带有符号数学的矩阵给出了一个符号答案，而不是数字答案 [英] Matrix with symbolic math gives a symbolic answer, not a numeric one

问题描述

考虑以下矩阵

Ja(t1, t2, t3, t4, t5, t6) =[ (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - sin(t1)/100 - (219*sin(t1)*sin(t2))/1000 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin)(t1)))/1000, (219*cos(t1)*cos(t2))/1000 + (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2)) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin)(t1)))/1000, (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) + cos(t4))*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (19*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 - (21*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos)(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2)- sin(t1)*sin(t2)) + cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (21)*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, -(cos(t5)*(cos(t3)*cos(t4)*(cos(t1)*cos()t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5，0][ cos(t1)/100 + (219*cos(t1)*sin(t2))/1000 + (29*cos(t1)*sin(t3))/1000 - (21*cos(t4)*(cos)(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 - (21*sin(t4)*(cos)(t1)*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 + (sin(t5)*(cos(t4))*(cos(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))) + sin(t4)*(cos(t1))*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))))/5 + (19*cos(t3)*(cos()t1)*cos(t2) - sin(t1)*sin(t2)))/100, (219*cos(t2)*sin(t1))/1000 - (sin(t5)*(cos(t3)*)cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 + (19*cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 + (21*cos)(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, (29*cos(t3)*sin(t1))/1000 - (21*cos(t4)*(cos(t3))*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (21*sin(t4)*(sin(t1))*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 - (19*sin(t3)*(c)os(t1)*sin(t2) + cos(t2)*sin(t1)))/100 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3))*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1))*sin(t2) + cos(t2)*sin(t1)))))/5, (21*sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos()t1)*sin(t2) + cos(t2)*sin(t1)))/1000 - (21*cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos()t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, (cos(t5)*(cos(t4)*(sin(t1)*sin(t3) - cos(t3)*)(cos(t1)*sin(t2) + cos(t2)*sin(t1)) + sin(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, 0][ 0, 0,(21*cos(t3)*cos(t4))/1000 - (29*cos(t3))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5, (21*cos(t3)*cos(t4))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5, -(cos(t5)*(cos(t3)*sin(t4) + cos(t4)*sin(t3)))/5, 0]

问题在于，当我输入参数时，MATLAB 不会以数字方式计算矩阵，而是以符号方式保留它.

结果如下:

Ja(q(1),q(2),q(3),q(4),q(5),q(6)) =[sin(63/100)/100 + (219*sin(528276371951843/1125899906842624)*sin(63/100))/1000 + (19*cos(157/125)*(cos(5218964084828404040826262624)1624)63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 + (sin(59/125)*(cos(157/125)*cos(157/252)*736/1125899906842624)*sin(63/100) - sin(528276371951843/11258999906842624)*cos(63/100)) - sin(157/125)*sin(157/125)*sin(157/261826182618261618261828161828161828181818181818181826181826182595918261826182618259182616之间63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(52195916264000000000000000)/5(63/100) -  SIN(1125899906842624分之528276371951843)* COS(63/100)))/1000  - (21 * SIN(125分之157)* SIN(250分之157)*(cos(1125899906842624分之528276371951843)*罪(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000，(219*cos(528276371951843/1125899626840)*cos(63/100)/1000)157/125)*(cos(528276371951843/11258999906842624)*sin(63/100) - sin(528276371951843/1125899906842624)/(525899906842624)*(5) cos(6)/10)/10)/10)/10)/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/11258999068420)*2)sin(1125899906842626)*206842620157/250)*(cos(528276371951843/11258999906842624)*sin(63/100) - sin(528276371951843/1125899906842624)/*cos(1125899906842624)/*205)/*205)/*2015)(157/250)*(cos(528276371951843/11258999906842624)*sin(63/100) - sin(528276371951843/1125899906842624)/106842624)/10*10s(6)/10s(10)/10s03)/10*10s030(157/250)*(cos(528276371951843/11258999906842624)*sin(63/100) - sin(528276371951843/1125899906842624)(528276371951843/1125899906842624)*10)/10)/10)/10)/10)s(6)/10)/100)(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)/1s5(ins5)*(528276371951843)(157)/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin)(63/17)*10)*10 cos1(63/10)*7(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/*25)*(2)*(5)(52827637)cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))(528276371951843/1125899906842624)*sin(63/100)*5)(15/100)(10)*2(5282763/100)+(528276)COS(1125899906842624分之528276371951843)* COS(63/100)+ SIN(1125899906842624分之528276371951843)* SIN(63/100)))/1000， - (SIN(59/125)*(cos(125分之157)*罪(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*1006842624)/1006842624)*100842623/100842623)*100842623/100842623/1006842623)*1007s/7(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))(2)*5(5282763/100)(528276371951843/1125899906842624)*sin(63/100))*5(5282763/100)()15/7s15(528276)*(cos(528276371951843/11258999906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*cos(157/250)*sin(157/125)*(cos(61658)625968282624)cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000，-(cos(59/125)*(cos(157/125)*cos(157/125)*cos(157/25)COS(1125899906842624分之528276371951843)* COS(63/100)+罪(1125899906842624分之528276371951843)*罪(63/100)) - 罪(125分之157)*罪(250分之157)*(COS(1125899906842624分之528276371951843)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5, 0][ cos(63/100)/100 + (219*sin(528276371951843/1125899906842624)*cos(63/100))/1000 + (29*cos(63/100)*sin5)/100(19*cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842626)2*1(1125899906842624)/11258999068426260)*10/10250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(5219591640340000)*(157/125)*(cos(528276371951843/1125899906842624)/100))))/1000 - (sin(59/125)*(cos(157/250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos()528276371951843/1125899906842624)*cos(63/100)+sin(528276371951843/1125899906842624)*sin(63/100)))/(63/100)5)+(sin)*5)7)+2(sin)1)*5)+250)/161/250*2161sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)//sin(528276371951843/1125899906842624)*2)/sin(5)/sin(528276842623)*10)/sin(5))*(cos(63/100)*cos(157/125)+sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100)+sin(52827637/199168358916848351840818201820100))))/1000, (19*cos(157/125)*(cos(528276371951843/11258999906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (219*cos(528276371951843/11258999906842624)/*sin(109)/*sin(1006)(63/100))/1006(+1006)/*sin506/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/11258999068426)*sin150)*2(sin10)40(1)157/250)*(cos(528276371951843/11258999906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*105899906842624)*cos(63/100)+sin(528276371951843/1125899906842624)*1050899906842624)*105023)*1005)/100)*10)50)6(157/250)*(cos(528276371951843/11258999906842624)*cos(63/100) + sin(528276371951843/1125899906842624)/10108999906842624)/10108999906842624)/101089999906842624)/101089999906842623)/1010s03)/10*10s03)(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)/109*2624)/109*10)/109*100()/109*100()/109*1000cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))(528276371951899906842624)*cos(63/100))(5282763/100)(63/100)(5282763/100)(5282763/100)(5282763/100)(5282763/100)(5282763/100))/19/10/100)(10)*21000 + (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63 sin) -(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1126884926))*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 + (sin(59/125)*(cos(157/250)*(cos(15)))*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/19120584)6(sin(5282763)/19120584)6(sin(5282763)6(19120584)6(sin(5282763)2)/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276376)*sin(52827637195184828482461628348216161616382616161683482616168261616848261683826168263638261682582582582526252524520号中63/100)))))/5, (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/112589990684262)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*125)) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/11258999068426240)/1125899906842630)*2)1)/10)/10)*(cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(157/125)8276371951843/1125899906842624)*cos(63/100))) - sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(162528)2019782378282828282828282828282828282826282628282828261826161682828282828282828282826999999999999999)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))))/5, -(cos(59/125)*(cos(157/250)*(sin(63/))100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(5282763719518583)*(cos(528276371951843)*sin(5282763719518583)6(sin(528276371951843)2016/100)157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100)*sin(63/100)-sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - 7 sin(52827625161826182828928282828929(63/100)))))/5, 0][ 0,0,(21*cos(157/125)*cos(157/250))/1000 - (29*cos(157/125))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5，(21*cos(157/125)*cos(157/250))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos)(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5, -(cos(59/125)*(cos(157/125)*sin()157/250) + cos(157/250)*sin(157/125)))/5, 0]

有没有办法得到实数?

