Matlab symbolic : calculate expression with vector of symbolic variables

Hello,

I need to calculate with Matlab symbolic the following expression :

"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 (varO1 in the code snippet).

Where is my error ?

Answer 1

[VBBV]

Use the element wise operator for / and ^ ... i.e. ./ and .^ as below

clear
    syms l_min l_max fsky Np var1D var2D varO1 varO2
    l_min = 10

l_min = 10

    l_max = 300

l_max = 300

    syms L
    %l = sym('l_',[1 (l_max - l_min)])
    C_l = sym('C_l_',[1 (l_max -l_min)])

C_l = 

    
    % First observable
    var1D = symsum(2/((2*L+1)*fsky*Np^2), L, l_min, l_max)

var1D = 

    varO1 = var1D/sum(C_l)^2

varO1 = 

    
    % Second observable
    var2D = symsum(((2*L+1)*fsky*Np^2), L, l_min, l_max)

var2D = 

    varO2 = var2D./symsum((2*L+1)*C_l, L, l_min, l_max).^2  % use element wise operator

varO2 = 

Answer 2

[petit]

have done some progress in investigation to compute the 2 variances :

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

Anyone could see a workaround ?

[petit]

a small up to know if someone could help me for the symbolic expression of varO2 ?

[VBBV]

@petit Use element wise division and power operators since they are now vectors