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Fix typos in least_squares notebook.

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PiperOrigin-RevId: 635696410
Change-Id: Iba9a2c8f121ca4994678ba933e19dce5323da27b
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Kevin Zakka
2024-05-20 23:47:38 -07:00
committed by Copybara-Service
parent f2732c336e
commit f0b633de6a
1 changed files with 4 additions and 4 deletions
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python/least_squares.ipynb
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@@ -2179,7 +2179,7 @@
"source": [ "source": [
"### Non-quadratic norms\n", "### Non-quadratic norms\n",
"\n", "\n",
"As explained in the background section, Least Squares can be generalized to norms other than the quadratic. We are now in a position to show how to define a non-quadratic norm, which is important in the estimation and system-identification contexts, where long-taled, disturbance-rejecting distributions are proportional to the exponent of a non-quadratic function.\n", "As explained in the background section, Least Squares can be generalized to norms other than the quadratic. We are now in a position to show how to define a non-quadratic norm, which is important in the estimation and system-identification contexts, where long-tailed, disturbance-rejecting distributions are proportional to the exponent of a non-quadratic function.\n",
"\n", "\n",
"Let's say that we wish the task residual i.e., the vector from the hand to the target, to be evaluated with the \"Smooth L2\" function $c(r)$ which, for a given smoothing radius $d \\gt 0$ is\n", "Let's say that we wish the task residual i.e., the vector from the hand to the target, to be evaluated with the \"Smooth L2\" function $c(r)$ which, for a given smoothing radius $d \\gt 0$ is\n",
"$$\n", "$$\n",
@@ -2193,7 +2193,7 @@
"H &=\\tfrac{\\partial^2 c}{\\partial r^2} = \\frac{I_{n_r} - g\\cdot g^T}{s}\n", "H &=\\tfrac{\\partial^2 c}{\\partial r^2} = \\frac{I_{n_r} - g\\cdot g^T}{s}\n",
"\\end{align}\n", "\\end{align}\n",
"$$\n", "$$\n",
"There is no particularly good reason to use this norm for this optimization task, it is meerly an example.\n", "There is no particularly good reason to use this norm for this optimization task, it is merely an example.\n",
"\n", "\n",
"Let's read the documentation of the `minimize.Norm` class:\n" "Let's read the documentation of the `minimize.Norm` class:\n"
] ]
@@ -2215,7 +2215,7 @@
"id": "3JGpR47DQ9S2" "id": "3JGpR47DQ9S2"
}, },
"source": [ "source": [
"Our sensors are 3 `r_pos` residual values for the hand-to-object vector followed by 21 `r_torque` actuator torques, for a total of `ns = 24` sensors. These are concatented for the entire trajectory, leading to a residual of size `24*N`, where `N` is the number of timesteps in a trajectory. After reshaping and slicing appropriately, the norm implementation looks like" "Our sensors are 3 `r_pos` residual values for the hand-to-object vector followed by 21 `r_torque` actuator torques, for a total of `ns = 24` sensors. These are concatenated for the entire trajectory, leading to a residual of size `24*N`, where `N` is the number of timesteps in a trajectory. After reshaping and slicing appropriately, the norm implementation looks as follows:"
] ]
}, },
{ {
@@ -2291,7 +2291,7 @@
"id": "J0brs9pG0-8Y" "id": "J0brs9pG0-8Y"
}, },
"source": [ "source": [
"Now that we are confident of our implemetation, we can see what the solution looks like:" "Now that we are confident in our implemetation, we can see what the solution looks like:"
] ]
}, },
{ {