diff --git a/doc/pub/week48/html/._week48-bs013.html b/doc/pub/week48/html/._week48-bs013.html index 1e97c32a4..1c2e7f207 100644 --- a/doc/pub/week48/html/._week48-bs013.html +++ b/doc/pub/week48/html/._week48-bs013.html @@ -289,7 +289,7 @@ $$ The minimization problem can be rewritten in terms of vectors and matrices as (with \( x \) and \( y \) being the unknowns) $$ -\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}3\\ 4 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. +\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}5\\ 3 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. $$ Similarly, we can now set up the inequalities (we need to change \( \geq \) to \( \leq \) by multiplying with \( -1 \) on bot sides) as the following matrix-vector equation diff --git a/doc/pub/week48/html/._week48-bs015.html b/doc/pub/week48/html/._week48-bs015.html index d78bf5373..557145499 100644 --- a/doc/pub/week48/html/._week48-bs015.html +++ b/doc/pub/week48/html/._week48-bs015.html @@ -278,7 +278,7 @@ $$
  1. With a given kernel we can thus define the matrix \( \boldsymbol{P} \).
  2. The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
    3. -
  3. The vector \( \boldsymbol{q} \) has all elements equal 1.
    4. +
  4. The vector \( \boldsymbol{q} \) has all elements equal -1.
  5. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).
  6. To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
diff --git a/doc/pub/week48/html/._week48-bs016.html b/doc/pub/week48/html/._week48-bs016.html index b36568daf..fc95a9a7b 100644 --- a/doc/pub/week48/html/._week48-bs016.html +++ b/doc/pub/week48/html/._week48-bs016.html @@ -286,7 +286,7 @@ $$ \lambda_3 \\ \dots \\ \lambda_n \\ -\end{bmatrix}= +\end{bmatrix}\wedge \begin{bmatrix} 0 \\ 0 \\ 0 \\ diff --git a/doc/pub/week48/html/week48-reveal.html b/doc/pub/week48/html/week48-reveal.html index a6d8cd3fb..79cdabc2c 100644 --- a/doc/pub/week48/html/week48-reveal.html +++ b/doc/pub/week48/html/week48-reveal.html @@ -720,7 +720,7 @@ $$ The minimization problem can be rewritten in terms of vectors and matrices as (with \( x \) and \( y \) being the unknowns)

 
$$ -\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}3\\ 4 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. +\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}5\\ 3 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. $$

 
@@ -809,7 +809,7 @@ $$

  1. With a given kernel we can thus define the matrix \( \boldsymbol{P} \).

  2. The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
    3. -

  3. The vector \( \boldsymbol{q} \) has all elements equal 1.
    4. +

  4. The vector \( \boldsymbol{q} \) has all elements equal -1.

  5. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).

