Solving an equation with two vectors
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I am trying to solve for an unknown using an equation with two vectors. I have tried using solve but the output is a 0x1 vector. I am trying to solve for p in the equation below and want a 37411x1 vector output with all the solutions. I considered using linsolve, but it looks like that only works for equations with one vector.
TotalDensity=WaterContent{:,2};%37411x1 vector
Drydensity=WaterContent{:,5};%37411x1 vector
syms p
eqn = TotalDensity==p*.99819+(1-p)*Drydensity;
S=solve(eqn,p);
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Torsten
2022-1-13
TotalDensity=WaterContent{:,2};%37411x1 vector
Drydensity=WaterContent{:,5};%37411x1 vector
TotalDensity = cell2mat(TotalDensity);
DryDensity = cell2mat(DryDensity);
p = (TotalDensity - DryDensity)./(.99819 - DryDensity)
回答（1 个）
You have 37411 equations in one single variable. There is no value, p, such that all of the equations are satisfied simultaneously.
solve() is for simultaneous equations. For example,
syms x y
solve([x + y == 5, 3*x + 4*y == 5])
Notice that this does not attempt to solve for ((x + y == 5) OR (3*x + 4*y == 5)) -- it solves for ((x + y == 5) AND (3*x + 4*y == 5))
There are two strategies:
- For linear equations and low-degree polynomials, solve a template and then subs() in the actual numeric values to get the vector of results; OR
- for nonlinear equations, loop doing one equation at a time, perhaps using arrayfun()
syms TD DD p
eqn = TD == p*.99819+(1-p)*DD;
S = solve(eqn, p)
%some numeric values for testing
TotalDensity = rand(4,1), Drydensity = rand(4,1).^2
%get numeric solutions
SN = double(subs(S, {TD, DD}, {TotalDensity, Drydensity}))
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2022-1-13
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