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Integrate Slice Sampling: Hyperrectangles-based Methods. #895

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@lorcandelaney lorcandelaney commented Aug 7, 2019

See #772

Includes:

  1. Hyperrectangles-based methods for Slice Sampling: Adaptive and Non-Adaptive. Both methods are in pints/pints/_mcmc/_slice_hyperrectangles.py.
  2. Tests for Hyperrectangles-based methods.
  3. Notebooks for Hyperrectangles-based methods.

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codecov bot commented Aug 7, 2019

Codecov Report

Merging #895 into master will not change coverage.
The diff coverage is 100%.

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@@          Coverage Diff          @@
##           master   #895   +/-   ##
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  Coverage     100%   100%           
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  Files          55     56    +1     
  Lines        5673   5772   +99     
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+ Hits         5673   5772   +99
Impacted Files Coverage Δ
pints/_mcmc/_slice_hyperrectangles.py 100% <100%> (ø)

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Hey @lorcandelaney ! For these and other PRs, please check how your docstrings render, and if you're using the correct syntax (:math:`1 + x` for maths, ``1 + x`` for code) everywhere!

See CONTRIBUTING.md for instructions on locally building and inspecting the docs

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Great stuff Lorcan -- looking really good! Apart from the inline comments, just one ask from me:

  • Can you go through the text in the notebook examples once more? I noticed a few spelling mistakes in there (these are hard to comment on in Github's interface).

@@ -46,10 +46,12 @@ relevant code.
- [Slice Sampling: Stepout MCMC](./sampling-slice-stepout-mcmc.ipynb)
- [Slice Sampling: Doubling MCMC](./sampling-slice-doubling-mcmc.ipynb)
- [Slice Sampling: Overrelaxation MCMC](./sampling-slice-overrelaxation-mcmc.ipynb)
- [Slice Sampling: Hyperrectangles MCMC](./sampling-slice-hyperrectangles-mcmc.ipynb)
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Can we sort this so it's alphabetical please (sorry)?

"metadata": {},
"source": [
"# Inference: Slice Sampling with Adaptive Hyperrectangles\n",
"This example shows you how to perform Bayesian inference on multiple toy problems, using\n",
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Change to, "This example shows how to perform Bayesian inference on multiple toy problems..."

"source": [
"# Inference: Slice Sampling with Adaptive Hyperrectangles\n",
"This example shows you how to perform Bayesian inference on multiple toy problems, using\n",
"Slice Sampling with Adaptive Hyperrectangles, as described in [1].\n",
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no capitalisation on slice sampling and adaptive hyperrectangles

" horizontal “slice”: $S = {x: y < f (x)}$. Note that $x_0$ is\n",
" always within $S$.\n",
"3. Find a hyperrectangle ($H = (L_1, R_1) ×···× (L_n, R_n)$) around\n",
" $x_0$, which preferably contains at least a big part of the slice.\n",
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This bit doesn't seem to be parseing for me. Can you check the formulae?

"\n",
"The implementation uses estimates (``width``) of the relative scales of the variables to randomly position a hyperrectangle with such dimensions uniformly over positions containing $x_0$ that lead to $H$.\n",
"\n",
"When a sample is rejected, the algorithm shrinks adaptively the hyperrectangle. Specifically, only the axis corresponding to the variable $x_i$ is shrunk, where $i$ maximises: $(R_i - L_i) |G_i|$, with $G$ being the gradient of $f(x)$ evaluated at the last rejectedvsample. By multiplying the magnitude of the component $i$ of the gradient by the width of the hyperrectangle in this direction, we get an estimate of the amount by which log $f(x)$ changes along axis $i$. The axis for which this change is thought to be largest is likely to be the best one to shrink in order to eliminate points outside the slice.\n",
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rejectedvsample -- think a spelling issue

3. Repeat:
a. for ``i = 1`` to ``n``:
- ``U_i \sim uniform(0,1)``
- ``x_{1_i} = L_i + U_i (R_i - L_i)``
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Where is R_i set?

always within S.
3. Find a hyperrectangle (``H = (L_1, R_1) ×···× (L_n, R_n)``) around
``x_0``, which preferably contains at least a big part of the slice.
4. Draw a new point (``x1``) from the part of the slice within this
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Is rejection sampling used for step 4? For example, if a point is drawn that is in the rectangle not in the slice, then it is rejected, right? Can we say this explicitly?

the gradient and the current dimensions of the hyperrectangle,
as described in [1] pp. 722. Specifically, only the axis corresponding
to the variable ``x_i`` is shrunk, where ``i`` maximises:
``(R_i - L_i) |G_i|``, with ``G`` being the gradient of ``f(x)` evaluated
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Is it the gradient of f(x) or of log f(x)?

``(R_i - L_i) |G_i|``, with ``G`` being the gradient of ``f(x)` evaluated
at the last rejected sample. By multiplying the magnitude of the component
``i`` of the gradient by the width of the hyperrectangle in this direction,
we get an estimate of the amount by which log ``f(x)`` changes along axis
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Again, is it the gradient of log f(x) of f(x)?

self._ready_for_tell = False

# Unpack reply
fx, grad = reply
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What happens if adaptation is turned off? Is None returned in grad?

}
],
"source": [
"import os\n",
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Please install PINTS, using e.g. pip install -e .[dev,test] (see the README and CONTRIBUTING).
After that these lines import os and os.chdir won't be necessary anymore and can be removed

"mcmc = pints.MCMCController(log_pdf, 3, xs, method=pints.SliceHyperrectanglesMCMC)\n",
"\n",
"# Add stopping criterion\n",
"mcmc.set_max_iterations(2000)\n",
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Do we really need 2000 iterations for a unimodal Gaussian? Keep in mind these notebooks should run quickly for users, and are tested regularly, so the faster the better!

