deciml-mathematics 0.0.3

Implementation of deciml library. Used for mathematical operations.

deciml_maths

pip install deciml_mathematics

Note - 'ret' argument is the 'r' argument of "retrn" function in "terminate" library.

Note - If 'chk' argument is False,

• Incorrect argument types (Below declaration snippets in README) result in error.
• Using List instead of Tuple can result in error.

If 'chk' is True,

• Decimal type can be replaced with float, int, or string.

Note - Detailed description of arguments is available in the docstring.

Use the "setpr" function to set the precision for a calculation ("getpr" to check the precision).

Increase the precision value by 2 more than the precision that you want for more accurate calculations

>>> from deciml_maths import setpr, getpr
>>> setpr(29)
>>> getpr()
29

Abbrevations

• c: class
• o: object
• sm: staticmethod
• cm: classmethod
• f: function
• s: setter
• g: getter

Matrix

matx

(o) matx(li, chk=True, ret='a'): Object that stores matrix properties

• li - tuple[ tuple[Decimal, ...] ] | tuple[Decimal, ...]

>>> from deciml_maths.matrix import matx
Imported deciml...
>>> from deciml.deciml import setpr
>>> setpr(3)
>>> matrix = matx([[1.924,2.25452,3.35157],[2.2585441,3.35844,4.25841],[3.58425,4.365258,5.694222],[4.6945485,5.5875155,6.557885]],True,'w')
'''
    [[1.924,2.25452,3.35157],[2.2585441,3.35844,4.25841],[3.58425,4.365258,5.694222],[4.6945485,5.5875155,6.557885]] - 2-D matrix
    True: Check argument types
    'w': Wait and exit if error
'''
>>> print(matrix)
matx(
_____|___[0]___|___[1]___|___[2]___|
 (0) | '1.924' | '2.255' | '3.352' | 
 (1) | '2.259' | '3.358' | '4.258' | 
 (2) | '3.584' | '4.365' | '5.694' | 
 (3) | '4.695' | '5.588' | '6.558' | 
)

i. (s) matx: Assign a new 2-D matrix

>>> matrix.matx = [1.5, 2.8257, 3.25541]
>>> matrix.pmatx
matx(
_____|__[0]__|___[1]___|___[2]___|
 (0) | '1.5' | '2.826' | '3.255' | 
)

ii. (g) matx -> tuple: Get the 2-D matrix as a tuple

>>> mat = matrix.matx
>>> mat
((Decimal('1.5'), Decimal('2.826'), Decimal('3.255')),)

iii. (g) rowlen -> int: Get the length of rows

>>> matrix.rowlen
3

iv. (g) collen -> int: Get the length of columns

>>> matrix.collen
1

v. (g) sqmatx -> bool: Get if square matrix

>>> matrix.sqmatx
False

vi. (g) pmatx: Print the matrix and return the matrix as a tuple

Note - Can be used to check for errors. :'/ Change the matx to pmatx

matrix.pmatx
matx(
_____|__[0]__|___[1]___|___[2]___|
 (0) | '1.5' | '2.826' | '3.255' | 
)

v. (f) dnant() -> Decimal: Get the determinant of matrix

>>> matrix = matx([[1,2,3,5],[2,4,4,5],[3,4,8,6],[7,5,6,7]])
>>> matrix.dnant()
Decimal('-155.000')

vi. (f) invsednant() -> Decimal: Get the determinant of the inverse matrix

>>> matrix.invsednant()
Decimal('-0.006452')

vii. (f) invse() -> matx: Get the inverse matrix of the matrix

>>> mat = matrix.invse()
>>> print(mat)
matx(
_____|____[0]_____|___[1]____|____[2]_____|____[3]_____|
 (0) | '-0.05161' | '-0.219' | '-0.04516' |    '0.232' | 
 (1) |   '-0.426' |  '0.690' |   '-0.123' | '-0.08387' | 
 (2) | '-0.09677' | '-0.161' |    '0.290' | '-0.06452' | 
 (3) |    '0.439' | '-0.135' |   '-0.116' |  '0.02581' | 
)

vii. (f) adjnt() -> matx: Get the adjoint matrix of the matrix

>>> mat = matrix.adjnt()
>>> print(mat)
matx(
_____|___[0]___|___[1]____|___[2]___|___[3]___|
 (0) |   '8.0' |   '34.0' |   '7.0' | '-36.0' | 
 (1) |  '66.0' | '-107.0' |  '19.0' |  '13.0' | 
 (2) |  '15.0' |   '25.0' | '-45.0' |  '10.0' | 
 (3) | '-68.0' |   '21.0' |  '18.0' |  '-4.0' | 
)

viii. (f) tpose() -> matx: Get the transpose matrix of the matrix

>>> mat = matrix.tpose()
>>> print(mat)
matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '7.0' | 
 (1) | '2.0' | '4.0' | '4.0' | '5.0' | 
 (2) | '3.0' | '4.0' | '8.0' | '6.0' | 
 (3) | '5.0' | '5.0' | '6.0' | '7.0' | 
)

ix. (f) cofacm() -> matx: Get the matrix of cofactors for the matrix

>>> mat = matrix.cofacm()
>>> print(mat)
matx(
_____|___[0]___|___[1]____|___[2]___|___[3]___|
 (0) |   '8.0' |   '66.0' |  '15.0' | '-68.0' | 
 (1) |  '34.0' | '-107.0' |  '25.0' |  '21.0' | 
 (2) |   '7.0' |   '19.0' | '-45.0' |  '18.0' | 
 (3) | '-36.0' |   '13.0' |  '10.0' |  '-4.0' | 
)

x. (f) mele(i, j, chk=True, ret='a') -> Decimal: Get an element of the matrix

• i - int
• j - int

>>> ele = matrix.mele(0,0,True,'e')
'''
  0 - Row index
  0 - Column index
  True - Check arguments
  'e' - Exit if error
'''
>>> ele
Decimal('1.0')

xi. (f) mrow(i, chk=True, ret='a') -> tuple[Decimal, ...]: Get a row of the matrix

• i - int

>>> row = matrix.mrow(0, True, 'c')
'''
  0 - Row index
  True - Check arguments
  'c' - Continue if error
'''
>>> row
(Decimal('1.0'), Decimal('2.0'), Decimal('3.0'), Decimal('5.0'))

xii. (f) mcol(j, chk=True, ret='a') -> tuple[Decimal, ...]: Get a column of the matrix

• j - int

>>> col = matrix.mcol(0, True, 'a')
'''
  0 - Column index
  True - Check arguments
  'a' - Ask to exit if error
'''
>>> col
(Decimal('1.0'), Decimal('2.0'), Decimal('3.0'), Decimal('7.0'))

xiii. (f) gele(a, r=False, chk=True, ret='a') -> tuple[ tuple[Decimal, ...] ]: Get the rows or columns of the matrix

• a - list[ int ]
• r - bool

>>> cols = matrix.gele([0,2], False, False, 'e')
'''
  [0,2] - Column indexes
  False - Get columns
  False - Skip arguments check
  'e' - Exit if error
'''
>>> cols
((Decimal('1.0'), Decimal('2.0'), Decimal('3.0'), Decimal('7.0')), (Decimal('3.0'), Decimal('4.0'), Decimal('8.0'), Decimal('6.0')))

xiv. (f) matxl() -> list[ list[ Decimal ] ]: Get the matrix as a list of Decimal objects

