Basic function for creating a holor

>>> holor [2,2] [1,2,3,4]
  1.0  2.0
  3.0  4.0
>>> holor [2,2] [1,2,3,4] :: Holor Int
  1  2
  3  4
>>> holor [2,2,4] [1 .. 16]
[0,:,:] =
  1.0  2.0  3.0  4.0
  5.0  6.0  7.0  8.0
[1,:,:] =
  9.0  10.0  11.0  12.0
  13.0  14.0  15.0  16.0

Creates a column-vector (2d-holor with shape [m,1])

>>> vector [1,2,3,4]
 1.0
 2.0
 3.0
 4.0

Creates a matrix (2d-holor)

>>> matrix [[1,2],[3,4]]
  1.0  2.0
  3.0  4.0

Creates a 2x1 holor from a tuple

Creates a 3x1 holor from a tuple

Creates a 4x1 holor from a tuple

Creates a 2x2 holor from nested tuples

Creates a 3x2 holor from nested tuples

Creates a 4x2 holor from nested tuples

Creates a 2x3 holor from nested tuples

Creates a 3x3 holor from nested tuples

Creates a 4x3 holor from nested tuples

Creates a 2x4 holor from nested tuples

Creates a 3x4 holor from nested tuples

Creates a 4x4 holor from nested tuples

Creates a holor for a given shape with all entries the same

>>> replicate [1,3] 0
  0.0  0.0  0.0

Shape of a holor

Number of holor entrys

Size of all holor elements in bytes (not equal to consumed memory of the holor)

Size of a single holor element in bytes

Dimension of a holor (length of shape)

>>> dim $ holor [2,2,2] [0..7]
3

Indexing a holor with shape (n,1) (column-vector) or (1,n) (row-vector)

>>> v = vector [5,6,7]
>>> v!1
6.0

Unsafe version of (!) without checking for row or column vector and not checking bounds

Indexing a single entry of a holor

>>> m = matrix [[2,3,4],[5,6,3],[9,0,2]]
>>> m|![0,2]
4.0

Unsafe version of (|!) without checking bounds

Extract a subholor by indices in the first dimension. Applied to a vector the result is a vector with the elements at the given element-indices. Applied to a matrix the result is a matrix with the rows at the given row-indices.

>>> h = holor [4,4] [1..16]
>>> h
  1.0  2.0  3.0  4.0
  5.0  6.0  7.0  8.0
  9.0  10.0  11.0  12.0
  13.0  14.0  15.0  16.0
>>> h||![1,3]
  5.0  6.0  7.0  8.0
  13.0  14.0  15.0  16.0

Unsafe version of (||!) without checking indices

Multidimensional indexing. For each dimension a list of indices define the axes to extract. This means multiindexing is done by a nested list of indices which has the same length as the shape. The dimension of the extracted subholor remains the same as that of the original holor.

>>> h = holor [4,4] [1..16]
>>> h
  1.0  2.0  3.0  4.0
  5.0  6.0  7.0  8.0
  9.0  10.0  11.0  12.0
  13.0  14.0  15.0  16.0
>>> h|||![[1,2,3],[0,1,1,2,3]]
  5.0  6.0  6.0  7.0  8.0
  9.0  10.0  10.0  11.0  12.0
  13.0  14.0  14.0  15.0  16.0

Unsafe version of (|||!) without checking multiindices

Map a function over all entries of a holor

Filter the values of a holor by a condition. The remaining elements are returned in a list.

>>> h = holor [3,3,3] [1 .. 27] :: Holor Int
>>> filter (\e -> mod e 3 == 0) h
[3,6,9,12,15,18,21,24,27]

Select all multiindices of a holor whose corresponding elements fulfill a condition.

>>> m = matrix [[-1,1],[-2,3]]
>>> selectBy (>0) m
  [[0,1],[1,1]]

Count elements of a holor that fulfill a condition

Accumulate the values of a holor by a function.

>>> v = vector [2,3,4,1] :: Holor Int
>>> accumulate (+) v
  [2,5,9,10]
>>> accumulate max v
  [2,3,4,4]

Flatten a holor to a column vector

Transpose a holor

Reshape a holor without changing the order of the underlying values

>>> h = holor [2,2,2] [1 .. 8]
>>> reshape [2,4] h
  1.0  2.0  3.0  4.0
  5.0  6.0  7.0  8.0

Get diagonal of a quadratical matrix (2d-holor) as a column vector

Returns the holor values in a list

Returns the values of an 2d-holor in a list of lists

Converts a holor with a single element to the element itself

Converts a holor to a 2-tuple if possible

Converts a holor to a 3-tuple if possible

Converts a holor to a 4-tuple if possible

Converts a holor to nested 2,2-tuple if possible

Converts a holor to nested 3,2-tuple if possible

Converts a holor to nested 4,2-tuple if possible

Converts a holor to nested 2,3-tuple if possible

Converts a holor to nested 3,3-tuple if possible

Converts a holor to nested 4,3-tuple if possible

Converts a holor to nested 2,4-tuple if possible

Converts a holor to nested 3,4-tuple if possible

Converts a holor to nested 4,4-tuple if possible

Modify a single entry of a holor

>>> v = vector [1,2,3]
>>> setElem [1,0] 22 v
  1.0  22.0  3.0

Modify many elements of a holor at once

>>> h = zeros [3,3] :: Holor Int
>>> setElems [[0,0],[1,1],[2,2]] [4,5,6] h
  4  0  0
  0  5  0
  0  0  6

Tests if a holor is instanced correctly, i.e. shape, strides and values fit together

Tests if a holor has shape n,1 or 1,n

Tests if a holor has the shape of a square matrix

Tests if a matrix A with shape [m,n] is of upper triangular form. If m<n, false is returned. If m>=n, all elements on the first diagonal must be unequal to zero and all elements below the first diagonal must be zero.