"outputs": [
{
"data": {
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Again, based on the trace plots it looks like 2000 iterations is massive overkill

"outputs": [
{
"data": {
"image/png": 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LzKJMT8t88sYQHmJphUQ6bXvgxjr3jKorgpO3PBljK2ljaCNqxexm4BgiEbKNv+vEILWGJWVfzz5ebnuZQDJQeC5qpkDR1jvSiKcVounCfcf8xwraThdOimkkHbFnCnUar32vbm1Lx4pf33CfHkeXhzmW1+k5MnCKqzJdAPMtWOZPg8+xALPZdm656Z1OXAXLxcVlfHY/NPY/lxmlsbGR5ubc6ntdXR0rV67MKlNVVVVEo1G2b98+6b67urrYv38/AM8++ywf+9jHbPuvv/563nnnHVpadFeNeDxOU1MT0WiUUCjEbbfdxqOPPkpdXaH71QcJIcRy4M+BX8zGeB6kLlAJT1Y4K5YIQpUZth7bSluobcrjWQW/gnGO/hpO7NTjc0zeflT/h56+uT9kV7bMpBShRIYfvdHMYNhSTNrs3iJQlnS+pdcvKpiDXayckBCfZ+WSxjjCIWbI2VqSm9fq0X3Zuc5E2nwnTKE3mnJwtzJc+lIoSOlszatLDbM5eBRVUx33j4nwcLQnxO6Tg1g1LJlXk8163TKarmBN+voIwfH0KK/Gu4yhffa+T7yMPPGS46FSSkJpXflKKvmFyiXsexjqf+NwoMb7PSEOtAcK9xU2HreFJrWiSn9a0bKLI2aSDvPcoukoTzU8xcGBgzSmA7wULeKSGO7T/xpKLIFO/Tc3nHMRzRx8gtSBwq+liag8ilqohHmyymBef6ZV2XJdGkcb8ScKLeia1D6QVqnJ4Ca5cHFxcZkksx30Ho1G+epXv0owGMTn83HxxRezZcsWFi9ezD333MPatWtZtWoV11133aT7vvzyy9m2bRtf/vKXueSSS/jKV75i219dXc3WrVv5/Oc/TyqlC9ibNm1iwYIF3HHHHSSTSaSUPPLIIwV9DwwMsG7dOsLhMB6Ph0cffZSGhgYWLpyeGiqzzKPAPwMLijUQQtwL3AtwwQWnFugtpCnGWITcIvKKIpPElTh7uvdw0aKLivc51YyBpgCbSYCvjKFIkmpLIox3W0c41DHK366/gLMWlgO5wrCjsTTnAT2BOGcb+4yzQUgNIcCrpSjtPQAjJeCNQWmlozCXnY6msLd7L9efdz3zSxzclfIF1bEULKeLajteklQ0OgfCHOkaZd2q6sL2Bj2BOIFYhrXLFxVtMx6KppBSdGG6bdhBcDeu+aueDmKJd4G1eXOX1KR0F7r07v+HeSs+om9f898mNgHjGiXTGezPnnFNkiGI6MJ9SlHRtFzq8fGeq3gmzonRE1xz1jUIIYinVXZFuynxCKi4AESROmfJEFK1u0u+3jCIr1wXYRVpKKIiz7dttL2wr6xldHxLy2hilKULzh2zzdu9b3PMf4y7195NqbfUtq+mM8BjgTa+dvOaAgtWQtEXJLoj3dTGDTdHRwXVOBch9GP9RomQUE82mUttVwBNwkfzjjQXKRwTpVjalCpRlox2AOeYQ9mOH4s3ut4AJc19kUR2ngA/e/9nXLz44qIJKvI5FVVstjOgThRXwXJxmSYmUuDXxWUqXHvttbz77ruO+zZt2sSmTZsKtu/Zsyf7euPGjWzcuLFgX0dHBx6Ph5/97GdjHn/TTTdx6FBhLMXBgwcLtlk555xz6OnpGbPN6UYI8Qcp5afGafMXwJCUskYIsbFYOynlFmALwLp1607pV19gCA5SUq4EKU0l0KRFefI3w1ADcDnmGvV4K8ZOCpb1tRC6/JkvWGmaRlRLsxCJP5ri6QNdfDac4IKlekyGP5oiqgzxTs8wt6y+jvllpVmrhgDi6iigKybRpGIZUxcor+vZhjzXULpHWo1zyc0QmT1FPTNasJXGQCMaGjevvHnMcybQiUyb8UPjWLCkpERNIL3280+kVSSwp2mI8xZXcp43DPOrwFL4OKNq/Paw/qyvXarq8WBVF485tdrBWgKpAJ+44BPZbU+feJrGoWGqud35oETO8hJSerOvg8kgg/FBLl2sj6kBdT1BLk8dYPG80kkrWMsSbQTk2dnN5rMlug6AEkdKyeNvt5PKaHRpo1xYXYqUMpug48sfv4gKICVVfJqK1+NlX88+2kJtnDP/HM6vPJ9nD/UwEE6yYrFe7Nq8PwXPcf9RUCSsvCm76XhfmDWr9etfWFtq/Dgn6ZQBUVPgZC7jaWI8d9T4CO0jR2DBWaTVNIMhheoFZdl051ammuSioTeIP5amyjzWtEpanr20kfUwn/5Q0hhbp2Uowu/f7+crG1dTWuJF0yRdo3Eu9b9GVSQCyfVQvgiBxKcmkHKe8zTzT8HfBGUrCtq1BFu4hYkpWCavd75OS6CFr1xlLPRpqm4591nqvWUSjtdqrjknugqWi4vL+HWyXFzOYIQQ1xTbBVw1gS42ALcLIW4DyoGFQohfSSnvmq45FpAVICRre7ejqgqadn1uf/12wskM+C7HJlBqGh5NQfMU/rw7pTFuGowQTyssKNUz9UlkQQxWTXKQQ/Fe/jYVIqHpgk4kabcoNMV303QCdrXU8x+3/R1NAX2lfSiSol97nY+mqwjE5nOyq5/FyR4kS2CM7IDWGCxVSiIJJVuPyimexYZ1e90z9Ax0MKqmHcey9RHu4+xYA4omcgkzjFmYc9mx/zhf9PyB14LL2XDb5zlrgW6V+9WBzlzzg1tIaQrajf/beX4GB/oPANgUrPFizNTWPdmzEJa5/7rx16hS5dJFqwFQVI2UotE1Emfx8lKHnopgKB4+NZ61VIFhwUrZE32kjAx08eAAYU1DW63xlpGA4pn3uviSlDwWOMaazte59cJbsy6EKSNGTsl/0LKZzK0LAAaJwt8kr/AipSSRMV0lTdNLoWtkINJLIhXmPN98o1/7szAUTjLc04x6jvUcx1kjiQxCuA3mLyWSTLO9xs/KZRV85prlhW0nEv+YpzT4E34OjvaQUFXLuRnKpEXBesXTRqUsYUNed70Bs8SB/v6dlhGu7HuOzNuVlP7Z/+JgxyjNg1Gu1pLGio4+ftnwUdb1Ps/A/L8FcopTzqqch03BHVvNsZaAkFJmE/eYfTcHmrP7pJQEmt4lOhSk8tZv5zoxXJPhs2OOdbpxY7BcXFxc/khZtWoVx44dG7/hmc8h4GHgP/L+PQwsHu9gKeU3pZTLpZSrgM8Bb86ocqUPaiSCkHjQBUbP8e025eG4U+r2hhf5SM84KcUtEtIbJwZ5v1sXXkURIbBXiQAQycTwegQ9ySO8quYUCvO4RcleSoPv8stjv6QzrO83E1yk1DiJjMqyRBtlaqTgWID6VC6WI2vjkipNAxEa+sJZYcxUlFqHIzzyehPt/hiPvN5ELO2cIjqQSBPLqIhQD/TaU7Br1tgiw9K1NN4M7z2Wm4vMvfCpSUZjaRakB2kZygnjwbhF4ZSSx0PHeeLYE9lNb/W85WBpmTwH20c51mfcL8uNVM3Mh5bEISCJpScZh2W4uUlkNvkEoFtL3/3PgqQkAEvjTZSFO9HQyCj69YwkFVqGovSHk7SMnATIutBlVOfsiFnB2+aa6JzsBGA4mqY/lOT/27cjq/APRZLEEvkxWfDsG//MjrcesCgx+lhmlseeYAIQ2fkDNAaaearhqQnEEgn2GZk8O0dyqerLlAjXd22ByAAikwQlVXAetr7zFKzfNP6Getllb5tVsOwLKFGRgdY3ebdjF/v79ttnJwSb6zbTHDnIa1ot7XE9rmsk6hzDVxLqpEH4icftLpZTccVLG9czmlR0pcnSR113kIzq3GdG04t8xxIJjvXmlOvu0XhB0py5iqtgubi4uLh80DkBfFlK+Wf5/4CJ5TifbbLLxTmB2TPSCkqKtJqmKZ2rbWMTN4absi9jeUkSxnJTahoMZwWXQsNCbsXZ5xFEYwcIyUIhdkF6gHLVuV5XznpWpO4VkvctCpZpwdJQsoqTNNqZ82kajOLRMhze/RL+1El6o3l1mPIYiHTTd+glRqKWZB0OspqaLwRb5jhV6v31Y9b0yY4lJT2B4tkZFTTeSOsxOwLnmB0ppU3hS2TylKxkyJZQxHa0UXjZ7MtEC3YWtK2P7qAt8bYxb33uVvfSbYkGfV9MT3jiNWKssjFTec+CCPdD3xFk7VMFM5DpmJ7NEVgab8OjKRzrCeGPplBkmrihSLYOxzjUNuxwYsa1UvWxNaP+2W+bfsurHa/iEQKJsM3/ZKCRSDrieN/b/FG6R/Xnra47SIe/0PI4L2O4c4Z6ofYp6D5o62swnKQvmLCsbIzh9pZtY7oIOjigdb1H3cnnOTJkr/Fl9jGQ1K1Dh9N6ohTVVg9PR5MavxzeR4sIcijm7JYupSSSjjAcL7zOndFh/v2NvYxEU4TiGX6yu4UDbSN0tDUy2n2C2sHa3HS7Cp8pE1Wqeh1Acs9AMJbm14fbafMXlkw4J1KPL1aYSfF04roIurh8wOkOFv+xNn3fp8Lm4NHcmyLxZ/dddd+U+3dxmUb+leILil+dTEdSyj3AnlObzviIrChmBiBJhtQEqVArrdFu2uJdrKbKnFTB8fNTQ4SOtzL/mk/pLlOWmBPTfc9KXzDJ0kqzO3t/5pHdkR7WpMtZmmhHjhE473w+znVgs5tkTpBKZFQShsAcyvTYTu83jb/h4ys+bhyicV7kKIvDBxhVJG95QqyhMIGKeXhXJkLV6EKO1vTw2Y8swiM8jsJzTGQKjhfA/PQgy5IDUCQXw3hMpFiyP5pGShjJdLCsZJVt33AkxSAxhoQu2AtDIE+MdJMJ9FCyZDlS00grGilL7aOCZAX12/VshNWXFoyvafmpVXRC8RTxkRjCGgqjpQhqvRiPjeHW5XSORvxWfgmIvOshELobojdlSUZh6eHIr6hMfYw1/l0Mzb+UtorSrBDu8wgwrCECDYlESocPveGeaLrQmqn5zcf5zYQ1ZjTvKtQ9qys4517FYFjvJ1qpkPKqyHIKyCrAHm/u0yxz16JtOEaFt5QPZ4dzUuCz6qf+x3R/LJIQJJVRUfIWVnLWYDNhhv5HtaWxF8Y2NftBTaRVMqpGideMjcu1fqrhKayohkvf082vcCIoKC/xUOWNs0iE6BqZx6JUL2heDg4cZN0568DfzMWdzxGafyMj8y8u+BzqWQjt53ZkqI73I6/y8XR+llBYFdjPssajcNn39I2RAag82/al83rn66TVNH9+0Z87XrvpZkIWLCHEn8z0RFxcXFxcXGYCKeV2KWVjkX07Zns+EyJrwZJZIeHFWAuvd+4iktZd7FQjCYZ0EGDXDu6grO89/c3ef4cG53TXYw1tYioGb/cdQbOkxO5Vxii+Gx3UY1TMPh361eds2Q9kNIk/lub1hkEiyhBRdSRrUUuFBoklksTSFmuBlGhIPFIhLVVCaorfd73OOy2DPPJ6E5rMiW6mcKtKyW8af8NzJ5/LxgNN5IJcNrST88LvAzAgQ0TSzqm+i1m6fIZQ3xfty7pQ5mMKwYHgDt29zBCC2/0xfnWg06ak+TR97nU7fshARwOMtvPz4+O4hwLDgRAH2kbY1TBIJq9WlGaJ/QM9eYcEajtH6A8ls5YiJxLDraSzMTX25CEFdO6nOt5sa5tzP8SiYNmP9RrJU8rUGCBIZKx1pMx+JP2hJO+1j2bTpGfPLx3nqBgmjF2J1lOTC5ozOcswaV2RDcbTdAYHaR16P