>>> matrix.matxl()
[[Decimal('1.0'), Decimal('2.0'), Decimal('3.0'), Decimal('5.0')], [Decimal('2.0'), Decimal('4.0'), Decimal('4.0'), Decimal('5.0')], [Decimal('3.0'), Decimal('4.0'), Decimal('8.0'), Decimal('6.0')], [Decimal('7.0'), Decimal('5.0'), Decimal('6.0'), Decimal('7.0')]]

xv. (f) pop(i, r=True, chk=True, ret='a') -> tuple[Decimal, ...]: Remove a row or column of the matrix

• i - int
• r - bool

>>> matrix.pop(0, False, True, 'c')
>>> popped = matrix.pop(0, False, True, 'c')
'''
    0 - Column index
    False - Pop column
    True - Check arguments
    'c' - Continue if error
'''
>>> popped
(Decimal('1.0'), Decimal('2.0'), Decimal('3.0'), Decimal('7.0'))
>>> print(matrix)
matx(
_____|__[0]__|__[1]__|__[2]__|
 (0) | '2.0' | '3.0' | '5.0' | 
 (1) | '4.0' | '4.0' | '5.0' | 
 (2) | '4.0' | '8.0' | '6.0' | 
 (3) | '5.0' | '6.0' | '7.0' | 
)

xvi. Get matx object using index slicing

>>> m = matx([[1,2,3,4],[1,2,5,6],[8,9,7,1]])
>>> m[2,1]
Decimal('9.0')
>>> m[:2]
matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '4.0' |
 (1) | '1.0' | '2.0' | '5.0' | '6.0' |
)

>>> m[:2,1]
matx(
_____|__[0]__|
 (0) | '2.0' |
 (1) | '2.0' |
)

>>> m[:2,:1]
matx(
_____|__[0]__|
 (0) | '1.0' |
 (1) | '1.0' |
)

>>> m[:2,:3]
matx(
_____|__[0]__|__[1]__|__[2]__|
 (0) | '1.0' | '2.0' | '3.0' |
 (1) | '1.0' | '2.0' | '5.0' |
)

matutils

(c) matutils: Methods used with matx

>>> from deciml_maths.matrix import matx, matutils
Imported deciml...

i. (sm) sclrm(n, el, chk=True, ret='a') -> matx: Get a matx object with a scalar matrix

• n - int
• el - Decimal

>>> from deciml_maths import setpr                
>>> setpr(3)
>>> mat = matutils.sclrm(4, 12.12345, True, 'e')
'''
    4 - Nummber of rows of square matrix
    12.12345 - Diagonal values
    True - Check arguments
    'e' - Exit if error
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]____|___[2]____|___[3]____|
 (0) | '12.123' |    '0.0' |    '0.0' |    '0.0' |
 (1) |    '0.0' | '12.123' |    '0.0' |    '0.0' |
 (2) |    '0.0' |    '0.0' | '12.123' |    '0.0' |
 (3) |    '0.0' |    '0.0' |    '0.0' | '12.123' |
)

ii. (sm) eqelm(m, n, i, chk=True, ret='a') -> matx: Get a matx object of matrix with equal elements

• m - int
• n - int
• i - Decimal

>>> mat = matutils.eqelm(4, 3, 12.12345, True, 'e')
'''
    4 - Number of rows
    3 - Number of columns
    12.12345 - Element value
    True - Check arguments
    'e' - Exit if error
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]____|___[2]____|
 (0) | '12.123' | '12.123' | '12.123' |
 (1) | '12.123' | '12.123' | '12.123' |
 (2) | '12.123' | '12.123' | '12.123' |
 (3) | '12.123' | '12.123' | '12.123' |
)

iii. *(sm) addmatx(a, b, r=False, chk=True, ret='a') -> matx: Get a matrix as a matx object for matrices of matx objects appended along row or column direction

• a - matx
• *b - matx
• r - bool

>>> mat1 = matx([[1,2,3,4],[12.1234, 1.2365, 3, 4]])
>>> mat2 = matx([[0.2365, 1.23641, 4.25631, 5],[5,6,7,8]])
>>> mat3 = matx([[1,2,3,4],[2,3,4,5]])
>>> mat = matutils.addmatx(mat1, mat2, mat3, r=True, chk=True, ret='w')
'''
    mat1, mat2, mat3 - matx objects
    True - Along row
    True - Check arguments
    'w' - Wait and exit if error
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]___|___[2]___|__[3]__|
 (0) |    '1.0' |   '2.0' |   '3.0' | '4.0' |
 (1) | '12.123' | '1.237' |   '3.0' | '4.0' |
 (2) |  '0.237' | '1.236' | '4.256' | '5.0' |
 (3) |    '5.0' |   '6.0' |   '7.0' | '8.0' |
 (4) |    '1.0' |   '2.0' |   '3.0' | '4.0' |
 (5) |    '2.0' |   '3.0' |   '4.0' | '5.0' |
)

>>> mat = matutils.addmatx(mat1, mat2, mat3, r=False, chk=True, ret='w')
'''
    mat1, mat2, mat3 - matx objects
    False - Along columns
    True - Check arguments
    'w' - Wait and exit if error
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]___|__[2]__|__[3]__|___[4]___|___[5]___|___[6]___|__[7]__|__[8]__|__[9]__|_[10]__|_[11]__|
 (0) |    '1.0' |   '2.0' | '3.0' | '4.0' | '0.237' | '1.236' | '4.256' | '5.0' | '1.0' | '2.0' | '3.0' | '4.0' |
 (1) | '12.123' | '1.237' | '3.0' | '4.0' |   '5.0' |   '6.0' |   '7.0' | '8.0' | '2.0' | '3.0' | '4.0' | '5.0' |
)

iv. (cm) maddval(a, x, chk=True, ret='a') -> matx: Get a matrix as a matx object with a number added to all the rows in the matrix of a matx object at the first index

• a - matx
• x - Decimal

>>> mat = matutils.maddval(mat1, 10.1234, True, 'a')
'''
    mat1 - matx object
    10.1234 - Number
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]____|___[2]___|__[3]__|__[4]__|
 (0) | '10.123' |    '1.0' |   '2.0' | '3.0' | '4.0' |
 (1) | '10.123' | '12.123' | '1.237' | '3.0' | '4.0' |
)

v. (sm) matlxtox(a, chk=True, ret='a') -> tuple[matx, ...]: Convert matx object to a tuple of matx objects with row matrix

• a - matx

>>> a = matutils.matlxtox(mat1, True, 'a')
'''
    mat1 - matx objects
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> for i in a:
...     print(i)
... 
matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '4.0' |
)

matx(
_____|___[0]____|___[1]___|__[2]__|__[3]__|
 (0) | '12.123' | '1.237' | '3.0' | '4.0' |
)

vi. (sm) matxtolx(a, chk=True, ret='a') -> matx: Convert a tuple of matx objects with row matrix to a matx object

• a - matx

>>> mat = matutils.matxtolx(a, True, 'a')
'''
    a - Tuple of matx objects with row matrix
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]___|__[2]__|__[3]__|
 (0) |    '1.0' |   '2.0' | '3.0' | '4.0' |
 (1) | '12.123' | '1.237' | '3.0' | '4.0' |
)

vii. (sm) gele(a, b, r=False, chk=True, ret='a') -> matx: Get the rows or columns of the matrix for a matx object as a matx object

• a - matx
• b - list[ int ]
• r - bool

>>> cols = matutils.gele(mat, [0,3], False, True, 'a')
'''
    mat - matx objects
    [0,3] - column indexes
    False - Get columns
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(cols)
matx(
_____|__[0]__|___[1]____|
 (0) | '1.0' | '12.123' |
 (1) | '4.0' |    '4.0' |
)

