Solve function not working - matlab

I'm currently trying to solve an equation with the solve function but I keep getting errors.
This is my code:
Dh=0.02;
Lc1=1.6;
Prw=9;
a=0.03*(Dh/Lc1)*Prw;
b=0.016*(Dh/Lc1)^(2/3)*Prw^(2/3);
c=9;
d=7.54;
syms Redh
eqn = (c*b-d*b)*Redh^(2/3)-a*Redh == d-c;
solRedh = solve(eqn,Redh);
When i run this i get the error
Warning: The solutions are
parameterized by the symbols: z2.
To include parameters and conditions
in the solution, specify the
'ReturnConditions' option.
In solve>warnIfParams (line 500)
In solve (line 356)
In Massflow_1 (line 105)
Warning: The solutions are valid under
the following conditions: 3*z2^2 + z2^3
- 59/50 == 0 & -pi/3 < angle(z2) &
angle(z2) <= pi/3.
To include parameters and conditions
in the solution, specify the
'ReturnConditions' option.
In solve>warnIfParams (line 507)
In solve (line 356)
In Massflow_1 (line 105)
I don't understand why the answer is parameterized by the symbol z2. There should be a solution containing a value. Even if i simplify it to an equation with the same powers of which I'm certain there is an answer to I get the same error.
Simpeler code
syms Redh
eqn = 0.0054*Redh^(2/3)-0.0034*Redh == -1.46;
solRedh = solve(eqn,Redh);
Does anybody know what is going wrong here and how I can fix it? It would be very helpful, thank you!

In your case, matlab use the symbol 'z2' to show that the solution use a complex number.(z2 ∈ Z)
You need to explain to matlab that you are not interested by a complex solution.
It should work without problem with:
% set an assumptions on symbolic variables! here our solution need to be a real number.
syms Redh real %check the doc for more informations about the assumptions.
eqn = 0.0054*Redh^(2/3)-0.0034*Redh == -1.46;
sol_sym = solve(eqn,Redh);
sol_nosym = double(sol_sym);

Related

"Unable to prove literally" error when trying to create a symbolic function based on an existing function

I need to find inverse of virtual value function of lognormal random variables. This is what I tried to do:
syms flogn(x,p1,p2)
% assume(p2<=0); %Adding this doesn't change the error
flogn(x,p1,p2) = x - logncdf(x,p1,p2,'upper')/lognpdf(x,p1,p2);
glogn = finverse(flogn,x);
But I got the error:
Error using symengine
Unable to prove 'p2 <= 0' literally. Use 'isAlways' to test the statement mathematically.
Error in sym/subsindex (line 810)
X = find(mupadmex('symobj::logical',A.s,9)) - 1;
Error in sym/privsubsasgn (line 1085)
L_tilde2 = builtin('subsasgn',L_tilde,struct('type','()','subs',{varargin}),R_tilde);
Error in sym/subsasgn (line 922)
C = privsubsasgn(L,R,inds{:});
Error in logncdf>locallogncdf (line 73)
sigma(sigma <= 0) = NaN;
Error in logncdf (line 47)
[varargout{1:max(1,nargout)}] = locallogncdf(uflag,x,varargin{:});
Error in Untitled5 (line 3)
flogn(x,p1,p2) = x - logncdf(x,p1,p2,'upper')/lognpdf(x,p1,p2);
I also tried with beta distribution, and got a similar error. How can I use logncdf with symbolic variables?
Note that you could have minimalize your sample code even more, like this:
syms flogn(x,p1,p2)
flogn(x,p1,p2) = logncdf(x,p1,p2);
It's shorter, produces the same error and helps us to focus on the source of the error message.
So, the error doesn't come from trying to inverse a function, but from trying to use an existing function for numerical calculations with symbolic variables.
The error comes from the fact that you want to create a symbolic function flogn based on existing function logncdf, and logncdf has a multiple comparisons.
With the command edit logncdf, you can read the source code of the function and see comparison at lines 73 and 76.
% Return NaN for out of range parameters.
sigma(sigma <= 0) = NaN;
% Negative data would create complex values, which erfc cannot handle.
x(x < 0) = 0;
Matlab cannot compare symbols so it throws errors.
Depending on what you really need, you can have different solutions.
Do you really need to symbolize the function flogn? Couldn't you just write it as a function then calculate the inverse of it (if it can be inversed...)?
If you really want to keep the symbolization, you can also rewrite your own function logncdf (with another name) so it does not have the comparisons. But it's still not guaranteed that you will find an inverse.

