Class: Cumo::NArray

Inherits:
Object
  • Object
show all
Defined in:
ext/cumo/narray/narray.c,
lib/cumo/narray/extra.rb

Overview

Cumo::NArray is the abstract super class for Numerical N-dimensional Array in the Ruby/Cumo module. Use Typed Subclasses of NArray (Cumo::DFloat, Int32, etc) to create data array instances.

Constant Summary collapse

@@warn_slow_dot = 
false

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.asarray(a) ⇒ Object 



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# File 'lib/cumo/narray/extra.rb', line 162

def self.asarray(a)
  case a
  when NArray
    (a.ndim == 0) ? a[:new] : a
  when Numeric,Range
    self[a]
  else
    cast(a)
  end
end

.cast(a) ⇒ Object

Convert the argument to an narray if not an narray.



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# File 'lib/cumo/narray/extra.rb', line 158

def self.cast(a)
  a.kind_of?(NArray) ? a : NArray.array_type(a).cast(a)
end

.column_stack(arrays) ⇒ Object

Stack 1-d arrays into columns of a 2-d array.

Examples:

x = Cumo::Int32[1,2,3]
y = Cumo::Int32[2,3,4]
p Cumo::NArray.column_stack([x,y])
# Cumo::Int32#shape=[3,2]
# [[1, 2],
#  [2, 3],
#  [3, 4]]


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# File 'lib/cumo/narray/extra.rb', line 608

def column_stack(arrays)
  arys = arrays.map do |a|
    a = cast(a)
    case a.ndim
    when 0; a[:new,:new]
    when 1; a[true,:new]
    else; a
    end
  end
  concatenate(arys,axis:1)
end

.concatenate(arrays, axis: 0) ⇒ Object

Examples:

p a = Cumo::DFloat[[1, 2], [3, 4]]
# Cumo::DFloat#shape=[2,2]
# [[1, 2],
#  [3, 4]]

p b = Cumo::DFloat[[5, 6]]
# Cumo::DFloat#shape=[1,2]
# [[5, 6]]

p Cumo::NArray.concatenate([a,b],axis:0)
# Cumo::DFloat#shape=[3,2]
# [[1, 2],
#  [3, 4],
#  [5, 6]]

p Cumo::NArray.concatenate([a,b.transpose], axis:1)
# Cumo::DFloat#shape=[2,3]
# [[1, 2, 5],
#  [3, 4, 6]]


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# File 'lib/cumo/narray/extra.rb', line 464

def concatenate(arrays,axis:0)
  klass = (self==NArray) ? NArray.array_type(arrays) : self
  nd = 0
  arrays = arrays.map do |a|
    case a
    when NArray
      # ok
    when Numeric
      a = klass[a]
    when Array
      a = klass.cast(a)
    else
      raise TypeError,"not Cumo::NArray: #{a.inspect[0..48]}"
    end
    if a.ndim > nd
      nd = a.ndim
    end
    a
  end
  if axis < 0
    axis += nd
  end
  if axis < 0 || axis >= nd
    raise ArgumentError,"axis is out of range"
  end
  new_shape = nil
  sum_size = 0
  arrays.each do |a|
    a_shape = a.shape
    if nd != a_shape.size
      a_shape = [1]*(nd-a_shape.size) + a_shape
    end
    sum_size += a_shape.delete_at(axis)
    if new_shape
      if new_shape != a_shape
        raise ShapeError,"shape mismatch"
      end
    else
      new_shape = a_shape
    end
  end
  new_shape.insert(axis,sum_size)
  result = klass.zeros(*new_shape)
  lst = 0
  refs = [true] * nd
  arrays.each do |a|
    fst = lst
    lst = fst + (a.shape[axis-nd]||1)
    refs[axis] = fst...lst
    result[*refs] = a
  end
  result
end

.diag_indices(m, n, k = 0) ⇒ Object

Return the k-th diagonal indices.



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# File 'lib/cumo/narray/extra.rb', line 1098

def self.diag_indices(m,n,k=0)
  x = Cumo::Int64.new(m,1).seq + k
  y = Cumo::Int64.new(1,n).seq
  (x.eq y).where
end

.dstack(arrays) ⇒ Object

Stack arrays in depth wise (along third axis).

Examples:

a = Cumo::Int32[1,2,3]
b = Cumo::Int32[2,3,4]
p Cumo::NArray.dstack([a,b])
# Cumo::Int32#shape=[1,3,2]
# [[[1, 2],
#   [2, 3],
#   [3, 4]]]

a = Cumo::Int32[[1],[2],[3]]
b = Cumo::Int32[[2],[3],[4]]
p Cumo::NArray.dstack([a,b])
# Cumo::Int32#shape=[3,1,2]
# [[[1, 2]],
#  [[2, 3]],
#  [[3, 4]]]


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# File 'lib/cumo/narray/extra.rb', line 591

def dstack(arrays)
  arys = arrays.map do |a|
    _atleast_3d(cast(a))
  end
  concatenate(arys,axis:2)
end

.hstack(arrays) ⇒ Object

Stack arrays horizontally (column wise).

