Determines a local minimum of a function of n independent variables with the Downhill Simplex method. Details
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accuracy controls the accuracy of the minimum. The method stops if two consecutive approximations differ no more than the value of accuracy. The default is 1E - 8. |
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Start is an array of points at which the optimization process is starting. These points form a simplex in n-dimension. |
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X is an array of strings representing the X variables. |
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f(X) is the string representing the function of the X variables. |
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Minimum is the determined local minimum in n-dimension. |
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f(Minimum) is the function value of f(X) at the determined minimum. |
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ticks is the time in milliseconds for the whole calculation. |
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error returns any error or warning condition from the VI. |
The Downhill Simplex algorithm, also called the Nelder and Mead method, works without partial derivatives. The Downhill Simplex algorithm consists of catching the minimum of the function, f(X), with the help of simple geometrical bodies, specifically a simplex. A simplex in 2D is a triangle, a simplex in 3D is a tetrahedron and so on. You must have (n + 1) starting points, each of dimension n, forming the initial simplex. The user must enter only one point of these (n + 1). The (n + 1) dimensional simplex is automatically constructed. For the example given below (f(x,y) = x^2 + y^2), you must enter two numbers (describing exactly one point in 2D). The algorithm generates a new simplex by some elementary operations like reflections, expansions, and contractions. In the end, the minimum is concentrated in a very small simplex.
The simplex sequence tending to the minimum (0,0) of the function
is shown in the following diagram. The function is entered on the front panel as: