Error : Matrix dimensions must agree

I dont know why it's giving can someone help ?

      function derivative_x = AIAA(t,x)
      derivative_x=zeros(5,1);

      A1 =[   -5.9690  -41.3275    1.3080   -1.0463   -0.4869
         -0.0078   -2.1282    0.9507  -20.8661   -0.0053
          2.0858   49.5871  -10.9028    1.2224   -0.1164
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A2 =[   -5.9690  -41.3275    1.3080   -1.0463   -0.4869
         -0.0078   -2.1282    0.9507  -20.8661   -0.0053
          2.0858   49.5871  -10.9028    1.2224   -0.1164
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A3 =[   -0.2132  -41.1168    0.9679   -1.0683    0.0097
          0.0051   -2.1951    1.0124  -20.8428   -0.0003
          0.4030   45.4138   -6.9930    2.6577   -0.0198
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A4 =[   -0.2142  -41.1032    1.0609   -1.0410    0.0365
         -0.0040   -2.1002    0.9922  -20.9089    0.0013
         -0.1534   51.2034   -8.2651   -1.3891    0.0643
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A5 =[   46.4754  -41.1787  -45.6425   -1.9833   -1.3092
         -0.2261   -2.1446    1.3133  -20.8828   -0.0024
        -33.7711   48.5222   29.6778    0.6092    0.4142
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A6 =[   -6.6983  -41.3450    1.3548   -1.0467   -0.5485
         -0.0106   -2.1288    0.9347  -20.8662   -0.0060
          2.2284   49.5581  -13.6275    1.2201   -0.1330
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A7 =[   -0.2534  -41.1302    0.9724   -1.0674    0.0073
          0.0071   -2.1944    1.0233  -20.8428   -0.0001
          0.5412   45.4620   -8.0555    2.6541   -0.0108
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A8 =[   -6.7972  -37.7358   -4.5678   -8.3716   13.8487
         -0.3353   -1.9333    0.6742  -21.2896    0.7127
        -17.5613   59.9487  -26.9974  -21.4951   37.5793
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A9 =[   54.4509  -25.8776   76.5925   -9.7710   16.3861
          0.0523   -2.1433    1.0735  -20.8769   -0.0662
        -20.1909  -63.2368  -35.7359    4.3123  -11.0777
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A10 =[   53.5818  -27.3231   75.3401   -9.8364   16.6126
         -0.3772   -2.1922    0.4696  -20.8736    0.2516
        -46.0467  -65.6067  -72.0813    4.5409    8.2318
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A11 =[    2.2818  -32.6618    3.1819   -9.5013    1.4445
         -0.0878   -2.5814    0.9246  -20.4504   -0.0835
         -6.3412  -87.0851  -13.3051   30.2435   -5.7179
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A12 =[    2.5007  -29.9855    3.4502  -11.1737    1.6224
          0.0743   -1.6826    1.0627  -21.2935    0.0767
          3.4620  -33.3368   -4.9838  -20.5278    3.9878
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A13 =[   67.0151  -24.5698   94.2833   -9.6220   19.9493
          0.0621   -2.1426    1.0873  -20.8758   -0.0798
        -24.9889  -63.7592  -44.2180    4.3141  -13.4387
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A14 =[   65.9082  -26.2945   92.6619   -9.7749   20.3256
         -0.4541   -2.1999    0.3613  -20.8809    0.3027
        -56.0385  -66.5172  -87.8631    4.0703    9.7567
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A15 =[    2.9873  -32.6748    4.1806   -9.4956    1.6515
         -0.1195   -2.5805    0.8903  -20.4506   -0.0945
         -8.5833  -87.0188  -17.5545   30.2301   -6.4803
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      A16 =[    3.3293  -29.7764    4.6105  -11.1986    1.8517
          0.1045   -1.6745    1.0962  -21.2946    0.0867
          4.9538  -32.9345   -5.1669  -20.5833    4.4969
               0         0    1.0000         0         0
               0   -2.6000         0    2.6000         0];

      derivative_x = A1.*x + A2.*x + A3.*x + A4.*x + A5.*x + A6.*x + A7.*x + A8.*x +A9.*x + A10.*x + A11.*x + A12.*x + A13.*x + A14.*x + A15.*x + A16.*x;

while running the above funtion in another matlab file i get this error

clc;
clf;
Initial_Time=0;
Final_Time=10;
[x1,x2] = meshgrid(-2:0.1:2);
 [t,x] = ode45(@AIAA, [Initial_Time Final_Time], [0.5 1 0.5 1]);
 figure(1);
%subplot(3,1,1);
plot(t,x(:,1));
%axis([0 10 -2 2]);
xlabel('time')
ylabel('state x1k')
figure(2);
%subplot(3,1,2);
plot(t,x(:,2));
xlabel('time')
ylabel('state x2k')
%axis([0 10 -3 3]);

Answer 1

[Walter Roberson]

In order to be able to use .* between a 5 by 5 matrix and "x", such as A1 .* x, then x would have to be scalar or x would have to be a 5 x 5 matrix itself. As this is ode45, the size of the output has to be the same size as your "x" input, so if x was in fact a scalar then you would get an error because the 5 x 5 result of your calculation would not be the same size as x. Therefore your x would have to be a 5 x 5 matrix.

However, in ode45, the x input is taken as a column vector the same length as your x0. Your x0 is [0.5 1 0.5 1] which is length 4, so the parameter that your function will receive will be a 4 x 1 vector. That cannot possibly be .* with a 5 x 5 array.

If you were to pass in an x0 which was length 5 then you might possibly intend your code to be

derivative_x = A1*x + A2*x + A3*x + A4*x + A5*x + A6*x + A7*x + A8*x +A9*x + A10*x + A11*x + A12*x + A13*x + A14*x + A15*x + A16*x;

which is to say that you would use Matrix multiplication instead of element-by-element multiplication. A 5 x 5 array matrix-multiply a 5 x 1 vector would give a 5 x 1 result, which is exactly what you need.

Note that if you do mean matrix multiplication like that, then by the rules of matrix multiplication, A1*x + A2*x = (A2+A2)*x and so you might as well calculate the sum of your A1 to A16 and matrix-multiply the result by x.