kmat
Kmat is a Ruby gem for matrix operations. Kmat uses BLAS/LAPACK as back-end.
Requirements
BLAS/LAPACK libraries are needed to build kmat. MKL can also be used. You need to modify extconf.rb to use the other BLAS/LAPACK compatible libraries (pull requests are welcome).
Installation
Kmat is available on RubyGems.org:
$ gem install kmat
or in your Gemfile:
gem 'kmat'
Usage
While the gem name is kmat, the top module of this gem is the class Mat. Most of the functions of kmat are defined under Mat (some monkey patches (e.g. Random#randn) are applied to built-in modules/classes).
Mat is a class of matricies. It has matrix operations as methods. Unlike numpy in Python, Mat cannot be a tensor with order other than 2. Mat with shape (n, 1) or (1, n) behaves as a vector (not be distinguished from each other) in some methods (e.g. Mat#iprod).
Matlab style expected return value comments appear in the following sample codes, but they are only in documents (kmat has no way to generate these strings from Mat instances nor way to generate Mat instances from these strings).
Construction of matricies
require 'kmat'
Mat[[1, 2], [3, 4]] #=> [1, 2; 3, 4]
Mat.ones(2, 2) #=> [1, 1; 1, 1]
Mat.eye(2, 2) #=> [1, 0; 0, 1]
Mat.randn(2, 2) #=> [-0.11, 0.25; 0.83, -0.03] (vary every call)
Mat.range(3) #=> [0; 1; 2]
Mat.new(2, 3){|i, j| i+j} #=> [0, 1, 2; 1, 2, 3]
Arithmetic operations
require 'kmat'
a = Mat.ones(2, 2); b = Mat[[2, 0], [0, 1]]
a+b #=> [3, 1; 1, 2]
a-b #=> [-1, 1; 1, 0]
a.mprod(b) #=> [2, 1; 2, 1] (matrix product)
a.e_mul(b) #=> [2, 0; 0, 1] (element-wise product)
b.under(a) #=> [0.5, 0.5; 1, 1] (like b\a in Matlab)
a.over(b) #=> [0.5, 1; 0.5, 1] (like a/b in Matlab)
a*b #=> ArgumentError (to avoid confusion of Mat#mprod vs Mat#e_mul)
using Mat::MatrixProductOperator
[a*b, a/b] #=> [ [2, 1; 2, 1], [0.5, 1; 0.5, 1] ] (refinements are available)
a.sin # Most of mathematical functions defined in math.h are available as element-wise operations
Destructive operation
require 'kmat'
a = Mat.ones(2, 2); b = Mat[[2, 0], [0, 1]]
a+b; a #=> [1, 1; 1, 1]
a.add!(b)
a #=> [3, 1; 1, 2]
c = Mat.new(2, 2)
c.mprod!(a, b)
c #=> [6, 1; 2, 2]
a.sub!(b); a.e_mul!(b); b.e_div!(a); c.under!(b, a)
Numpy-like broadcasting
require 'kmat'
a = Mat.eye(2, 2); b = Mat.range(2)
a+b #=> [1, 0; 1, 2]
a.add!(a.broadcast(b)) # For destructive operation, you need to fit shape using Mat#broadcast
a.s_add!(1.5) # Or use Mat#s_xxx! for element-wise opertion with broadcasted scalar value
0.5 * a # Numeric#* can be used as scalar multiplication (others like Numeric+Mat are not available)
Element or submatrix accessing
rquire 'kmat'
a = Mat[[1, 2], [3, 4]]
a[1, 0] #=> 3.0
a[0, -1] #=> 2.0 (negative indexing is available)
a[nil, 1] #=> [2; 4] (nil works like `:' in numpy)
a[[1, 0], 0..1] #=> [3, 4; 1, 2]
a[a.gt(2)] #=> [3; 4] (boolean indexing returns a vector)
vidx = Mat.new(1, 2, :object){ |i, j| [j, i] }
a[vidx] #=> [1, 3] (=[a[0, 0], a[1, 0]])
b = a[0, nil] # a submatrix is like a `view' of numby
a[0, 0] = 5
b #=> [5, 2]
b[0, 1] = -1 # but it's writable and may change the `supermatrix'
a #=> [5, -1; 3, 4]
b.freeze # use Object#freeze to avoid it
a[0, 0] = -3 # but, freezing submatrix do not freeze the `supermatrix'
b #=> [-3, -1]
a.deep_freeze # use `supermatrix'.deep_freeze to freeze all the related matricies
b[0, 0] = 7 #=> FrozenError
c = a[0, nil] # submatrix made from frozen matrix is pre-frozen
c[0, 0] = 9 #=> FrozenError
a = Mat[[1, 2], [3, 4]]
a[nil, 0] = Mat.range(2) # multi-entry substitution is also available
a #=> [0, 2; 1, 4]
a.map(&:-@) #=> [0, -2; -1, -4]
a.map_with_index!{|e, i, j| e+j}
a.diag #=> [0; 5] (returns diagonal elements as a vector)
a[] #=> [0, 3; 1, 5] (with no argument is equivalent to a[nil, nil])
Mat.range(3)[2] #=> 2.0 (with single integer or single integer array is available for vectors)
Value types
Mat in kmat has 5 value types.