>>> rows = matutils.gele(mat, [0], True, True, 'a')
'''
    mat - matx object
    [0] - Row indexes
    True - Get rows
    True - Check arguments
    'a' - Ask to exit if error
'''   
>>> print(rows)
matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '4.0' |
)

viii. (cm) tpose(a, chk=True, ret='a') -> matx: Get the transpose matrix as a matx object for matrix of a matx object

>>> tmat = matutils.tpose(mat, True, 'a')
'''
    mat - matx object
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(tmat)
matx(
_____|__[0]__|___[1]____|
 (0) | '1.0' | '12.123' |
 (1) | '2.0' |  '1.237' |
 (2) | '3.0' |    '3.0' |
 (3) | '4.0' |    '4.0' |
)

ix. (cm) cofac(a, b, c, chk=True, ret='a') -> matx: Get the matrix of cofactors as a matx object for matrix of a matx object

• a - matx
• b - int
• c - int

>>> cofac = matutils.cofac(mat, 0, 0, True, 'a')
Invalid command: matutils.cofac()
Error: Not a square matrix 

exit? y/n
n
>>> mat = matx([[1,2,3],[2,4,4],[1,3,5]])
>>> cofac = matutils.cofac(mat, 0, 0, True, 'a')
'''
    mat - matx object
    0 - Row index
    0 - Column index
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> cofac
Decimal('8.0')

x. (cm) dnant(a, chk=True, ret='a') -> Decimal: Get the determinant of matrix for a matx object

• a - matx

>>> det = matutils.dnant(mat, True, 'a')
'''
    mat - matx object
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> det
Decimal('2.0')

xi. (cm) adjnt(a, chk=True, ret='a') -> matx: Get the adjoint of matrix for a matx object

• a - matx

>>> adjmat = matutils.adjnt(mat, True, 'a')
'''
    mat - matx object
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(adjmat)
matx(
_____|__[0]___|__[1]___|__[2]___|
 (0) |  '8.0' | '-1.0' | '-4.0' |
 (1) | '-6.0' |  '2.0' |  '2.0' |
 (2) |  '2.0' | '-1.0' |  '0.0' |
)

xii. (cm) invse(a, chk=True, ret='a') -> matx: Get the inverse matrix as a matx object for matrix of a matx object

• a - matx

>>> invmat = matutils.invse(mat, True, 'a')
'''
    mat - matx object
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(invmat)
matx(
_____|__[0]___|___[1]___|__[2]___|
 (0) |  '4.0' | '-0.50' | '-2.0' |
 (1) | '-3.0' |   '1.0' |  '1.0' |
 (2) |  '1.0' | '-0.50' |  '0.0' |
)

xiii. (cm) invsednant(a, chk=True, ret='a') -> Decimal: Get the determinant of the inverse matrix for matrix of a matx object

• a - matx

>>> mat = matx([[1,2,3],[2.256245,4,4],[1,3.2358,5.332526]])
>>> mat.invse().dnant()                                     
Decimal('0.449')
>>> invdet = matutils.invsednant(mat, True, 'a')
'''
    mat - matx object
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> invdet
Decimal('0.449')

xiv. (cm) tform(a, b, c, d, r=False, chk=True, ret='a') -> matx: Get a matx object with matrix for matrix of a matx object after a row or column transformation

• a - matx
• b - int
• c - int
• d - Decimal

Note - Transformation is [b] -> [b] + c*[d]

>>> mat = matx([[1,2,3],[2,4,4],[1,3,5]])
>>> mat = matutils.tform(mat, 1, 2, 1.2487, False, True, 'a')
'''
    mat - matx object
    1 - Index
    2 - Index
    1.2487 - Factor
    False - Column transformation
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|__[0]__|___[1]___|__[2]__|
 (0) | '1.0' | '5.747' | '3.0' |
 (1) | '2.0' | '8.996' | '4.0' |
 (2) | '1.0' | '9.245' | '5.0' |
)

xv. (sm) madd(a, b, sumr=None, chk=True, ret='a') -> matx | tuple[Decimal, ...]: Get the matrix as a matx object after matrix addition for matrices of two matx objects

• a - matx
• b - matx
• sumr - bool/None

>>> mat1 = matx([[5,6,7],[3,4,1],[5,4,1]])
>>> mat = matutils.madd(mat, mat1, chk=True, ret='a')
'''
    mat, mat1 - matx objects
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|__[0]__|___[1]____|__[2]___|
 (0) | '6.0' | '11.747' | '10.0' |
 (1) | '5.0' | '12.996' |  '5.0' |
 (2) | '6.0' | '13.245' |  '6.0' |
)

>>> sum_of_rows = matutils.madd(mat, mat1, False, True, 'a')
'''
    mat, mat1 - matx objects
    False - Return sum of elements at a row index in each column
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> sum_of_rows
(Decimal('45.747'), Decimal('30.996'), Decimal('35.245'))

xvi. (cm) saddcnst(a, b, r=False, sumr=None, chk=True, ret='a') -> matx | tuple[Decimal, ...]: Get the matrix as matx object after addition of a constant to each row or column in matrix of a matx object

• a - list[ Decimal ] | tuple[Decimal, ...] | Decimal
• b - matx
• r - bool/None
• sumr - bool/None

>>> mat = matutils.saddcnst(0.4826, mat, None, chk=True, ret='a')
'''
    0.4826 - Number
    mat - matx object
    None - Add to all elements
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|___[0]___|___[1]____|___[2]____|
 (0) | '6.483' | '12.230' | '10.483' |
 (1) | '5.483' | '13.479' |  '5.483' |
 (2) | '6.483' | '13.728' |  '6.483' |
)

>>> mat = matutils.saddcnst([0.1,0.2,0.3], mat, True, chk=True, ret='a')
'''
    [0.1,0.2,0.3] - Numbers
    mat - matx object
    True - Add to rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|___[0]___|___[1]____|___[2]____|
 (0) | '6.583' | '12.330' | '10.583' |
 (1) | '5.683' | '13.679' |  '5.683' |
 (2) | '6.783' | '14.028' |  '6.783' |
)

xvii. (sm) msub(a, b, sumr=None, chk=True, ret='a') -> matx | tuple[Decimal, ...]: Get the matrix as a matx object after matrix subtraction for matrices of two matx objects

• a - matx
• b - matx
• sumr - bool/None

>>> mat1 = matx([[1.1234,2.2123,12.2541,3],[1,5,4,2],[3,1,2,2]])
>>> mat2 = matx([[2,3,1,1],[3,3,5,6],[2,3,1,1]])
>>> mat = matutils.msub(mat1, mat2, chk=True, ret='a')
'''
    mat1, mat2 - matx objects
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]____|___[2]____|__[3]___|
 (0) | '-0.877' | '-0.788' | '11.254' |  '2.0' |
 (1) |   '-2.0' |    '2.0' |   '-1.0' | '-4.0' |
 (2) |    '1.0' |   '-2.0' |    '1.0' |  '1.0' |
)

xviii. (sm) smult(a, b, sumr=None, chk=False, ret='a') -> matx | tuple[Decimal, ...]: Get the matrix as matx object after multiplication of a number

• a - matx
• b - matx
• sumr - bool/None

>>> mat = matutils.smult(0.1595, mat)
'''
    0.1595 - Number
    mat - matx object
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]____|___[2]___|___[3]____|
 (0) |  '-0.14' | '-0.126' | '1.795' |  '0.319' |
 (1) | '-0.319' |  '0.319' | '-0.16' | '-0.638' |
 (2) |   '0.16' | '-0.319' |  '0.16' |   '0.16' |
)

xix. (cm) smultfac(a, b, r=True, sumr=None, chk=True, ret='a') -> matx | tuple[Decimal, ...]: Get the matrix as a matx object after multiplication of a number to each row or column in matrix of a matx object

