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POSolve non-linear system of equation in Mathematica
 

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  1. POSolve non-linear system of equation in Mathematica
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    <p>I'm trying to solve non-linear system of equations in Mathemtica. I tried Solve and NSolve, I also tried to define a_{ij} and b_{ij} and m33=1 numerical to simplify equation, but Mathematica seems to work too long or I doing something wrong.In Mathematica I just trying to find solution, but I also need some c/c++ lib to do this in my code.</p> <p>Main equation in "operators":</p> <pre><code>M[A[(x,y)]]=B[M[(x,y)]] </code></pre> <p>where "operator" is perspective transform:</p> <pre><code>u= (m13 + m11*x + m12*y)/(m33 + m31*x + m32*y); v= (m23 + m21*x +m22*y)/(m33 + m31*x + m32*y); </code></pre> <p>My input in Mathematica:</p> <pre><code>Solve[(b13 + (b11 (m13 + m11 x1 + m12 y1))/(m33 + m31 x1 + m32 y1) + (b12 (m23 + m21 x1 + m22 y1))/(m33 + m31 x1 + m32 y1))/(b33 + (b31 (m13 + m11 x1 + m12 y1))/(m33 + m31 x1 + m32 y1) + (b32 (m23 + m21 x1 + m22 y1))/(m33 + m31 x1 + m32 y1)) == (m13 + (m11 (a13 + a11 x1 + a12 y1))/(a33 + a31 x1 + a32 y1) + (m12 (a23 + a21 x1 + a22 y1))/(a33 + a31 x1 + a32 y1))/(m33 + (m31 (a13 + a11 x1 + a12 y1))/(a33 + a31 x1 + a32 y1) + (m32 (a23 + a21 x1 + a22 y1))/(a33 + a31 x1 + a32 y1)) &amp;&amp; (b23 + (b21 (m13 + m11 x1 + m12 y1))/(m33 + m31 x1 + m32 y1) + (b22 (m23 + m21 x1 + m22 y1))/(m33 + m31 x1 + m32 y1))/(b33 + (b31 (m13 + m11 x1 + m12 y1))/(m33 + m31 x1 + m32 y1) + (b32 (m23 + m21 x1 + m22 y1))/(m33 + m31 x1 + m32 y1)) == (m23 + (m21 (a13 + a11 x1 + a12 y1))/(a33 + a31 x1 + a32 y1) + (m22 (a23 + a21 x1 + a22 y1))/(a33 + a31 x1 + a32 y1))/(m33 + (m31 (a13 + a11 x1 + a12 y1))/(a33 + a31 x1 + a32 y1) + (m32 (a23 + a21 x1 + a22 y1))/(a33 + a31 x1 + a32 y1)) &amp;&amp; (b13 + (b11 (m13 + m11 x2 + m12 y2))/(m33 + m31 x2 + m32 y2) + (b12 (m23 + m21 x2 + m22 y2))/(m33 + m31 x2 + m32 y2))/(b33 + (b31 (m13 + m11 x2 + m12 y2))/(m33 + m31 x2 + m32 y2) + (b32 (m23 + m21 x2 + m22 y2))/(m33 + m31 x2 + m32 y2)) == (m13 + (m11 (a13 + a11 x2 + a12 y2))/(a33 + a31 x2 + a32 y2) + (m12 (a23 + a21 x2 + a22 y2))/(a33 + a31 x2 + a32 y2))/(m33 + (m31 (a13 + a11 x2 + a12 y2))/(a33 + a31 x2 + a32 y2) + (m32 (a23 + a21 x2 + a22 y2))/(a33 + a31 x2 + a32 y2)) &amp;&amp; (b23 + (b21 (m13 + m11 x2 + m12 y2))/(m33 + m31 x2 + m32 y2) + (b22 (m23 + m21 x2 + m22 y2))/(m33 + m31 x2 + m32 y2))/(b33 + (b31 (m13 + m11 x2 + m12 y2))/(m33 + m31 x2 + m32 y2) + (b32 (m23 + m21 x2 + m22 y2))/(m33 + m31 x2 + m32 y2)) == (m23 + (m21 (a13 + a11 x2 + a12 y2))/(a33 + a31 x2 + a32 y2) + (m22 (a23 + a21 