Class: Mat

Inherits:
Object
  • Object
show all
Includes:
Enumerable
Defined in:
lib/kmat.rb,
lib/kmat/misc.rb,
lib/kmat/arith.rb,
lib/kmat/linalg.rb,
lib/kmat/random.rb,
lib/kmat/logical.rb,
lib/kmat/version.rb,
lib/kmat/accessor.rb,
lib/kmat/statistics.rb

Defined Under Namespace

Modules: MatrixProductOperator Classes: InternalError, MismatchedDimensionError, NotImplementedYetError, SharingError, UncomputableMatrixError, ValueTypeError

Constant Summary collapse

VERSION = 
"0.1.0"

Class Method Summary collapse

Instance Method Summary collapse

Methods included from Enumerable

#argsort, #argsort_by

Class Method Details

.blocks(args) ⇒ Object

for example, Mat.blocks([a, b], [c, d]) returns a single matrix of [a, b; c, d]



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# File 'lib/kmat/accessor.rb', line 121

def blocks(args)
  vstack(*(args.map do |row|
    hstack(*row)
  end))
end

.hilb(n, type = :float) ⇒ Object 



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# File 'lib/kmat/misc.rb', line 2

def hilb(n, type=:float)
  self.new(n, n, type) do |i, j|
    1.quo(i+j+1)
  end
end

.hstack(*mats) ⇒ Object 



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# File 'lib/kmat/accessor.rb', line 146

def hstack(*mats)
  m, n = mats[0].shape
  1.upto(mats.size-1) do |i|
    mat = mats[i]
    raise MismatchedDimensionError, 'row-sizes must be the same' if mat.row_size != m
    n += mat.col_size
  end
  ret = Mat.new(m, n, mats[0].vtype)
  k = 0
  m = Mat.irange(m)
  mats.each do |mat|
    ret[m, Mat.new(mat.col_size, 1, :int) do |i, j|
      i+k
    end] = mat
    k += mat.col_size
  end
  ret
end

.load(file) ⇒ Object 



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# File 'lib/kmat/misc.rb', line 7

def load(file)
  case file
  when String
    ret = nil
    File.open(file) do |f|
      ret = Marshal.load(f)
    end
    ret
  when IO
    Marshal.load(file)
  else
    raise ArgumentError, 'the argument must be a filepath or an IO object'
  end
end

.max(*args) ⇒ Object Also known as: maximum 



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# File 'lib/kmat/arith.rb', line 159

def max(*args)
  case args.size
  when 0
    nil
  when 1
    args[0]
  else
    ret = args[0].dup
    1.upto(args.size-1) { |i|
      ret.maximum!(args[i])
    }
    ret
  end
end

.min(*args) ⇒ Object Also known as: minimum 



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# File 'lib/kmat/arith.rb', line 174

def min(*args)
  case args.size
  when 0
    nil
  when 1
    args[0]
  else
    ret = args[0].dup
    1.upto(args.size-1) { |i|
      ret.minimum!(args[i])
    }
    ret
  end
end

.rand(m = 1, n = 1, random: $MatRandom) ⇒ Object 



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# File 'lib/kmat/random.rb', line 100

def rand(m=1, n=1, random: $MatRandom)
  _rand0(m, n, random)
end

.rand_orth(n, random: $MatRandom) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 69

def self.rand_orth(n, random: $MatRandom)
  Mat.new(n, n, :float).rand_orth(random: random)
end

.randn(m = 1, n = 1, random: $MatRandom) ⇒ Object 



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# File 'lib/kmat/random.rb', line 103

def randn(m=1, n=1, random: $MatRandom)
  _randn0(m, n, random)
end

.vstack(*mats) ⇒ Object 



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# File 'lib/kmat/accessor.rb', line 127

def vstack(*mats)
  m, n = mats[0].shape
  1.upto(mats.size-1) do |i|
    mat = mats[i]
    raise MismatchedDimensionError, 'column-sizes must be the same' if mat.col_size != n
    m += mat.row_size
  end
  ret = Mat.new(m, n, mats[0].vtype)
  k = 0;
  n = Mat.irange(n)
  mats.each do |mat|
    ret[Mat.new(mat.row_size, 1, :int) do |i, j|
      i+k
    end, n] = mat
    k += mat.row_size
  end
  ret
end

