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