Examples:

a = Cumo::Int32[1,2,3]
b = Cumo::Int32[2,3,4]
p Cumo::NArray.hstack([a,b])
# Cumo::Int32#shape=[6]
# [1, 2, 3, 2, 3, 4]

a = Cumo::Int32[[1],[2],[3]]
b = Cumo::Int32[[2],[3],[4]]
p Cumo::NArray.hstack([a,b])
# Cumo::Int32#shape=[3,2]
# [[1, 2],
#  [2, 3],
#  [3, 4]]


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# File 'lib/cumo/narray/extra.rb', line 561

def hstack(arrays)
  klass = (self==NArray) ? NArray.array_type(arrays) : self
  nd = 0
  arys = arrays.map do |a|
    a = klass.cast(a)
    nd = a.ndim if a.ndim > nd
    a
  end
  dim = (nd >= 2) ? 1 : 0
  concatenate(arys,axis:dim)
end

.parse(str, split1d: /\s+/, split2d: /;?$|;/, split3d: /\s*\n(\s*\n)+/m) ⇒ Object

parse matrix like matlab, octave

Examples:

a = Cumo::DFloat.parse %[
 2 -3 5
 4 9 7
 2 -1 6
]
=> Cumo::DFloat#shape=[3,3]
[[2, -3, 5],
 [4, 9, 7],
 [2, -1, 6]]


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# File 'lib/cumo/narray/extra.rb', line 185

def self.parse(str, split1d:/\s+/, split2d:/;?$|;/,
               split3d:/\s*\n(\s*\n)+/m)
  a = []
  str.split(split3d).each do |block|
    b = []
    #print "b"; p block
    block.split(split2d).each do |line|
      #p line
      line.strip!
      if !line.empty?
        c = []
        line.split(split1d).each do |item|
          c << eval(item.strip) if !item.empty?
        end
        b << c if !c.empty?
      end
    end
    a << b if !b.empty?
  end
  if a.size==1
    self.cast(a[0])
  else
    self.cast(a)
  end
end

.tril_indices(m, n, k = 0) ⇒ Object

Return the indices for the lower-triangle on and below the k-th diagonal.



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# File 'lib/cumo/narray/extra.rb', line 1082

def self.tril_indices(m,n,k=0)
  x = Cumo::Int64.new(m,1).seq + k
  y = Cumo::Int64.new(1,n).seq
  (x>=y).where
end

.triu_indices(m, n, k = 0) ⇒ Object

Return the indices for the uppler-triangle on and above the k-th diagonal.



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# File 'lib/cumo/narray/extra.rb', line 1043

def self.triu_indices(m,n,k=0)
  x = Cumo::Int64.new(m,1).seq + k
  y = Cumo::Int64.new(1,n).seq
  (x<=y).where
end

.vstack(arrays) ⇒ Object

Stack arrays vertically (row wise).

Examples:

a = Cumo::Int32[1,2,3]
b = Cumo::Int32[2,3,4]
p Cumo::NArray.vstack([a,b])
# Cumo::Int32#shape=[2,3]
# [[1, 2, 3],
#  [2, 3, 4]]

a = Cumo::Int32[[1],[2],[3]]
b = Cumo::Int32[[2],[3],[4]]
p Cumo::NArray.vstack([a,b])
# Cumo::Int32#shape=[6,1]
# [[1],
#  [2],
#  [3],
#  [2],
#  [3],
#  [4]]


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# File 'lib/cumo/narray/extra.rb', line 538

def vstack(arrays)
  arys = arrays.map do |a|
    _atleast_2d(cast(a))
  end
  concatenate(arys,axis:0)
end

Instance Method Details

#append(other, axis: nil) ⇒ Object

Append values to the end of an narray.

Examples:

a = Cumo::DFloat[1, 2, 3]
p a.append([[4, 5, 6], [7, 8, 9]])
# Cumo::DFloat#shape=[9]
# [1, 2, 3, 4, 5, 6, 7, 8, 9]

a = Cumo::DFloat[[1, 2, 3]]
p a.append([[4, 5, 6], [7, 8, 9]],axis:0)
# Cumo::DFloat#shape=[3,3]
# [[1, 2, 3],
#  [4, 5, 6],
#  [7, 8, 9]]

a = Cumo::DFloat[[1, 2, 3], [4, 5, 6]]
p a.append([7, 8, 9], axis:0)
# in `append': dimension mismatch (Cumo::NArray::DimensionError)


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# File 'lib/cumo/narray/extra.rb', line 278

def append(other,axis:nil)
  other = self.class.cast(other)
  if axis
    if ndim != other.ndim
      raise DimensionError, "dimension mismatch"
    end
    return concatenate(other,axis:axis)
  else
    a = self.class.zeros(size+other.size)
    a[0...size] = self[true]
    a[size..-1] = other[true]
    return a
  end
end

#at(*indices) ⇒ Cumo::NArray

Multi-dimensional array indexing. Same as [] for one-dimensional NArray. Similar to numpy’s tuple indexing, i.e., ‘a[,[3,4,..]]` (This method will be rewritten in C)

Examples:

p x = Cumo::DFloat.new(3,3,3).seq
# Cumo::DFloat#shape=[3,3,3]
# [[[0, 1, 2],
#   [3, 4, 5],
#   [6, 7, 8]],
#  [[9, 10, 11],
#   [12, 13, 14],
#   [15, 16, 17]],
#  [[18, 19, 20],
#   [21, 22, 23],
#   [24, 25, 26]]]

p x.at([0,1,2],[0,1,2],[-1,-2,-3])
# Cumo::DFloat(view)#shape=[3]
# [2, 13, 24]

Returns:



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# File 'lib/cumo/narray/extra.rb', line 67

def at(*indices)
  if indices.size != ndim
    raise DimensionError, "argument length does not match dimension size"
  end
  idx = nil
  stride = 1
  (indices.size-1).downto(0) do |i|
    ix = Int64.cast(indices[i])
    if ix.ndim != 1
      raise DimensionError, "index array is not one-dimensional"
    end
    ix[ix < 0] += shape[i]
    if ((ix < 0) & (ix >= shape[i])).any?
      raise IndexError, "index array is out of range"
    end
    if idx
      if idx.size != ix.size
        raise ShapeError, "index array sizes mismatch"
      end
      idx += ix * stride
      stride *= shape[i]
    else
      idx = ix
      stride = shape[i]
    end
  end
  self[idx]
end

#concatenate(*arrays, axis: 0) ⇒ Object

Examples:

p a = Cumo::DFloat[[1, 2], [3, 4]]
# Cumo::DFloat#shape=[2,2]
# [[1, 2],
#  [3, 4]]

p b = Cumo::DFloat[[5, 6]]
# Cumo::DFloat#shape=[1,2]
# [[5, 6]]

p a.concatenate(b,axis:0)
# Cumo::DFloat#shape=[3,2]
# [[1, 2],
#  [3, 4],
#  [5, 6]]

p a.concatenate(b.transpose, axis:1)
# Cumo::DFloat#shape=[2,3]
# [[1, 2, 5],
#  [3, 4, 6]]


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# File 'lib/cumo/narray/extra.rb', line 663

def concatenate(*arrays,axis:0)
  axis = check_axis(axis)
  self_shape = shape
  self_shape.delete_at(axis)
  sum_size = shape[axis]
  arrays.map! do |a|
    case a
    when NArray
      # ok
    when Numeric
      a = self.class.new(1).store(a)
    when Array
      a = self.class.cast(a)
    else
      raise TypeError,"not Cumo::NArray: #{a.inspect[0..48]}"
    end
    if a.ndim > ndim
      raise ShapeError,"dimension mismatch"
    end
    a_shape = a.shape
    sum_size += a_shape.delete_at(axis-ndim) || 1
    if self_shape != a_shape
      raise ShapeError,"shape mismatch"
    end
    a
  end
  self_shape.insert(axis,sum_size)
  result = self.class.zeros(*self_shape)
  lst = shape[axis]
  refs = [true] * ndim
  refs[axis] = 0...lst
  result[*refs] = self
  arrays.each do |a|
    fst = lst
    lst = fst + (a.shape[axis-ndim] || 1)
    refs[axis] = fst...lst
    result[*refs] = a
  end
  result
end

#cov(y = nil, ddof: 1, fweights: nil, aweights: nil) ⇒ Object

under construction



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# File 'lib/cumo/narray/extra.rb', line 1270

def cov(y=nil, ddof:1, fweights:nil, aweights:nil)
  if y
    m = NArray.vstack([self,y])
  else
    m = self
  end
  w = nil
  if fweights
    f = fweights
    w = f
  end
  if aweights
    a = aweights
    w = w ? w*a : a
  end
  if w
    w_sum = w.sum(axis:-1, keepdims:true)
    if ddof == 0
      fact = w_sum
    elsif aweights.nil?
      fact = w_sum - ddof
    else
      wa_sum = (w*a).sum(axis:-1, keepdims:true)
      fact = w_sum - ddof * wa_sum / w_sum
    end
    if (fact <= 0).any?
      raise StandardError,"Degrees of freedom <= 0 for slice"
    end
  else
    fact = m.shape[-1] - ddof
  end
  if w
    m -= (m*w).sum(axis:-1, keepdims:true) / w_sum
    mw = m*w
  else
    m -= m.mean(axis:-1, keepdims:true)
    mw = m
  end
  mt = (m.ndim < 2) ? m : m.swapaxes(-2,-1)
  mw.dot(mt.conj) / fact
end

#deg2rad ⇒ Object

Convert angles from degrees to radians.



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# File 'lib/cumo/narray/extra.rb', line 30

def deg2rad
  self * (Math::PI/180)
end

#delete(indice, axis = nil) ⇒ Object

Examples:

a = Cumo::DFloat[[1,2,3,4], [5,6,7,8], [9,10,11,12]]
p a.delete(1,0)
# Cumo::DFloat(view)#shape=[2,4]
# [[1, 2, 3, 4],
#  [9, 10, 11, 12]]

p a.delete((0..-1).step(2),1)
# Cumo::DFloat(view)#shape=[3,2]
# [[2, 4],
#  [6, 8],
#  [10, 12]]

p a.delete([1,3,5])
# Cumo::DFloat(view)#shape=[9]
# [1, 3, 5, 7, 8, 9, 10, 11, 12]


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# File 'lib/cumo/narray/extra.rb', line 313

def delete(indice,axis=nil)
  if axis
    bit = Bit.ones(shape[axis])
    bit[indice] = 0
    idx = [true]*ndim
    idx[axis] = bit.where
    return self[*idx].copy
  else
    bit = Bit.ones(size)
    bit[indice] = 0
    return self[bit.where].copy
  end
end

#diag(k = 0) ⇒ Object

Return a matrix whose diagonal is constructed by self along the last axis.



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# File 'lib/cumo/narray/extra.rb', line 1105

def diag(k=0)
  *shp,n = shape
  n += k.abs
  a = self.class.zeros(*shp,n,n)
  a.diagonal(k).store(self)
  a
end

#diag_indices(k = 0) ⇒ Object

Return the k-th diagonal indices.



