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
