From ee2c3e2428aee8be6685299da362311d8a2a4d43 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Mon, 10 Apr 2017 16:34:08 -0400 Subject: [PATCH] fix HW6 gradient of cost equation --- HW6/README.md | 6 +- lecture_17/octave-workspace | Bin 5146 -> 153 bytes lecture_18/octave-workspace | Bin 2001 -> 153 bytes lecture_19/octave-workspace | Bin 10815 -> 153 bytes lecture_20/octave-workspace | Bin 0 -> 11 bytes .../lecture_21-checkpoint.ipynb | 6 + lecture_21/lecture_21.ipynb | 430 ++++++++++++++++++ lecture_21/q1.png | Bin 0 -> 28691 bytes lecture_21/q2.png | Bin 0 -> 36399 bytes lecture_21/reduce_noise.png | Bin 0 -> 7390788 bytes 10 files changed, 440 insertions(+), 2 deletions(-) create mode 100644 lecture_20/octave-workspace create mode 100644 lecture_21/.ipynb_checkpoints/lecture_21-checkpoint.ipynb create mode 100644 lecture_21/lecture_21.ipynb create mode 100644 lecture_21/q1.png create mode 100644 lecture_21/q2.png create mode 100644 lecture_21/reduce_noise.png diff --git a/HW6/README.md b/HW6/README.md index 1f3c86c..c72ba05 100644 --- a/HW6/README.md +++ b/HW6/README.md @@ -34,12 +34,14 @@ variable is failure (1=fail, 0=pass). Create a function called `cost_logistic.m` takes the vector `a`, and independent variable `x` and dependent variable `y`. Use the function, $\sigma(t)=\frac{1}{1+e^{-t}}$ where $t=a_{0}+a_{1}x$. Use the cost function, - $J(a_{0},a_{1})=\sum_{i=1}^{n}\left[-y_{i}\log(\sigma(t_{i}))-(1-y_{i})\log((1-\sigma(t_{i})))\right]$ + $J(a_{0},a_{1})=1/m\sum_{i=1}^{n}\left[-y_{i}\log(\sigma(t_{i}))-(1-y_{i})\log((1-\sigma(t_{i})))\right]$ and gradient $\frac{\partial J}{\partial a_{i}}= - 1/m\sum_{k=1}^{N}\left(\sigma(t_{k})-y_{k}\right)t_{k}$ + 1/m\sum_{k=1}^{N}\left(\sigma(t_{k})-y_{k}\right)x_{k}^{i}$ + + where $x_{k}^{i} is the k-th value of temperature raised to the i-th power (0, and 1) a. edit `cost_logistic.m` so that the output is `[J,grad]` or [cost, gradient] diff --git a/lecture_17/octave-workspace b/lecture_17/octave-workspace index c9ec2aa3f1753ebfc595762a3c1c99b8573c1bf4..8c437bb6e55a5d1b6115661b3a20e86870909d32 100644 GIT binary patch delta 20 bcmbQGF_V$oKe;5aELGP~*N0*9e6~ISLiq+~ literal 5146 zcmb7Hd05O_A8$lOO1l=)q6H0-5OEIOibyI%MMAPWZCYohJzBiyG=2SXpZERa?RkDP&n&+)=X}1OExQfA?tUIzW9||$j+mI3Grh#b zeoD}X?e4zbTm1Wf{`|R-z8XR=NqP;-oxil1W@)YvXq~PO@_SqlMzE0DI 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+ ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```matlab\n", + "% Define function ...\n", + "function collar_potential_energy(x,theta)\n", + " % function to evaluate E_total\n", + " Etotal = m*x*g.*sin(theta)+K/2*(0.5-sqrt(0.5^2+(0.5-x).^2);\n", + "end\n", + "\n", + "% solve for x\n", + "\n", + "x=goldmin(@(x) collar_potential_energy(x,theta),xl,xu)\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## HW #5\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Initial Value Problem" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Octave", + "language": "octave", + "name": "octave" + }, + "language_info": { + "file_extension": ".m", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "octave", + "version": "0.19.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/lecture_21/q1.png b/lecture_21/q1.png new file mode 100644 index 0000000000000000000000000000000000000000..3145b8d50745f1e76b825a3abe1d4de86684ecd5 GIT binary patch literal 28691 zcmdpdcTkgG)FxO!L_m=uU8G9~=|u(Uy(1+ENDIA&j;KiQy-Ozq2rYyb0@9>QFQG{9 zAe}&fjlbXbeLFj|yED79e{E)%T#`5Uz4yN7o_o&oJSSXJU4iH!^+OyS93myfciK2O zcaS(ZxbhG1u%B2uoabZT?zzh-={~@|{2zP_!~Rd@A!q2J<818#GIz7Wv2k*CwBmNR zbhEN@a<_H%IJk?H#=&`xqx9~ru6Ne%e1JdG#{13d+?p+5LY!g|ueP%G)~h1z#VT!4 zMKO-#?_`jY`vgXD8KbjHWAvO^clEt%N8Rc9{*c)(th*O9D`j?oPXQ96iR_1kFo8}V8&kP-^N!_K4vueKi}eiV@CedSZ<43 zHTd_p&k`^X|8^2~S2n@yZ{vaM2gM`KzYRv>NB`B?h#0z}&?Qqf&7Z1_j;%D|Fr6=b zj=3+>^kcHgbWATbv(C&e2(D3)#!BI0DTMt})mEKhG#@>lAMmJQtUPx~GZ-0phjl}KQJP_(A#=dxi?Vw4?%emNnvJyzBT zn1j!?&$D?*#!Fvb`982^iJ3nINRI5jB)H`nf#_1^8C5vC_UQj)eabv~U)bxxBs=R} 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