dnncTensorFunctions.md

DNNC functions to mimic numpy using Eigen

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Most remarkable fluid features (Array creation):

Legends ✔️: ToBeDone, ✅:Done, 🚫:Rejected

✅a = numpy.array([1,2,3])

✅numpy.array([1,2]) #1D
✅numpy.array([[1,2],[10,20]]) #2D

# For complex types
🚫numpy.array([1,2], dtype=complex) #1D complex

# For randomized 3d array
🚫Array3d = numpy.random.randint(10, size=(3, 4, 5))

# generate uniformly distributed numbers
✅a = numpy.random.rand(3,2)   #(3 rows, 2 cols)

# Create empty 2D array (2 rows, 3 columns)
✅a_empty = numpy.empty(2,3)

# Create 0 initiallized 2D array (3 rows, 2 columns)
✅numpy.zeros(3,2) 

# Create 1 initiallized 2D array (3 rows, 2 columns)
✅numpy.ones(3,2) 

# Create a range of elements
✅array = numpy.arange(3) # array will contain 0,1,2

# Create a Numpy array from Python sequence of elements
✔️a = numpy.asarray([1,2])

# Create an array with values that are evenly spaced
✔️a = numpy.array(0,6,2) # create 0-5, 2 apart, returns [0,2,4]

# Ccreate an array where the values are linearly spaced between an interval    numpy.linspace(first, last, number)
✔️a = numpy.linspace(0,10,5) # returns [0,2.5,5,7.5,10]

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Some advanced features (Array manipulation)

# Add
a = [3,4,5]
a = numpy.append(a, [1,2]) #returns [3,4,5,1,2]

#Join
numpy.concatenate(a,b)
numpy.stack(a,b)
numpy.hstack(a,b)
numpy.vstack(a,b)

# Delete
a = numpy.delete(array,2) # 2 is going to be deleted from the array

# Sort
numpy.sort(array1, axis=1, kind = 'quicksort', order ='column name')

# Deep copy
new_array = numpy.copy(array)

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Array functions and attributes

Shape and Dimension

# Shape
array = numpy.array([[..],[..]])
array.shape

# Reshape by setting shape property
array.shape = (1,2) # (1 row, 2 columns)
# resize(x,y) can also be used to resize an array

# Dimensions of an array:
array.dim

# Find length of each element of an array:
array.itemsize

Slicing

array = numpy.arange(100)

# Get 3rd element:
array[2]

# Get items within indexes
array[3:5] #3 is start, 5 is end

# Get 3-10 element, step size 4 increments:
array[2:9:4]

# Get all elements from 2nd element onwards
array[1:]

# Can also pass in N-Dimensional Index
array[[0,1],[1,2]]

# Get all NAN elements
array[numpy.isnan(array)]

# Using where()
numpy.where(array > 5) # will return all elements that meet the criteria

Broadcasting

# 5 rows, 3 columns array
bigger_array = arange(5,3) 

# 5 rows, 1 column array
smaller_array = arange(5)

final_array = bigger_array + smaller_array

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Mathematical functions

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Can be done through DNNC opearators:

• ✔️ numpy.sin()
• ✔️ numpy.cos()
• ✔️ numpy.tan()
• ✔️ numpy.sinh()
• ✔️ numpy.cosh()
• ✔️ numpy.tanh()
• ✔️ numpy.arcsin()
• ✔️ numpy.arccos()
• ✔️ numpy.arctan()
• ✔️ numpy.arcsinh()
• ✔️ numpy.arccosh()
• ✔️ numpy.arctanh()
• ✔️ numpy.add()
• ✔️ numpy.subtract()
• ✔️ numpy.cross()
• ✔️ numpy.divide()
• ❌ numpy.power()
• ✔️ numpy.round()
• ✔️ numpy.floor()
• ✔️ numpy.ceil()
• ✔️ numpy.exp()
• ✔️ numpy.log()
• ✔️ numpy.sqrt()
• ✔️ numpy.absolute()
• ❌ numpy.clip()
• ❌ numpy.convolve()

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Have to be implemented:

• numpy.dot()

  dot product of 2 arrays

• numpy.inner()

  inner product of 2 arrays

• numpy.determinant()

  determinant of an array

• numpy.transpose()

  permute the dimensions of matrix

• numpy.inverse()

  inverse of a matrix

• numpy.solve()

  solves matrix equation

• numpy.multiply()

  element wise multiplication of 2 arrays (not to be confused with matrix multiplication)

• numpy.true_divide()

  element wise division of 2 arrays (uses / in python)

• numpy.floor_divide()

  element wise division of 2 arrays (uses // in python)

• numpy.degrees() / numpy.rad2deg()

  radian to degree converter

• numpy.radians() / numpy.deg2rad()

  degree to radian converter

• numpy.median()

  Finds the median

• numpy.average()

  Finds average

• numpy.mean()

  Finds mean

• numpy.var()

  Finds variance

• numpy.rint()

  round elements of the array to the nearest integer

• numpy.fix()

  round elements of the array to the nearest integer towards zero

• numpy.trunc()

  returns the truncated value of the elements of array

• numpy.log10()

  return the base 10 logarithm of the input array, element-wise

• numpy.log2()

  return the base 10 logarithm of the input array, element-wise

• numpy.expm1()

  calculate exp(x) – 1 for all elements in the array

• numpy.exp2()

  calculate (2^p) for all p in the input array

• numpy.logaddexp()

  logarithm of the sum of exponentiations of the inputs

• numpy.logaddexp2()

  logarithm of the sum of exponentiations of the inputs in base-2

• numpy.reciprocal()

  calculate (1/x) for all x in the input array

• numpy.positive()

  make every element positive

• numpy.negetive()

  make every element negetive

• numpy.remainder()

  return element wise remainder of division

• numpy.divmod()

  return element-wise quotient and remainder simultaneously

• numpy.isreal()

  test element-wise whether it is a real number or not(not infinity or not Not a Number) and return the result as a boolean array

• numpy.conj()

  The conjugate of a complex number is obtained by changing the sign of its imaginary part. If the complex number is (2+5j) then its conjugate is (2-5j)

• numpy.cbrt()

  mathematical function helps user to calculate cube root of x for all x being the array elements

• numpy.square()

  return the non-negative square-root of an array, element-wise

• numpy.maximum()

  find the element-wise maximum of array elements

• numpy.minimum()

  find the element-wise minimum of array elements

• numpy.interp()

  returns the one-dimensional piecewise linear interpolant to a function with given discrete data points (xp, fp), evaluated at x

• numpy.nan_to_num()

  replace NaN with zero and infinity with large finite numbers

• numpy.real_if_close()

  if complex input returns a real array if complex parts are close to zero

• numpy.heaviside()

  heaviside(x1, x2) = {0 if x1 < 0}, {x2 if x1 == 0}. {1 if x1 > 0}

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Resource:

• Basic Functions are taken from Medium
• Mathematical functions are taken from GeeksForGeeks