backup

.vscode/settings.json

@@ -0,0 +1,3 @@
+{
+    "python.formatting.provider": "black"
+}

_config.yml

@@ -36,10 +36,11 @@ html:
   use_issues_button: true
   use_repository_button: true
 
+# https://github.com/QuantEcon/lecture-python-advanced.myst/blob/3a0b5b40dc627f9dfabdd7e84c0c67a171bca690/lectures/_config.yml#L71
 # https://jupyterbook.org/en/stable/content/math.html
-#sphinx:
-#  config:
-#    mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
+sphinx:
+  config:
+    mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
 
 
 parse:
@@ -57,13 +58,14 @@ sphinx:
     mathjax_config:
       tex:
         macros:
+          "argmax": "arg\\,max"
+          "argmin": "arg\\,min"
           "covMat": "\\boldsymbol{\\Sigma}"
           "data": "\\mathcal{D}"
           "defeq": "\\triangleq"
           "diag": "\\mathrm{diag}"
           "discreteState": "s"
           "dotstar": "\\odot"
-          "dynamicsFn": "\\mathbf{f}"
           "floor": ["\\lfloor#1\\rfloor", 1]
           "gainMatrix": "\\mathbf{K}"
           "gainMatrixReverse": "\\mathbf{G}"
@@ -82,14 +84,12 @@ sphinx:
           "inputs": "\\input"
           "inv": ["{#1}^{-1}", 1]
           "keyword": ["\\textbf{#1}", 1]
-          "ldsDyn": "\\mathbf{F}"
-          "ldsDynIn": "\\mathbf{B}"
           "initMean": "\\boldsymbol{\\mean}_0"
           "initCov": "\\boldsymbol{\\covMat}_0"
           "ldsObs": "\\mathbf{H}"
           "ldsObsIn": "\\mathbf{D}"
-          "ldsTrans": "\\ldsDyn"
-          "ldsTransIn": "\\ldsDynIn"
+          "ldsTrans": "\\mathbf{F}"
+          "ldsTransIn": "\\mathbf{B}"
           "obsCov": "\\mathbf{R}"
           "obsNoise": "\\boldsymbol{r}"
           "map": "\\mathrm{map}"
@@ -115,6 +115,7 @@ sphinx:
           "trans": "\\mathsf{T}"
           "transpose": ["{#1}^{\\trans}", 1]
           "transCov": "\\mathbf{Q}"
+          "transFn": "\\mathbf{f}"
           "transNoise": "\\mathbf{q}"
           "valpha": "\\boldsymbol{\\alpha}"
           "vbeta": "\\boldsymbol{\\beta}"

chapters/ssm/lds.ipynb

@@ -64,7 +64,7 @@
     "the input $\\inputs_t \\in \\real^{\\ninputs}$,\n",
     "and some random $\\keyword{process noise}$ $\\transNoise_t \\in \\real^{\\nhidden}$ \n",
     "\\begin{align}\n",
-    "\\hidden_t &= \\dynamicsFn(\\hidden_{t-1}, \\inputs_t, \\transNoise_t)  \n",
+    "\\hidden_t &= \\transFn(\\hidden_{t-1}, \\inputs_t, \\transNoise_t)  \n",
     "\\end{align}\n",
     "where $\\transNoise_t$ is drawn from the distribution such\n",
     "that the induced distribution\n",
@@ -80,7 +80,7 @@
     "If we assume additive Gaussian noise,\n",
     "the model becomes\n",
     "\\begin{align}\n",
-    "\\hidden_t &= \\dynamicsFn(\\hidden_{t-1}, \\inputs_t) +  \\transNoise_t  \\\\\n",
+    "\\hidden_t &= \\transFn(\\hidden_{t-1}, \\inputs_t) +  \\transNoise_t  \\\\\n",
     "\\obs_t &= \\measurementFn(\\hidden_{t}, \\inputs_t) + \\obsNoise_t\n",
     "\\end{align}\n",
     "where $\\transNoise_t \\sim \\gauss(\\vzero,\\transCov_t)$\n",
@@ -88,7 +88,7 @@
     "We will call these $\\keyword{Gaussian SSMs}$.\n",
     "\n",
     "If we additionally assume\n",
-    "the transition function $\\dynamicsFn$\n",
+    "the transition function $\\transFn$\n",
     "and the observation function $\\measurementFn$ are both linear,\n",
     "then we can rewrite the model as follows:\n",
     "\\begin{align}\n",

chapters/ssm/nlds.ipynb

@@ -143,7 +143,7 @@
     "but the process noise and observation noise are Gaussian.\n",
     "That is, \n",
     "\\begin{align}\n",
-    "\\hidden_t &= \\dynamicsFn(\\hidden_{t-1}, \\inputs_t) +  \\transNoise_t  \\\\\n",
+    "\\hidden_t &= \\transFn(\\hidden_{t-1}, \\inputs_t) +  \\transNoise_t  \\\\\n",
     "\\obs_t &= \\obsFn(\\hidden_{t}, \\inputs_t) + \\obsNoise_t\n",
     "\\end{align}\n",
     "where $\\transNoise_t \\sim \\gauss(\\vzero,\\transCov)$\n",
@@ -202,7 +202,7 @@
     "\\underbrace{\n",
     "  \\begin{pmatrix} \\hiddenScalar_{1,t-1} + \\hiddenScalar_{2,t-1} \\Delta  \\\\\n",
     "    \\hiddenScalar_{2,t-1} -g \\sin(\\hiddenScalar_{1,t-1}) \\Delta  \\end{pmatrix}\n",
-    "  }_{\\dynamicsFn(\\hidden_{t-1})}\n",
+    "  }_{\\transFn(\\hidden_{t-1})}\n",
     "+\\transNoise_{t-1}\n",
     "\\end{align}\n",
     "where $\\transNoise_{t-1} \\sim \\gauss(\\vzero,\\transCov)$ with\n",