Question

我正在尝试使用python来解决一个由6个非线性方程组成的系统。有9个变量，其中3个是预定的（留下6个方程的系统，有6个未知数）。问题是，它可能是任何3，我事先无法知道。

以下是方程式（如果您有兴趣）。

c11 * c12 + c21 * c22 + c31 * c32 = 0

c11 * c13 + c21 * c23 + c31 * c33 = 0

c12 * c13 + c22 * c23 + c32 * c33 = 0

c11 * c21 + c12 * c22 + c13 * c23 = 0

c11 * c31 + c12 * c32 + c13 * c33 = 0

c21 * c31 + c22 * c32 + c23 * c33 = 0

注意：这是我认为最快/最容易解决的方式。另一种可能的表达方式是：

    |c11 c21 c31|
A = |c12 c22 c32|
    |c13 c23 c33|

    |c11 c12 c13|
B = |c21 c22 c23|
    |c31 c32 c33|

      |1 0 0|
A*B = |0 1 0|
      |0 0 1|

我的问题是：无论如何将其中的3个设置为固定，并使用scipy.optimize.fsolve（或更合适的模块？）解决其余参数？

Answer 1

所以，我自己找到了一个有效的解决方案。不确定它是否是最佳解决方案，但它的功能。

为了回答我的问题，scipy.optimize.fsolve接受一个参数args =（这里有额外的参数）。我把预定的参数放在这里。调用该函数时，首先解析args并将3个预定值放在适当的位置。

其余6个变量在列表中传递，并迭代以填充剩余的间隙。由于参数没有改变，每个变量总是放在矩阵的同一个位置。

使用此方法，可以预先确定任何3个矩阵元素，并且fsolve将尝试确定余数。

fsolve的调用语句如下所示：

paramSolve1, infodict, ier, mesg = scipy.optimize.fsolve(func,(i,i,i,i,i,i),args = (knownVals[0],knownVals[1],knownVals[2]), full_output = True, warning = False)

knwonVals是一个预定参数列表，我是一个开始猜测（所有6个缺失参数得到相同的起始猜测）。 full_output允许返回可选输出，warning = False将关闭未找到解决方案时出现的警告消息。有关详细信息，请查看http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html

对于那些感兴趣的人，问题的完整代码如下。

import scipy
from scipy.optimize import fsolve

def func(params, *args):
    c = propMatrix(createMatrix(args), params)

    ans =(scipy.dot(c[:, 0],c[:, 1]), scipy.dot(c[:, 1],c[:, 2]), scipy.dot(c[:, 0],c[:, 2]),scipy.dot(c[:, 0],c[:, 0])-1,scipy.dot(c[:, 1],c[:, 1])-1,scipy.dot(c[:, 2],c[:, 2])-1)
    return ans

def createMatrix(knownVals):

    c = [['____', '____', '____'],['____', '____', '____'], ['____', '____', '____']]  

    for element in knownVals:
        x, y, val = element
        c[y][x] = float(val)
    return c

def propMatrix(c, params):
    for p in params:
        assign = True
        for x in range(3):
            for y in range(3):
                if c[x][y]=='____' and assign:
                    c[x][y] = float(p)
                    assign = False

    return scipy.array(c)

def test(c):
    v1 = c[:, 0]
    v2 = c[:, 1]
    v3 = c[:, 2]
    h1 = c[0, :]
    h2 = c[1, :]
    h3 = c[2, :]
    ans = (scipy.dot(v1,v1)-1, scipy.dot(v1,v2), scipy.dot(v1, v3), scipy.dot(v2, v2)-1, scipy.dot(v2, v3), scipy.dot(v3,v3)-1, scipy.dot(h1,h1)-1, scipy.dot(h1,h2), scipy.dot(h1, h3), scipy.dot(h2, h2)-1, scipy.dot(h2, h3), scipy.dot(h3,h3)-1)
    return ans

def getInput():
    knownVals = []
    print """\n\nThis module analytically solves for the rotation matrix\n
    First, enter 3 known values of the matrix:\n
                 x
            1    2    3   
       1 | c11  c12  c13 |
    y  2 | c21  c22  c23 |
       3 | c31  c32  c33 |\n\n"""

    for i in range(3):
        invalid = True
        print "Point Number %i:"%(i)
        while invalid:
            x = int(raw_input("\tx-coordinate:"))-1
            if x>2 or x<0:
                print "\tInvalid x-coordinate."
            else:
                invalid = False
        invalid = True
        while invalid:
            y = int(raw_input("\ty-coordinate:"))-1
            if y>2 or y<0:
                print "\tInvalid y-coordinate."
            else:
                invalid = False
        invalid = True
        while invalid:
            val = float(raw_input("\tValue:"))
            if val>1 or val<-1:
                print "\tInvalid value. Must be -1 <= value <= 1"
            else:
                invalid = False
        knownVals.append((x, y, val))
    c = createMatrix(knownVals)
    print "Input Matrix:\n\n", scipy.array(c)
    choice = raw_input("\nIs this correct (y/n)?  ")
    if choice == "y":
        return knownVals
    elif choice == "n":
        return getInput()

def Main():
    solution = False
    knownVals = getInput()
    for i in (-1,-.5,0,.5,1):
        paramSolve1, infodict, ier, mesg = scipy.optimize.fsolve(func,(i,i,i,i,i,i),args = (knownVals[0],knownVals[1],knownVals[2]), full_output = True, warning = False)
        if ier == 1:
            print "\nInitial value: %r"%(i) 
            print propMatrix(createMatrix(knownVals),paramSolve1)
            solution = True
    if not solution:
        print "Could not find a valid solution"

scipy.set_printoptions(precision = 4, suppress = True)
Main()

将预定参数传递给scipy.optimize.fsolve

1 个答案: