matlab - Matrix with symbolic Math does not make the calculus -
consider 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 when put arguments, matlab doesn't calculate matrix.
this 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 way can real numbers ?
short answer: evaluate symbolic expression numerically using eval or convert specific type using one of these options, f.e. double or vpa.
note eval may twice slow using double, faster too
explanation
the problem matlab not evaluate symbolic expression numerically, simplifies expression mathematically.
example:
syms x my_function(x) = cos(x) % exact algebraic solution 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 numerically approximated: my_function(3.1415) % returns cos(6283/2000) my_function(1) % returns cos(1) so, matlab able simplify cos expression when result known. in general, result of cos can numerically evaluated, therefore matlab displays cos in answer.
if want numerical result can use 1 of following options:
eval: evaluates matrix numericallydouble: converts double precisionsingle: converts single precisionint8: converts 8 bit integers (alternativesint16,int32,int64)vpa: converts variable-precision arithmetic, i.e. allows specify desired accuracy (number of significant digits) of result
see conversion between symbolic , numeric more information
is using eval option?
as pointed out sardar usama, using eval (to evaluate string) bad practice:
but, same eval?
no, don't think so. help sym/eval returns (in contrast help eval):
eval evaluate symbolic expression. eval(s) evaluates character representation of symbolic expression s in caller's workspace.
also using matlab debugger points out different function. however, full explanation mentions evaluates character representation of expression, can seen in source code:
s = evalin('caller',vectorize(map2mat(char(x))));
so, uses internally evalin, similar eval, evaluate string. may not efficient.
so, should avoid sym/eval too?
maybe not, double uses eval internally evaluate string:
xstr = mupadmex('symobj::double', s.s, 0); x = eval(xstr);
the difference sym/eval uses eval (evalin) original character representation, i.e. whole expression, whereas double uses parse final result, i.e. numerically evaluated value.
conclusion: example double seems appropriate method twice fast using eval. however, following example eval faster (~15%):
my_function(x) = cos(x); i=2:100 my_function(x) = my_function(x) + cos(i*x); end 
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