Shape Manipulation

Changing the shape of any array

numpy

hmatrix

>>> a = np.floor(10*np.random.random((3,4)))
>>> a
array([[ 2.,  8.,  0.,  6.],
       [ 4.,  5.,  1.,  1.],
       [ 8.,  9.,  3.,  6.]])
>>> a.shape
(3, 4)
>>> a.ravel()  # returns the array, flattened
array([ 2.,  8.,  0.,  6.,  4.,  5.,  1.,  1.,  8.,  9.,  3.,  6.])
>>> a.reshape(6,2)  # returns the array with a modified shape
array([[ 2.,  8.],
       [ 0.,  6.],
       [ 4.,  5.],
       [ 1.,  1.],
       [ 8.,  9.],
       [ 3.,  6.]])
>>> a.T  # returns the array, transposed
array([[ 2.,  4.,  8.],
       [ 8.,  5.,  9.],
       [ 0.,  1.,  3.],
       [ 6.,  1.,  6.]])
>>> a.T.shape
(4, 3)
>>> a.shape
(3, 4)

>>> import Numeric.LinearAlgebra.HMatrix (Seed, RandDist(..), randomVector, rand)
>>> let rand' seed r c = reshape c (randomVector seed Uniform (r*c))
>>> let a = cmap (floor . (*10)) (rand' 1 3 4) :: Matrix Z
>>> a
(3><4)
 [ 2, 8, 0, 6
 , 4, 5, 1, 1
 , 8, 9, 3, 6 ]
>>> size a
(3,4)
>>> flatten a
[2,8,0,6,4,5,1,1,8,9,3,6]
>>> ((reshape 2) . flatten) a
(6><2)
 [ 2, 8
 , 0, 6
 , 4, 5
 , 1, 1
 , 8, 9
 , 3, 6 ]
>>> tr a
(4><3)
 [ 2, 4, 8
 , 8, 5, 9
 , 0, 1, 3
 , 6, 1, 6 ]
>>> size (tr a)
(4,3)
>>> size a
(3,4)

numpy

hmatrix

>>> a
array([[ 2.,  8.,  0.,  6.],
       [ 4.,  5.,  1.,  1.],
       [ 8.,  9.,  3.,  6.]])
>>> a.resize((2,6))
>>> a
array([[ 2.,  8.,  0.,  6.,  4.,  5.],
       [ 1.,  1.,  8.,  9.,  3.,  6.]])
>>> a.reshape(3,-1)
array([[ 2.,  8.,  0.,  6.],
       [ 4.,  5.,  1.,  1.],
       [ 8.,  9.,  3.,  6.]])

>>> a
(3><4)
 [ 2, 8, 0, 6
 , 4, 5, 1, 1
 , 8, 9, 3, 6 ]
>>> let a' = ((reshape 6) . flatten) a
>>> a'
(2><6)
 [ 2, 8, 0, 6, 4, 5
 , 1, 1, 8, 9, 3, 6 ]
>>> (tr . (reshape 3) . flatten . tr) a
(3><4)
 [ 2, 8, 0, 6
 , 4, 5, 1, 1
 , 8, 9, 3, 6 ]

Stacking together different arrays

numpy

hmatrix

>>> a = np.floor(10*np.random.random((2,2)))
>>> a
array([[ 8.,  8.],
       [ 0.,  0.]])
>>> b = np.floor(10*np.random.random((2,2)))
>>> b
array([[ 1.,  8.],
       [ 0.,  4.]])
>>> np.vstack((a,b))
array([[ 8.,  8.],
       [ 0.,  0.],
       [ 1.,  8.],
       [ 0.,  4.]])
>>> np.hstack((a,b))
array([[ 8.,  8.,  1.,  8.],
       [ 0.,  0.,  0.,  4.]])