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# File 'lib/cumo/narray/extra.rb', line 1089

def diag_indices(k=0)
  if ndim < 2
    raise NArray::ShapeError, "must be >= 2-dimensional array"
  end
  m,n = shape[-2..-1]
  NArray.diag_indices(m,n,k)
end

#diff(n = 1, axis: -1)) ⇒ Object

Calculate the n-th discrete difference along given axis.

Examples:

p x = Cumo::DFloat[1, 2, 4, 7, 0]
# Cumo::DFloat#shape=[5]
# [1, 2, 4, 7, 0]

p x.diff
# Cumo::DFloat#shape=[4]
# [1, 2, 3, -7]

p x.diff(2)
# Cumo::DFloat#shape=[3]
# [1, 1, -10]

p x = Cumo::DFloat[[1, 3, 6, 10], [0, 5, 6, 8]]
# Cumo::DFloat#shape=[2,4]
# [[1, 3, 6, 10],
#  [0, 5, 6, 8]]

p x.diff
# Cumo::DFloat#shape=[2,3]
# [[2, 3, 4],
#  [5, 1, 2]]

p x.diff(axis:0)
# Cumo::DFloat#shape=[1,4]
# [[-1, 2, 0, -2]]


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# File 'lib/cumo/narray/extra.rb', line 983

def diff(n=1,axis:-1)
  axis = check_axis(axis)
  if n < 0 || n >= shape[axis]
    raise ShapeError,"n=#{n} is invalid for shape[#{axis}]=#{shape[axis]}"
  end
  # calculate polynomial coefficient
  c = self.class[-1,1]
  2.upto(n) do |i|
    x = self.class.zeros(i+1)
    x[0..-2] = c
    y = self.class.zeros(i+1)
    y[1..-1] = c
    c = y - x
  end
  s = [true]*ndim
  s[axis] = n..-1
  result = self[*s].dup
  sum = result.inplace
  (n-1).downto(0) do |i|
    s = [true]*ndim
    s[axis] = i..-n-1+i
    sum + self[*s] * c[i] # inplace addition
  end
  return result
end

#dot(b) ⇒ Cumo::NArray

Dot product of two arrays.

Parameters:

Returns:



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# File 'lib/cumo/narray/extra.rb', line 1134

def dot(b)
  t = self.class::UPCAST[b.class]
  if self.ndim == 0 and b.ndim == 0
    return self * b
  end
  if [SFloat, DFloat, SComplex, DComplex].include?(t)
    b = self.class.asarray(b)
    case self.ndim
    when 1
      case b.ndim
      when 1
        self.mulsum(b, axis:-1)
      else
        self[:new, false].gemm(b).flatten
      end
    else
      case b.ndim
      when 1
        self.gemm(b[false, :new]).flatten
      else
        self.gemm(b)
      end
    end
  else
    b = self.class.asarray(b)
    case b.ndim
    when 1
      mulsum(b, axis:-1)
    else
      case ndim
      when 0
        b.mulsum(self, axis:-2)
      when 1
        self[true,:new].mulsum(b, axis:-2)
      else
        unless @@warn_slow_dot
          nx = 200
          ns = 200000
          am,an = shape[-2..-1]
          bm,bn = b.shape[-2..-1]
          if am > nx && an > nx && bm > nx && bn > nx &&
              size > ns && b.size > ns
            @@warn_slow_dot = true
            warn "\nwarning: matrix dot for #{t} is slow. Consider SFloat, DFloat, SComplex, or DComplex to use cuBLAS.\n\n"
          end
        end
        self[false,:new].mulsum(b[false,:new,true,true], axis:-2)
      end
    end
  end
end

#dsplit(indices_or_sections) ⇒ Object 



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# File 'lib/cumo/narray/extra.rb', line 809

def dsplit(indices_or_sections)
  split(indices_or_sections, axis:2)
end

#each_over_axis(axis = 0) ⇒ Object

Iterate over an axis @ example

> a = Cumo::DFloat.new(2,2,2).seq
> p a
Cumo::DFloat#shape=[2,2,2]
[[[0, 1],
  [2, 3]],
 [[4, 5],
  [6, 7]]]

> a.each_over_axis{|i| p i}
Cumo::DFloat(view)#shape=[2,2]
[[0, 1],
 [2, 3]]
Cumo::DFloat(view)#shape=[2,2]
[[4, 5],
 [6, 7]]

> a.each_over_axis(1){|i| p i}
Cumo::DFloat(view)#shape=[2,2]
[[0, 1],
 [4, 5]]
Cumo::DFloat(view)#shape=[2,2]
[[2, 3],
 [6, 7]]



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# File 'lib/cumo/narray/extra.rb', line 238

def each_over_axis(axis=0)
  unless block_given?
    return to_enum(:each_over_axis,axis)
  end
  if ndim == 0
    if axis != 0
      raise ArgumentError,"axis=#{axis} is invalid"
    end
    niter = 1
  else
    axis = check_axis(axis)
    niter = shape[axis]
  end
  idx = [true]*ndim
  niter.times do |i|
    idx[axis] = i
    yield(self[*idx])
  end
  self
end

#fliplr ⇒ Object

Flip each row in the left/right direction. Same as ‘a[true, (-1..0).step(-1), …]`.



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# File 'lib/cumo/narray/extra.rb', line 36

def fliplr
  reverse(1)
end

#flipud ⇒ Object

Flip each column in the up/down direction. Same as ‘a[(-1..0).step(-1), …]`.



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# File 'lib/cumo/narray/extra.rb', line 42

def flipud
  reverse(0)
end

#hsplit(indices_or_sections) ⇒ Object 



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# File 'lib/cumo/narray/extra.rb', line 805

def hsplit(indices_or_sections)
  split(indices_or_sections, axis:1)
end

#inner(b, axis: -1)) ⇒ Cumo::NArray

Inner product of two arrays. Same as ‘(a*b).sum(axis:-1)`.

Parameters:

  • b (Cumo::NArray)
  • axis (Integer) (defaults to: -1)) —

    applied axis

Returns:



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# File 'lib/cumo/narray/extra.rb', line 1192

def inner(b, axis:-1)
  mulsum(b, axis:axis)
end

#insert(indice, values, axis: nil) ⇒ Object

Insert values along the axis before the indices.

Examples:

p a = Cumo::DFloat[[1, 2], [3, 4]]
a = Cumo::Int32[[1, 1], [2, 2], [3, 3]]

p a.insert(1,5)
# Cumo::Int32#shape=[7]
# [1, 5, 1, 2, 2, 3, 3]

p a.insert(1, 5, axis:1)
# Cumo::Int32#shape=[3,3]
# [[1, 5, 1],
#  [2, 5, 2],
#  [3, 5, 3]]

p a.insert([1], [[11],[12],[13]], axis:1)
# Cumo::Int32#shape=[3,3]
# [[1, 11, 1],
#  [2, 12, 2],
#  [3, 13, 3]]

p a.insert(1, [11, 12, 13], axis:1)
# Cumo::Int32#shape=[3,3]
# [[1, 11, 1],
#  [2, 12, 2],
#  [3, 13, 3]]

p a.insert([1], [11, 12, 13], axis:1)
# Cumo::Int32#shape=[3,5]
# [[1, 11, 12, 13, 1],
#  [2, 11, 12, 13, 2],
#  [3, 11, 12, 13, 3]]

p b = a.flatten
# Cumo::Int32(view)#shape=[6]
# [1, 1, 2, 2, 3, 3]

p b.insert(2,[15,16])
# Cumo::Int32#shape=[8]
# [1, 1, 15, 16, 2, 2, 3, 3]

p b.insert([2,2],[15,16])
# Cumo::Int32#shape=[8]
# [1, 1, 15, 16, 2, 2, 3, 3]

p b.insert([2,1],[15,16])
# Cumo::Int32#shape=[8]
# [1, 16, 1, 15, 2, 2, 3, 3]

p b.insert([2,0,1],[15,16,17])
# Cumo::Int32#shape=[9]
# [16, 1, 17, 1, 15, 2, 2, 3, 3]

p b.insert(2..3, [15, 16])
# Cumo::Int32#shape=[8]
# [1, 1, 15, 2, 16, 2, 3, 3]

p b.insert(2, [7.13, 0.5])
# Cumo::Int32#shape=[8]
# [1, 1, 7, 0, 2, 2, 3, 3]

p x = Cumo::DFloat.new(2,4).seq
# Cumo::DFloat#shape=[2,4]
# [[0, 1, 2, 3],
#  [4, 5, 6, 7]]

p x.insert([1,3],999,axis:1)
# Cumo::DFloat#shape=[2,6]
# [[0, 999, 1, 2, 999, 3],
#  [4, 999, 5, 6, 999, 7]]


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# File 'lib/cumo/narray/extra.rb', line 398

def insert(indice,values,axis:nil)
  if axis
    values = self.class.asarray(values)
    nd = values.ndim
    midx = [:new]*(ndim-nd) + [true]*nd
    case indice
    when Numeric
      midx[-nd-1] = true
      midx[axis] = :new
    end
    values = values[*midx]
  else
    values = self.class.asarray(values).flatten
  end
  idx = Int64.asarray(indice)
  nidx = idx.size
  if nidx == 1
    nidx = values.shape[axis||0]
    idx = idx + Int64.new(nidx).seq
  else
    sidx = idx.sort_index
    idx[sidx] += Int64.new(nidx).seq
  end
  if axis
    bit = Bit.ones(shape[axis]+nidx)
    bit[idx] = 0
    new_shape = shape
    new_shape[axis] += nidx
    a = self.class.zeros(new_shape)
    mdidx = [true]*ndim
    mdidx[axis] = bit.where
    a[*mdidx] = self
    mdidx[axis] = idx
    a[*mdidx] = values
  else
    bit = Bit.ones(size+nidx)
    bit[idx] = 0
    a = self.class.zeros(size+nidx)
    a[bit.where] = self.flatten
    a[idx] = values
  end
  return a
end

#kron(b) ⇒ Cumo::NArray

Kronecker product of two arrays.

kron(a,b)[k_0, k_1, ...] = a[i_0, i_1, ...] * b[j_0, j_1, ...]
   where:  k_n = i_n * b.shape[n] + j_n

Examples:

Cumo::DFloat[1,10,100].kron([5,6,7])
=> Cumo::DFloat#shape=[9]
[5, 6, 7, 50, 60, 70, 500, 600, 700]
Cumo::DFloat[5,6,7].kron([1,10,100])
=> Cumo::DFloat#shape=[9]
[5, 50, 500, 6, 60, 600, 7, 70, 700]
Cumo::DFloat.eye(2).kron(Cumo::DFloat.ones(2,2))
=> Cumo::DFloat#shape=[4,4]
[[1, 1, 0, 0],
 [1, 1, 0, 0],
 [0, 0, 1, 1],
 [0, 0, 1, 1]]

Parameters:

Returns:



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# File 'lib/cumo/narray/extra.rb', line 1256

def kron(b)
  b = NArray.cast(b)
  nda = ndim
  ndb = b.ndim
  shpa = shape
  shpb = b.shape
  adim = [:new]*(2*[ndb-nda,0].max) + [true,:new]*nda
  bdim = [:new]*(2*[nda-ndb,0].max) + [:new,true]*ndb
  shpr = (-[nda,ndb].max..-1).map{|i| (shpa[i]||1) * (shpb[i]||1)}
  (self[*adim] * b[*bdim]).reshape(*shpr)
end

#new_fill(value) ⇒ Object

Return an array filled with value with the same shape and type as self.



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# File 'lib/cumo/narray/extra.rb', line 20

def new_fill(value)
  self.class.new(*shape).fill(value)
end

#new_narray ⇒ Object

Return an unallocated array with the same shape and type as self.



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# File 'lib/cumo/narray/extra.rb', line 5

def new_narray
  self.class.new(*shape)
end

#new_ones ⇒ Object

Return an array of ones with the same shape and type as self.



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# File 'lib/cumo/narray/extra.rb', line 15

def new_ones
  self.class.ones(*shape)
end

#new_zeros ⇒ Object

Return an array of zeros with the same shape and type as self.



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# File 'lib/cumo/narray/extra.rb', line 10

def new_zeros
  self.class.zeros(*shape)
end

#outer(b, axis: nil) ⇒ Cumo::NArray

Outer product of two arrays. Same as ‘self * b`.

Examples:

a = Cumo::DFloat.ones(5)
=> Cumo::DFloat#shape=[5]
[1, 1, 1, 1, 1]
b = Cumo::DFloat.linspace(-2,2,5)
=> Cumo::DFloat#shape=[5]
[-2, -1, 0, 1, 2]
a.outer(b)
=> Cumo::DFloat#shape=[5,5]
[[-2, -1, 0, 1, 2],
 [-2, -1, 0, 1, 2],
 [-2, -1, 0, 1, 2],
 [-2, -1, 0, 1, 2],
 [-2, -1, 0, 1, 2]]

Parameters:

  • b (Cumo::NArray)
  • axis (Integer) (defaults to: nil) —

    applied axis (default=-1)

Returns:



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# File 'lib/cumo/narray/extra.rb', line 1217

def outer(b, axis:nil)
  b = NArray.cast(b)
  if axis.nil?
    self[false,:new] * ((b.ndim==0) ? b : b[false,:new,true])
  else
    md,nd = [ndim,b.ndim].minmax
    axis = check_axis(axis) - nd
    if axis < -md
      raise ArgumentError,"axis=#{axis} is out of range"
    end
    adim = [true]*ndim
    adim[axis+ndim+1,0] = :new
    bdim = [true]*b.ndim
    bdim[axis+b.ndim,0] = :new
    self[*adim] * b[*bdim]
  end
end

#rad2deg ⇒ Object

Convert angles from radians to degrees.



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# File 'lib/cumo/narray/extra.rb', line 25

def rad2deg
  self * (180/Math::PI)
end

#repeat(arg, axis: nil) ⇒ Object

Examples:

p Cumo::NArray[3].repeat(4)
# Cumo::Int32#shape=[4]
# [3, 3, 3, 3]

p x = Cumo::NArray[[1,2],[3,4]]
# Cumo::Int32#shape=[2,2]
# [[1, 2],
#  [3, 4]]

p x.repeat(2)
# Cumo::Int32#shape=[8]
# [1, 1, 2, 2, 3, 3, 4, 4]

p x.repeat(3,axis:1)
# Cumo::Int32#shape=[2,6]
# [[1, 1, 1, 2, 2, 2],
#  [3, 3, 3, 4, 4, 4]]

p x.repeat([1,2],axis:0)
# Cumo::Int32#shape=[3,2]
# [[1, 2],
#  [3, 4],
#  [3, 4]]


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# File 'lib/cumo/narray/extra.rb', line 921

def repeat(arg,axis:nil)
  case axis
  when Integer
    axis = check_axis(axis)
    c = self
  when NilClass
    c = self.flatten
    axis = 0
  else
    raise ArgumentError,"invalid axis"
  end
  case arg
  when Integer
    if !arg.kind_of?(Integer) || arg<1
      raise ArgumentError,"argument should be positive integer"
    end
    idx = c.shape[axis].times.map{|i| [i]*arg}.flatten
  else
    arg = arg.to_a
    if arg.size != c.shape[axis]
      raise ArgumentError,"repeat size shoud be equal to size along axis"
    end
    arg.each do |i|
      if !i.kind_of?(Integer) || i<0
        raise ArgumentError,"argument should be non-negative integer"
      end
    end
    idx = arg.each_with_index.map{|a,i| [i]*a}.flatten
  end
  ref = [true] * c.ndim
  ref[axis] = idx
  c[*ref].copy
end

#rot90(k = 1, axes = [0,1]) ⇒ Object

Rotate in the plane specified by axes.

