals - Program made for educational intent, can be freely distributed
# and can be used for economical intent. I will not take legal actions
# unless my intelectual propperty, the code, is stolen or change without permission.
# Copyright (C) 2020 VItor Hideyoshi Nakazone Batista
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License version 2 as published by
# the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
import csv
def numpy(array, path):
with open(path, mode='w') as sistema_linear:
solution_writer = csv.writer(sistema_linear, delimiter=',', quotechar='"', quoting=csv.QUOTE_MINIMAL)
solution_writer.writerows(array)
return array
def pandas(df, path):
df.to_csv(path)

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import setuptools
with open("README.md", "r") as fh:
long_description = fh.read()
setuptools.setup(
name="yoshi-seals",
version="1.3.3.1",
author="Vitor Hideyoshi",
author_email="vitor.h.n.batista@gmail.com",
description="Numeric Calculus python module in the topic of Linear Algebra",
long_description=long_description,
long_description_content_type="text/markdown",
url="https://github.com/HideyoshiNakazone/Seals-NumericCalculus.git",
packages=setuptools.find_packages(),
classifiers=[
"Programming Language :: Python :: 3",
"License :: OSI Approved :: GNU General Public License v2 (GPLv2)",
"Operating System :: OS Independent"
],
python_requires='>=3.6',
install_requires=[
'numpy',
'pandas',
],
)

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Metadata-Version: 2.1
Name: yoshi-seals
Version: 1.3.3.1
Summary: Numeric Calculus python module in the topic of Linear Algebra
Home-page: https://github.com/HideyoshiNakazone/Seals-NumericCalculus.git
Author: Vitor Hideyoshi
Author-email: vitor.h.n.batista@gmail.com
License: UNKNOWN
Description: # Seals - Numeric Calculus
This python namespace is made for applied Numeric Calculus of Linear Algebra. It is made with the following objectives in mind:
* Scan *csv* files to make a numpy matrix.
* Write a matrix into a *csv* file.
* Insert user input into a matrix or a vector.
* Calculate Eigenvalues and his Eigenvectors.
* Use methods to proccess the matrices.
* Identity Matrix
* Gauss Elimination
* Inverse Matrix
* Cholesky Decomposition
* LU Decomposition
* Cramer
## Syntax
To call the package *scan* use the syntax: `from Seals import scan`. The package also has a function for *Numpy* arrays and *Pandas* dataframes, and used the following syntax `scan.np(path)` for *Numpy* and `scan.pd(path)` for *Pandas*, where `path` is the path to your directory.
To call the package *write* use the syntax: `from Seals import write`. The package also has a function for *Numpy* arrays and *Pandas* dataframes, and uses the following syntax `write.np(array,path)` for *Numpy*, where `array` is the matrix that you desire to output and `path` is the path to your directory, and `write.pd(df,path)` for *Pandas*, where `df` is the matrix that you desire to output and `path` is the path to your directory.
To call the package *insert* use the syntax: `from Seals import insert`. The package also has a function for *matrix* and another for *vector*, and it has the following syntax `insert.function(array)`, where `insert` is the *Python Module* and `function` is either a `matrix` or a `vector` and `array` is either a *matrix* or a *vector*.
There is also a function that given a matrix it return all real eigenvalues and all real eigenvectors, this function uses the power method to find the eigenvalues and inverse power method for the eigenvector.
### Processes
To call the module `process` use the syntax: `from Seals import process as sl`, where `sl` is an instance and to use a function you have to append the desired function in front of the instance like: `sl.identity(array)`.
* The function *identity* returns a *numpy* identity matrix of the order of the matrix passed into to it, and it has the following syntax `sl.identity(array)`, which `array` is a square matrix.
* The function *gauss* returns a *numpy* vector containing the vector of variables from the augmented matrix. `sl.gauss(matrix)`, which `matrix` is the augmented matrix.
* The function *inverse* returns a *numpy* inverse matrix of the matrix passed into to it, and it has the following syntax `sl.inverse(matrix)`, which `matrix` is a square matrix.
* The function *cholesky* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector.
* The function *decomposition* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector.
* The function *cramer* returns a *numpy* vector containing the vector of variables from the coefficient matrix and the constants vector, and it has the following syntax `sl.cholesky(A,b)`, which `A` is the coefficient matrix and `b` is the constants vector.
## Installation
To install the package from source `cd` into the directory and run:
`pip install .`
or run
`pip install yoshi-seals`
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 3
Classifier: License :: OSI Approved :: GNU General Public License v2 (GPLv2)
Classifier: Operating System :: OS Independent
Requires-Python: >=3.6
Description-Content-Type: text/markdown

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README.md
setup.py
Seals/__init__.py
Seals/eigen/__init__.py
Seals/eigen/eigen.py
Seals/insert/__init__.py
Seals/insert/insert.py
Seals/process/__init__.py
Seals/process/process.py
Seals/scan/__init__.py
Seals/scan/scan.py
Seals/write/__init__.py
Seals/write/write.py
yoshi_seals.egg-info/PKG-INFO
yoshi_seals.egg-info/SOURCES.txt
yoshi_seals.egg-info/dependency_links.txt
yoshi_seals.egg-info/requires.txt
yoshi_seals.egg-info/top_level.txt

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numpy
pandas

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Seals