Class: Matrix::LUPDecomposition

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 154
def initialize a
 raise TypeError, "Expected Matrix but got #{a.class}" unless a.is_a?(Matrix )
 # Use a "left-looking", dot-product, Crout/Doolittle algorithm.
 @lu = a.to_a
 @row_count = a.row_count
 @column_count = a.column_count
 @pivots = Array .new(@row_count)
 @row_count.times do |i|
 @pivots[i] = i
 end
 @pivot_sign = 1
 lu_col_j = Array .new(@row_count)
 # Outer loop.

 @column_count.times do |j|
 # Make a copy of the j-th column to localize references.

 @row_count.times do |i|
 lu_col_j[i] = @lu[i][j]
 end
 # Apply previous transformations.

 @row_count.times do |i|
 lu_row_i = @lu[i]
 # Most of the time is spent in the following dot product.

 kmax = [i, j].min
 s = 0
 kmax.times do |k|
 s += lu_row_i[k]*lu_col_j[k]
 end
 lu_row_i[j] = lu_col_j[i] -= s
 end
 # Find pivot and exchange if necessary.

 p = j
 (j+1).upto(@row_count-1) do |i|
 if (lu_col_j[i].abs > lu_col_j[p].abs)
 p = i
 end
 end
 if (p != j)
 @column_count.times do |k|
 t = @lu[p][k]; @lu[p][k] = @lu[j][k]; @lu[j][k] = t
 end
 k = @pivots[p]; @pivots[p] = @pivots[j]; @pivots[j] = k
 @pivot_sign = -@pivot_sign
 end
 # Compute multipliers.

 if (j < @row_count && @lu[j][j] != 0)
 (j+1).upto(@row_count-1) do |i|
 @lu[i][j] = @lu[i][j].quo(@lu[j][j])
 end
 end
 end
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 63
def pivots
 @pivots
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 79
def det
 if (@row_count != @column_count)
 Matrix .Raise Matrix ::ErrDimensionMismatch
 end
 d = @pivot_sign
 @column_count.times do |j|
 d *= @lu[j][j]
 end
 d
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 22
def l
 Matrix .build (@row_count, [@column_count, @row_count].min) do |i, j|
 if (i > j)
 @lu[i][j]
 elsif (i == j)
 1
 else
 0
 end
 end
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 48
def p
 rows = Array .new(@row_count){Array .new(@row_count, 0)}
 @pivots.each_with_index{|p, i| rows[i][p] = 1}
 Matrix .send :new, rows, @row_count
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 67
def singular?
 @column_count.times do |j|
 if (@lu[j][j] == 0)
 return true
 end
 end
 false
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 95
def solve b
 if (singular?)
 Matrix .Raise Matrix ::ErrNotRegular, "Matrix is singular."
 end
 if b.is_a? Matrix 
 if (b.row_count != @row_count)
 Matrix .Raise Matrix ::ErrDimensionMismatch
 end
 # Copy right hand side with pivoting
 nx = b.column_count
 m = @pivots.map{|row| b.row(row).to_a}
 # Solve L*Y = P*b
 @column_count.times do |k|
 (k+1).upto(@column_count-1) do |i|
 nx.times do |j|
 m[i][j] -= m[k][j]*@lu[i][k]
 end
 end
 end
 # Solve U*m = Y
 (@column_count-1).downto(0) do |k|
 nx.times do |j|
 m[k][j] = m[k][j].quo(@lu[k][k])
 end
 k.times do |i|
 nx.times do |j|
 m[i][j] -= m[k][j]*@lu[i][k]
 end
 end
 end
 Matrix .send :new, m, nx
 else # same algorithm, specialized for simpler case of a vector
 b = convert_to_array(b)
 if (b.size != @row_count)
 Matrix .Raise Matrix ::ErrDimensionMismatch
 end
 # Copy right hand side with pivoting
 m = b.values_at(*@pivots)
 # Solve L*Y = P*b
 @column_count.times do |k|
 (k+1).upto(@column_count-1) do |i|
 m[i] -= m[k]*@lu[i][k]
 end
 end
 # Solve U*m = Y
 (@column_count-1).downto(0) do |k|
 m[k] = m[k].quo(@lu[k][k])
 k.times do |i|
 m[i] -= m[k]*@lu[i][k]
 end
 end
 Vector .elements (m, false)
 end
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 56
def to_ary
 [l, u, p]
end

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# File 'opal/stdlib/matrix/lup_decomposition.rb', line 36
def u
 Matrix .build ([@column_count, @row_count].min, @column_count) do |i, j|
 if (i <= j)
 @lu[i][j]
 else
 0
 end
 end
end