Matlab, cannot turn sym to double

I am trying to solve a variable in an equation (syms x), I've simplified the equation. I am trying to store the value in P_9, a 1x1000 matrix by converting from a symbol to a double and am getting the error below. It is giving me a symbol of 0x0, which is where I think my error lies.
Please help me troubleshoot my code. Many thanks!
number = 1000;
P_9 = zeros(1,number);
A_t=0.67;
A_e = linspace(0,10,number);
for n=1:number
%% find p9
syms x
eqn = x + 5 == A_t/A_e(n);
solx = solve(eqn,x);
P_9(n) = double(solx);
end
Warning: Explicit solution could not be found.
In solve at 179
In HW4 at 74
In an assignment A(I) = B, the number of elements in B and I must be the same.
Error in HW4 (line 76)
P_9(n) = double(solx);
You certainly have an equation, where x can't be isolated.
For example it is impossible to isolate x in tan(x) + x == 1. So if you try to solve this equation analyticaly, matlab will tell you that x can't be isolated and therefore there is no explicit analytical solution.
So instead of using an analytical method to solve your equation, you need to use a numerical method, it's less "sexy" but this time you will be able to solve your equation.
Life is well done, matlab already integrate a numerical solver: vpasolve.
So your code will look like:
for n=1:number
%% find p9
syms x
eqn = x + 5 == A_t/A_e(n);
solx = vpasolve(eqn,x);
P_9(n) = double(solx);
end

Getting conversion error while using solve function on an expression generated using for loop in MATLAB?

I am trying to find the first term 'p' of a geometric series with common ratio 1.05 in MATLAB as follows. However the solve function is giving the error as below (posted right after the code). I can't seem to figure out the reason for this error, because when I display the expression for 'sum', it is correctly showing an expression in terms of'p', but the problem arises when I try to equate that to a value, and solve for 'p'. Any insights would be appreciated! Thanks.
clear all;
clc;
t=20; %no. of terms in geometric series
sum =0;
jackpot = 1000; %sum of geometric series
%p is first term
syms p
for x=1:t
sum = sum + p*((1.05)^(x-1));
end
disp(sum);
eqn1 = sum == jackpot;
solve(eqn1,p);
Output:
(18614477322052275759*p)/562949953421312000
??? Error using ==> char
Conversion to char from logical is not possible.
Error in ==> solve>getEqns at 169
vc = char(v);
Error in ==> solve at 67
[eqns,vars] = getEqns(varargin{:});
Error in ==> geometric_trial at 13
solve(eqn1,p);
So, I got the answer for this from a user Walter Roberson on another forum. Posting here, from his answer.
I was trying this on a version of MATLAB which is really old i.e. R2010a. In this, using 'symbolic_expression == symbolic_expression' does not set up an equation for later solving, but instead compares the two expressions for literal equality and returns a logical value immediately.
In versions that old, the easiest fix is to change
eqn1 = sum == jackpot
to
eqn1 = (sum) - (jackpot)
and let solve() deal with the implicit equality to 0.

Solving an inequality with Matlab

I have to solve an inequality but it is too hard to do it by hand. Therefore, I would like to use Matlab. Let a = [(k-3)*sqrt(v)]/s and b = 1.08148*a^2-epsilon, where epsilon = 10^(-6). The inequality that needs to be solved is:
q(a,b) < s*sqrt(v)
where s and v are known. More precisely I want to solve the above inequality for k (which occurs in a and b). Now, the problem is that q(a,b) is the greatest real root of the quartic polynomial:
(48*a^2+16*b)*x^4 - (40*a^3+168*a*b)*x^3+(-45*a^4+225*a^2*b+72*b)*x^3+(27*a^2*b-162*a*b^2)*x+27*b^3
I tried to run this:
syms x z
av = ((x-3)*sqrt(v))/s;
Q = max(roots([48*z^2+16*(1.08148*z-eps), -40*z^3-168*z*(1.08148*z-eps), -45*z^4+225*z^2*(1.08148*z-eps)+72*(1.08148*z-eps)^2, 27*z^3*(1.08148*z-eps)-162*z*(1.08148*z-eps)^2, 27*(1.08148*z-eps)^3]));
F = compose(Q,av);
solve(F-skew*sqrt(var)<0, x)
but Matlab keeps giving the following error:
Error using sym/max (line 97)
Input arguments must be convertible
to floating-point numbers.
Error in Testt (line 13)
R = max(roots([2048,
-6912*((x-3)sqrt(var)/skew)^2,
8088((x-3)sqrt(var)/skew)^4,
-3600((x-3)sqrt(var)/skew)^6,
375((x-3)*sqrt(var)/skew)^8]));
Perhaps someone has a better idea to solve it? The best way would be if I had an explicit expression for the greatest real root q of the quartic in function of a and b. However, this explicit expression is too lengthy to use.
The error information seemed to say the max() function do not support sym x z.
Because the returned result of roots() includes x and z.But Matlab doesn't know the value of x and z,so it can't calculate the value of the roots and then can't compare them.
Maybe you should improve your algorithm.