• a - list[ Decimal ] | tuple[Decimal, ...]
• b - matx
• r - bool
• sumr - bool/None

>>> mat = matutils.smultfac([1,2,3,10], mat, False)
'''
    [1,2,3,10]
    mat
    False
'''
>>> print(mat)
matx(
_____|___[0]____|___[1]____|___[2]____|___[3]____|
 (0) | '-0.140' | '-0.252' |  '5.385' |  '3.190' |
 (1) | '-0.319' |  '0.638' | '-0.480' | '-6.380' |
 (2) |  '0.160' | '-0.638' |  '0.480' |  '1.600' |
)

xx. (cm) mmult(a, b, t=(False, False), sumr=None, chk=True, ret='a') -> matx | tuple[Decimal, ...]: Get the matrix as a matx object after matrix multiplication for matrices of two matx objects

• a - matx
• b - matx
• t - tuple[bool, bool]
• sumr - bool/None

>>> mat = matutils.mmult(mat, mat1, (False, True))
'''
    mat, mat1 - matx objects
    (False, True) - Use transpose of 'mat1'
'''
>>> print(mat)
matx(
_____|____[0]____|____[1]____|____[2]____|
 (0) |  '74.843' |  '26.520' |  '16.478' |
 (1) | '-23.969' | '-11.809' | '-14.039' |
 (2) |   '9.450' |   '2.090' |   '4.002' |
)
>>> mat = matutils.mmult(mat1, mat2, (False, True), False)
>>> mat
(Decimal('137.5470'), Decimal('96.0'), Decimal('60.0'))

xxi. (sm) melmult(a, b, t=(False, False), sumr=None, chk=True, ret='a') -> matx | tuple[Decimal, ...]: Get the matrix as a matx object after multipling the elements at the same indexes of the matrices of two matx objects

• a - matx
• b - matx
• t - tuple[bool, bool]
• sumr - bool/None

>>> mat = matutils.melmult(mat1, mat2)
'''
    mat1, mat2 - matx objects
'''
>>> print(mat)
matx(
_____|___[0]___|___[1]___|___[2]____|__[3]___|
 (0) | '2.246' | '6.636' | '12.254' |  '3.0' |
 (1) |   '3.0' |  '15.0' |   '20.0' | '12.0' |
 (2) |   '6.0' |   '3.0' |    '2.0' |  '2.0' |
)

xxii. (sm) uldcompose(a, chk=True, ret='a') -> tuple[matx, matx, matx]: Get a tuple with matx objects of upper triangular, diagonal, and lower triangular matrices for a matrix of a matx

• a - matx

>>> u,l,d = matutils.uldcompose(matutils.gele(mat, [0,1,2], False))
'''
    matutils.gele(mat, [0,1,2], False) - matx object to decompose
'''
>>> print("{}{}{}".format(u,l,d))
matx(
_____|__[0]__|__[1]__|__[2]__|
 (0) | '0.0' | '3.0' | '6.0' |
 (1) | '0.0' | '0.0' | '3.0' |
 (2) | '0.0' | '0.0' | '0.0' |
)
matx(
_____|___[0]____|__[1]___|__[2]__|
 (0) |    '0.0' |  '0.0' | '0.0' |
 (1) |  '6.636' |  '0.0' | '0.0' |
 (2) | '12.254' | '20.0' | '0.0' |
)
matx(
_____|___[0]___|__[1]___|__[2]__|
 (0) | '2.246' | '15.0' | '2.0' |
)

xxiii. (cm) dpose(a, li, r=False, chk=True, ret='a') -> tuple[matx, ...]: Get a tuple of matrices after decomposing a matrix of a matx object along the row or column direction

• a - matx
• li - list[ int ] | tuple[int, ...]
• r - bool

>>> mats = matutils.dpose(mat, [2,2])
'''
    mat - matx object
    [2,2] - Number of columns to decompose
'''
>>> for i in mats:print(i, end="")
... 
matx(
_____|___[0]___|__[1]___|__[2]__|
 (0) | '2.246' |  '3.0' | '6.0' |
 (1) | '6.636' | '15.0' | '3.0' |
)
matx(
_____|___[0]____|__[1]___|__[2]__|
 (0) | '12.254' | '20.0' | '2.0' |
 (1) |    '3.0' | '12.0' | '2.0' |
)

xix. (sm) moperate(a, chk=True, ret='a') -> matx | tuple[matx, ...]: Returns the result after performing specified operations.

• a: tuple[str, tuple[matx|tuple, ...]]
  • 1^st element is the operation to perform
  • If no operation is to be performed then the elements are matx objects
  • Operations:
    • "add": Perform addition of matrices in matx objects
    • "sub": Perform subtraction of matrices in matx objects from matrix in first matx object
    • "mul": Perform multiplication of matrices in matx objects
    • "invse": Get the inverse matrices for the matrices in matx objects
    • "lxtox": Convert matrices into row matrices of rows of matrices in matx objects
    • "xtolx": Convert row matrices in matx objects into matrix with rows as the rows in row matrices
    • "tpose": Get the transpose matrix of matrices in matx objects

>>> mat1=matx([1.2311,2.23514,3.2365])
>>> mat2=matx([2.3254,5.2364,3.2541])
>>> mat3=matx([2.3121,2.3214,5.3211])
>>> mat=matutils.moperate(('add', (('xtolx', (mat1, mat2, mat3)), ('invse', (('xtolx', (mat2, mat1, mat3)),)))), True, 'a')
'''
    ('add', (('xtolx', (mat1, mat2, mat3)), ('invse', (('xtolx', (mat2, mat1, mat3)),)))) - Operation sequence
    True - Check arguments
     'a' - Ask to exit if error
'''
>>> print(mat)
matx(
_____|___[0]___|___[1]____|___[2]___|
 (0) | '1.811' | '-0.453' | '4.518' |
 (1) | '2.449' |  '5.878' | '2.788' |
 (2) | '2.006' |  '3.209' | '5.156' |
)

melutils

(c) melutils: Methods for operations on rows/columns in matrix of a matx object

i. (sm) add(a, li, r=False, chk=True, ret='a') -> matx: Get a matx object with matrix of rows as sum of elements in rows or columns in a matrix of a matx object

• a - matx
• li - tuple[tuple[int, ...]] | list[list[ int ]] | 'all'
• r - bool

>>> mat=matx([[1.0121, 2.3202, 5.3214], [2.3202, 4.2555, 6.3111], [5.3236, 3.5895, 4.2314]])
>>> mat1=melutils.add(mat, [[1,2],[0,2]], False, True, 'a')
'''
    mat - matx object
    [[1,2],[0,2]] - List of list of column indexes of columns to add
    False - For columns
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]___|___[1]____|___[2]___|
 (0) | '7.641' | '10.567' | '7.821' |
 (1) | '6.333' |  '8.631' | '9.555' |
)

>>> mat1=melutils.add(mat, [[1,2],[0,2]], True, True, 'a')
'''
    mat - matx object
    [[1,2],[0,2]] - List of list of row indexes of rows to add
    True - For rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]___|___[1]___|___[2]____|
 (0) | '7.644' | '7.846' | '10.542' |
 (1) | '6.336' | '5.910' |  '9.552' |
)

ii. (sm) mult(a, li, r=False, chk=True, ret='a') -> matx: Get a matx object with matrix of rows as multiplication of elements in rows or columns in a matrix of a matx object

• a - matx
• li - tuple[tuple[int, ...]] | list[list[ int ]] | 'all'
• r - bool

>>> mat1=melutils.mult(mat, [[1,2],[0,2]], False, True, 'a')
'''
    mat - matx object
    [[1,2],[0,2]] - List of list of column indexes of columns to multiply
    False - For columns
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]____|___[1]____|___[2]____|
 (0) | '12.345' |  '26.86' | '15.189' |
 (1) |  '5.385' | '14.642' | '22.526' |
)