2tFy55zJleQ2UoyrVKmGp+Pxj9kt/dEiif9GcsVUTM/5yOtRFMKcdMq2Vtra9czGuNoj34O80q9Rr9mH7m+ANRC/crWHmBPo26lOu4/TnPoOM5IajsDHOoIZK9EeYmX+cGTXN3/a8qz87B0HPMTlEkOxl4irAygSY10uB8S+tzTSobOEcvn/PgO2o0yFFHGKDYOEOym+8B/kujQY8sToV6ah4+RVJIOKf1njolasH4mhCgFtgLPSCmD47R3cflAMS0ZAtvfOkVr0odOfQ4uLi5nBMJw9aL2yWysTb6i4Oxsl8Mmrw2dQJzn9B0i8/5aVroN5U4A8YzKyf4IDb6cG99L0TbuyyQZTtqFTsDiqvihbJ+qZheXzSxnVkJxXXhKZlTSMidg+bQkgc7jJL0LERf+qd4204fmuQTIWXPeTvbTGa6kLnSSCs41zsV+/Uo8nqx4fXJUjw8iGcrWmHK6QkLaFYs62UlJ/0v8t8u/btsezPSwZ3gAHL5Q6CQcAAAgAElEQVTONakRSoXY0VJcpzcv/YLUAHARaBnwlBGIOwmV0i60hnpQFp1vV1QcaB2OIoHGwSgXeGOsKYFIIkMinCQS6+cN0cmVspp4WjISSbF4XglmxkdF1c1C5rjlSk4cPP7Wdg4uuZCV5R9hsS+X6CGazLC/dQRK9ePe7wpy6egezgsH9L6MdomMqiduqSicvQRDWdK3h2Wc0UzEtt/836MpdIZTDJEkmlSoKM2JuqONL9MhQni0Nmh5Q0/wdOGfIgRoQthHHTwOF1zPE++0UxfZzkc9ndy3+MoiV9VOc2sTi7Wc8l7czVRaXmkONk59f38olb3m9b0hfP2/4LrP/R9oetXWulSLUZkeYjCczFqBs3FsVqW16TVU7TL7UJkklFbaNoUS+idlb89e+kMJlvJp/RnNm2hBwhILXuH8TTWMLg+FlD4ODe6n+5hRy+vCP6VpMMJwJE32KRo6gbrwfMqVEFJA+0gM8qohmFNSEgFeirQSOvQ891at5803vkOvR+XsS2+m3OtgapwhJqRgSSk/JoS4BPgScFgIcRB4Qkr5+ozOzsXFJcvycM34jaYJm/vfRMjPQmgSCMGfffPUJzTXmO7iyhO4Rg8++CDPPPMMXq8Xj8fDY489xvr166d3HhY2btzIww8/zLp166bcx9NPP833v/99ACorK/npT3/Khz/84XGOcgFs2pFZBFSXYaRFwRIIBzG6nSAJobJazrf1k7V+SAnBLlh4nuPQmgQ63oH2fXDj1xFm8L9PMhCzx10kMnGOBvdQquasWaETb7KwvER3qyvzEkupSAkv1Oe+V7JWt2x8l74tYQTFe4RAkznrg6lAeWUGj+HuqEkNFa+hAGk2645XCAwDn8VFKnc9TQXLZ8Ti0F/8O09KmKcGkQ7uh2AvCNyWeId0qosV8+bZrI+gpxN/+sTTDv1LWkeGeLMvZ2XMphFXM9kU1YpM0SpyCs3SRAfd+/OKi6vOiTT8CT9d4S6uOfsa2zMR0ZLsinfTWtNCvMLDRUtaiYkMIZkirejCaEbVsu5u+QpAVbw1+zohFDSp0pc6yiLf+aZnK92jMQ60jXDNZYKRaIq+UJCuuD1eTko9ZXhIGGn886w5EkkslVNy/YTAcE4sURN6Qd4K3VLilRlepYOUR+MGs/aAgWL57ERb3iWUzLBIc4plMw+wLwLUJoe40nDTGyRGHOfrXaLmFlNlviIMxRM1SOPcPR5jnkZ7KdHQ2D7QxhIqqNBKoNM5RmpeJsyuE3brsW0IgN4a1IrL8KlJypQognKUQ7+k8fJ/tLXVHOYZTA9BWcHmgrEEMESc0rzyZPpOfaNXKnikQnvfuzaFpCTlL4gxVLQMi5PdvCMUjoSHYaFKUOmmL7iGi4F4WuUXL+/lmvR+UqpGIB3lVwc6SQQjRESaZZqC8M1eMvcJx2BJKZuFEN8CDgM/Aq4Wuj/Cv0gpX5ipCbq4uLj8sbN//3527txJbW0tZWVl+P1+0ulx3CTmABdeeCF79+5lyZIl/OEPf+Dee+/lvffeOy1zEXqRneullM5SyRym1OshjqoLO1aXQCDnXJej3qNbmaR0LnacivjxjHRQoiRZFltGRWaETFnO4iClpLdzH0u0DBWZOCpaLgQkTxY96q9HAGfFch6Y4aRCZZkvu3Kt9wmH/a9zdr6IbgnCSio5AVoIPYOgEx41AyndeqEJUxA1XNPQlcdy5RJkyTm2K2MKuSVegSk2ezzOkRLdSpTBof9EJZf0wUkM31y3mdTwJ0lpMcJKv31npB8ycSMzn0Bd2KXH0Hjs8TMnByI8UfMOC5fkLHbSjODQcq5sXcnDVAq7wO8bqre972lroDSeAgExMpSTS+YglQxXL7o4ex0WJXvpVFvolCPEvQNUsAbzWdLyxfJssWZzfoUWJhWpK8Ca3e3Suggwr28/56cG0Mpy11VKfTyB1dKR+1+3tkVY4q2EJfoxHkuEy9mxBsqP/oqRq26nUYyyRi7JWmFLho/B4deybSNp/XouTg1xpNdH2KMQC0QM4d8pSNBrqzd2IDmAGtSf9fc8/czDi9Nn0IqiWq5WOg5dB9jZayivMmFJ4a5B3TMQ7KLzyv9hJNHQjxwKp2jyd1OTHKZazOOj8nzof99xPFX4iFuU0fy4OvOvqmlc6s9dm3Z/jGeOHKDSWORYmmhnec/LxD/8Rf1SKCmu79rCb6vLWLX8XBJplQXl1qQoZmIdc5ugQfi5Or+sQnwU2vYCUJEZYXngbTyZMNK8pWqGBU2/ZklCtyinUOjIhJFaNR6pogiJXyTQ4gfxBF7Er9zFxUBvOM4V4ZcJo8ICEBIWJnuzn3XNsZDzzDHRGKwrhRCPoGdiugn4tJTycuP1IzM4PxcXF5c/evr7+6mqqqKsTF82rKqq4rzzdOvDAw88wHXXXcef/MmfcO+992Z/xDZu3MjXvvY1brzxRi6//HIOHTrEZz7zGS655BK+9a1vAXqh4csuu4wvfvGLXHnllfzVX/0V8XhhJrbXXnuNj370o1xzzTX89V//NdGobq34xje+wYc+9CGuvPJKvv71rxccd8MNN7BkiS4RXX/99ae16LCUUkNPzX5GYBX1FDQ6CFksMbqg4CdBbfi3DKZPZttarSmK1Hj0wK9pDASNPgWBWJoTfSEGIimQGiuD77E00WEbWwIvRZrZHm0FTUWxWIdknoZVM3zEVo+p8DzM4Pniws0AMWqTwwxYXAY1CRKLwmURYD3Nr0NfHZrUa0FJwGMVnmLDXDKkC46D4aQlwYC+22tRqmTH29BTo7ugWbLtvZXoRaS7CywUQZL8KnVCn5NxkzJagobY7+lO1hhzNVCSEO6HQCcEOlCaXtWLsuahZ/zTLTTZuWYtWEq2T1UWpjf35CWOsGYMfMfTSxqLm1hfLeE9j2TT0a8e3ctoOMhQNEVaJmlPvIvWp5+DBEoSVpdJI912SqE7mCClFCq/aVTOjRxleagGsNRTMzNCtr+FlFCRCeDkAmh7LXMKs2bE2aUsKdS9DuLrs62v0ihGUSy9+UYabRk3Gwb0lN8eBO959PMbHexlnv8YEl0ZSasa4aR53yXtCT3tuaJJgokMmbg98Wi+WqZYgptUNEa0RG5GvTXQupvBoP6sZwxl1B9NcaQroFuWgRdqe/OySUoC8WTBtbJSlzSsy0LYEsqoeYqF+R2hapJSSxxlJJ2hO1lryyJaGe1ka/3PASiN6HNbFDpBT0cLx3rDKJpmM00NRSzKdV7ZB7NV9PBzjEaT2e+GEjVhTwAjVXYm26nI6LXoDoh+Xol1IDNRPBarti+jZw1cEDnBCAl+72nDTyK7OFCRCfKhod/nvoOkOqFEM9PFRC1YPwZ+jm6tyt5xKWWfYdVycXE5RcaKzzpT2Rw8WjTDILhZBifKLbfcwgMPPMCaNWv45Cc/yZ133snHP/5xAO6//36+853vAPCFL3yBnTt38ulPfxqA0tJS9u3bxw9/+EPuuOMOampqWLp0KatXr+ZrX/saAI2NjTz++ONs2LCBL33pS2zevNmmLPn9fjZt2sSuXbuYP38+3//+9/nBD37A/fffz4svvsjJkycRQhAMjh2a+/jjj/OpT31qJi7PZHhNCPFZ4AU5fnGb00fe1I5JP0c9IyylBMPhSN/u8VMVTzIsPMAykkqSHb2d2aXTfi1ObV8jMtTNpUsWI4RgIJy0KSvmKyFVru/aQufi9QyEzgIhiGpp0FQymoIQsDA1wFn+A3lztfZSiBm7lK3T5CDgHPT0szhTUmBtsr5flmgzjtYQ8aCeTEHYLSkBmaRK6osQpoBpFXbNlj6vvrNlMIwyMoxvnsQfTZFUCtv2CGucj6RXFCb2qI/+zn7OBS10MlKDmN88QV2J8Hgp8ZoCoMSXd/S7x5pJLNJYOt+5WHB+Msf8zHwaeja9eFqhQknx2+F2rjCzT5K7fn1KB0kW0Y1+flLY7+mADLGAChJp/bqHE4WucQrW62d1TTXiiLrbCaQzltK1ZlsYVhN0CSPFv+kmR/EnK1/BklJyrDdgGLhyo4vRFnbFc7WkzBT8XgRDxBDAopS+8BNnKSOWWLcF5bm7UaaEGUokUSUkh9rsIXZmnJ+UDI/8nO/87rLszI+KYY5EM3ys4rzs+QxFklBiP7OEopE4+gLywirbdutntSAbZB6/HtA/IxUZPS2+P93GYLqBj+SV7BtKJNkX60XxSeJCUit6+bRcRdzBvdRqKy9JjiDRCzWXhDtgwTKIByEdw6mcoOEhmlXYJJBSVA63j1CmRJEWN0N7vOhJrERJs4BySvoOO86uXmun1JjjkIizUi5ECF2Jhpwlaba/8idaB+s29OQWCdBdLYQQehiilE+NeaSLi4uLyylRWVlJTU0NW7Zsobq6mjvvvJOtW7cCsHv3btavX8/atWt58803OX48l+np9ttvB2Dt2rVcccUVnHvuuZSVlXHRRRfR3a0nJlixYgUbNmwA4K677uLtt9+2jX3gwAEaGhrYsGEDV111Fdu2baOzs5OFCxdSXl7O3XffzQsvvEBFRUXR+e/evZvHH388G491GvlfwG+BtBAiLISICCGcCzedTjQlK5wAWStEIq0SjNldQ8tUu8B/3JNbXX8jbS9Smi9gyFiurRnjtDL4Hm+eHCKpGG0bdjBPKyGtaMxTAgRUp8yBxQWX6kAtIAuK7GYFYMt7ay96jEpui1dLZ+c5EkszaKyUe6SexU0iSKRVhhTdAnuSUbxaCmFJXGCev8/QSoLhsJ5UAWzKlZVmkcuMZrbIn1sBeUpPOKlbfepTuuBLIgD+5mwMjTnH/mCSnqEASxId+DTdWjFw/En+q9WMcS0cMz/1uSfPrVICPYE473eHyKhaNgNbnAwjJPJaFnsHJ8Qgg+Ss257u/ZQr9o9Ov8i5OF469EpBbxGLdTUhFQ4J3aVyJJriSDKvppJxHvlubQtSZmyR/byfCzU7zj2T59iZNCySPV6lSB2xvFmn9Oe9Ot5sZoG3jSzQY+GQEq9MI5MtaKE/MN9QckYNB7WM1O0qyYxK63CMsJpzJ1UtLnzvtY/yfk8ITerzM597AJEKZcccDyEEXclDpLSYrphJe191KT+VkRaaxSjDIkF9YtSx6G9B7FjekyGCHfkj248nVxtNSknTYNTxozMcTpExF0NSEds+gSCZUbOFkXNzyt0QUxVW0AwLVs5WZbVgzSYTVbB2Yc+JU2FsK4oQ4pdCiCEhxDHLtqVCiNeFEM3G3yXGdiGE+JEQokUIcVQIcc1kT8TFxcXlg4zX62Xjxo1873vf48c//jHPP/88yWSS++67j+3bt1NfX88999xDMplzszJdCj0eT/a1+V5RDNejPAGtoFaNlNx8883U1dVRV1dHQ0MDjz/+OD6fj4MHD/LZz36WHTt2cOuttzrO++jRo9x999289NJLLFu2bFquxVSRUi6QUnqklCVSyoXGe+fMBacTtdAVDPRV7uahCFqyUCcsujprbD7QPsqv3m0jGM/kWTmchaqsvhHzEx5RiWdUFsky6o26zJboKsdEG9b+F6QGCaSGHUerSPRn21n3KkWUGIEkZbjBlahxpOkQJPQU7yYBklzd84T9TCUcE8NUhuphVF/tzxcYTUIO6dtNu4iiSkq0BL74ILWNHQXtNGm3NphKXDBjCLjJsJ7GHiARNO6d3n5JojMrnAMc8gwwkDqBEIKEWmglzrdglal24VRDZt3drIkVdosu3vH0Fr1zEsmopVgxUpJGzV7Pno63qYo3W3fbWJjqy77Ofz4kkqOaP6uQZTRJwDKWhgRDIY9rmWwCFIC4OkQKlQWpwVwhX6AtEcmL4dJR8tzj0lmlqlBNsc4ZIBBLM9ReT8FzmPe2TI3gU+OODczny4NgNJYmEM3QR5S+ZC52ri+kK7rHxDAJFBIZlaF0k01ZLlOjzG8xk6CMr2JVpIazGR5VqSL9rZwTyY0ZTSnUD25m1IgvS2U0ToiRsbuX8IqnzWkzIVLkx+WZ3WharlC4LzHCPu1YVtEFaBchEkJhKJoqLIptmW8+ImvlFPgMdSaFkrWkmhYsa6H02WSiCla5lDK7bGW8Lr5cqbMVyP/F/QbwhpTyEuAN4z3Ap4BLjH/3Aj+d4LxcXFzmIN3BRPbf/tYR2z+XydPY2Ehzc06YqaurY+XKlVllqqqqimg0yvbt24t1UZSuri7279djDJ599lk+9rGP2fZff/31vPPOO7S0tAAQj8dpamoiGo0SCoW47bbbePTRR6mrq3Ps+zOf+QxPPfUUa9asmfTcphtjMe8uIcS3jfcrhBAfOd3zKsBXhjj/Wqujk2237DpQeAyFAkQyoyKQDIk4/USN2Bg7YcOiIYRVEJVZH7uYliEpckJPgZCSihRK17Y56dan9qjd7addhNCQ+EYPmCPaxLODgWdJaTE8UsnLoCoJxXVh6+zYCSpS/dkp5/OKpw3V4lIpgTYRYqRvO4R0wdKM1/COIbOmVWfXt8xQM9XxpqwVzUpvKJldkTf3BPNSrcfSCj0nD+If3E9EGSSfTnKK9EC8G0VOPrGNhnS8P6rhAtguQsYW053KOaV2vpK0L2ZXRkLJnII0jn3PNo5JJGU/Hk0loSk0GrXGzP5qlHr2i15SKCxLtBWxQuWstUOxFKqUhBKZPDf8whnmW//iGdVWsNlEABnyLIWWQt7CotSZz5dZ6gBgWOSSV1jpFhFe83QQJElfqt62ELI42V1wSCKj5qw+eVT1PJXN8Hho+E1SEbuFMJLS1ZC05XPfLezKOUAok0FNJ/QU7gYZVbPFaWVUjb2ebsunzE5FVPeWkBKWxFpJCIXXPB20SnsdOU2C37DQOz0/+fFTo9pQdk+f4bobI8Nbnp4CK6PepyxYQJxJJhqDFRNCXCOlrAUQQlwLjBkwIqXcJ4RYlbf5DmCj8XobsAf4v43tTxo+8QeEEIuFEOdKKfNS8ri4uLjMAWY59Xw0GuWrX/0qwWAQn8/HxRdfzJYtW1i8eDH33HMPa9euZdWqVVx33XWT7vvyyy9n27ZtfPnLX+aSSy7hK1/5im1/dXU1W7du5fOf/zyplL6qv2nTJhYsWMAdd9xBMplESskjjxTmO3rggQcYGRnhvvv0WDufz8fhw/l+9LPKZnRPr5uAfwOiwE+AyV+4mcTjhUUroHt/gUJzTvQ4cmmh0U1i1CiykFQ0PEZihBYRYHlmAZTZj20QukXKmxnBXHOVFgFxW/gE3SJhjGHp35RThk4gygrra9lq5Rgp0xekBijR9L66RJhKWUJNeFR3j8k3Emgqo5lOlkfsmdKElAQtmfTeVd7j4yyjQhm1tzP+vpnpoiMrOBoughZh2BSAPUKgjrPCnUGlTYQozVubPi9SR6ykisC8lTaBv3UoymVOS9EJfa6hRAYJ1LQ8QazcLF+Qm8P7nlySiZNDA1Mq1dErIpQb8TFjnZ1XS7M8XINnoT5hazr4tJJTFNNifDerpFDolKHs+8r0EKVK1Cb0RpKKbd0grqi5TJVSQriXSDpNIJ6msrwEa+bMsEhz3LC2nBPJOkllu0tZlJ+TwRD+khRp47NhxpaNlZgln3zlUiA5IfR7mHNWc+5P5qkdqpAoUuP8SB0j81aTKCmMXdrn6QHOLthuVdYA6rqDugXTQWd4Cz2ubFGyh4YBhcuLpO/PpyIzQkk65zpcIwZQOnuoLPPlziH/s+pw6lJCLK1Sjo/l3Tv1bZgeEvoBUZwt9YF42lbewMS0UmWvuUUhHhS6BTEscnX0YkLR14rGON+ZZKIK1v8EfiuEMJcszgXunMJ4Z5tKk5SyXwhxlrH9fMBaqbDH2FagYAkh7kW3cnHBBc4paF1cZoxi9Z5MjAKYLpNgvJpSH8Q6WpPk2muv5d13nbOLb9q0iU2bNhVs37NnT/b1xo0b2bhxY8G+jo4OPB4PP/vZz8Y8/qabbuLQoUMFbQ4ePDjmvH/xi1/wi1/8Ysw2s8x6KeU1QogjAFLKgBDCOXvAaeatFj/VkSQHhkd1QcGaZAuHlOEWIWee9JEQukB1TlSPyQuIFMud3AGNv0vjbTSylNUsplQNE5e6hWVeSS6leKYweTdAESuCGeAuqUwPEU+uYFGq17ZfEVp2lT7f6lGiJZAOTjYCjQ5b2JwsmFUkpWTdBQelpR6R0SyWUJHzcnMYiqRs7oXFGDUVOweJskIJEGAlixO5uLf56SGoyEVXZDQ9HsWj6kKgqdSpUjI/7SftrSiIqTMZCjtbr5yER+u2JhFgVCaBpfo5UFjcGaDUcHHLtyyZ8wY4IfyoQhvfPAWc9NgV3qWJDqxqrsewR5hdWe+hRMKJnRzrixD