x2 + a22 y2))/(a33 + a31 x2 + a32 y2))/(m33 + (m31 (a13 + a11 x2 + a12 y2))/(a33 + a31 x2 + a32 y2) + (m32 (a23 + a21 x2 + a22 y2))/(a33 + a31 x2 + a32 y2)) &amp;&amp; (b13 + (b11 (m13 + m11 x3 + m12 y3))/(m33 + m31 x3 + m32 y3) + (b12 (m23 + m21 x3 + m22 y3))/(m33 + m31 x3 + m32 y3))/(b33 + (b31 (m13 + m11 x3 + m12 y3))/(m33 + m31 x3 + m32 y3) + (b32 (m23 + m21 x3 + m22 y3))/(m33 + m31 x3 + m32 y3)) == (m13 + (m11 (a13 + a11 x3 + a12 y3))/(a33 + a31 x3 + a32 y3) + (m12 (a23 + a21 x3 + a22 y3))/(a33 + a31 x3 + a32 y3))/(m33 + (m31 (a13 + a11 x3 + a12 y3))/(a33 + a31 x3 + a32 y3) + (m32 (a23 + a21 x3 + a22 y3))/(a33 + a31 x3 + a32 y3)) &amp;&amp; (b23 + (b21 (m13 + m11 x3 + m12 y3))/(m33 + m31 x3 + m32 y3) + (b22 (m23 + m21 x3 + m22 y3))/(m33 + m31 x3 + m32 y3))/(b33 + (b31 (m13 + m11 x3 + m12 y3))/(m33 + m31 x3 + m32 y3) + (b32 (m23 + m21 x3 + m22 y3))/(m33 + m31 x3 + m32 y3)) == (m23 + (m21 (a13 + a11 x3 + a12 y3))/(a33 + a31 x3 + a32 y3) + (m22 (a23 + a21 x3 + a22 y3))/(a33 + a31 x3 + a32 y3))/(m33 + (m31 (a13 + a11 x3 + a12 y3))/(a33 + a31 x3 + a32 y3) + (m32 (a23 + a21 x3 + a22 y3))/(a33 + a31 x3 + a32 y3)) &amp;&amp; (b13 + (b11 (m13 + m11 x4 + m12 y4))/(m33 + m31 x4 + m32 y4) + (b12 (m23 + m21 x4 + m22 y4))/(m33 + m31 x4 + m32 y4))/(b33 + (b31 (m13 + m11 x4 + m12 y4))/(m33 + m31 x4 + m32 y4) + (b32 (m23 + m21 x4 + m22 y4))/(m33 + m31 x4 + m32 y4)) == (m13 + (m11 (a13 + a11 x4 + a12 y4))/(a33 + a31 x4 + a32 y4) + (m12 (a23 + a21 x4 + a22 y4))/(a33 + a31 x4 + a32 y4))/(m33 + (m31 (a13 + a11 x4 + a12 y4))/(a33 + a31 x4 + a32 y4) + (m32 (a23 + a21 x4 + a22 y4))/(a33 + a31 x4 + a32 y4)) &amp;&amp; (b23 + (b21 (m13 + m11 x4 + m12 y4))/(m33 + m31 x4 + m32 y4) + (b22 (m23 + m21 x4 + m22 y4))/(m33 + m31 x4 + m32 y4))/(b33 + (b31 (m13 + m11 x4 + m12 y4))/(m33 + m31 x4 + m32 y4) + (b32 (m23 + m21 x4 + m22 y4))/(m33 + m31 x4 + m32 y4)) == (m23 + (m21 (a13 + a11 x4 + a12 y4))/(a33 + a31 x4 + a32 y4) + (m22 (a23 + a21 x4 + a22 y4))/(a33 + a31 x4 + a32 y4))/(m33 + (m31 (a13 + a11 x4 + a12 y4))/(a33 + a31 x4 + a32 y4) + (m32 (a23 + a21 x4 + a22 y4))/(a33 + a31 x4 + a32 y4)) &amp;&amp; m33 == 1, {m11, m12, m13, m21, m22, m23, m31, m32}] </code></pre>
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    1. COYou're using a program to generate that Mathematica input, right? ;)
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    2. COI do substitutions with Mathematica to get two equations and then copy-paste it 4 times to get 8 equations for 4 points (x1,y1),...,(x4,y4).
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    3. CO@mrgloom Could you please clarify where are `u,v` entering the top equation ?
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