{"id":22421978,"url":"https://github.com/auralius/jacobian-hessian-cpp","last_synced_at":"2025-03-27T05:21:30.420Z","repository":{"id":148342420,"uuid":"80675836","full_name":"auralius/jacobian-hessian-cpp","owner":"auralius","description":"Jacobian and Hessian of a vector 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\"cells\": [\n  {\n   \"cell_type\": \"markdown\",\n   \"metadata\": {},\n   \"source\": [\n    \"This codes calculate numerically the Jacobian and the Hessian of a vector of function.  \\n\",\n    \"For matrix operation, Armadillo is used: http://arma.sourceforge.net/  \\n\",\n    \"To install, do the follwoing:\\n\",\n    \"\\n\",\n    \"```\\n\",\n    \"mkdir build  \\n\",\n    \"cd build  \\n\",\n    \"cmake ..  \\n\",\n    \"make  \\n\",\n    \"```\\n\",\n    \"\\n\",\n    \"There is an example provided.  \\n\",\n    \"\\n\",\n    \"To understand the concept, let's take an example of a function of vector, with 3 input parameters and 2 output parameters:   \\n\",\n    \"\\n\",\n    \"$y=\\\\begin{bmatrix} f_1(x_1,x_2,x_3) \\\\\\\\ f_2(x_1,x_2,x_3) \\\\end{bmatrix}$\\n\",\n    \"\\n\",\n    \"$Jac(y) = \\\\begin{bmatrix}\\n\",\n    \"\\\\frac{\\\\partial f_1}{\\\\partial x_1} \u0026 \\\\frac{\\\\partial f_1}{\\\\partial x_2} \u0026 \\\\frac{\\\\partial f_1}{\\\\partial x_3} \\\\\\\\ \\n\",\n    \"\\\\frac{\\\\partial f_2}{\\\\partial x_1} \u0026 \\\\frac{\\\\partial f_2}{\\\\partial x_2} \u0026 \\\\frac{\\\\partial f_2}{\\\\partial x_3} \\n\",\n    \"\\\\end{bmatrix}$ \\n\",\n    \"\\n\",\n    \"$Hess(y(1)) = \\\\begin{bmatrix}\\n\",\n    \"\\\\frac{\\\\partial^2 f_1}{\\\\partial x_1^2} \u0026 \\\\frac{\\\\partial^2 f_1}{\\\\partial x_1 \\\\partial x_2} \u0026 \\\\frac{\\\\partial^2 f_1}{\\\\partial x_1 \\\\partial x_3} \\\\\\\\\\n\",\n    \"\\\\frac{\\\\partial^2 f_1}{\\\\partial x_2 \\\\partial x_1} \u0026 \\\\frac{\\\\partial^2 f_1}{\\\\partial x_2^2} \u0026 \\\\frac{\\\\partial^2 f_1}{\\\\partial x_2 \\\\partial x_3}  \\\\\\\\\\n\",\n    \"\\\\frac{\\\\partial^2 f_1}{\\\\partial x_3 \\\\partial x_1} \u0026 \\\\frac{\\\\partial^2 f_1}{\\\\partial x_3 \\\\partial x_2} \u0026 \\\\frac{\\\\partial^2 f_1}{\\\\partial x_3^2}\\n\",\n    \"\\\\end{bmatrix}$\\n\",\n    \"\\n\",\n    \"$Hess(y(2)) = \\\\begin{bmatrix}\\n\",\n    \"\\\\frac{\\\\partial^2 f_2}{\\\\partial x_1^2} \u0026 \\\\frac{\\\\partial^2 f_2}{\\\\partial x_1 \\\\partial x_2} \u0026 \\\\frac{\\\\partial^2 f_2}{\\\\partial x_1 \\\\partial x_3} \\\\\\\\\\n\",\n    \"\\\\frac{\\\\partial^2 f_2}{\\\\partial x_2 \\\\partial x_1} \u0026 \\\\frac{\\\\partial^2 f_2}{\\\\partial x_2^2}             \u0026 \\\\frac{\\\\partial^2 f_2}{\\\\partial x_2 \\\\partial x_3} \\\\\\\\\\n\",\n    \"\\\\frac{\\\\partial^2 f_2}{\\\\partial x_3 \\\\partial x_1} \u0026 \\\\frac{\\\\partial^2 f_2}{\\\\partial x_3 \\\\partial x_2}  \u0026 \\\\frac{\\\\partial^2 f_2}{\\\\partial x_3^2}\\n\",\n    \"\\\\end{bmatrix}$\"\n   ]\n  }\n ],\n \"metadata\": {\n  \"kernelspec\": {\n   \"display_name\": \"Python 2\",\n   \"language\": \"python\",\n   \"name\": \"python2\"\n  },\n  \"language_info\": {\n   \"codemirror_mode\": {\n    \"name\": \"ipython\",\n    \"version\": 2\n   },\n   \"file_extension\": \".py\",\n   \"mimetype\": \"text/x-python\",\n   \"name\": \"python\",\n   \"nbconvert_exporter\": \"python\",\n   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