Instance Method Details

#*(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 59

def *(other)
  if other.kind_of?(Mat)
    raise ArgumentError, "Mat#* is available only for scalar multiplication. To use Mat#*(Mat) for matrix product, call `using Mat::MatrixProductOperator'"
  else
    self.dup.s_mul!(other)
  end
end

#**(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 111

def **(other)
  case other
  when Integer
    ret, temp = self.dup, self.dup
    ret.eye
    if 0 <= other
      a = self.dup
    else
      a = self.inv
      other = -other
    end
    loop do
      if other % 2 == 1
        temp.mprod!(ret, a)
        temp, ret = ret, temp
      end
      other = other.div(2)
      break if other == 0
      temp.mprod!(a, a)
      temp, a = a, temp
    end
    ret
  when Float
    if self.symmetry?
      v, d = self.symmetrize.sym_evd
      d.diag.s_pow!(other)
      foo = v.mprod(d)
      d.mprod!(foo, v.t!)
    else
      raise UncomputableMatrixError, "cannot compute float power of non-symmetric matrcies"
    end
  when Rational
    self ** other.to_f
  else
    raise ArgumentError, "Mat powered by #{other.class} is not supported"
  end
end

#/(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 70

def /(other)
  if other.kind_of?(Mat)
    raise ArgumentError, "Mat#/ is available only for scalar multiplication with reciprocal. To use Mat#/(Mat) as an alias of Mat#over, call `using Mat::MatrixProductOperator`"
  else
    self.dup.s_div!(other)
  end
end

#<(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 59

def <(other)
  return false if self.equal?(other)
  unless other.kind_of?(Mat)
    raise ArgumentError, "Mat < #{other.class} is not defined"
  end
  if self.vtype != other.vtype
    raise ValueTypeError, "value types must be the same"
  elsif self.size != other.size
    raise MismatchedDimensionError, "the sizes must be the same, (#{self.size.join(', ')}) != (#{other.size.join(', ')})"
  end
  each_with_index do |e, i, j|
    return false unless e < other[i, j]
  end
  true
end

#<=(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 74

def <=(other)
  return false if self.equal?(other)
  unless other.kind_of?(Mat)
    raise ArgumentError, "Mat <= #{other.class} is not defined"
  end
  if self.vtype != other.vtype
    raise ValueTypeError, "value types must be the same"
  elsif self.size != other.size
    raise MismatchedDimensionError, "the sizes must be the same, (#{self.size.join(', ')}) != (#{other.size.join(', ')})"
  end
  each_with_index do |e, i, j|
    return false unless e <= other[i, j]
  end
  true
end

#==(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 47

def ==(other)
  return true if self.equal?(other)
  return false unless other.kind_of?(Mat)
  if self.vtype == other.vtype && self.size == other.size
    each_with_index do |e, i, j|
      return false unless e == other[i, j]
    end
    true
  else
    false
  end
end

#===(other) ⇒ Object 



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# File 'lib/kmat/accessor.rb', line 2

def ===(other)
  if other.kind_of?(Mat)
    self == other
  else
    false
  end
end

#>(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 89

def >(other)
  return false if self.equal?(other)
  unless other.kind_of?(Mat)
    raise ArgumentError, "Mat > #{other.class} is not defined"
  end
  if self.vtype != other.vtype
    raise ValueTypeError, "value types must be the same"
  elsif self.size != other.size
    raise MismatchedDimensionError, "the sizes must be the same, (#{self.size.join(', ')}) != (#{other.size.join(', ')})"
  end
  each_with_index do |e, i, j|
    return false unless e > other[i, j]
  end
  true
end

#>=(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 104

def >=(other)
  return false if self.equal?(other)
  unless other.kind_of?(Mat)
    raise ArgumentError, "Mat > #{other.class} is not defined"
  end
  if self.vtype != other.vtype
    raise ValueTypeError, "value types must be the same"
  elsif self.size != other.size
    raise MismatchedDimensionError, "the sizes must be the same, (#{self.size.join(', ')}) != (#{other.size.join(', ')})"
  end
  each_with_index do |e, i, j|
    return false unless e >= other[i, j]
  end
  true
end

