Module: MyMathGem::LinearAlgebra

Defined in:
lib/my_math_gem/linear_algebra.rb

Class Method Summary collapse

Class Method Details

.cross(v1, v2) ⇒ Object

Cross product dua vektor 3D

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 29

def self.cross(v1, v2)
  raise ArgumentError, "Cross product hanya untuk vektor 3 dimensi" unless v1.length == 3 && v2.length == 3
  [
    v1[1]*v2[2] - v1[2]*v2[1],
    v1[2]*v2[0] - v1[0]*v2[2],
    v1[0]*v2[1] - v1[1]*v2[0]
  ]
end

.determinant_2x2(m) ⇒ Object

Determinan matriks 2x2

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 71

def self.determinant_2x2(m)
  raise ArgumentError, "Matriks harus 2x2" unless m.length == 2 && m.all? { |row| row.length == 2 }
  m[0][0]*m[1][1] - m[0][1]*m[1][0]
end

.determinant_3x3(m) ⇒ Object

Determinan matriks 3x3

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 77

def self.determinant_3x3(m)
  raise ArgumentError, "Matriks harus 3x3" unless m.length == 3 && m.all? { |row| row.length == 3 }
  a, b, c = m[0]
  d, e, f = m[1]
  g, h, i = m[2]
  a*(e*i - f*h) - b*(d*i - f*g) + c*(d*h - e*g)
end

.dot(v1, v2) ⇒ Object

Dot product dua vektor (array angka)

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 11

def self.dot(v1, v2)
  raise ArgumentError, "Vektor harus sama panjang" unless v1.length == v2.length
  v1.zip(v2).map { |a, b| a * b }.sum
end

.inverse_2x2(m) ⇒ Object

Invers matriks 2x2

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 86

def self.inverse_2x2(m)
  det = determinant_2x2(m)
  raise ArgumentError, "Matriks singular, determinan = 0" if det == 0
  inv_det = 1.0 / det
  [
    [ m[1][1]*inv_det, -m[0][1]*inv_det ],
    [ -m[1][0]*inv_det, m[0][0]*inv_det ]
  ]
end

.inverse_3x3(m) ⇒ Object

Invers matriks 3x3 (menggunakan metode kofaktor)

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 97

def self.inverse_3x3(m)
  det = determinant_3x3(m)
  raise ArgumentError, "Matriks singular, determinan = 0" if det == 0
  inv_det = 1.0 / det

  cofactors = Array.new(3) { Array.new(3, 0) }

  # Hitung kofaktor untuk tiap elemen
  (0..2).each do |row|
    (0..2).each do |col|
      minor = minor_2x2(m, row, col)
      cofactors[row][col] = ((row + col).even? ? 1 : -1) * determinant_2x2(minor)
    end
  end

  # Transpose kofaktor untuk dapat adjoin matrix
  adjugate = transpose(cofactors)

  # Kalikan dengan 1/det
  adjugate.map { |row| row.map { |val| val * inv_det } }
end

.matrix_multiply(m1, m2) ⇒ Object

Perkalian matriks (mxn) dengan matriks (nxp) atau vektor (n)



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# File 'lib/my_math_gem/linear_algebra.rb', line 39

def self.matrix_multiply(m1, m2)
  # Jika m2 adalah vektor
  if m2.is_a?(Array) && !m2.empty? && !m2[0].is_a?(Array)
    raise ArgumentError, "Jumlah kolom m1 harus sama dengan panjang vektor m2" unless m1[0].length == m2.length

    m1.map do |row|
      dot(row, m2)
    end
  else
    raise ArgumentError, "Jumlah kolom m1 harus sama dengan jumlah baris m2" unless m1[0].length == m2.length

    result = Array.new(m1.length) { Array.new(m2[0].length, 0) }
    m1.length.times do |i|
      m2[0].length.times do |j|
        sum = 0
        m2.length.times do |k|
          sum += m1[i][k] * m2[k][j]
        end
        result[i][j] = sum
      end
    end
    result
  end
end

.minor_2x2(m, row_to_remove, col_to_remove) ⇒ Object

Helper: matriks minor 2x2 dengan menghilangkan baris row_to_remove dan kolom col_to_remove



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# File 'lib/my_math_gem/linear_algebra.rb', line 120

def self.minor_2x2(m, row_to_remove, col_to_remove)
  m.each_with_index
   .reject { |_, r| r == row_to_remove }
   .map { |row, _| row.each_with_index.reject { |_, c| c == col_to_remove }.map(&:first) }
end

.norm(v) ⇒ Object

Norm (magnitude) vektor



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# File 'lib/my_math_gem/linear_algebra.rb', line 17

def self.norm(v)
  Math.sqrt(v.map { |x| x**2 }.sum)
end

.normalize(v) ⇒ Object

Normalisasi vektor (unit vector)

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 22

def self.normalize(v)
  n = norm(v)
  raise ArgumentError, "Vektor nol tidak dapat dinormalisasi" if n == 0
  v.map { |x| x.to_f / n }
end

.square_matrix?(m) ⇒ Boolean

Validasi matriks (array of arrays) persegi

Returns:

  • (Boolean) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 4

def self.square_matrix?(m)
  return false unless m.is_a?(Array) && !m.empty?
  n = m.length
  m.all? { |row| row.is_a?(Array) && row.length == n }
end

.transpose(m) ⇒ Object

Transpose matriks

Raises:

  • (ArgumentError) 


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# File 'lib/my_math_gem/linear_algebra.rb', line 65

def self.transpose(m)
  raise ArgumentError, "Input harus matriks (array of arrays)" unless m.is_a?(Array) && m.all? { |row| row.is_a?(Array) }
  m[0].length.times.map { |i| m.map { |row| row[i] } }
end