>>> mat1=melutils.mult(mat, [[1,2],[0,2]], True, True, 'a')
'''
    mat - matx object
    [[1,2],[0,2]] - List of list of row indexes of rows to multiply
    True - For rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]____|___[1]____|___[2]____|
 (0) | '12.352' | '15.279' | '26.702' |
 (1) |  '5.388' |  '8.329' | '22.513' |
)

iii. (sm) pow(an, a, li, r=False, chk=True, ret='a') -> matx: Get a matx object with matrix of rows as exponentiation of elements in rows or columns in a matrix of a matx object

• an - tuple[Decimal, Decimal]
• a - matx
• li - tuple[int, ...] | list[ int ] | 'all'
• r - bool

>>> mat1=melutils.pow((2, 2), mat, [0,1], False, True, 'a')
'''
    (2, 2) - Factor to multiply and power
    mat - matx object
    [0,1] - List of column indexes of columns to exponentiate
    False - For columns
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]___|___[1]____|___[2]____|
 (0) | '4.097' |  '21.53' | '113.38' |
 (1) | '21.53' | '72.454' | '51.552' |
)

>>> mat1=melutils.pow((2, 2), mat, [0,1], True, True, 'a')
'''
    (2, 2) - Factor to multiply and power
    mat - matx object
    [0,1] - List of row indexes of rows to exponentiate
    True - For rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]___|___[1]____|____[2]____|
 (0) | '4.097' |  '21.53' | '113.252' |
 (1) | '21.53' | '72.454' | '159.315' |
)

iv. (sm) log(an, a, li, r=False, chk=True, ret='a') -> matx: Get a matx object with matrix of rows as logarithm of elements in rows or columns in a matrix of a matx object

• an - tuple[Decimal, Decimal]
• a - matx
• li - tuple[int, ...] | list[ int ] | 'all'
• r - bool

>>> mat1=melutils.log((2, 2), mat, [0,1], True, True, 'a')
'''
    (2, 2) - Factor to multiply and base
    mat - matx object
    [0,1] - List of row indexes of rows for logarithm
    True - For rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]___|___[1]___|___[2]___|
 (0) | '1.017' | '2.214' | '3.412' |
 (1) | '2.214' | '3.089' | '3.658' |
)

>>> mat1=melutils.log((2, 2), mat, [0,1], False, True, 'a')
'''
    (2, 2) - Factor to multiply and base
    mat - matx object
    [0,1] - List of column indexes of columns for logarithm
    False - For columns
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]___|___[1]___|___[2]___|
 (0) | '1.017' | '2.214' | '3.413' |
 (1) | '2.214' | '3.089' | '2.844' |
)

v. (sm) expo(an, a, li, r=False, chk=True, ret='a') -> matx: Get a matx object with matrix of rows as exponentiation of a number by elements in rows or columns in a matrix of a matx object

• an - tuple[Decimal, Decimal]
• li - tuple[int, ...] | list[ int ] | 'all'
• r - bool

>>> mat1=melutils.expo((2, 2), mat, [0,1], False, True, 'a')
'''
    (2, 2) - Number to exponentiate and factor to multiply
    mat - matx object
    [0,1] - List of column indexes of columns for exponentiation
    False - For columns
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]____|____[1]____|____[2]_____|
 (0) |  '4.067' |  '24.933' | '1604.602' |
 (1) | '24.933' | '365.063' |  '145.009' |
)

>>> mat1=melutils.expo((2, 2), mat, [0,1], True, True, 'a')
'''
    (2, 2) - Number to exponentiate and factor to multiply
    mat - matx object
    [0,1] - List of row indexes of rows for exponentiation
    True - For rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]____|____[1]____|____[2]_____|
 (0) |  '4.067' |  '24.933' | '1597.943' |
 (1) | '24.933' | '365.063' | '6303.774' |
)

vi. (sm) trig(n, a, li, r=False, f='cos', chk=True, ret='a') -> matx: Get a matx object with matrix of rows as trignometric function values for elements in rows or columns in a matrix of a matx object

• n - Decimal
• a - matx
• li - tuple[int, ...] | list[ int ] | 'all'
• r - bool
• f - str
  • 'sin', 'cos', 'tan', 'cosec', 'sec', 'cot', 'asin', 'acos', 'atan', 'asec', 'acosec', 'acot', 'sinh', 'cosh', 'tanh', 'sech', 'cosech', 'coth'

>>> mat1=melutils.trig(2, mat, [0,1], False, 'tan', True, 'a')
'''
    2 - Factor to multiply
    mat - matx object
    [0,1] - List of column indexes of columns for trignometric operation
    False - For columns
    'tan' - Use the "tan" function
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]____|___[1]____|___[2]___|
 (0) | '-2.053' | '13.790' | '2.760' |
 (1) | '13.790' | '-1.294' | '1.252' |
)

>>> mat1=melutils.trig(2, mat, [0,1], False, 'sinh', False, 'a')
'''
    2 - Factor to multiply
    mat - matx object
    [0,1] - List of column indexes of columns for trignometric operation
    False - For columns
    'sinh' - Use the "sinh" function
    False - Check arguments
    'a' - Ask to exit if error
'''
>>> print(mat1)
matx(
_____|___[0]____|____[1]_____|_____[2]_____|
 (0) |  '3.718' |   '51.767' | '21054.143' |
 (1) | '51.767' | '2487.050' |   '656.454' |
)

matstat

(c) matstat: Methods for statistical analysis using matx object

>>> from deciml_maths.matrix import matstat, matx
Imported deciml...
>>> from deciml_maths import setpr
>>> setpr(3)

i. (sm) amean(a, el='row', chk=True, ret='a') -> tuple[Decimal, ...] | Decimal: Get the arithmatic mean for all rows/columns/elements of matrix in matx object

• a - matx
• el - str
  • 'row'/'col'/'all'

>>> mat=matx([[1.2312, 2.321, 5.3214, 3.23651, 5.2514, 5.3652, 4.32145],[12, 13.2642, 5.3251, 8.2569, 6.25412, 7.25631, 1.23651]])
>>> arith_mean_rows = matstat.amean(mat, 'row', True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> arith_mean_rows
(Decimal('3.864'), Decimal('7.656'))
>>> arith_mean_cols = matstat.amean(mat, 'col', True, 'a')
'''
    mat - matx object
    'col' - For all columns
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> arith_mean_cols
(Decimal('6.616'), Decimal('7.793'), Decimal('5.323'), Decimal('5.747'), Decimal('5.753'), Decimal('6.311'), Decimal('2.779'))
>>> arith_mean = matstat.amean(mat, 'all', True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> arith_mean
Decimal('5.760')

ii. gmean(a, el='row', chk=True, ret='a') -> tuple[Decimal, ...] | Decimal: Get the geometric mean for all rows/columns/elements of matrix in matx object

• a - matx
• el - str
  • 'row'/'col'/'all'

>>> geo_mean_rows = matstat.gmean(mat, 'row', True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> geo_mean_rows
(Decimal('3.466'), Decimal('6.301'))
>>> geo_mean_cols = matstat.gmean(mat, 'col', True, 'a')
'''
    mat - matx object
    'col' - For all columns
    True - Check arguments
    'a' - Ask to exit if error
'''       
>>> geo_mean_cols
(Decimal('3.843'), Decimal('5.549'), Decimal('5.323'), Decimal('5.17'), Decimal('5.731'), Decimal('6.239'), Decimal('2.312'))
>>> geo_mean = matstat.gmean(mat, 'all', True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> geo_mean
Decimal('4.671')

iii. hmean(a, el='row', chk=True, ret='a') -> tuple[Decimal, ...] | Decimal: Get the harmonic mean for all rows/columns/elements of matrix in matx object

• a - matx
• el - str
  • 'row'/'col'/'all'

>>> harm_mean_rows = matstat.hmean(mat, 'row', True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> harm_mean_rows
(Decimal('0.426'), Decimal('0.635'))
>>> harm_mean = matstat.hmean(mat, 'all', True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> harm_mean
Decimal('0.255')

iv. qmean(a, el='row', chk=True, ret='a') -> tuple[Decimal, ...] | Decimal: Get the quadratic mean of all rows/columns/elements of matrix in matx object

• a - matx
• el - str
  • 'row'/'col'/'all'

>>> quad_mean_rows = matstat.qmean(mat, 'row', True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> quad_mean_rows
(Decimal('3.466'), Decimal('6.301'))
>>> quad_mean = matstat.qmean(mat, 'all', True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> quad_mean
Decimal('4.671')

v. var(a, el='row', samp=True, chk=True, ret='a') -> tuple[Decimal, ...] | Decimal: Get the sample or population variance of all rows/columns/elements of matrix in matx object

• a - matx
• el - str
  • 'row'/'col'/'all'
• samp - bool

>>> samp_var_rows = matstat.var(mat, 'row', True, True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Sample variance
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> samp_var_rows
(Decimal('2.703'), Decimal('16.574'))
>>> popul_var = matstat.var(mat, 'all', False, True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    False - Population variance
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> popul_var
Decimal('11.857')

vi. sd(a, el='row', samp=True, chk=True, ret='a') -> tuple[Decimal, ...] | Decimal: Get the sample or population standard deviation for all rows/columns/elements of matrix in matx object

• a - matx
• el - str
  • 'row'/'col'/'all'
• samp - bool

>>> std_dev_rows = matstat.sd(mat, 'row', True, True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Sample standard deviation
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> std_dev_rows
(Decimal('1.644'), Decimal('4.071'))
>>> popul_std_dev = matstat.sd(mat, 'all', False, True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    False - Population standard deviation
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> popul_std_dev
Decimal('3.443')

vii. median(a, el='row', chk=True, ret='a') -> tuple[Decimal, ...] | Decimal

• a - matx
• el - str
  • 'row'/'col'/'all'

>>> median_rows = matstat.median(mat, 'row', True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> median_rows
(Decimal('4.321'), Decimal('7.256'))
>>> median = matstat.median(mat, 'all', True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> median
Decimal('5.323')

viii. mode(a, el='row', chk=True, ret='a') -> tuple[dict, ...] | dict

• a - matx
• el - str
  • 'row'/'col'/'all'

>>> mat = matx([[1,2,4,6,4,3,4,5,6,4,3,4,5,6,4,4,4],[4,5,6,23,4,65,7,4,23,4,5,6,8,6,4,2,5]])
>>> mode_rows = matstat.mode(mat, 'row', True, 'a')
'''
    mat - matx object
    'row' - For all rows
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> mode_rows
({'values': (Decimal('4.0'),), 'mode': 8}, {'values': (Decimal('4.0'),), 'mode': 5})
>>> mode = matstat.mode(mat, 'all', True, 'a')
'''
    mat - matx object
    'all' - For all elements in matrix
    True - Check arguments
    'a' - Ask to exit if error
'''
>>> mode
{'values': (Decimal('4.0'),), 'mode': 13}

Data

data

(o) data: Data object to store data values for independent (x) and dependent (y) variables

>>> from deciml_maths.data import data
>>> dat = data([[1,2,3,4],[2,3,4,5],[3,4,5,6],[5,6,7,4],[9,8,7,0]], [1,2,3,4,5])

i. (s) x_labels: Set the x labels

>>> dat.x_labels = ["A", "B", "C", "D"]

ii. (g) x_labels -> tuple[str, ...]: Get the x labels

>>> dat.x_labels
('A', 'B', 'C', 'D')

iii. (s) y_label: Set the y label

>>> dat.y_label = "Y Value"

iv. (g) y_label -> str: Get the y label

>>> dat.y_label
'Y Value'

v. (f) get_label_index(labels) -> tuple[int, ...]: Get the index

• labels - tuple[str, ...] | list[str]

>>> dat.get_label_index(["A", "C", "D"])
'''
    ["A", "C", "D"] - List of column names
'''
[0, 2, 3]

vi. get data object using index slicing

>>> dat[:,["A","B"]]
data[
___|____A_____|____B_____||_Y Value__|
 0 |   1.0    |   2.0    ||   1.0    |
 1 |   2.0    |   3.0    ||   2.0    |
 2 |   3.0    |   4.0    ||   3.0    |
 3 |   5.0    |   6.0    ||   4.0    |
 4 |   9.0    |   8.0    ||   5.0    |
]
>>> dat[:,0]
data[
___|____A_____||_Y Value__|
 0 |   1.0    ||   1.0    |
 1 |   2.0    ||   2.0    |
 2 |   3.0    ||   3.0    |
 3 |   5.0    ||   4.0    |
 4 |   9.0    ||   5.0    |
]
>>> dat[0,:]
data[
___|____A_____|____B_____|____C_____|____D_____||_Y Value__|
 0 |   1.0    |   2.0    |   3.0    |   4.0    ||   1.0    |
]
>>> dat[1:4,:]
data[
___|____A_____|____B_____|____C_____|____D_____||_Y Value__|
 0 |   2.0    |   3.0    |   4.0    |   5.0    ||   2.0    |
 1 |   3.0    |   4.0    |   5.0    |   6.0    ||   3.0    |
 2 |   5.0    |   6.0    |   7.0    |   4.0    ||   4.0    |
]

vii. (g) data -> tuple[matx, tuple[Decimal, ...]]: Get the data as a tuple with matx object of x values and tuple of y values

>>> dat.data
(matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '4.0' |
 (1) | '2.0' | '3.0' | '4.0' | '5.0' |
 (2) | '3.0' | '4.0' | '5.0' | '6.0' |
 (3) | '5.0' | '6.0' | '7.0' | '4.0' |
 (4) | '9.0' | '8.0' | '7.0' | '0.0' |
)
, (Decimal('1.0'), Decimal('2.0'), Decimal('3.0'), Decimal('4.0'), Decimal('5.0')))

viii. (g) datalen -> int: Get the length of data

>>> dat.datalen
5

ix. (g) xvars -> int: Get the number of x variables

>>> dat.xvars
4

x. (g) pdata: Print the data

>>> dat.pdata
data[
  0: '1.0', '2.0', '3.0', '4.0' | 1.0
  1: '2.0', '3.0', '4.0', '5.0' | 2.0
  2: '3.0', '4.0', '5.0', '6.0' | 3.0
  3: '5.0', '6.0', '7.0', '4.0' | 4.0
  4: '9.0', '8.0', '7.0', '0.0' | 5.0
]

xi. (f) getax() -> matx: Get all x values as a matx object

>>> dat.getax()
matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '4.0' |
 (1) | '2.0' | '3.0' | '4.0' | '5.0' |
 (2) | '3.0' | '4.0' | '5.0' | '6.0' |
 (3) | '5.0' | '6.0' | '7.0' | '4.0' |
 (4) | '9.0' | '8.0' | '7.0' | '0.0' |
)

xii. (f) getay() -> tuple[Decimal, ...]: Get all y values as a tuple

>>> dat.getay()
(Decimal('1.0'), Decimal('2.0'), Decimal('3.0'), Decimal('4.0'), Decimal('5.0'))

xiii. (f) getx(li, chk=True, ret='a') -> matx: Get the x values at indexes

• li - list[int] | tuple[int, ...]
• chk - bool
• ret - str

>>> dat.getx([0, 1, 3, 4])
'''
    [0, 1, 3, 4] - Row indexes
'''
matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '4.0' |
 (1) | '2.0' | '3.0' | '4.0' | '5.0' |
 (2) | '5.0' | '6.0' | '7.0' | '4.0' |
 (3) | '9.0' | '8.0' | '7.0' | '0.0' |
)

xiv. (f) gety(li, chk=True, ret='a') -> tuple[Decimal, ...]: Get the y values at indexes

