埃ぇиョノ跑猭Transformation盢计厩家锣传Θ絬┦把计家ㄒ安砞家 $$ y=ae^{bx} $$
礛癸计眔
$$ \ln y = \ln a + bx $$$\ln a$ の $b$ 跑Θ絬┦把计иノ¨程キよ猭〃тㄤ叫ǎㄏノ跑猭絛ㄒ
瓃瓜い材瓜琌 $\ln y$ 癸 $x$ 瓜τ材玥琌 $y$ 癸 $x$ 瓜叫疭猔種竒パ跑猭ぇ程キよ猭┮眔程羆キよ粇畉琌 $$ E'=\sum_{i=1}^m (\ln y_i - \ln a - bx_i)^2 $$
τぃ琌家羆キよ粇畉 $$ E=\sum_{i=1}^m (y_i - ae^{bx_i})^2 $$
硄盽 $E'$ 程$E$ ぃ﹚琌程硄盽ョ瞒程ョぃ环╫璝璶弘痲―弘ノ fminsearch ― $E$ 程跑程キよ猭眔 a の b 穓碝癬翴叫ǎ絛ㄒ
パ瓃絛ㄒиㄏノ跑猭т菠把计礛ノ fminsearch ㄓ癸粇畉キよ㎝秈︽程て眔粇畉キよ㎝穦ゑ玡絛ㄒノ跑猭临璶讽礛硂絛ㄒいи﹚竡ゲ斗砆程て粇畉羆㎝ㄧΑ errorMeasure3.m竊絞碩ㄤず甧ぃ弄叫︽把σ盒い郎
ㄆ龟癬ㄓ琌獶絬┦癹耴家竒筁ㄇ锣传碞穦跑Θ絬┦癹耴家碞ㄏノи硂竊┮弧跑猭ㄓ秈︽絬┦癹耴把计―琌ㄇ跑猭ノ獶絬┦家の闽锣传よ猭
絪腹 獶絬┦家 锣传絬┦家 把计锣传そΑ 1 $y=\frac{ax}{1+bx}$ $\underbrace{\frac{1}{y}}_Y=\underbrace{\frac{1}{a}}_\alpha \frac{1}{x}+\underbrace{\frac{b}{a}}_\beta$ $a=\frac{1}{\alpha}$, $b=\frac{\beta}{\alpha}$ 2 $y=\frac{a}{x+b}$ $\underbrace{\frac{1}{y}}_Y=\underbrace{\frac{1}{a}}_\alpha x+\underbrace{\frac{b}{a}}_\beta$ $a=\frac{1}{\alpha}$, $b=\frac{\beta}{\alpha}$ 3 $y=\frac{ax}{x^2+b^2}$ $\underbrace{\frac{1}{y}}_Y=\underbrace{\frac{1}{a}}_\alpha x+\underbrace{\frac{b^2}{a}}_\beta \frac{1}{x}$ $a=\frac{1}{\alpha}$, $b=\pm\sqrt{\frac{\beta}{\alpha}}$ 4 $y=ax^b$ $\underbrace{\ln y}_Y = \underbrace{b}_\alpha \ln x + \underbrace{\ln a}_\beta$ $a=e^\beta, b=\alpha$ 5 $y=\frac{1}{1+ax^b}$ $\underbrace{\ln \frac{1-y}{y}}_Y = \underbrace{b}_\alpha \ln x + \underbrace{\ln a}_\beta$ $a=e^\beta, b=\alpha$ 6 $y=\frac{1}{1+exp\left(\frac{ax}{b+x}\right)}$ $\underbrace{\left[\ln \frac{1-y}{y}\right]^{-1}}_Y=\underbrace{\frac{b}{a}}_\alpha \frac{1}{x}+\underbrace{\frac{1}{a}}_\beta$ $a=\frac{1}{\beta}, b=\frac{\alpha}{\beta}$ 7 $y=\ln a + x - \ln (e^x+b)$ $\underbrace{e^{-y}}_Y=\underbrace{\frac{b}{a}}_\alpha e^x+\underbrace{\frac{1}{a}}_\beta$ $a=\frac{1}{\beta}, b=\frac{\alpha}{\beta}$ 8 $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $\underbrace{y^2}_Y=\underbrace{-\frac{b^2}{a^2}}_\alpha x^2+\underbrace{b^2}_\beta$ $a^2=-\frac{\beta}{\alpha}, b^2=\beta$ 9 $(x-a)^2+(y-b)^2=c^2$ $\underbrace{x^2+y^2}_Y=\underbrace{2a}_\alpha x+\underbrace{2b}_\beta y+\underbrace{c^2-a^2-b^2}_\gamma$ $a=\alpha/2, b=\beta/2\\c=\gamma+\frac{\alpha^2}{4}+\frac{\beta^2}{4}$ 10 $y=a e^{\left[-\left(\frac{x-c}{b}\right)^2\right]}$ $\underbrace{\ln y}_Y = \underbrace{-\frac{1}{b^2}}_\alpha x^2+ \underbrace{\frac{2c}{b^2}}_\beta x+\underbrace{\ln a-\frac{c^2}{b^2}}_\gamma$ $a=exp \left( \gamma - \frac{\beta^2}{4}\right)\\b=\pm \sqrt{-\frac{1}{\alpha}}\\c=-\frac{\beta}{2\alpha}$ 11 $y=\frac{a}{\sqrt{(1+bx^2)^2+c}}$ $\underbrace{\frac{1}{y^2}}_Y=\underbrace{\frac{b^2}{a^2}}_\alpha x^4+\underbrace{\frac{2b}{a^2}}_\beta x^2+\underbrace{\frac{c+1}{a^2}}_\gamma$ $a=\pm\frac{\sqrt{4\alpha}}{\beta}\\b=\frac{2\alpha}{\beta}\\c=\frac{4\alpha\gamma}{\beta^2}-1$
MATLAB祘Α砞璸秈顶絞![]()