Function comb

Synopse

Create a grid of impulses image.

g = comb(shape, delta, offset)
- g: Image.

shape: Image. output image dimensions (1-D, 2-D or 3-D).
delta: Image. interval between the impulses in each dimension (1-D, 2-D or 3-D).
offset: Image. offset in each dimension (1-D, 2-D or 3-D).



In [1]:

    
import numpy as np
def comb(shape, delta, offset):

    shape = np.array(shape)
    assert shape.size <= 3
    g = np.zeros(shape) 
    if shape.size == 1:
        g[offset::delta] = 1
    elif shape.size == 2:
        g[offset[0]::delta[0], offset[1]::delta[1]] = 1
    elif shape.size == 3:
        g[offset[0]::delta[0], offset[1]::delta[1], offset[2]::delta[2]] = 1
    return g

Examples



In [1]:

    
testing = (__name__ == "__main__")
if testing:
    ! jupyter nbconvert --to python comb.ipynb
    import numpy as np
    import sys,os
    import matplotlib.image as mpimg
    ia898path = os.path.abspath('../../')
    if ia898path not in sys.path:
        sys.path.append(ia898path)
    import ia898.src as ia









    



[NbConvertApp] Converting notebook comb.ipynb to python
[NbConvertApp] Writing 3044 bytes to comb.py

Example 1



In [2]:

    
if testing:
    u1 = ia.comb(10, 3, 2)
    print('u1=',u1)
    u2 = ia.comb((10,), 3, 2)
    print('u2=',u2)









    



u1= [ 0.  0.  1.  0.  0.  1.  0.  0.  1.  0.]
u2= [ 0.  0.  1.  0.  0.  1.  0.  0.  1.  0.]

Example 2



In [3]:

    
if testing:
    u3 = ia.comb((7,9), (1,2), (0,1))
    print('u3=\n',u3)









    



u3=
 [[ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
 [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
 [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
 [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
 [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
 [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
 [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]]

Example 3



In [4]:

    
if testing:
    u4 = ia.comb((4,5,9), (2,1,2), (1,0,1))
    print(u4)









    



[[[ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]]

 [[ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]]

 [[ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]
  [ 0.  0.  0.  0.  0.  0.  0.  0.  0.]]

 [[ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]
  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.]]]

Equation

One dimension:

$$ \begin{matrix} u(x)=\sum _{i=0}^{\infty}\delta \left( x-\left( ki+o\right) \right)\\ x\in [0,S_0-1] \end{matrix} $$

$$\begin{matrix} where\quad \delta (i)=\left\{ \begin{array}{ll} 1, & i=0\\ 0, & otherwise \end{array}\right. \end{matrix} $$

N-dimension:

$$ \begin{matrix} u\left( x_{0},x_{1},\cdots ,x_{N-1}\right) =\sum _{i_{0}=0}^{\infty}\sum _{i_{1}=0}^{\infty}\cdots \sum _{i_{N-1}=0}^{\infty}\delta \left( x_{0}-\left( k_{0}i_{0}+o_{0}\right) ,x_{1}-\left( k_{1}i_{1}+o_{1}\right) ,\cdots ,x_{N-1}-\left(k_{N-1}i_{N-1}+o_{N-1}\right) \right)\\ \left( x_{0},x_{1},\cdots ,x_{N-1}\right) \in \left[ \left( 0,0,\cdots ,0\right) ,\left( S_{0}-1,S_{1}-1,\cdots ,S_{N-1}-1\right) \right] \end{matrix} $$

$$\begin{matrix} where\quad \delta (i_0,i_1,\ldots,i_{N-1})=\left\{ \begin{array}{ll} 1, & i_0=i_1=i_2=\ldots=i_{N-1}=0\\ 0, & otherwise \end{array}\right. \end{matrix} $$



In [5]:

    
if testing:
    print('testing comb')
    print(repr(ia.comb(10, 3, 2)) == repr(np.array(
           [0., 0., 1., 0., 0., 1., 0., 0., 1., 0.])))
    print(repr(ia.comb((7,9), (3,4), (3,2))) == repr(np.array(
          [[0., 0., 0., 0., 0., 0., 0., 0., 0.],
           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
           [0., 0., 1., 0., 0., 0., 1., 0., 0.],
           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
           [0., 0., 1., 0., 0., 0., 1., 0., 0.]])))









    



testing comb
True
True



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