Module: Maxima

Defined in:
lib/maxima/core.rb,
lib/maxima/unit.rb,
lib/maxima/float.rb,
lib/maxima/helper.rb,
lib/maxima/boolean.rb,
lib/maxima/command.rb,
lib/maxima/complex.rb,
lib/maxima/version.rb,
lib/maxima/function.rb,
lib/maxima/rational.rb,
lib/maxima/histogram.rb,
lib/maxima/polynomial.rb

Defined Under Namespace

Modules: Helper Classes: Boolean, Command, Complex, Float, Function, Histogram, Polynomial, Rational, Unit

Constant Summary collapse

VERSION = 
"1.1.0"

Class Method Summary collapse

Class Method Details

.bin_op(e_1, e_2, bin_op) ⇒ Object 



2
3
4
 
# File 'lib/maxima/core.rb', line 2

def self.bin_op(e_1, e_2, bin_op)
  Maxima::Function.new("((#{Maxima.mformat(e_1)}) #{bin_op} (#{Maxima.mformat(e_2)}))")
end

.Complex(real, imaginary) ⇒ Object 



3
4
5
 
# File 'lib/maxima/complex.rb', line 3

def self.Complex(real, imaginary)
  Complex.new(real, imaginary)
end

.diff(function, v: "x") ⇒ Object 



35
36
37
38
39
40
 
# File 'lib/maxima/core.rb', line 35

def self.diff(function, v: "x")
  Command.output(diff: Function) do |c|
    c.let :function, function
    c.let :diff, "derivative(function, #{v})"
  end
end

.equivalence(expression_one, expression_two) ⇒ Object 



83
84
85
86
87
88
89
90
 
# File 'lib/maxima/core.rb', line 83

def self.equivalence(expression_one, expression_two)
  Command.output(:is_equal => Boolean) do |c|
    formatted_expression_one = mformat(expression_one)
    formatted_expression_two = mformat(expression_two)

    c.let :is_equal, "is(equal(#{formatted_expression_one}, #{formatted_expression_two}))"
  end
end

.Float(real) ⇒ Object 



3
4
5
 
# File 'lib/maxima/float.rb', line 3

def self.Float(real)
  Float.new(real)
end

.integrate(function, t0 = nil, t1 = nil, v: "x") ⇒ Object 



26
27
28
29
30
31
32
33
 
# File 'lib/maxima/core.rb', line 26

def self.integrate(function, t0 = nil, t1 = nil, v: "x")
  expression = (t0 && t1) ? "integrate(function, #{v}, #{t0}, #{t1})" : "integrate(function, #{v})"

  Command.output(integral: Function) do |c|
    c.let :function, function
    c.let :integral, expression
  end
end

.lagrangian(minimize_function, variables, constraint_function, initial_guess, iterations: 5) ⇒ Object 



92
93
94
95
96
97
98
99
100
101
102
103
104
105
 
# File 'lib/maxima/core.rb', line 92

def self.lagrangian(minimize_function, variables, constraint_function, initial_guess, iterations: 5)
  Command.output(variables => Unit) do |c|
    variables           = mformat(variables)
    initial_guess       = mformat(initial_guess)
    constraint_function = mformat(Array(constraint_function))
    optional_args       = mformat(niter: iterations)

    c.dependencies << "lbfgs"
    c.dependencies << "augmented_lagrangian"

    c.let :output, "augmented_lagrangian_method(#{minimize_function}, #{variables}, #{constraint_function}, #{initial_guess}, #{optional_args})"
    c.let variables, "sublis(output[1], #{variables})"
  end
end

.lagrangian_interpolation(array) ⇒ Object

c.let :output, “fmin_cobyla(#minimize_function, #mformat(variables), #initial_guess,constraints = #constraint_function)”

  c.let variables, "sublis(output[1], #{variables})"
end

end



18
19
20
21
22
23
24
 
# File 'lib/maxima/core.rb', line 18

def self.lagrangian_interpolation(array)
  Command.output(function: Function) do |c|
    c.dependencies << "interpol"
    c.let :array, array
    c.let_simplified :function, "lagrange(array)"
  end
end