1qJT6PKhIhii0/HgtmRXNme/xdGefnAyaYxFcYRT1nYrTmEBk52u6tMWVkYJsfdbzsipgZqKUhal+EiWLCo7BOCIf8z4IYIQEoyRZIsvH1CAWpAfxaWkCSqHLqxXzei1NdCAtqdeHRYLFlDgflIfV3TaUyLDA+JyMVYTYiWi6UIlPKhqVDm0B5mf8BduKuRrOuSyCUspDQojLgEvRb+VJKR3yhU4dpzN2vCNSyi3AFoB169bNrkOli4tB0Yx/R15jxeJ5zvtcXFxONxkhhFm4BiFENc7ljU474aTC/JSzkKC7fdm3DYViLPLrFg5TuSo4TgkAOYEu/we00TOKKjVWBA/zlpKiVM2AZZU5IRQ82YPGFlSC8XS2aDDA/GhnoduZFDblTLG4KwkpOSt+YswxAHxaypbIoCeYsI1jjd0w3akE+gq3eQpObmBO5ITlQoRU8UjVFj/l1DYQz6B5oNxjd7ucnxlBUNw65FxSGlvqcpNknpXJLxIsD9cQL/GSGUdBSsrilo600PAW3Ts2FYFdtIlcnJJATyVu6qoqVrc6Xbk3lZLReAYEHBB9CLmk6BgZrVCJUPM+3h1Zt8tiNqdCRL7iJAoV0e7kfqpjTQWfClVIW7FrKyVanMr0kMMeva6cv2K1bVtXMA4eva93PL2OxzkxTwmM2yY5xrMH+j1xLLWgpnKWLdu1zimWfanYxAOSHDC/F3KWK/3V/HShYmUf3SR3V+aiiyDoLhSrjGOuFkIgpXxykuMNmq5/QohzAfPJ6gFb5s7lQF/B0S4uLi4u08aqVas4duzY+A0/OPwIeBE4SwjxIPBXwLdP75Sc0QVqmX1tpWs0RmmZVWKRBHubyWTGXqXWgGXxVuIlS83DdIHbQrGkD9Y+QI9LSqsapV4PJelQQbtEnuCfTKUpy2szIhLMUwz3wzyr0OJkNxPlsGcg+3qs2ccsK+P+WBoj4/SESVBc+Uh5F7AgNVCwPZywr0UrmkZSUWyKTFLRwDu19eL6kaAtPfpYxIus6usYAvE403BINDchDnjsIl2LCNhk7qDIPbsSSbsSolHYrWDWeeZT7vPYlHXzPJS89qaL42TE7PPy3FQ9FOoL89P+MZO9tAwXxjcBVKSdzhFK1Rhezf7sREXx+KRTJd/imM9QOFlg5a2ONcPCnO1ZQaNETTIvEyJaWg1AXCjsERP/LI+F+X1oPoOmu7Fj2zlgfpmQgiWEeApYDdRBVs2VwGQVrN8BXwT+X+PvS5bt9wshngPWAyE3/srlTOVMqmc11lynyxJXEDfQbuk3UCiYubjMFFLKp4UQNcAn0GWs/y6lHN9MMsfQpD3l9fz0CPMzw2McoSORzFOCOQXLQVRrFyEWkpqQEDcYSbFi8TxK06Ei0RQ5nKwzflH8+2cs4WmqmOfULPQV/QXpQoVoLEzXLqdro3jKHPeMF9dVMDkHlodrSKk4Omrt9uguiQtladFU82ca7yUHUTTJgCh0Z5ynFK+3Z1VIcjFP9oQMFLSYGp48FSs/QYYVVUr93kzSeHJ2zP7VlFv8mF3tIZVRHV1oy9QwaOU2ZXZJUn8eJ/L5nawtaeI2R3tbe8KLuWfBWgd8aDKFGYUQz6IntKgSQvQA30VXrH4jhPgHoAv4a6P5K+i1tlqAOPD3Ex3HxcXFxcVlIgghnpJSfgE46bDtjCH/h3hJsnNKxznVvQEIy8kqN+OLBqVqbMz9sykymhn0KjLFV+0nOx9rFjkrsbx4krGlqOLC38JE65iZxXx4GI46x1dNBNP6Mhv3YbwxpjIHKQtT1ENxi2yB298kEGqacum13S7PGP0pqjaGcjBxgd90wZvI9ZnO+5hvjS6G1UVwMklEJkpAjG2ht3GmWLCAY8A5OCSdKIaU8vNFdn3Coa0E/mmifbu4uMw8s2HdcnGZZa6wvjHisa49TXMZB0GMDL/ztBTsmcxKbl6XAJQYRWz9sZRtl8y+nnj/oUSGqOIrcP+bNHNAILLSM8b3n9Nas5AaFFGyrGQ0CcLpZMe+AKVqgsQYsviog7Vnasz8jRj3+ZVMycerXCn0iLBmQ5wuPELgLVCMiisho/EMxSLHSrWxFx6smMpiflyZE5NNLDFVIkkla02fyLyszOQcrTMx71QwnqacSShpp8hEFawqoEEIcRBys5NS3j4js3JxcZnTnElukC4uQohvAv8CzBNChMn95qYxkibNJUwBPulb4Lwq7yigj49Zu8cpO59VIPFpiaLZ7PIJpxTKcI4vmQxzTL8aE6e5OmUyK4aTO5lnnCQDUSZfA2symNa82YhdySUrcN4/FEmybP7kkntONFHJdJE/9fE+L1NeFLFgxtpNypIzJSY+V6ursjXerUwtLIae3/dEMneeKtbslP2hJLHYxL7XpoOJKlj/OpOTcHFxcTmT2Fy3eVr7u++q+8Zt8+CDD/LMM8/g9XrxeDw89thjrF+/flrnYWXjxo08/PDDrFu3bsp9vPTSS3z729/G4/Hg8/l49NFHCwoZzwZSyoeAh4QQD0kpJ533XwixAj3m+Bx0XWSLlPKH0zzNLJo0UjFXXFQQYH8qtGWLyubSPTvRk2ma9eIxYydgmGPMgFzoc8iAZ2WqSvVkyXdpnAnGUzYymmQgMnuWhslyMDXIgGdyFjJApNwAACAASURBVMPUOAr0RDBrPM1VmhyTkpxedolOFqEr65WhJjzLzpm1sSeapn2vEGIlcImUcpcQogKmnK3TxcXFBYDNwaPjthlf9fjgs3//fnbu3EltbS1lZWX4/X7S6bn9YwvwiU98gttvvx0hBEePHuVv/uZvOHny5PgHzhz/RwhxF3ChlPLfDM
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Comment doesn't match code (and again, do we need 2000?)