• li - list[int] | tuple[int, ...]
• chk - bool
• ret - str

>>> dat.gety([0, 1, 3, 4])
'''
    [0, 1, 3, 4] - Row indexes
'''
(Decimal('1.0'), Decimal('2.0'), Decimal('4.0'), Decimal('5.0'))

xv. (f) getd(li, chk=True, ret='a') -> tuple[matx, tuple[Decimal, ...]]: Get a tuple with matx object of x values and tuple of y values for indexes

• li - list[int] | tuple[int, ...]
• chk - bool
• ret - str

>>> dat.getd([0, 1, 3, 4])
'''
    [0, 1, 3, 4] - Row indexes
'''
(matx(
_____|__[0]__|__[1]__|__[2]__|__[3]__|
 (0) | '1.0' | '2.0' | '3.0' | '4.0' |
 (1) | '2.0' | '3.0' | '4.0' | '5.0' |
 (2) | '5.0' | '6.0' | '7.0' | '4.0' |
 (3) | '9.0' | '8.0' | '7.0' | '0.0' |
)
, (Decimal('1.0'), Decimal('2.0'), Decimal('4.0'), Decimal('5.0')))

xvi. (f) getlx(li, chk=True, ret='a') -> matx: Get the x values as a matx object for x variable at indexes

• li - list[int] | tuple[int, ...]
• chk - bool
• ret - str

>>> dat.getlx(dat.get_label_index(["A", "C", "D"]))
'''
    dat.get_label_index(["A", "C", "D"]) - Column indexes
'''
matx(
_____|__[0]__|__[1]__|__[2]__|
 (0) | '1.0' | '3.0' | '4.0' |
 (1) | '2.0' | '4.0' | '5.0' |
 (2) | '3.0' | '5.0' | '6.0' |
 (3) | '5.0' | '7.0' | '4.0' |
 (4) | '9.0' | '7.0' | '0.0' |
)

datautils

(c) datautils: Methods to use with data object

>>> from deciml_maths.data import datautils

i. dataval(d, x, chk=True, ret='a') -> data: Add a x variable with constant value to data

• d - data
• x - Decimal
• chk - bool
• ret - str

>>> datautils.dataval(dat, 12.123)
'''
    dat - data object
    12.123 - Column's values
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____||____Y_____|
 0 |  12.123  |   1.0    |   2.0    |   3.0    |   4.0    ||   1.0    |
 1 |  12.123  |   2.0    |   3.0    |   4.0    |   5.0    ||   2.0    |
 2 |  12.123  |   3.0    |   4.0    |   5.0    |   6.0    ||   3.0    |
 3 |  12.123  |   5.0    |   6.0    |   7.0    |   4.0    ||   4.0    |
 4 |  12.123  |   9.0    |   8.0    |   7.0    |   0.0    ||   5.0    |
]

ii. addata(d, *a, chk=True, ret='a') -> data: Add x variables to data object

• d - data
• *a - matx
• chk - bool
• ret - str

>>> datautils.addata(dat, matx([[1],[3],[5],[7],[9]]), matx([[1,1],[2,2],[3,3],[4,4],[5,5]]))
'''
    dat - data object
    matx([[1],[3],[5],[7],[9]]), matx([[1,1],[2,2],[3,3],[4,4],[5,5]]) - matx objects
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____|____5_____|____6_____||____Y_____|
 0 |   1.0    |   2.0    |   3.0    |   4.0    |   1.0    |   1.0    |   1.0    ||   1.0    |
 1 |   2.0    |   3.0    |   4.0    |   5.0    |   3.0    |   2.0    |   2.0    ||   2.0    |
 2 |   3.0    |   4.0    |   5.0    |   6.0    |   5.0    |   3.0    |   3.0    ||   3.0    |
 3 |   5.0    |   6.0    |   7.0    |   4.0    |   7.0    |   4.0    |   4.0    ||   4.0    |
 4 |   9.0    |   8.0    |   7.0    |   0.0    |   9.0    |   5.0    |   5.0    ||   5.0    |
]

iii. datalx(d, li, chk=True, ret='a') -> data: Get a data object with x variables at indexes

• d - data
• li - list[int] | tuple[int,...]
• chk - bool
• ret - str

>>> datautils.datalx(dat, [0,1,3])
'''
    dat - data object
    [0,1,3] - Column indexes
'''
data[
___|____0_____|____1_____|____2_____||____Y_____|
 0 |   1.0    |   2.0    |   4.0    ||   1.0    |
 1 |   2.0    |   3.0    |   5.0    ||   2.0    |
 2 |   3.0    |   4.0    |   6.0    ||   3.0    |
 3 |   5.0    |   6.0    |   4.0    ||   4.0    |
 4 |   9.0    |   8.0    |   0.0    ||   5.0    |
]

iv. multlx(d, li, chk=True, ret='a') -> data: Get a data object with multiplication of x variables at indexes as added x variables

• d - data
• li - list[list[int]] | tuple[tuple[int,...]] | str
• chk - bool
• ret - str

>>> datautils.multlx(dat, [[0,1],[1,2]])
'''
    dat - data object
    [[0,1],[1,2]] - Columns to multiply
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____|____5_____||____Y_____|
 0 |   1.0    |   2.0    |   3.0    |   4.0    |   2.0    |   6.0    ||   1.0    |
 1 |   2.0    |   3.0    |   4.0    |   5.0    |   6.0    |   12.0   ||   2.0    |
 2 |   3.0    |   4.0    |   5.0    |   6.0    |   12.0   |   20.0   ||   3.0    |
 3 |   5.0    |   6.0    |   7.0    |   4.0    |   30.0   |   42.0   ||   4.0    |
 4 |   9.0    |   8.0    |   7.0    |   0.0    |   72.0   |   56.0   ||   5.0    |
]

v. aaddlx(d, li, chk=True, ret='a') -> data: Get a data object with addition of x variables at indexes as added x variables

• d - data
• li - list[list[int]] | tuple[tuple[int,...]] | str
• chk - bool
• ret - str

>>> datautils.addlx(dat, [[0,1],[1,2]])
'''
    dat - data object
    [[0,1],[1,2]] - Columns to add
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____|____5_____||____Y_____|
 0 |   1.0    |   2.0    |   3.0    |   4.0    |   3.0    |   5.0    ||   1.0    |
 1 |   2.0    |   3.0    |   4.0    |   5.0    |   5.0    |   7.0    ||   2.0    |
 2 |   3.0    |   4.0    |   5.0    |   6.0    |   7.0    |   9.0    ||   3.0    |
 3 |   5.0    |   6.0    |   7.0    |   4.0    |   11.0   |   13.0   ||   4.0    |
 4 |   9.0    |   8.0    |   7.0    |   0.0    |   17.0   |   15.0   ||   5.0    |
]

vi. powlx(d, an, li, chk=True, ret='a') -> data: Get a data object with exponentiated x variables as added x variables

• d - data
• an - tuple[Decimal, Decimal]
• li - list[int] | tuple[int,...] | str
• chk - bool
• ret - str