.lsquares_estimation(points, variables, equation, outputs, equation_for_mse: equation) ⇒ Object 



65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
 
# File 'lib/maxima/core.rb', line 65

def self.lsquares_estimation(points, variables, equation, outputs, equation_for_mse: equation)
  Command.output(outputs => Complex, :mse => Float) do |c|
    formatted_points    = points.map { |a| mformat(a) }.join(",")
    formatted_variables = mformat(variables)
    formatted_outputs   = mformat(outputs)

    c.dependencies << "lsquares"
    c.let :M, "matrix(#{formatted_points})"
    c.let :lsquares_estimation, "lsquares_estimates(M, #{formatted_variables}, #{equation}, #{formatted_outputs})"
    if outputs.count == 1
      c << "map (lhs, lsquares_estimation) :: map (rhs, lsquares_estimation)"
    else
      c << "map (lhs, lsquares_estimation[1]) :: map (rhs, lsquares_estimation[1])"
    end
    c.let :mse, "lsquares_residual_mse(M, #{formatted_variables}, #{equation_for_mse}, first (lsquares_estimation))"
  end
end

.mformat(variable) ⇒ Object 



107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
 
# File 'lib/maxima/core.rb', line 107

def self.mformat(variable)
  case variable
  when String
    variable # the only truly `valid` input is a string
  when Hash
    variable.map do |key,value|
      "#{mformat(key)} = #{mformat(value)}"
    end.join(", ")
  when Array, Histogram
    "[" + variable.to_a.map { |v| mformat(v) }.join(",") + "]"
  when ::Complex
    mformat Complex.new(variable.real, variable.imag)
  when Numeric
    mformat Float(variable)
  when Complex, Float, Function
    variable.to_maxima_input
  when nil
    throw :cannot_format_nil
  else # Symbol, etc.
    variable.to_s
  end
end

.plot(*maxima_objects, from_x: nil, from_y: nil) ⇒ Object 



42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
 
# File 'lib/maxima/core.rb', line 42

def self.plot(*maxima_objects, from_x: nil, from_y: nil)
  maxima_objects << [[from_x.min, 0], [from_x.max, 0]] if from_x
  maxima_objects << [[0, from_y.min], [0, to_y.max]] if from_y

  maxima_objects = maxima_objects.map do |k|
    if k.respond_to?(:to_gnu_plot)
      k.to_gnu_plot
    elsif k.is_a?(Array) && !k.first.is_a?(String)
      [*k.transpose, w: "points"]
    else
      k
    end
  end

  Helper.stfu do
    Numo.gnuplot do |c|
      c.debug_on
      c.set title: "Maxima Plot"
      c.plot(*maxima_objects)
    end
  end
end

.solve_polynomial(equations, variables_to_solve_for, ignore: nil, real_only: false) ⇒ Object 



130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
 
# File 'lib/maxima/core.rb', line 130

def self.solve_polynomial(equations, variables_to_solve_for, ignore: nil, real_only: false)
  variables_to_solve_for = Array(variables_to_solve_for)
  equations = Array(equations)

  throw :all_equations_must_include_equivalence unless equations.all? { |e| e.include?("=") }

  # regex match extract
  output = Command.output(output: Unit) do |c|
    c.with_options(real_only: real_only)

    variables = mformat(variables_to_solve_for)
    equations = mformat(equations)

    c.let :output, "algsys(#{equations},#{variables})"
  end

  output = output[:output]

  variables_to_solve_for -= Array(ignore)

  variable_regexes = variables_to_solve_for.map do |variable|
    "#{variable}=(-?.*?)(?:\,|\\])"
  end

  regex = Regexp.new(variable_regexes.reduce(&:+))

  output = output.to_s.gsub(" ", "")

  output.scan(regex).map { |row| variables_to_solve_for.zip(row.map { |v| Unit.parse(v) }).to_h }
end