IDL最优估计(OE)函数中的几个例子 RGB 3S博客

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IDL最优估计(OE)函数中的几个例子 RGB 3S博客

#IDL最优估计(OE)函数中的几个例子 RGB 3S博客| 来源: 网络整理| 查看: 265

1 LMFIT函数 LMFIT函数对具有任意数量参数的函数进行非线性最小二乘拟合。LMFIT使用Levenberg-Marquardt算法，该算法结合了最速下降法和反黑塞斯函数拟合方法。该函数可以是任何非线性函数。算法执行迭代，直到三个连续的迭代未能将卡方值变化低于指定的阈值为止，或者直到执行了最大数量的迭代为止。例子：使用LM算法拟合公式：f(x)=a[0] * exp(a[1]*x) + a[2] + a[3] * sin(x) 偏导数计算公式： dF(x)/dA(0) = exp(A(1)*X) dF(x)/dA(1) = A(0)*X*exp(A(1)*X) = bx * X dF(x)/dA(2) = 1.0 dF(x)/dA(3) = sin(x)

FUNCTION myfunct, X, A ; First, define a return function for LMFIT: bx = A[0]*EXP(A[1]*X) RETURN,[ [bx+A[2]+A[3]*SIN(X)], [EXP(A[1]*X)], [bx*X], $ [1.0] ,[SIN(X)] ] END PRO lmfit_example ; Compute the fit to the function we have just defined. First, ; define the independent and dependent variables: X = FINDGEN(40)/20.0 Y = 8.8 * EXP(-9.9 * X) + 11.11 + 4.9 * SIN(X) measure_errors = 0.05 * Y ; Provide an initial guess for the function's parameters: A = [10.0, -0.1, 2.0, 4.0] fita = [1,1,1,1] ; Plot the initial data, with error bars: PLOTERR, X, Y, measure_errors coefs = LMFIT(X, Y, A, MEASURE_ERRORS=measure_errors, /DOUBLE, $ FITA = fita, FUNCTION_NAME = 'myfunct') ; Overplot the fitted data: OPLOT, X, coefs END

图1.png 2 CURVEFIT函数 CURVEFIT函数使用梯度扩展算法来计算与具有任意数量参数的用户提供的函数的非线性最小二乘拟合。用户提供的函数可以是偏导数已知或可以近似的任何非线性函数。执行迭代，直到卡方小于指定的阈值，或者直到执行了最大数量的迭代为止。例子1：拟合公式：F(x) = a * exp(b*x) + c 偏导数计算： df/da = EXP(b*x) df/db = a * x * EXP(b*x) df/dc = 1.0

PRO gfunct, X, A, F, pder bx = EXP(A[1] * X) F = A[0] * bx + A[2] ;If the procedure is called with four parameters, calculate the ;partial derivatives. IF N_PARAMS() GE 4 THEN $ pder = [[bx], [A[0] * X * bx], [replicate(1.0, N_ELEMENTS(X))]] END Pro CURVEFIT X = FLOAT(INDGEN(10)) Y = [12.0, 11.0, 10.2, 9.4, 8.7, 8.1, 7.5, 6.9, 6.5, 6.1] ;Define a vector of weights. weights = 1.0/Y ;Provide an initial guess of the function’s parameters. A = [10.0,-0.1,2.0] ;Compute the parameters. yfit = CURVEFIT(X, Y, weights, A, SIGMA, FUNCTION_NAME='gfunct') ;Print the parameters returned in A. PRINT, 'Function parameters: ', A End

输出结果： Function parameters: 9.91120 -0.100883 2.07773 最终拟合结果： f (x) = 9.91120(e-0.100883x) + 2.07773 例子2：拟合公式Z = A X^B + C X Y + D Y^E

PRO mymulticurvefit, XY, A, F, PDER X = XY[*,0] Y = XY[*,1] F = A[0]*X^A[1] + A[2]*X*Y + A[3]*Y^A[4] PDER = [[X^A[1]], [A[0]*X^A[1]*ALOG(X)], $ [X*Y], [Y^A[4]], [A[3]*Y^A[4]*ALOG(Y)]] END Pro CurvefitTest2 seed = 1 n = 1000 X = 2*RANDOMU(seed, n) Y = 2*RANDOMU(seed, n) XY = [[X], [Y]] A = [-3, 2, 5, 3, 3] noise = RANDOMN(seed, n) Z = A[0]*X^A[1] + A[2]*X*Y + A[3]*Y^A[4] + noise ;Provide an initial guess of the function's parameters. A = [1d, 1, 1, 1, 1] ;Compute the parameters. yfit = CURVEFIT(XY, Z, weights, A, $ FUNCTION_NAME='mymulticurvefit') PRINT, 'Function parameters: ', A ; Plot the original data as scattered points. iPlot, X, Y, Z, /SCATTER ; Create a 2D surface of the final fit. X1 = 2*FINDGEN(101)/100 X = REBIN(X1, 101, 101) Y = TRANSPOSE(X) Z = A[0]*X^A[1] + A[2]*X*Y + A[3]*Y^A[4] iSurface, Z, X1, X1, /OVERPLOT END

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IDL最优估计(OE)函数中的几个例子 RGB 3S博客

IDL最优估计(OE)函数中的几个例子 RGB 3S博客

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