Examples:

p a = Cumo::Int32.new(2,2).seq
# Cumo::Int32#shape=[2,2]
# [[0, 1],
#  [2, 3]]

p a.rot90
# Cumo::Int32(view)#shape=[2,2]
# [[1, 3],
#  [0, 2]]

p a.rot90(2)
# Cumo::Int32(view)#shape=[2,2]
# [[3, 2],
#  [1, 0]]

p a.rot90(3)
# Cumo::Int32(view)#shape=[2,2]
# [[2, 0],
#  [3, 1]]


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# File 'lib/cumo/narray/extra.rb', line 117

def rot90(k=1,axes=[0,1])
  case k % 4
  when 0
    view
  when 1
    swapaxes(*axes).reverse(axes[0])
  when 2
    reverse(*axes)
  when 3
    swapaxes(*axes).reverse(axes[1])
  end
end

#split(indices_or_sections, axis: 0) ⇒ Object

Examples:

p x = Cumo::DFloat.new(9).seq
# Cumo::DFloat#shape=[9]
# [0, 1, 2, 3, 4, 5, 6, 7, 8]

pp x.split(3)
# [Cumo::DFloat(view)#shape=[3]
# [0, 1, 2],
#  Cumo::DFloat(view)#shape=[3]
# [3, 4, 5],
#  Cumo::DFloat(view)#shape=[3]
# [6, 7, 8]]

p x = Cumo::DFloat.new(8).seq
# Cumo::DFloat#shape=[8]
# [0, 1, 2, 3, 4, 5, 6, 7]

pp x.split([3, 5, 6, 10])
# [Cumo::DFloat(view)#shape=[3]
# [0, 1, 2],
#  Cumo::DFloat(view)#shape=[2]
# [3, 4],
#  Cumo::DFloat(view)#shape=[1]
# [5],
#  Cumo::DFloat(view)#shape=[2]
# [6, 7],
#  Cumo::DFloat(view)#shape=[0][]]


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# File 'lib/cumo/narray/extra.rb', line 732

def split(indices_or_sections, axis:0)
  axis = check_axis(axis)
  size_axis = shape[axis]
  case indices_or_sections
  when Integer
    div_axis, mod_axis = size_axis.divmod(indices_or_sections)
    refs = [true]*ndim
    beg_idx = 0
    mod_axis.times.map do |i|
      end_idx = beg_idx + div_axis + 1
      refs[axis] = beg_idx ... end_idx
      beg_idx = end_idx
      self[*refs]
    end +
    (indices_or_sections-mod_axis).times.map do |i|
      end_idx = beg_idx + div_axis
      refs[axis] = beg_idx ... end_idx
      beg_idx = end_idx
      self[*refs]
    end
  when NArray
    split(indices_or_sections.to_a,axis:axis)
  when Array
    refs = [true]*ndim
    fst = 0
    (indices_or_sections + [size_axis]).map do |lst|
      lst = size_axis if lst > size_axis
      refs[axis] = (fst < size_axis) ? fst...lst : -1...-1
      fst = lst
      self[*refs]
    end
  else
    raise TypeError,"argument must be Integer or Array"
  end
end

#tile(*arg) ⇒ Object

Examples:

p a = Cumo::NArray[0,1,2]
# Cumo::Int32#shape=[3]
# [0, 1, 2]

p a.tile(2)
# Cumo::Int32#shape=[6]
# [0, 1, 2, 0, 1, 2]

p a.tile(2,2)
# Cumo::Int32#shape=[2,6]
# [[0, 1, 2, 0, 1, 2],
#  [0, 1, 2, 0, 1, 2]]

p a.tile(2,1,2)
# Cumo::Int32#shape=[2,1,6]
# [[[0, 1, 2, 0, 1, 2]],
#  [[0, 1, 2, 0, 1, 2]]]

p b = Cumo::NArray[[1, 2], [3, 4]]
# Cumo::Int32#shape=[2,2]
# [[1, 2],
#  [3, 4]]

p b.tile(2)
# Cumo::Int32#shape=[2,4]
# [[1, 2, 1, 2],
#  [3, 4, 3, 4]]

p b.tile(2,1)
# Cumo::Int32#shape=[4,2]
# [[1, 2],
#  [3, 4],
#  [1, 2],
#  [3, 4]]

p c = Cumo::NArray[1,2,3,4]
# Cumo::Int32#shape=[4]
# [1, 2, 3, 4]

p c.tile(4,1)
# Cumo::Int32#shape=[4,4]
# [[1, 2, 3, 4],
#  [1, 2, 3, 4],
#  [1, 2, 3, 4],
#  [1, 2, 3, 4]]


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# File 'lib/cumo/narray/extra.rb', line 860

def tile(*arg)
  arg.each do |i|
    if !i.kind_of?(Integer) || i<1
      raise ArgumentError,"argument should be positive integer"
    end
  end
  ns = arg.size
  nd = self.ndim
  shp = self.shape
  new_shp = []
  src_shp = []
  res_shp = []
  (nd-ns).times do
    new_shp << 1
    new_shp << (n = shp.shift)
    src_shp << :new
    src_shp << true
    res_shp << n
  end
  (ns-nd).times do
    new_shp << (m = arg.shift)
    new_shp << 1
    src_shp << :new
    src_shp << :new
    res_shp << m
  end
  [nd,ns].min.times do
    new_shp << (m = arg.shift)
    new_shp << (n = shp.shift)
    src_shp << :new
    src_shp << true
    res_shp << n*m
  end
  self.class.new(*new_shp).store(self[*src_shp]).reshape(*res_shp)
end

