項目里需要求出兩個表達式之間的關系，涉及到3個未知數，就用Ruby寫了一個算法，利用了Ruby的BigDecimal，算法本身應該不算復雜，也可以方便的擴展到N元線性方程。之前用JS也寫了一個，但JS的浮點精度不夠，換成了RUBY，都放在了github上(https://github.com/caiqingfeng/formula-solver)，如果有用就直接拿過去了，free to copy and commercial use:-)

formula-solver.rb代碼如下：

require "bigdecimal"

?

#solver for a three variables linear formula (three dimensional matrix)?

# matrix M=

# a11 a12 a13

# a21 a22 a23

# a31 a32 a33

# variables = (x, y, z)

# res = (A, B, C)

# res = M * variables;

class FormulaSolver

def findAnswer(matrixInput, resInput)

#combine matrix with resInput

matrix = Array.new(3) {Array.new(4) {BigDecimal.new("0.0")}}

for ii in 0..2

for jj in 0..2

matrix[ii][jj] =? BigDecimal.new(matrixInput[ii][jj].to_s)/BigDecimal.new("1.0")

end

matrix[ii][3] =? BigDecimal.new(resInput[ii].to_s)/BigDecimal.new("1.0")

end

#step 1: row2 or row3+row1*something to get a21 and a31 0

#matrix[0][0] should not be zero, otherwise to reset it by row+row

#reset matrix to guarantee matrix[0][0]!=0

if matrix[0][0] == 0

line = 1;

if matrix[1][0] == 0?

if matrix[2][0] == 0

puts "this formula cannot be solved!"

return

end

line = 2;

end

for ii in 0..3

matrix[0][ii] = matrix[0][ii]+matrix[line][ii]

end

end

for ii in 1..2

if matrix[ii][0] != 0

factor = matrix[ii][0]/matrix[0][0]

for jj in 0..3

matrix[ii][jj] = matrix[ii][jj] - matrix[0][jj]*factor

end

end

end

?

#step 2: set matrix[2][1] = 0

if matrix[1][1] == 0

if matrix[2][1] == 0

puts "this formula cannot be solved!"

return

end

for ii in 1..3

matrix[1][ii] = matrix[1][ii]+matrix[2][ii]

end

end

for ii in 2..2

factor = matrix[ii][1]/matrix[1][1]

if matrix[ii][1] != 0?

for jj in 1..3

matrix[ii][jj] = matrix[ii][jj] - matrix[1][jj]*factor

end

end

end

?

#step 3: set matrix[0][2], matrix[1][2] = 0

if matrix[2][2] == 0

puts "this formula cannot be solved!"

return

end

for ii in 0..1

factor = matrix[ii][2]/matrix[2][2]

if matrix[ii][2] != 0?

for jj in 2..3

matrix[ii][jj] = matrix[ii][jj] - matrix[2][jj]*factor

end

end

end

?

#step 4: set matrix[0][1] = 0

for ii in 0..0

factor = matrix[ii][1]/matrix[1][1]

if matrix[ii][1] != 0?

for jj in [1, 3]

matrix[ii][jj] = matrix[ii][jj] - matrix[1][jj]*factor

end

end

end

?

#step 5: set [0][0]=1, [1][1]=1, [2][2]=1

for ii in 0..2

matrix[ii][3] = matrix[ii][3]/matrix[ii][ii]

matrix[ii][ii] = 1.0

end

matrix

end

end

?

測試代碼：test.rb

require_relative "formula-solver"

?

matrix = [[1, 113.9231311, 22.5034716], [1, 113.95313110000001, 22.5034716], [1, 113.95313110000001, 22.533471600000002]]

#res = [113.93454840179, 113.96456293154, 113.96454575759]

res = [113.93454840179, 113.96454575759, 113.96454575759]

puts FormulaSolver.new.findAnswer(matrix, res)

?

matrix = [[1, 113.9231311, 22.5034716], [1, 113.95313110000001, 22.5034716], [1, 113.95313110000001, 22.533471600000002]]

#res = [22.506156406299, 22.506279984718, 22.536277316988]

res = [22.506279984718, 22.506279984718, 22.536277316988]

puts FormulaSolver.new.findAnswer(matrix, res)

?

運行ruby test.rb得到輸出：(略)

轉載于:https://www.cnblogs.com/mobileinternet/archive/2012/06/10/2543879.html

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