#[](*idx) ⇒ Object 



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# File 'lib/kmat/accessor.rb', line 10

def [](*idx)
  if block_given?
    tmp = self.bracket(*idx)
    ret = yield(tmp)
    tmp.__send__(:_kill)
    ret
  else
    self.bracket(*idx)
  end
end

#add(other) ⇒ Object Also known as: + 



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# File 'lib/kmat/arith.rb', line 11

def add(other)
  if other.kind_of?(Mat)
    self.dup.add!(broadcast(other))
  else
    self.dup.s_add!(other)
  end
end

#add_times(other, alpha) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 78

def add_times(other, alpha)
  if other.kind_of?(Mat)
    self.dup.add_times!(broadcast(other), alpha)
  else
    self.dup.s_mul!(other*alpha)
  end
end

#all?(*args) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/kmat/logical.rb', line 2

def all?(*args)
  if block_given?
    each do |ent|
      return false unless yield(ent, *args)
    end
  elsif args.size == 0
    if self.vtype == :bool
      each do |ent|
        return false unless ent
      end
    else
      return enum_for(__method__)
    end
  else
    each do |ent|
      args.each do |arg|
        return false unless arg === ent
      end
    end
  end
  return true
end

#any?(*args) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/kmat/logical.rb', line 24

def any?(*args)
  if block_given?
    each do |ent|
      return true if yield(ent, *args)
    end
  elsif args.size == 0
    if self.vtype == :bool
      each do |ent|
        return true if ent
      end
    else
      return enum_for(__method__)
    end
  else
    each do |ent|
      args.each do |arg|
        return true if arg === ent
      end
    end
  end
  return false
end

#broadcast(other, vt = nil) ⇒ Object

extend ‘other’ to fit the shape of self this is similar to Python’s numpy broadcasting



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# File 'lib/kmat/accessor.rb', line 42

def broadcast(other, vt=nil)
  if other.kind_of?(Mat)
    if other.row_size == 1
      if other.col_size == 1
        other.repmat(row_size(), col_size())
      elsif other.col_size == self.col_size
        other.repmat(self.row_size, 1)
      else
        raise MismatchedDimensionError, "can't broadcast from (#{other.size.join(', ')}) to (#{self.size.join(', ')})"
      end
    elsif other.row_size == self.row_size
      if other.col_size == 1
        other.repmat(1, col_size())
      elsif other.col_size == self.col_size
        other
      else
        raise MismatchedDimensionError, "can't broadcast from (#{self.size.join(', ')}) to (#{other.size.join(', ')})"
      end
    else
      raise MismatchedDimensionError, "can't broadcast from (#{self.size.join(', ')}) to (#{other.size.join(', ')})"
    end
  else
    vt = vtype() if vt.nil?
    Mat.new(row_size(), col_size(), vt).fill(other)
  end
end

#coerce(other) ⇒ Object

to define Numeric * Mat as Mat#scalar(Numeric) remaining Mat * Mat is undefined, this returns non‐standard value



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# File 'lib/kmat/arith.rb', line 4

def coerce(other)
  if caller.first[/`([^']*)'/, 1] == '*'
    [self, other]
  else
    raise TypeError, "Mat can't be coerced into #{other.class}"
  end
end

#diag(k = 0) ⇒ Object 



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# File 'lib/kmat/accessor.rb', line 114

def diag(k=0)
  _diag_ul(k)
end

#distance(other) ⇒ Object

distance (Frobenius norm of the difference)



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# File 'lib/kmat/linalg.rb', line 229

def distance(other)
  self.dup.sub!(other).normf
end

#e_div(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 34

def e_div(other)
  if other.kind_of?(Mat)
    self.dup.e_div!(broadcast(other))
  else
    self.dup.s_div!(other)
  end
end

#e_mul(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 27

def e_mul(other)
  if other.kind_of?(Mat)
    self.dup.e_mul!(broadcast(other))
  else
    self.dup.s_mul!(other)
  end
end

#eigen_values ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 130

def eigen_values
  if symmetry?
    symmetrize().sym_eigen_values()
  else
    ge_eigen_values()
  end
end