>>> import Numeric.LinearAlgebra.HMatrix (Seed, RandDist(..), randomVector, rand)
>>> let rand' seed r c = reshape c (randomVector seed Uniform (r*c))
>>> let a = cmap (floor . (*10)) (rand' 1 2 2) :: Matrix Z
>>> a
(2><2)
 [ 8, 8
 , 0, 0 ]
>>> let b = cmap (floor . (*10)) (rand' 2 2 2) :: Matrix Z
>>> b
(2><2)
 [ 1, 8
 , 0, 4 ]
>>> a === b
(4><2)
 [ 8, 8
 , 0, 0
 , 1, 8
 , 0, 4 ]
>>> a ||| b
(2><4)
 [ 8, 8, 1, 8
 , 0, 0, 0, 4 ]

numpy

hmatrix

>>> from numpy import newaxis
>>> np.column_stack((a,b))     # with 2D arrays
array([[ 8.,  8.,  1.,  8.],
       [ 0.,  0.,  0.,  4.]])
>>> a = np.array([4.,2.])
>>> b = np.array([3.,8.])
>>> np.column_stack((a,b))     # returns a 2D array
array([[ 4., 3.],
       [ 2., 8.]])
>>> np.hstack((a,b))           # the result is different
array([ 4., 2., 3., 8.])
>>> a[:,newaxis]               # this allows to have a 2D columns vector
array([[ 4.],
       [ 2.]])
>>> np.column_stack((a[:,newaxis],b[:,newaxis]))
array([[ 4.,  3.],
       [ 2.,  8.]])
>>> np.hstack((a[:,newaxis],b[:,newaxis]))   # the result is the same
array([[ 4.,  3.],
       [ 2.,  8.]])
   >>> np.r_[1:4,0,4]
   array([1, 2, 3, 0, 4])

>>> let a = fromList [4,2] :: Vector Z
>>> let b = fromList [3,8] :: Vector Z
>>> fromColumns [a,b]
(2><2)
 [ 4, 3
 , 2, 8 ]
>>> vjoin [a,b]
[4,2,3,8]
>>> asColumn a
(2><1)
 [ 4
 , 2 ]
>>> fromBlocks [fmap asColumn [a,b]]
(2><2)
 [ 4, 3
 , 2, 8 ]
>>> fromList ([1..3] ++ [0] ++ [4]) :: Vector Z
[1,2,3,0,4]

Splitting one array into several smaller ones

numpy

hmatrix

>>> a = np.floor(10*np.random.random((2,12)))
>>> a
array([[ 9.,  5.,  6.,  3.,  6.,  8.,  0.,  7.,  9.,  7.,  2.,  7.],
       [ 1.,  4.,  9.,  2.,  2.,  1.,  0.,  6.,  2.,  2.,  4.,  0.]])
>>> np.hsplit(a,3)   # Split a into 3
[array([[ 9.,  5.,  6.,  3.],
       [ 1.,  4.,  9.,  2.]]), array([[ 6.,  8.,  0.,  7.],
       [ 2.,  1.,  0.,  6.]]), array([[ 9.,  7.,  2.,  7.],
       [ 2.,  2.,  4.,  0.]])]
>>> np.hsplit(a,(3,4))   # Split a after the third and the fourth column
[array([[ 9.,  5.,  6.],
       [ 1.,  4.,  9.]]), array([[ 3.],
       [ 2.]]), array([[ 6.,  8.,  0.,  7.,  9.,  7.,  2.,  7.],
       [ 2.,  1.,  0.,  6.,  2.,  2.,  4.,  0.]])]

>>> import Numeric.LinearAlgebra.HMatrix (Seed, RandDist(..), randomVector, rand)
>>> let rand' seed r c = reshape c (randomVector seed Uniform (r*c))
>>> let a = cmap (floor . (*10)) (rand' 1 2 12) :: Matrix Z
>>> a
(2><12)
 [ 9, 5, 6, 3, 6, 8, 0, 7, 9, 7, 2, 7
 , 1, 4, 9, 2, 2, 1, 0, 6, 2, 2, 4, 0 ]
>>> toBlocksEvery 2 4 a -- we could do @toBlocksEvery (rows a) ((floor . (/3) . fromIntegral . cols) a) a@
[[(2><4)
 [ 9, 5, 6, 3
 , 1, 4, 9, 2 ],(2><4)
 [ 6, 8, 0, 7
 , 2, 1, 0, 6 ],(2><4)
 [ 9, 7, 2, 7
 , 2, 2, 4, 0 ]]]
>>> toBlocks [2] [3, 4-3, cols a - 4] a
[[(2><3)
 [ 9, 5, 6
 , 1, 4, 9 ],(2><1)
 [ 3
 , 2 ],(2><8)
 [ 6, 8, 0, 7, 9, 7, 2, 7
 , 2, 1, 0, 6, 2, 2, 4, 0 ]]]