Why does the following expression result in error?

Disclaimer. I am familiar with Mathematica but not Matlab, so I apologize if this is a neophyte question.
I am getting a strange error on Matlab on the the following at using Matlab's solve command:
solve(0.2 = (1.4+1/2)^((1.4+1)/(2*(1.4-1)))*(M)/((1+(1.4-1)/2*M^2))^((1.4+1)/(2*(1.4-1))), M)
The error is:
Error: The expression to the left of the equals sign is not a valid target for an assignment.
The equivalent Solve command in Mathematica (using the same expression) works perfectly, so I don't think my expression itself is invalid.
Moreover, I get the same error when I try to use the examples on the doc site: http://www.mathworks.com/help/symbolic/mupad_ref/solve.html
Is it a configuration problem or is there something about the syntax of the command I am misinterpreting?
Edit: I also tried with == instead of =, and I get a different error:
Undefined function or variable 'M'.
Also, as a note, I am running Matlab R2011b (7.13.0.564) 64-bit (glnxa64).
Edit2: I tried the first suggested solution with syms:
>> syms M
>> solve(0.2 == (1.4+1/2)^((1.4+1)/(2*(1.4-1)))*(M)/((1+(1.4-1)/2*M^2))^((1.4+1)/(2*(1.4-1))), M)
Error using char
Conversion to char from logical is not possible.
Error in solve>getEqns (line 245)
vc = char(v);
Error in solve (line 141)
[eqns,vars,options] = getEqns(varargin{:});
Edit3: I have been able to reproduce this issue with even the simplest of equations
>> syms x
>> solve(x^2 -4 == 0, x)
Error using char
Conversion to char from logical is not possible.
Error in solve>getEqns (line 245)
vc = char(v);
Error in solve (line 141)
[eqns,vars,options] = getEqns(varargin{:});
Moreover, I tried the solution suggested here too: MATLAB examples are failing
Matlab's fsolve command assumes the expression is set to zero. If solving numerically, you would not do:
x=solve(2=x+1,x)
but rather:
x=fsolve(#(x) x+1-2,0)
Where the equation is already set to zero, #(x) is what you are solving for, and 0 is the initial guess. Which you must include.
Using solve symbolically, it looks like this:
syms x
val=solve(x+1-2)
Or for your system:
syms M
solve(-0.2+ (1.4+1/2)^((1.4+1)/(2*(1.4-1)))*(M)/((1+(1.4-1)/2*M^2))^((1.4+1)/(2*(1.4-1))))
ans =
4.7161724968093348297842999805458
0.029173662296926424763929809009225
- 3.8716404782846254923900841980317 - 3.4984412176176158766571497649425*i
1.4989673987314948651159693032542 + 5.5784387926679222829321168661041*i
1.4989673987314948651159693032542 - 5.5784387926679222829321168661041*i
- 3.8716404782846254923900841980317 + 3.4984412176176158766571497649425*i
you should define M as sym, and use == instead of =
syms M
solve(0.2 == (1.4+1/2)^((1.4+1)/(2*(1.4-1)))*(M)/((1+(1.4-1)/2*M^2))^((1.4+1)/(2*(1.4-1))), M)
ans =
4.7161724968093348297842999805458
0.029173662296926424763929809009225
- 3.8716404782846254923900841980317 - 3.4984412176176158766571497649425*i
1.4989673987314948651159693032542 + 5.5784387926679222829321168661041*i
1.4989673987314948651159693032542 - 5.5784387926679222829321168661041*i
- 3.8716404782846254923900841980317 + 3.4984412176176158766571497649425*i