"outputs": [
{
"data": {
"image/png": 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Never say something's obvious! (or trivial etc.)
If readers get it you're wasting space, if they don't you're making them feel bad

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Again please have a look at the number of iterations in all these examples

"2. Draw a real value ($y$) uniformly from $(0, f(x_0))$, defining a\n",
" horizontal “slice”: $S = {x: y < f (x)}$. Note that $x_0$ is\n",
" always within $S$.\n",
"3. Find a hyperrectangle ($H = (L_1, R_1) ×···× (L_n, R_n)$) around\n",
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See Ben's comments on previous notebook

This is a multivariate method, which generates n-dimensional samples of
the form ``x = (x_1, ..., x_n)`` by sampling uniformly from the area of an
axis-aligned hyperrectangle:
``H = {x: L_i < x_i < R_i for all i = 1, ..., n}``.
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This should be :math:`stuff` , same goes for rest of code!



if __name__ == '__main__':
print('Add -v for more debug output')
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Please remove these lines, as the debug variable isn't used anywhere.

import pints
import pints.toy

debug = False
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Please remove

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Hi @lorcandelaney , have made some initial suggestions to go with @ben18785 's comments.
Overall, it's looking very good!

One question: it seems the two notebooks are very similar, and mostly showcase the same code (just with the adaptive option switched on and off). Would it be better to replace this with a single notebook that shows how the adaptive method is better/worse in selected cases?

@MichaelClerx MichaelClerx mentioned this pull request Sep 3, 2019
49 tasks
be a single number or an array with the same number of elements
as the number of variables to update.
"""
if type(w) == int or float:
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This means if (type(w) == int) or float)
and if float == True...

use np.isscalar(w) instead

"""
if type(w) == int or float:
w = np.full((len(self._x0)), w)
if any(n < 0 for n in w):
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if np.any(w < 0)

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3 participants