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Computationallinearalgebracourse.pdf

@@ -687,7 +687,7 @@ <h2><span class="section-number">2.6. </span>Householder triangulation<a class="
 done so, you will need to modified
 <a class="reference internal" href="cla_utils.html#cla_utils.exercises3.householder" title="cla_utils.exercises3.householder"><code class="xref py py-func docutils literal notranslate"><span class="pre">cla_utils.exercises3.householder()</span></code></a> to use the <code class="docutils literal notranslate"><span class="pre">kmax</span></code>
 argument. You may make use of the built-in triangular solve
-algorithm <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+2083.8dd161d)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> (we shall consider
+algorithm <a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+2084.abafdff)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> (we shall consider
 triangular matrix algorithms briefly later). The test script
 <code class="docutils literal notranslate"><span class="pre">test_exercises3.py</span></code> in the <code class="docutils literal notranslate"><span class="pre">test</span></code> directory will also test this
 function.</p>
@@ -799,7 +799,7 @@ <h2><span class="section-number">2.7. </span>Application: Least squares problems
 appropriate augmented matrix <span class="math notranslate nohighlight">\(\hat{A}\)</span>, calling
 <a class="reference internal" href="cla_utils.html#cla_utils.exercises3.householder" title="cla_utils.exercises3.householder"><code class="xref py py-func docutils literal notranslate"><span class="pre">cla_utils.exercises3.householder()</span></code></a> and extracting appropriate
 subarrays using slice notation, before using
-<a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+2083.8dd161d)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> to solve the resulting upper triangular
+<a class="reference external" href="http://scipy.github.io/devdocs/reference/generated/scipy.linalg.solve_triangular.html#scipy.linalg.solve_triangular" title="(in SciPy v1.8.0.dev0+2084.abafdff)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.linalg.solve_triangular()</span></code></a> to solve the resulting upper triangular
 system, before returning the solution <span class="math notranslate nohighlight">\(x\)</span>. The test script
 <code class="docutils literal notranslate"><span class="pre">test_exercises3.py</span></code> in the <code class="docutils literal notranslate"><span class="pre">test</span></code> directory will also test this
 function.</p>

L2_QR_factorisation.html

@@ -519,12 +519,13 @@ <h2><span class="section-number">4.2. </span>Pivoting<a class="headerlink" href=
     </div><div class="proof-content">
 <p>The function <a class="reference internal" href="cla_utils.html#cla_utils.exercises7.perm" title="cla_utils.exercises7.perm"><code class="xref py py-func docutils literal notranslate"><span class="pre">cla_utils.exercises7.perm()</span></code></a> has been left
 unimplemented. It should take an <span class="math notranslate nohighlight">\(m\times m\)</span> permutation matrix
-<span class="math notranslate nohighlight">\(P\)</span>, stored as a vector of indices <span class="math notranslate nohighlight">\(p\in\mathbb{N}^m\)</span> so that
-<span class="math notranslate nohighlight">\((Px)_i = x_{p_i}\)</span>, <span class="math notranslate nohighlight">\(i=1,2,\ldots, m\)</span>, and replace it with the
-matrix <span class="math notranslate nohighlight">\(P_{i,j}P\)</span> (also stored as a vector of indices) where
-<span class="math notranslate nohighlight">\(P_{i,j}\)</span> is the permutation matrix that exchanges the entries <span class="math notranslate nohighlight">\(i\)</span>
-and <span class="math notranslate nohighlight">\(j\)</span>. The test script <code class="docutils literal notranslate"><span class="pre">test_exercises7.py</span></code> in the <code class="docutils literal notranslate"><span class="pre">test</span></code>
-directory will test this function.</p>
+<span class="math notranslate nohighlight">\(P\)</span>, stored as an (integer-valued) array of indices
+<span class="math notranslate nohighlight">\(p\in\mathbb{N}^m\)</span> so that <span class="math notranslate nohighlight">\((Px)_i = x_{p_i}\)</span>, <span class="math notranslate nohighlight">\(i=1,2,\ldots, m\)</span>,
+and replace it with the matrix <span class="math notranslate nohighlight">\(P_{i,j}P\)</span> (also stored as a array
+of indices) where <span class="math notranslate nohighlight">\(P_{i,j}\)</span> is the permutation matrix that
+exchanges the entries <span class="math notranslate nohighlight">\(i\)</span> and <span class="math notranslate nohighlight">\(j\)</span>. The test script
+<code class="docutils literal notranslate"><span class="pre">test_exercises7.py</span></code> in the <code class="docutils literal notranslate"><span class="pre">test</span></code> directory will test this
+function.</p>
 </div></div><div class="proof proof-type-exercise" id="id8">
 
     <div class="proof-title">

L4_LU_decomposition.html

@@ -498,12 +498,13 @@ complete pivoting, `PAQ=LU`.
 
    The function :func:`cla_utils.exercises7.perm` has been left
    unimplemented. It should take an `m\times m` permutation matrix
-   `P`, stored as a vector of indices `p\in\mathbb{N}^m` so that
-   `(Px)_i = x_{p_i}`, `i=1,2,\ldots, m`, and replace it with the
-   matrix `P_{i,j}P` (also stored as a vector of indices) where
-   `P_{i,j}` is the permutation matrix that exchanges the entries `i`
-   and `j`. The test script ``test_exercises7.py`` in the ``test``
-   directory will test this function.
+   `P`, stored as an (integer-valued) array of indices
+   `p\in\mathbb{N}^m` so that `(Px)_i = x_{p_i}`, `i=1,2,\ldots, m`,
+   and replace it with the matrix `P_{i,j}P` (also stored as a array
+   of indices) where `P_{i,j}` is the permutation matrix that
+   exchanges the entries `i` and `j`. The test script
+   ``test_exercises7.py`` in the ``test`` directory will test this
+   function.
 
 
 .. proof:exercise::

_sources/L4_LU_decomposition.rst.txt

@@ -27,4 +27,6 @@ repositories for Autumn 2021. An up to date version is in the
 6. Corrected the upper limit of the sum in the algorithm for forward
    substitution.
 
-7. Corrected the sign of inequalities in :code:`test_solve_U` and :code:`test_solve_L`.
+7. Corrected the sign of inequalities in :code:`test_solve_U` and
+   :code:`test_solve_L`. And then uncorrected them again, they were right
+   in the first place.

_sources/errata.rst.txt

@@ -67,7 +67,9 @@ <h1>Errata for 2021/22<a class="headerlink" href="#errata-for-2021-22" title="Pe
 test so that <span class="math notranslate nohighlight">\(k\)</span> corresponds to the column being operated on.</p></li>
 <li><p>Corrected the upper limit of the sum in the algorithm for forward
 substitution.</p></li>
-<li><p>Corrected the sign of inequalities in <code class="code docutils literal notranslate"><span class="pre">test_solve_U</span></code> and <code class="code docutils literal notranslate"><span class="pre">test_solve_L</span></code>.</p></li>
+<li><p>Corrected the sign of inequalities in <code class="code docutils literal notranslate"><span class="pre">test_solve_U</span></code> and
+<code class="code docutils literal notranslate"><span class="pre">test_solve_L</span></code>. And then uncorrected them again, they were right
+in the first place.</p></li>
 </ol>
 </section>