#to_c ⇒ Object 



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# File 'lib/cumo/narray/extra.rb', line 148

def to_c
  if size==1
    Complex(self.extract_cpu)
  else
    # convert to DComplex?
    raise TypeError, "can't convert #{self.class} into Complex"
  end
end

#to_f ⇒ Object 



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# File 'lib/cumo/narray/extra.rb', line 139

def to_f
  if size==1
    self.extract_cpu.to_f
  else
    # convert to DFloat?
    raise TypeError, "can't convert #{self.class} into Float"
  end
end

#to_i ⇒ Object 



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# File 'lib/cumo/narray/extra.rb', line 130

def to_i
  if size==1
    self.extract_cpu.to_i
  else
    # convert to Int?
    raise TypeError, "can't convert #{self.class} into Integer"
  end
end

#trace(offset = nil, axis = nil, nan: false) ⇒ Object

Return the sum along diagonals of the array.

If 2-D array, computes the summation along its diagonal with the given offset, i.e., sum of ‘a`. If more than 2-D array, the diagonal is determined from the axes specified by axis argument. The default is axis=.

Parameters:

  • offset (Integer) (defaults to: nil) —

    (optional, default=0) diagonal offset

  • axis (Array) (defaults to: nil) —

    (optional, default=) diagonal axis

  • nan (Bool) (defaults to: false) —

    (optional, default=false) nan-aware algorithm, i.e., if true then it ignores nan.



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# File 'lib/cumo/narray/extra.rb', line 1123

def trace(offset=nil,axis=nil,nan:false)
  diagonal(offset,axis).sum(nan:nan,axis:-1)
end

#tril(k = 0) ⇒ Object

Lower triangular matrix. Return a copy with the elements above the k-th diagonal filled with zero.



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# File 'lib/cumo/narray/extra.rb', line 1051

def tril(k=0)
  dup.tril!(k)
end

#tril!(k = 0) ⇒ Object

Lower triangular matrix. Fill the self elements above the k-th diagonal with zero.



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# File 'lib/cumo/narray/extra.rb', line 1057

def tril!(k=0)
  if ndim < 2
    raise NArray::ShapeError, "must be >= 2-dimensional array"
  end
  if contiguous?
    idx = triu_indices(k+1)
    *shp,m,n = shape
    reshape!(*shp,m*n)
    self[false,idx] = 0
    reshape!(*shp,m,n)
  else
    store(tril(k))
  end
end

#tril_indices(k = 0) ⇒ Object

Return the indices for the lower-triangle on and below the k-th diagonal.



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# File 'lib/cumo/narray/extra.rb', line 1073

def tril_indices(k=0)
  if ndim < 2
    raise NArray::ShapeError, "must be >= 2-dimensional array"
  end
  m,n = shape[-2..-1]
  NArray.tril_indices(m,n,k)
end

#triu(k = 0) ⇒ Object

Upper triangular matrix. Return a copy with the elements below the k-th diagonal filled with zero.



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# File 'lib/cumo/narray/extra.rb', line 1012

def triu(k=0)
  dup.triu!(k)
end

#triu!(k = 0) ⇒ Object

Upper triangular matrix. Fill the self elements below the k-th diagonal with zero.



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# File 'lib/cumo/narray/extra.rb', line 1018

def triu!(k=0)
  if ndim < 2
    raise NArray::ShapeError, "must be >= 2-dimensional array"
  end
  if contiguous?
    *shp,m,n = shape
    idx = tril_indices(k-1)
    reshape!(*shp,m*n)
    self[false,idx] = 0
    reshape!(*shp,m,n)
  else
    store(triu(k))
  end
end

#triu_indices(k = 0) ⇒ Object

Return the indices for the uppler-triangle on and above the k-th diagonal.



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# File 'lib/cumo/narray/extra.rb', line 1034

def triu_indices(k=0)
  if ndim < 2
    raise NArray::ShapeError, "must be >= 2-dimensional array"
  end
  m,n = shape[-2..-1]
  NArray.triu_indices(m,n,k)
end

#vsplit(indices_or_sections) ⇒ Object

Examples:

p x = Cumo::DFloat.new(4,4).seq
# Cumo::DFloat#shape=[4,4]
# [[0, 1, 2, 3],
#  [4, 5, 6, 7],
#  [8, 9, 10, 11],
#  [12, 13, 14, 15]]

pp x.hsplit(2)
# [Cumo::DFloat(view)#shape=[4,2]
# [[0, 1],
#  [4, 5],
#  [8, 9],
#  [12, 13]],
#  Cumo::DFloat(view)#shape=[4,2]
# [[2, 3],
#  [6, 7],
#  [10, 11],
#  [14, 15]]]

pp x.hsplit([3, 6])
# [Cumo::DFloat(view)#shape=[4,3]
# [[0, 1, 2],
#  [4, 5, 6],
#  [8, 9, 10],
#  [12, 13, 14]],
#  Cumo::DFloat(view)#shape=[4,1]
# [[3],
#  [7],
#  [11],
#  [15]],
#  Cumo::DFloat(view)#shape=[4,0][]]


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# File 'lib/cumo/narray/extra.rb', line 801

def vsplit(indices_or_sections)
  split(indices_or_sections, axis:0)
end