解决方案

简短回答:使用 eval 以数字方式评估您的符号表达式或使用 eval 将其转换为特定类型a href="https://mathworks.com/help/symbolic/functionlist.html#btgyshe-1" rel="nofollow noreferrer">这些选项之一，fedouble 或 vpa.

请注意，eval 可能比使用 double 慢两倍，但有时也稍微快一些

说明

问题在于 MATLAB 不会以数字方式计算您的符号表达式，它只会在数学上简化您的表达式.

示例:

syms xmy_function(x) = cos(x)% 精确代数解已知:my_function(0) % 返回 1my_function(pi) % 返回 -1my_function(pi/2) % 返回 0my_function(pi/6) % 返回 3^(1/2)/2% 结果只能用数字近似:my_function(3.1415) % 返回 cos(6283/2000)my_function(1) % 返回 cos(1)

因此，当结果完全已知时，MATLAB 能够简化 cos 表达式.一般情况下，cos 的结果只能用数值计算，因此MATLAB 在它的答案中显示cos.

如果您想要数字结果，可以使用以下选项之一:

• eval:以数字方式评估您的矩阵
• double:转换为双精度
• single:转换为单精度
• int8 :转换为 8 位整数(替代 int16、int32、int64)
• vpa:转换为可变精度算术，即它允许您指定结果的所需精度(有效位数)

有关详细信息，请参阅符号和数字之间的转换><小时>

使用 eval 是个好选择吗?

正如 Sardar Usama 所指出的，使用 eval(评估字符串)通常是不好的做法:

• 逃避评估.
• eval 函数的替代方案

但是，这是同一个eval吗?

不，我不这么认为.help sym/eval 返回(相对于 help eval):

<块引用>

eval 评估一个符号表达式.eval(S) 评估字符的表示调用者工作区中的符号表达式 S.

同样使用 MATLAB 调试器指出它是一个不同的函数.然而，完整的解释提到它评估表达式的字符表示，这也可以在源代码中看到:

<块引用>

s = evalin('caller',vectorize(map2mat(char(x))));

因此，它在内部使用了类似于 eval 的 evalin 来计算字符串.这可能不是很有效.

所以，我们也应该避免sym/eval?

也许不是，double 也在内部使用 eval 来计算字符串:

<块引用>

Xstr = mupadmex('symobj::double', S.s, 0);X = 评估(Xstr)；

区别在于 sym/eval 使用 eval (evalin) 作为原始字符表示，即整个表达式，而 double 使用它来解析最终结果，即数值计算的值.

结论:对于您的示例，double 似乎是合适的方法，因为它的速度是使用 eval 的两倍.但是，对于以下示例，eval 稍微快一些(~15%):

my_function(x) = cos(x);对于 i=2:100my_function(x) = my_function(x) + cos(i*x);结尾

Consider the following matrix

Ja(t1, t2, t3, t4, t5, t6) =

[                                                                                                             (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - sin(t1)/100 - (219*sin(t1)*sin(t2))/1000 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000, (219*cos(t1)*cos(t2))/1000 + (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000,                                                                                                             (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) + cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (19*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 - (21*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000,                                                                                 (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) + cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (21*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000,                                        -(cos(t5)*(cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5, 0]
[ cos(t1)/100 + (219*cos(t1)*sin(t2))/1000 + (29*cos(t1)*sin(t3))/1000 - (21*cos(t4)*(cos(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 - (21*sin(t4)*(cos(t1)*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 + (sin(t5)*(cos(t4)*(cos(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))) + sin(t4)*(cos(t1)*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))))/5 + (19*cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100, (219*cos(t2)*sin(t1))/1000 - (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 + (19*cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 + (21*cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, (29*cos(t3)*sin(t1))/1000 - (21*cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (21*sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 - (19*sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, (21*sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 - (21*cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, (cos(t5)*(cos(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) + sin(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, 0]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                     0,                                                                                                                                                                                                                                                                                                                                           0,                                                                                                                                                                                                                                                                                                (21*cos(t3)*cos(t4))/1000 - (29*cos(t3))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5,                                                                                                                                                                                                                                 (21*cos(t3)*cos(t4))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5,                                                                                                                -(cos(t5)*(cos(t3)*sin(t4) + cos(t4)*sin(t3)))/5, 0]

The problem is that when I put my arguments, MATLAB doesn't calculate the matrix numerically, rather it leaves it symbolically.

This is the result:

Ja(q(1),q(2),q(3),q(4),q(5),q(6)) = 

[                                                                                                                                                          sin(63/100)/100 + (219*sin(528276371951843/1125899906842624)*sin(63/100))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000, (219*cos(528276371951843/1125899906842624)*cos(63/100))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000,                                                                                                                                                        - (19*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (sin(59/125)*(cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) + cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 - (21*cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000,                                                                                                                   - (sin(59/125)*(cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) + cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 - (21*cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000,                                                           -(cos(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5, 0]
[ cos(63/100)/100 + (219*sin(528276371951843/1125899906842624)*cos(63/100))/1000 + (29*cos(63/100)*sin(157/125))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (21*cos(157/250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/1000 - (sin(59/125)*(cos(157/250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))) + sin(157/250)*(cos(63/100)*cos(157/125) + sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))))/5 - (21*sin(157/250)*(cos(63/100)*cos(157/125) + sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/1000, (19*cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (219*cos(528276371951843/1125899906842624)*sin(63/100))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000, (19*sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 - (29*cos(157/125)*sin(63/100))/1000 + (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 + (sin(59/125)*(cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) - sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 + (sin(59/125)*(cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) - sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, -(cos(59/125)*(cos(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) + sin(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, 0]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             0,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  0,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 (21*cos(157/125)*cos(157/250))/1000 - (29*cos(157/125))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     (21*cos(157/125)*cos(157/250))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5,                                                                                                                                                                                                                                                                           -(cos(59/125)*(cos(157/125)*sin(157/250) + cos(157/250)*sin(157/125)))/5, 0]

Is there a way I can get real numbers ?

解决方案

Short answer: evaluate your symbolic expression numerically using eval or convert it to a specific type using one of these options, f.e. double or vpa.

Note that eval may be twice as slow as using double, but is sometimes slightly faster too

Explanation

The problem is that MATLAB does not evaluate your symbolic expression numerically, it only simplifies your expression mathematically.

Example:

syms x
my_function(x) = cos(x)
% exact algebraic solution is known:
my_function(0) % returns 1
my_function(pi) % returns -1
my_function(pi/2) % returns 0
my_function(pi/6) % returns 3^(1/2)/2
% result can only be numerically approximated:
my_function(3.1415) % returns cos(6283/2000)
my_function(1) % returns cos(1)

So, MATLAB is able to simplify the cos expression when the result is exactly known. In general, the result of cos can only be numerically evaluated, therefore MATLAB displays cos in it answer.

If you want a numerical result you can use one of the following options:

• eval: evaluates your matrix numerically
• double: converts to double precision
• single: converts to single precision
• int8 : converts to 8 bit integers (alternatives int16, int32, int64)
• vpa: converts to variable-precision arithmetic, i.e. it allows you to specify the desired accuracy (number of significant digits) of the result

See Conversion Between Symbolic and Numeric for more information

---

Is using eval a good option?

As pointed out by Sardar Usama, using eval (to evaluate a string) is often bad practice:

• Evading eval.
• Alternatives to the eval Function

But, is this the same eval?

No, I don't think so. help sym/eval returns (in contrast to help eval):

eval  Evaluate a symbolic expression.
    eval(S) evaluates the character representation of the
    symbolic expression S in the caller's workspace.

Also using the MATLAB debugger points out that it is a different function. However, the full explanation mentions that it evaluates the character representation of the expression, which can also be seen in the source code:

s = evalin('caller',vectorize(map2mat(char(x))));

So, it uses internally evalin, which is similar to eval, to evaluate a string. This may not be very efficient.

So, we should avoid sym/eval too?

Maybe not, also double uses eval internally to evaluate a string:

Xstr = mupadmex('symobj::double', S.s, 0);
X = eval(Xstr);

The difference is that sym/eval uses eval (evalin) for the original character representation, i.e. the whole expression, whereas double uses it to parse the final result, i.e. the numerically evaluated value.

Conclusion: for your example double seems to be the appropriate method as it is twice as fast as using eval. However, for the following example eval is somewhat faster (~15%):

my_function(x) = cos(x);
for i=2:100
  my_function(x) = my_function(x) + cos(i*x);
end

这篇关于带有符号数学的矩阵给出了一个符号答案，而不是数字答案的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！