Float
The default value type is :float. Values are double in C language and it is compatible with Float in Ruby. Most of linear argebraic operations are available only on float matricies.
Complex
:complex is available to deal with complex floats. Some operations are defined but the number of available operations is limitted.
Int
:int can be used as row or column index array. Values are int in C language, so it is not useful for matrix operations with large integer elements. We recomend to use :object with Integer for such usage.
Bool
:bool can be used as boolean indexing. Logical operations are available. In some operations, elements in boolean matricies behave as a finite filed with order 2 (+ is exclusive disjunction and * is logical conjunction).
Object
:object matricies can contain arbitrary Ruby objects. Operation behaviors are dependent on methods defined for the objects. For example, Mat#solve works if K#==, K#quo, K#* and K#- are defined appropriately, where K is a class of the elements.
:object matricies with 2-length Arrays are used as indecies for other Mats.
rquire 'kmat'
Mat.new(2, 2, :float){|i, j| i+j}
Mat.new(2, 2, :complex){|i, j| Complex.rect(i, j)}
Mat.new(2, 2, :int){|i, j| i-j}
Mat.new(2, 2, :bool){|i, j| i==j}
Mat.new(2, 2, :object){|i, j| Rational(i, j+1) }
Mat.new(1, 1).vtype #=> :float (Mat#vtype returns its value type as a Symbol above)
Sort, stacking and logical operations
require 'kmat'
a = Mat[[3, 2, 1], [5, -3, 7]]
a.sort(:row) #=> [1, 2, 3; -3, 5, 7]
a.rsort(:col) #=> [5, 2, 7; 3, -3, 1]
a.flip(:both) #=> [7, -3, 5; 1, 2, 3]
a.t #=> [3, 5; 2, -3; 1, 7] (transpose)
b = Mat.range(2)
Mat.blocks([[a, b], [b, a]]) #=> [3, 2, 1, 0; 5, -3, 7, 1; 0, 3, 2, 1; 1, 5, -3, 7]
Mat.vstack(a, a); Mat.hstack(a, b)
a.gt(b) #=> [true, true, true; true, false, true] (numpy-like broadcasting)
a.eq(b); a.ge(b); a.lt(b); a.le(b)
a.max #=> 7
a.maximum(b) #=> [3, 2, 1; 5, 1, 7]
Mat.maximum(a, b.repmat(1, 3), Mat.randn(2, 3))
#=> Mat.maximum can recieve arbitrary number of arguments but do not broadcast automatically
Linear algebraic operations
Most of them are useing BLAS/LAPACK as a back-end.
require 'kmat'
a, b = Mat.randn(3, 3), Mat.rand(3, 1)
a.ls(b) # ls means least_squares, the return x mimimize a.mprod(x)-b
a.evd # eigendecomposition
a.svd # singular value decomposition
a.lup # LUP decomposition
a.det # determinant
a.qr # QR decomposition
Mat.rand_orth(3) # Random orthogonal matrix
a.tr # trace
Copying elements
require 'kmat'
a, b = Mat.randn(2, 2), Mat.randn(2, 2)
a.dup # dup/clone are like Array#dup/clone
a.copy_from(b) # it is equivalent to a[] = b, value type is dependent on the reciever
a.replace(b[]) # Mat#replace copies submatrix relation and value type (Mat#copy_from do not)
a.fill(1.5) #=> [1.5, 1.5; 1.5, 1.5] (destructive)
Marshal.load(Marshal.dump(a))
# Marshal.dump/load are available
Random
require 'kmat'
Mat.randn(2, 2, random: Random.new) # In kmat, methods using random value, the generator can be specified by keyword `random'
$MatRandom = Random.new # Or substitute into $MatRandom
Random.new.randn # Random#randn returns a random value following N(0, 1)
randn() # Kernel#randn is equivalent to $MatRandom.randn
Contributing
Bug reports and pull requests are welcome on GitHub at https://github.com/cycloawaodorin/kmat.
License
Kmat is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version3 of the License, or (at your option) any later version.
Kmat is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with the gem; see the file LICENSE.md. If not, see the website of GPL.
/ext/lapack_headers/*.h
The header files under /ext/lapack_headers/ directory are modified or copied version of an Azalea Clive's product or Intel Corp's products. The original versions are distributed at the following.
blas.h is distributed at BLASの簡単な使い方.
lapacke.h, lapacke_config.h, lapacke_mangling.h and lapacke_utils.h are distributed at the website of LAPACKE under modified BSD license.