  6. To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
@@ -841,7 +841,7 @@ $$ \lambda_3 \\ \dots \\ \lambda_n \\ -\end{bmatrix}= +\end{bmatrix}\wedge \begin{bmatrix} 0 \\ 0 \\ 0 \\ diff --git a/doc/pub/week48/html/week48-solarized.html b/doc/pub/week48/html/week48-solarized.html index 225b53558..baa2fd991 100644 --- a/doc/pub/week48/html/week48-solarized.html +++ b/doc/pub/week48/html/week48-solarized.html @@ -743,7 +743,7 @@ $$ The minimization problem can be rewritten in terms of vectors and matrices as (with \( x \) and \( y \) being the unknowns) $$ -\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}3\\ 4 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. +\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}5\\ 3 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. $$ Similarly, we can now set up the inequalities (we need to change \( \geq \) to \( \leq \) by multiplying with \( -1 \) on bot sides) as the following matrix-vector equation @@ -820,7 +820,7 @@ $$
  1. With a given kernel we can thus define the matrix \( \boldsymbol{P} \).
  2. The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
    3. -
  3. The vector \( \boldsymbol{q} \) has all elements equal 1.
    4. +
  4. The vector \( \boldsymbol{q} \) has all elements equal -1.
  5. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).
  6. To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
@@ -850,7 +850,7 @@ $$ \lambda_3 \\ \dots \\ \lambda_n \\ -\end{bmatrix}= +\end{bmatrix}\wedge \begin{bmatrix} 0 \\ 0 \\ 0 \\ diff --git a/doc/pub/week48/html/week48.html b/doc/pub/week48/html/week48.html index 32f5f77ef..cad0f3ffa 100644 --- a/doc/pub/week48/html/week48.html +++ b/doc/pub/week48/html/week48.html @@ -748,7 +748,7 @@ $$ The minimization problem can be rewritten in terms of vectors and matrices as (with \( x \) and \( y \) being the unknowns) $$ -\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}3\\ 4 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. +\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}5\\ 3 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. $$ Similarly, we can now set up the inequalities (we need to change \( \geq \) to \( \leq \) by multiplying with \( -1 \) on bot sides) as the following matrix-vector equation @@ -825,7 +825,7 @@ $$
  1. With a given kernel we can thus define the matrix \( \boldsymbol{P} \).
  2. The matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \). Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up.
    3. -
  3. The vector \( \boldsymbol{q} \) has all elements equal 1.
    4. +
  4. The vector \( \boldsymbol{q} \) has all elements equal -1.
  5. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \).
  6. To set up the matrix \( \boldsymbol{G} \) we note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into \( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
@@ -855,7 +855,7 @@ $$ \lambda_3 \\ \dots \\ \lambda_n \\ -\end{bmatrix}= +\end{bmatrix}\wedge \begin{bmatrix} 0 \\ 0 \\ 0 \\ diff --git a/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz b/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz index 990f429ba..138637831 100644 Binary files a/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz and b/doc/pub/week48/ipynb/ipynb-week48-src.tar.gz differ diff --git a/doc/pub/week48/ipynb/week48.ipynb b/doc/pub/week48/ipynb/week48.ipynb index 4b000801a..3a1874f38 100644 --- a/doc/pub/week48/ipynb/week48.ipynb +++ b/doc/pub/week48/ipynb/week48.ipynb @@ -675,7 +675,7 @@ "metadata": {}, "source": [ "$$\n", - "\\frac{1}{2}\\begin{bmatrix} x\\\\ y \\end{bmatrix}^T \\begin{bmatrix} 1 & 0\\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} x \\\\ y \\end{bmatrix} + \\begin{bmatrix}3\\\\ 4 \\end{bmatrix}^T \\begin{bmatrix}x \\\\ y \\end{bmatrix}.\n", + "\\frac{1}{2}\\begin{bmatrix} x\\\\ y \\end{bmatrix}^T \\begin{bmatrix} 1 & 0\\\\ 0 & 0 \\end{bmatrix} \\begin{bmatrix} x \\\\ y \\end{bmatrix} + \\begin{bmatrix}5\\\\ 3 \\end{bmatrix}^T \\begin{bmatrix}x \\\\ y \\end{bmatrix}.\n", "$$" ] }, @@ -816,7 +816,7 @@ "\n", "2. The matrix $\\boldsymbol{P}$ has matrix elements $p_{ij}=y_iy_jK(\\boldsymbol{x}_i,\\boldsymbol{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up.\n", "\n", - "3. The vector $\\boldsymbol{q}$ has all elements equal 1.\n", + "3. The vector $\\boldsymbol{q}$ has all elements equal -1.\n", "\n", "4. The constraint $\\boldsymbol{y}^T\\boldsymbol{\\lambda}=0$ leads to $f=0$ and $\\boldsymbol{A}=\\boldsymbol{y}$.\n", "\n", @@ -850,7 +850,7 @@ "\\lambda_3 \\\\\n", "\\dots \\\\\n", "\\lambda_n \\\\\n", - "\\end{bmatrix}=\n", + "\\end{bmatrix}\\wedge \n", "\\begin{bmatrix} 0 \\\\\n", "0 \\\\\n", "0 \\\\\n", diff --git a/doc/src/week48/week48.do.txt b/doc/src/week48/week48.do.txt index 80e972ea3..912b85ef8 100644 --- a/doc/src/week48/week48.do.txt +++ b/doc/src/week48/week48.do.txt @@ -498,7 +498,7 @@ Let us show how to perform the optmization using a simple case. Assume we want t The minimization problem can be rewritten in terms of vectors and matrices as (with $x$ and $y$ being the unknowns) !bt \[ -\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}3\\ 4 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. +\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}5\\ 3 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}. \] !et Similarly, we can now set up the inequalities (we need to change $\geq$ to $\leq$ by multiplying with $-1$ on bot sides) as the following matrix-vector equation @@ -575,7 +575,7 @@ We have the general problem o With a given kernel we can thus define the matrix $\bm{P}$. o The matrix $\bm{P}$ has matrix elements $p_{ij}=y_iy_jK(\bm{x}_i,\bm{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up. -o The vector $\bm{q}$ has all elements equal 1. +o The vector $\bm{q}$ has all elements equal -1. o The constraint $\bm{y}^T\bm{\lambda}=0$ leads to $f=0$ and $\bm{A}=\bm{y}$. o To set up the matrix $\bm{G}$ we note that the inequalities $0\leq \lambda_i \leq C$ can be split up into $0\leq \lambda_i$ and $\lambda_i \leq C$. These two inequalities define then the matrix $\bm{G}$ and the vector $\bm{h}$. @@ -603,7 +603,7 @@ can be written as \lambda_3 \\ \dots \\ \lambda_n \\ -\end{bmatrix}= +\end{bmatrix}\wedge \begin{bmatrix} 0 \\ 0 \\ 0 \\