Matlab symbolic : calculate expression with vector of symbolic variables-CodePudding

This

"l" is a vector of symbolic variables and "C_l" also (same length than "l", that is to say, l_max -l_min = 3000-10=2990).

To calculate this, I did :

clear syms l_min l_max fsky Np var1D varO1 l_min = 10 l_max = 3000 l = sym('l_',[1 (l_max - l_min)]) C_l = sym('C_l_',[1 (l_max -l_min)]) % First observable var1D = symsum(2/((2*l 1)*fsky*Np^2), l, l_min, l_max) varO1 = var1D/symsum(C_l, l_min, l_max)^2 Error using symengine Invalid operands. Error in sym/privBinaryOp (line 1030) Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:}); Error in / (line 373) X = privBinaryOp(A, B, 'symobj::mrdivide'); Error in inequality (line 9) var1D = symsum(2/((2*l 1)*fsky*Np^2), l, l_min, l_max)

I don't know to proceed to compute the expression of sigma_o,1^2 just above.

Update 1

The first variance sigma_{o,1}^2 has been correctly coded. Now, I have difficulties with the second one but I have done some progress in investigation to compute this second variance (sigma_{o,2}^2) :

Now, I did :

clear syms l_min l_max fsky Np var1D var2D varO1 varO2 l_min = 10 l_max = 3000 syms l %l = sym('l_',[1 (l_max - l_min)]) C_l = sym('C_l_',[1 (l_max -l_min)]) % First observable var1D = symsum(2/((2*l 1)*fsky*Np^2), l, l_min, l_max) varO1 = var1D/sum(C_l)^2 % Second observable var2D = symsum(((2*l 1)*fsky*Np^2), l, l_min, l_max) varO2 = var2D/symsum((2*l 1)*C_l, l, l_min, l_max)^2

But I still get an error at the last line :

var2D = 9005901*Np^2*fsky Error using symengine Not a square matrix. Error in sym/privBinaryOp (line 1030) Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:}); Error in ^ (line 330) B = privBinaryOp(A, p, 'symobj::mpower'); Error in inequality (line 15) varO2 = var2D/symsum((2*l 1)*C_l, l, l_min, l_max)^2

The issue is that I don't know how to mix the classical "sum" function and the "symsum" symbolic function because I have the following expression in divider :

varO2 = var2D/symsum((2*l 1)*C_l, l, l_min, l_max)^2

Is a workaround available here?

Update 2

@CrisLuengo :

Following your suggestion, I tried :

clear syms l_min l_max fsky Np var1D var2D varO1 varO2 l_min = 10 l_max = 15 syms l %l = sym('l_',[1 (l_max - l_min)]) C_l = sym('C_l_',[1 (l_max -l_min)]) assume(C_l > 0) % First observable var1D = symsum(2/((2*l 1)*fsky*Np^2), l, l_min, l_max) varO1 = var1D/sum(C_l)^2 % Second observable var2D = symsum(((2*l 1)*fsky*Np^2), l, l_min, l_max) varO2 = var2D/(symsum(((2*l 1)*C_l), l, l_min, l_max)).^2

and get the error :

varO1 = 45894056/(97698825*Np^2*fsky*(C_l_1 C_l_2 C_l_3 C_l_4 C_l_5)^2) var2D = 156*Np^2*fsky Error using symengine Invalid operands. Error in sym/privBinaryOp (line 1030) Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:}); Error in / (line 373) X = privBinaryOp(A, B, 'symobj::mrdivide'); Error in inequality (line 16) varO2 = var2D/(symsum(((2*l 1)*C_l), l, l_min, l_max)).^2

I just want to express symbolically the following quantity (I have a set of data of couples (l, C_l), that is to say, I have for each "l" value an associated "C_l" value.

Where might the error come from ?

Update 3

There may be a confusion about the expression of second quantity above. I have i=1:N couples of values (l_i, C_l_i), and the quantity appears like this :

Unfortunately, when I am doing :

% Second observable var2D = symsum(((2*l 1)*fsky*Np^2), l, l_min, l_max) varO2 = var2D./(sum(symsum(((2*l 1).*C_l), l, l_min, l_max))).^2

I get on terminal Matlab :

As you can see, I have the factor 156 which appears for each C_l and this is wrong since I would like to have as real values the factor (2*l 1) for each C_l : computation of (2*l 1) must be done with a real value, not as symbolic coefficients.

Update 4

I have badly expressed my issue : with the solution suggested in answer by @drakon101, I have always the same weighting values.

What I would like to get is the following symbolic expression for the divider :

How to make change the variable "l" to make it replaced by real values (3, then 5, 7, ...., 5999) ?

CodePudding user response：

I don't know what output you're looking for, but according to the equations you have displayed above, your second observable lines should be:

% Second observable var2D = 2*symsum(((2*l 1)), l, l_min, l_max)./(fsky.*Np.^2) varO2 = var2D./(symsum(((2.*l 1).*C_l), l, l_min, l_max)).^2

CodePudding user response：

(Posted solution in behalf of the question author to move it to the answer space).

I have found the following solution by coding :

clc clear all syms fsky Np l l_min = 10 l_max = 15 C_l = sym('C_l_',[1 (l_max)]); assume(C_l > 0); % Second observable var2D = symsum(((2*l 1)*fsky*Np^2), l, l_min, l_max) below=0; for l=l_min:l_max below= below (2*l 1)*C_l(l); end varO2= var2D/(below)^2