#eq(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 120

def eq(other)
  unless other.kind_of?(Mat) && other.size == self.size
    other = broadcast(other)
  end
  Mat.new(row_size(), col_size(), :bool).eq!(self, other)
end

#evd ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 137

def evd
  if symmetry?
    symmetrize().sym_evd()
  else
    ge_evd()
  end
end

#flip(dim = :both) ⇒ Object

flip row, column or both axis ‘dim’ Symbol specifies fliping axis (:row, :col, :both, :none are available)



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# File 'lib/kmat/accessor.rb', line 85

def flip(dim=:both)
  dim = dim.to_sym if dim.respond_to?(:to_sym)
  m, n = *shape()
  case dim
  when :both, :b
    ri = Mat.new(m, 1, :int) do |i, j|
      m-i-1
    end
    ci = Mat.new(n, 1, :int) do |i, j|
      n-i-1
    end
    self[ri, ci]
  when :row, :r
    ri = Mat.new(m, 1, :int) do |i, j|
      m-i-1
    end
    self[ri, nil]
  when :col, :c
    ci = Mat.new(n, 1, :int) do |i, j|
      n-i-1
    end
    self[nil, ci]
  when :none, :n
    self[]
  else
    raise ArgumentError, "unknown axis symbol #{dim.inspect}"
  end
end

#ge(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 144

def ge(other)
  unless other.kind_of?(Mat) && other.size == self.size
    other = broadcast(other)
  end
  Mat.new(row_size(), col_size(), :bool).ge!(self, other)
end

#geo_mean(arg = :all) ⇒ Object 



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# File 'lib/kmat/statistics.rb', line 87

def geo_mean(arg=:all)
  foo = self.log.mean(arg)
  if foo.kind_of?(Mat)
    foo.exp!
  elsif arg.kind_of?(Mat)
    arg.exp!
    arg[0, 0]
  else
    Math.exp(foo)
  end
end

#geo_normalize(arg = :all) ⇒ Object 



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# File 'lib/kmat/misc.rb', line 48

def geo_normalize(arg=:all)
  self.dup.geo_normalize!(arg)
end

#geo_normalize!(arg = :all) ⇒ Object 



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# File 'lib/kmat/misc.rb', line 38

def geo_normalize!(arg=:all)
  self.log!
  foo = self.mean(arg)
  if foo.kind_of?(Mat)
    self.sub!(self.broadcast(foo))
  else
    self.s_sub!(foo)
  end
  self.exp!
end

#gt(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 138

def gt(other)
  unless other.kind_of?(Mat) && other.size == self.size
    other = broadcast(other)
  end
  Mat.new(row_size(), col_size(), :bool).gt!(self, other)
end

#hypot(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 149

def hypot(other)
  if other.kind_of?(Mat)
    self.dup.hypot!(broadcast(other))
  else
    self.dup.s_hypot!(other)
  end
end

#iprod(*args, inverse: false) ⇒ Object Also known as: inner_product

inner product let x and y are column vectors and M is a square matrix the following is available (1) x.iprod => x’*x (2) x.iprod(y) => x’*y (3) M.iprod(x) => x’*M*x (4) M.iprod(x, y) => x’*M*y if ‘inverse’ is true, M is replaced by its Moore–Penrose inverse in case (1) or (2), ‘inverse’ is ignored if x or y is row vector, take transpose automatically



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# File 'lib/kmat/linalg.rb', line 155

def iprod(*args, inverse: false)
  case  args.size
  when 0
    if vector? # case 1
      _iprod(self)
    else
      raise MismatchedDimensionError, "self must be a vector"
    end
  when 1
    o = args[0]
    if o.vector?
      if vector? # case 2
        _iprod(o)
      else # case 3
        if !square?
          raise MismatchecDimensionError, "M must be square for M.iprod(x)"
        elsif inverse
          temp = Mat.new(row_size, 1, vtype)
          if o.col_size == 1
            begin
              temp.solve!(self, o)
            rescue UncomputableMatrixError
              temp.ls!(self, o)
            end
          else
            begin
              temp.tsolve!(self, o)
            rescue UncomputableMatrixError
              temp.tls!(self, o)
            end
          end
        else
          temp = Mat.new(row_size, 1, vtype)
          if o.col_size == 1
            temp.mprod!(self, o)
          else
            temp.mprod!(o, self)
          end
        end
        temp.__send__(:_iprod, o)
      end
    else
      raise MismatchedDimensionError, "as iprod with single argument, x.iprod(y) and M.iprod(x) are available, not x.iprod(M) or others"
    end
  when 2 # case 4
    x, y = *args
    if !square? || !x.vector? || !y.vector? || x.length != row_size || y.length != row_size
      raise MismatchecDimensionError, "as iprod with 2 arguments, only M.iprod(x, y) is available, not others"
    end
    temp = Mat(row_size, 1, vtype)
    if y.col_size == 1
      temp.mprod!(y)
    else
      if y.frozen?
        y = y.dup
        y.transpose
        temp.mprod!(y)
      else
        begin
          y.transpose
          temp.mprod!(y)
        ensure
          y.transpose
        end
      end
    end
    x.__send__(:_iprod, temp)
  else
    raise ArgumentError, "wrong number of arguments (given #{args.size}, expected 0..2)"
  end
end

#le(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 132

def le(other)
  unless other.kind_of?(Mat) && other.size == self.size
    other = broadcast(other)
  end
  Mat.new(row_size(), col_size(), :bool).le!(self, other)
end

#least_squares(b, tor: nil, weight: nil, transpose: false) ⇒ Object Also known as: ls 



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# File 'lib/kmat/linalg.rb', line 18

def least_squares(b, tor: nil, weight: nil, transpose: false)
  if tor
    raise ArgumentError, "tor and weight must not specify at once" if weight
    raise ArgumentError, "for conjugate LS, auto-transpose is not available" if transpose
    ls_conj(b, tor)
  elsif weight
    raise ArgumentError, "for weighted LS, auto-transpose is not available" if transpose
    wls(b, weight)
  else
    if transpose
      tls(b)
    else
      Mat.new(*b.shape, :float).__send__(:_ls, self, b)
    end
  end
end

#least_squares!(a, b, tor: nil, weight: nil, transpose: false) ⇒ Object Also known as: ls! 



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# File 'lib/kmat/linalg.rb', line 2

def least_squares!(a, b, tor: nil, weight: nil, transpose: false)
  if tor
    raise ArgumentError, "tor and weight must not specify at once" if weight
    raise ArgumentError, "for conjugate LS, auto-transpose is not available" if transpose
    _ls_conj(a, b, tor)
  elsif weight
    raise ArgumentError, "for weighted LS, auto-transpose is not available" if transpose
    wls!(a, b, weight)
  else
    if transpose
      tls!(a, b)
    else
      _ls(a, b)
    end
  end
end

#ls_conj(b, tor: Float::EPSILON) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 40

def ls_conj(b, tor: Float::EPSILON)
  Mat.new(self.col_size, 1, :float).ls_conj!(self, b, tor: tor)
end

#ls_conj!(a, b, tor: Float::EPSILON) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 37

def ls_conj!(a, b, tor: Float::EPSILON)
  _ls_conj(a, b, tor)
end

#lt(other) ⇒ Object 



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# File 'lib/kmat/logical.rb', line 126

def lt(other)
  unless other.kind_of?(Mat) && other.size == self.size
    other = broadcast(other)
  end
  Mat.new(row_size(), col_size(), :bool).lt!(self, other)
end

#maximum(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 86

def maximum(other)
  if other.kind_of?(Mat)
    self.dup.maximum!(broadcast(other))
  else
    self.dup.s_maximum!(other)
  end
end

#mean(arg = :all) ⇒ Object 



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# File 'lib/kmat/statistics.rb', line 17

def mean(arg=:all)
  foo = sum(arg)
  if foo.kind_of?(Mat)
    if foo.row_size != self.row_size
      foo.e_div(self.row_size)
    else
      foo.e_div(self.col_size)
    end
  elsif arg.kind_of?(Mat)
    arg.e_div(self.length)
    arg[0, 0]
  else
    foo.quo(self.length)
  end
end

#minimum(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 93

def minimum(other)
  if other.kind_of?(Mat)
    self.dup.minimum!(broadcast(other))
  else
    self.dup.s_minimum!(other)
  end
end

#norm(type = :two, elementwise: false) ⇒ Object

matrix norm ‘type’ Symbol or Integer specifies norm definition if ‘elementwise’ is true, return induced norm if ‘elementwise’ is false, return elementwise norm if ‘type’ is :fro, return Frobenius norm



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# File 'lib/kmat/linalg.rb', line 241

def norm(type=:two, elementwise: false)
  if elementwise
    case type
    when :one, :o, 1
      norm_e1()
    when :infinity, :i, :inf, :infty, Float::INFINITY
      norm_einf()
    when :two, :t, 2, :frobenius, :f, :fro
      normf()
    end
  else
    case type
    when :one, :o, 1
      norm1()
    when :infinity, :i, :inf, :infty, Float::INFINITY
      normi()
    when :two, :t, 2
      norm2()
    when :frobenius, :f, :fro
      normf()
    end
  end
end

#normalize ⇒ Object 



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# File 'lib/kmat/misc.rb', line 65

def normalize
  self.dup.normalize!
end

#normalize! ⇒ Object 



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# File 'lib/kmat/misc.rb', line 51

def normalize!
  if self.vector?
    self.s_div!(self.normf)
  elsif self.square?
    ev = self.eigen_values
    if ev[0] < 0
      self.diag.s_add!(ev[0]*(-2))
      ev.s_add!(ev[0]*(-2))
    end
    self.s_div!(Math.exp(ev.log!.mean))
  else
    raise MismatchedDimensionError, "normalize is available only for vectors or square matricies"
  end
end

#over(other) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 95

def over(other)
  if other.square?
    begin
      other.tsolve(self).t!
    rescue UncomputableMatrixError
      other.tls(self).t!
    end
  else
    other.tls(self).t!
  end
end

#over!(a, b) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 106

def over!(a, b)
  if b.square?
    begin
      tsolve!(b, a).t!
    rescue UncomputableMatrixError
      tls!(b, a).t!
    end
  else
    tls!(b, a).t!
  end
end

#pinv ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 117

def pinv
  n = self.size.min
  i = Mat.I(n)
  if square?
    begin
      solve(i)
    rescue UncomputableMatrixError
      ls(i)
    end
  else
    ls(i)
  end
end

#pow(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 101

def pow(other)
  if other.kind_of?(Mat)
    self.dup.pow!(broadcast(other))
  else
    self.dup.s_pow!(other)
  end
end

#rand(arg = nil, random: $MatRandom) ⇒ Object 



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# File 'lib/kmat/random.rb', line 92

def rand(arg=nil, random: $MatRandom)
  _rand0(random, arg)
end

#rand_orth(random: $MatRandom) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 66

def rand_orth(random: $MatRandom)
  _rand_orth(random)
end

#randn(random: $MatRandom) ⇒ Object 



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# File 'lib/kmat/random.rb', line 95

def randn(random: $MatRandom)
  _randn0(random)
end

#rcond(type = :two) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 265

def rcond(type=:two)
  case type
  when :one, :o, 1
    _rcondoi(:one)
  when :infinity, :i, :inf, :infty, Float::INFINITY
    _rcondoi(:infinity)
  when :two, :t, 2
    _rcond2()
  when :frobenius, :f, :fro
    _rcondf()
  end
end

#replace_rep(src) ⇒ Object

replace self by repeated ‘src’ self will be left-top of infinitly repeated ‘src’



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# File 'lib/kmat/accessor.rb', line 71

def replace_rep(src)
  ri = Mat.new(row_size(), 1, :int) do |i, j|
    i % src.row_size
  end
  ci = Mat.new(col_size(), 1, :int) do |i, j|
    i % src.col_size
  end
  src[ri, ci] do |m|
    self.copy_from(m)
  end
end

#repmat(row_repeat, col_repeat) ⇒ Object

for example, A.repmat(2, 3) returns [A, A, A: A, A, A]



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# File 'lib/kmat/accessor.rb', line 28

def repmat(row_repeat, col_repeat)
  ri = Mat.new(row_size()*row_repeat, 1, :int) do |i, j|
    i % row_size()
  end
  ci = Mat.new(col_size()*col_repeat, 1, :int) do |i, j|
    i % col_size()
  end
  self[ri, ci] do |m|
    m.dup
  end
end

#rpow(other) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 108

def rpow(other)
  other.dup.pow!(other.broadcast(self))
end

#save(file) ⇒ Object 



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# File 'lib/kmat/misc.rb', line 24

def save(file)
  case file
  when String
    File.open(file, 'w') do |f|
      Marshal.dump(self, f)
    end
  when IO
    Marshal.dump(self, file)
  else
    raise ArgumentError, 'the argument must be a filepath or an IO object'
  end
  nil
end

#scalar(alpha) ⇒ Object 



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# File 'lib/kmat/arith.rb', line 66

def scalar(alpha)
  self.dup.s_mul!(alpha)
end

#squared_distance(other) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 232

def squared_distance(other)
  self.dup.sub!(other).iprod
end

#std(arg = :all, ddof: 0) ⇒ Object Also known as: stddev, standard_deviation 



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# File 'lib/kmat/statistics.rb', line 73

def std(arg=:all, ddof: 0)
  foo = var(arg, ddof: ddof)
  if foo.kind_of?(Mat)
    foo.sqrt!
  elsif arg.kind_of?(Mat)
    arg.sqrt!
    arg[0, 0]
  else
    Math.sqrt(arg)
  end
end

#sub(other) ⇒ Object Also known as: - 



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# File 'lib/kmat/arith.rb', line 19

def sub(other)
  if other.kind_of?(Mat)
    self.dup.sub!(broadcast(other))
  else
    self.dup.s_sub!(other)
  end
end

#sum(arg = :all) ⇒ Object 



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# File 'lib/kmat/statistics.rb', line 2

def sum(arg=:all)
  case arg
  when Mat
    _sum(arg)
  when :all, :a
    _sum(Mat.new(1, 1, self.vtype))
  when :col, :c
    _sum(Mat.new(1, col_size, self.vtype))
  when :row, :r
    _sum(Mat.new(row_size, 1, self.vtype))
  when :none, :n
    self.dup
  end
end

#temp ⇒ Object 



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# File 'lib/kmat/accessor.rb', line 21

def temp
  ret = yield(self)
  _kill
  ret
end

#under(other) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 73

def under(other)
  if square?
    begin
      solve(other)
    rescue UncomputableMatrixError
      ls(other)
    end
  else
    ls(other)
  end
end

#under!(a, b) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 84

def under!(a, b)
  if a.square?
    begin
      solve!(a, b)
    rescue UncomputableMatrixError
      ls!(a, b)
    end
  else
    ls!(a, b)
  end
end

#var(arg = :all, ddof: 0) ⇒ Object Also known as: variance 



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# File 'lib/kmat/statistics.rb', line 48

def var(arg=:all, ddof: 0)
  foo = mean(arg)
  if foo.kind_of?(Mat)
    bar = foo.repmat(self.row_size.div(foo.col_size), self.col_size.div(foo.col_size))
    bar.sub!(self).e_mul!(bar)
  else
    unless arg.kind_of?(Mat)
      arg = Mat.new(1, 1, self.vtype) do
        foo
      end
    end
    bar = Mat.new(self.row_size, self.col_size, self.vtype)
    bar.fill(foo)
  end
  bar.sub!(self)
  bar.e_mul!(bar)
  bar.__send__(:_mean, arg, ddof)
  if foo.kind_of?(Mat)
    bar
  else
    bar[0, 0]
  end
end

#wls(b, w) ⇒ Object 



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# File 'lib/kmat/linalg.rb', line 62

def wls(b, w)
  Mat.new(self.col_size, 1, :f).wls!(self, b, w)
end

#wls!(a, b, w) ⇒ Object

weighted least squares weight ‘w’ is a vector consists of standard deviations of errors a; (m, n)-matrix b: m-vector x: n-vector



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# File 'lib/kmat/linalg.rb', line 49

def wls!(a, b, w)
  nw = w.length
  diag = Mat.new(nw, nw, :f)
  diag.diag.temp do |dd|
    begin
      dd.copy_from(w)
    rescue MismatchedDimensionError
      dd.tcopy_from(w)
    end
    dd.sqrt!
  end
  glm!(a, diag, b)
end