Skip to content

Commit 8b50e30

Browse files
scheinermanscheinerman
committed
various
1 parent 9128fe4 commit 8b50e30

File tree

14 files changed

+77
-11
lines changed

14 files changed

+77
-11
lines changed

‎development/dual_basic_vector.jl‎

Lines changed: 7 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,18 +1,24 @@
11
using SimplexTableaux, LinearAlgebraX
22

33
function dual_basic_vector(T::Tableau, B)
4-
A = T.A
4+
A = T.A
55
c = T.c
66
A_B = A[:, B]
77
c_B = c[B]
88
yT = c_B' * invx(A_B)
99
return yT'
1010
end
1111

12+
"""
13+
dual_basic_vector(T::Tableau)
14+
15+
Return the dual basic vector for `T`.
16+
"""
1217
function dual_basic_vector(T::Tableau)
1318
B = get_basis(T)
1419
if 0 ∈ B
1520
error("No basis set for this tableau")
1621
end
1722
return dual_basic_vector(T, B)
1823
end
24+

‎docs/build/.documenter-siteinfo.json‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1 +1 @@
1-
{"documenter":{"julia_version":"1.11.6","generation_timestamp":"2025-09-04T13:57:19","documenter_version":"1.10.1"}}
1+
{"documenter":{"julia_version":"1.11.7","generation_timestamp":"2025-09-17T15:53:42","documenter_version":"1.10.1"}}

‎docs/build/bases/index.html‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -39,4 +39,4 @@
3939
[1, 3, 4]
4040
[1, 3, 5]
4141
[2, 3, 4]
42-
[3, 4, 5]</code></pre><p>Note that <code>find_all_bases</code> is rather inefficient as it considers all possible <code>m</code>-element subsets of the columns.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../create/">« Creating Tableaux</a><a class="docs-footer-nextpage" href="../pivot/">Pivoting Tableaux »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Thursday 4 September 2025 13:57">Thursday 4 September 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
42+
[3, 4, 5]</code></pre><p>Note that <code>find_all_bases</code> is rather inefficient as it considers all possible <code>m</code>-element subsets of the columns.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../create/">« Creating Tableaux</a><a class="docs-footer-nextpage" href="../pivot/">Pivoting Tableaux »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Wednesday 17 September 2025 15:53">Wednesday 17 September 2025</span>. Using Julia version 1.11.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

‎docs/build/create/index.html‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -64,4 +64,4 @@
6464
├──────────┼───┼─────┼─────┼─────┼─────┤
6565
│ Cons 1 │ 0 │ 1 │ 2 │ 3 │ 1 │
6666
│ Cons 2 │ 0 │ 4 │ 5 │ 6 │ 2 │
67-
└──────────┴───┴─────┴─────┴─────┴─────┘</code></pre><p>Notice that the third constraint has been (silently) removed.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Overview</a><a class="docs-footer-nextpage" href="../bases/">Bases »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Thursday 4 September 2025 13:57">Thursday 4 September 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
67+
└──────────┴───┴─────┴─────┴─────┴─────┘</code></pre><p>Notice that the third constraint has been (silently) removed.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Overview</a><a class="docs-footer-nextpage" href="../bases/">Bases »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Wednesday 17 September 2025 15:53">Wednesday 17 September 2025</span>. Using Julia version 1.11.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

‎docs/build/dual/index.html‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -25,4 +25,4 @@
2525
│ Cons 1 │ 0 │ -11 │ -8 │ -8 │ -6 │ -4 │ -2 │ -1 │ 0 │ 0 │ -3 │
2626
│ Cons 2 │ 0 │ -2 │ -6 │ -8 │ -5 │ -1 │ 1 │ 0 │ -1 │ 0 │ -4 │
2727
│ Cons 3 │ 0 │ -11 │ -9 │ -5 │ -8 │ -2 │ -4 │ 0 │ 0 │ -1 │ -7 │
28-
└──────────┴───┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘</code></pre><p>The result of <code>simplex_solve!(dT)</code> is <span>$-15/2$</span>. </p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../solve/">« Solving LPs</a><a class="docs-footer-nextpage" href="../other/">Other Functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Thursday 4 September 2025 13:57">Thursday 4 September 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
28+
└──────────┴───┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘</code></pre><p>The result of <code>simplex_solve!(dT)</code> is <span>$-15/2$</span>. </p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../solve/">« Solving LPs</a><a class="docs-footer-nextpage" href="../other/">Other Functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Wednesday 17 September 2025 15:53">Wednesday 17 September 2025</span>. Using Julia version 1.11.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

‎docs/build/index.html‎

Lines changed: 1 addition & 1 deletion
Large diffs are not rendered by default.

‎docs/build/objects.inv‎

11 Bytes
Binary file not shown.

‎docs/build/other/index.html‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -38,4 +38,4 @@
3838
{\Large\strut}$0$ &amp; $1$ &amp; $\frac{1}{2}$ &amp; $0$ &amp; $\frac{9}{2}$ &amp; $\frac{-1}{2}$ &amp; $\frac{9}{2}$\\
3939
{\Large\strut}$0$ &amp; $0$ &amp; $\frac{1}{2}$ &amp; $-1$ &amp; $\frac{1}{2}$ &amp; $\frac{3}{2}$ &amp; $\frac{5}{2}$\\
4040
\hline
41-
\end{tabular}</code></pre><p>Here is the LaTeX output:</p><p><img src="../tableau.png" alt/></p><h2 id="Other-Public-Functions"><a class="docs-heading-anchor" href="#Other-Public-Functions">Other Public Functions</a><a id="Other-Public-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Other-Public-Functions" title="Permalink"></a></h2><p>Presently, these functions are exported in <code>SimplexTableaux</code> but might be hidden in future releases. They are not likely to be useful to the users of this module. See the doc strings for more information:</p><ul><li><code>big_M_tableau</code></li><li><code>check_basis</code></li><li><code>find_pivot_column</code></li><li><code>infer_basis!</code></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../dual/">« Dual LP</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Thursday 4 September 2025 13:57">Thursday 4 September 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
41+
\end{tabular}</code></pre><p>Here is the LaTeX output:</p><p><img src="../tableau.png" alt/></p><h2 id="Other-Public-Functions"><a class="docs-heading-anchor" href="#Other-Public-Functions">Other Public Functions</a><a id="Other-Public-Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Other-Public-Functions" title="Permalink"></a></h2><p>Presently, these functions are exported in <code>SimplexTableaux</code> but might be hidden in future releases. They are not likely to be useful to the users of this module. See the doc strings for more information:</p><ul><li><code>big_M_tableau</code></li><li><code>check_basis</code></li><li><code>find_pivot_column</code></li><li><code>infer_basis!</code></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../dual/">« Dual LP</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.10.1 on <span class="colophon-date" title="Wednesday 17 September 2025 15:53">Wednesday 17 September 2025</span>. Using Julia version 1.11.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

0 commit comments

Comments
 (0)