>>> datautils.powlx(dat, (2, 3), [0,1,2])
'''
    dat - data object
    (2, 3) - Multiplication factor and exponent
    [0,1,2] - Column indexes
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____|____5_____|____6_____||____Y_____|
 0 |   1.0    |   2.0    |   3.0    |   4.0    |   8.0    |   64.0   |  216.0   ||   1.0    |
 1 |   2.0    |   3.0    |   4.0    |   5.0    |   64.0   |  216.0   |  512.0   ||   2.0    |
 2 |   3.0    |   4.0    |   5.0    |   6.0    |  216.0   |  512.0   |  1000.0  ||   3.0    |
 3 |   5.0    |   6.0    |   7.0    |   4.0    |  1000.0  |  1728.0  |  2744.0  ||   4.0    |
 4 |   9.0    |   8.0    |   7.0    |   0.0    |  5832.0  |  4096.0  |  2744.0  ||   5.0    |
]

vii. loglx(d, an, li, chk=True, ret='a') -> data: Get a data object with logarithm of x variables as added x variables

• d - data
• an - tuple[Decimal,Decimal]
• li - list[int] | tuple[int,...] | str
• chk - bool
• ret - str

>>> datautils.loglx(dat, (2, 2), [0,1,2])
'''
    dat - data object
    (2, 2) - Factor and base
    [0,1,2] - Column indexes
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____|____5_____|____6_____||____Y_____|
 0 |   1.0    |   2.0    |   3.0    |   4.0    |   1.0    |   2.0    |  2.585   ||   1.0    |
 1 |   2.0    |   3.0    |   4.0    |   5.0    |   2.0    |  2.585   |   3.0    ||   2.0    |
 2 |   3.0    |   4.0    |   5.0    |   6.0    |  2.585   |   3.0    |  3.322   ||   3.0    |
 3 |   5.0    |   6.0    |   7.0    |   4.0    |  3.322   |  3.585   |  3.807   ||   4.0    |
 4 |   9.0    |   8.0    |   7.0    |   0.0    |   4.17   |   4.0    |  3.807   ||   5.0    |
]

viii. expolx(d, an, li, chk=True, ret='a') -> data: Get a data object with exponentiation using x variables as added x variables

• d - data
• an - tuple[Decimal,Decimal]
• li - list[int] | tuple[int,...] | str
• chk - bool
• ret - str

>>> datautils.expolx(dat, (2, 2), [0,1,2])
'''
    dat - data object
    (2, 2) - Base and factor
    [0,1,2] - Column indexes
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____|____5_____|____6_____||____Y_____|
 0 |   1.0    |   2.0    |   3.0    |   4.0    |   4.0    |   16.0   |   64.0   ||   1.0    |
 1 |   2.0    |   3.0    |   4.0    |   5.0    |   16.0   |   64.0   |  256.0   ||   2.0    |
 2 |   3.0    |   4.0    |   5.0    |   6.0    |   64.0   |  256.0   |  1024.0  ||   3.0    |
 3 |   5.0    |   6.0    |   7.0    |   4.0    |  1024.0  |  4096.0  | 16384.0  ||   4.0    |
 4 |   9.0    |   8.0    |   7.0    |   0.0    | 262144.0 | 65536.0  | 16384.0  ||   5.0    |
]

ix. triglx(d, n, li, f='cos', chk=True, ret='a') -> data: Ge a data object with x variables after operation with a trignometric function as added x variables

• d - data
• n - Decimal
• li - list[int] | tuple[int,...] | str
• f - str
  • 'sin', 'cos', 'tan', 'cosec', 'sec', 'cot', 'asin', 'acos', 'atan', 'asec', 'acosec', 'acot', 'sinh', 'cosh', 'tanh', 'sech', 'cosech', 'coth'
• chk - bool
• ret - str

>>> datautils.triglx(dat, 2, [0,1,2], 'cos')
'''
    dat - data object
    2 - Factor
    [0,1,2] - Column indexes
    'cos' - Trignometric operation
'''
data[
___|____0_____|____1_____|____2_____|____3_____|____4_____|____5_____|____6_____||____Y_____|
 0 |   1.0    |   2.0    |   3.0    |   4.0    |  -0.416  |  -0.654  |  0.960   ||   1.0    |
 1 |   2.0    |   3.0    |   4.0    |   5.0    |  -0.654  |  0.960   |  -0.146  ||   2.0    |
 2 |   3.0    |   4.0    |   5.0    |   6.0    |  0.960   |  -0.146  |  -0.839  ||   3.0    |
 3 |   5.0    |   6.0    |   7.0    |   4.0    |  -0.839  |  0.844   |  0.137   ||   4.0    |
 4 |   9.0    |   8.0    |   7.0    |   0.0    |  0.660   |  -0.958  |  0.137   ||   5.0    |
]

Functions

axn

(o) axn: Get the object for a exponentiated variable

• __f1 - Decimal
• __f2 - Decimal
• ret - str

>>> from deciml_maths.functions import axn
>>> fun = axn(2,5.5)
'''
    2 - Coefficient
    5.5 - Power
'''

i. (f) f(__a)

• __a: The value of the variable

>>> fun.f(2)
Decimal('90.51')

ii. (f) df(__a)

• __a: The value of the variable
• __pr: The precision

>>> fun.df(2)
Decimal('248.901')

iii. (g) getf

>>> fun.getf
(Decimal('2.0'), Decimal('5.5'))

iv. (g) getdf

>>> fun.getdf
(Decimal('11.0'), Decimal('4.5'))

poly

(o) poly: Get the object for a polynomial function

• *__f - tuple[Decimal,Decimal]|list[Decimal]
• ret - str

>>> from deciml_maths.functions import poly
fun = poly((Decimal('2.0'), Decimal('3.0')), (Decimal('2.0'), Decimal('5.5')))
'''
    (Decimal('2.0'), Decimal('3.0')), (Decimal('2.0'), Decimal('5.5')) - Coefficients and exponent
'''

i. (f) f(__a)

• __a: The value of the variable

>>> fun.f(2)
Decimal('106.51')

ii. (f) df(__a)

• __a: The value of the variable

>>> fun.df(2)
Decimal('272.902')

iii. (g) getf

>>> fun.getf
((Decimal('2.0'), Decimal('3.0')), (Decimal('2.0'), Decimal('5.5')))

iv. (g) getdf

>>> fun.getdf
((Decimal('6.0'), Decimal('2.0')), (Decimal('11.0'), Decimal('4.5')))

apolyn

(o) apolyn: Get the object for a exponentiated polynomial function

• __a - Decimal
• __n - Decimal
• *__f - tuple[Decimal,Decimal]|list[Decimal]
• ret - str

from deciml_maths.functions import apolyn
f = apolyn('5.5', '2.5', (2.3, 4), (5, 3))
'''
    '5.5' - Coefficient
    '2.5' - Exponent
    (2.3, 4), (5, 3) - Coefficients and exponent
'''

i. (f) f(__a, __pr=getpr())

• __a: The value of the variable
• __pr: The precision

Decimal('284292.721')

ii. (f) df(__a, __pr=getpr())

• __a: The value of the variable
• __pr: The precision

Decimal('1236377.205')

iii. (g) getf

((Decimal('5.5'), Decimal('2.5')), ((Decimal('2.3'), Decimal('4.0')), (Decimal('5.0'), Decimal('3.0'))))

iv. (g) getdf

((Decimal('13.75'), Decimal('1.5')), ((Decimal('2.3'), Decimal('4.0')), (Decimal('5.0'), Decimal('3.0'))), ((Decimal('9.20'), Decimal('3.0')), (Decimal('15.0'), Decimal('2.0'))))