SQL functions for linear algebra.
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| float8 | norm1 (float8[] x) |
| | 1-norm of a vector More...
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| float8 | norm2 (float8[] x) |
| | 2-norm of a vector More...
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| float8 | dist_norm1 (float8[] x, float8[] y) |
| | 1-norm of the difference between two vectors More...
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| float8 | dist_norm2 (float8[] x, float8[] y) |
| | 2-norm of the difference between two vectors More...
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| float8 | squared_dist_norm2 (float8[] x, float8[] y) |
| | Squared 2-norm of the difference between two vectors. More...
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| float8 | dist_angle (float8[] x, float8[] y) |
| | Angle between two vectors. More...
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| float8 | dist_tanimoto (float8[] x, float8[] y) |
| | Tanimoto distance between two vectors. More...
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| closest_column_result | closest_column (float8[][] m, float8[] x, regproc dist="squared_dist_norm2") |
| | Given matrix \( M \) and vector \( \vec x \) compute the column of \( M \) that is closest to \( \vec x \). More...
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| closest_columns_result | closest_columns (float8[][] m, float8[] x, integer num, regproc dist="squared_dist_norm2") |
| | Given matrix \( M \) and vector \( \vec x \) compute the columns of \( M \) that are closest to \( \vec x \). More...
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| aggregate float8[] | avg (float8[] x) |
| | Compute the average of vectors. More...
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| aggregate float8[] | normalized_avg (float8[] x) |
| | Compute the normalized average of vectors. More...
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| aggregate float8[] | matrix_agg (float8[] x) |
| | Combine vectors to a matrix. More...
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| float8[] | matrix_column (float8[][] matrix, integer col) |
| | Return the column of a matrix. More...
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- See Also
- For an overview of linear-algebra functions, see the module description Linear-Algebra Operations.
Definition in file linalg.sql_in.
| aggregate float8 [] avg |
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float8[] |
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Given vectors \( x_1, \dots, x_n \), compute the average \( \frac 1n \sum_{i=1}^n x_i \).
- Parameters
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- Returns
- Average \( \frac 1n \sum_{i=1}^n x_i \)
Definition at line 301 of file linalg.sql_in.
| closest_column_result closest_column |
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float8 |
m[][], |
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float8[] |
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regproc |
dist = "squared_dist_norm2" |
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- Parameters
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| M | Matrix \( M = (\vec{m_0} \dots \vec{m_{l-1}}) \in \mathbb{R}^{k \times l} \) |
| x | Vector \( \vec x \in \mathbb R^k \) |
| dist | The metric \( \operatorname{dist} \). This needs to be a function with signature DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION. |
- Returns
- A composite value:
columns_id INTEGER - The 0-based index of the column of \( M \) that is closest to \( x \). In case of ties, the first such index is returned. That is, columns_id is the minimum element in the set \( \arg\min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \).distance DOUBLE PRECISION - The minimum distance between any column of \( M \) and \( x \). That is, \( \min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \).
Definition at line 196 of file linalg.sql_in.
| closest_columns_result closest_columns |
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float8 |
m[][], |
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float8[] |
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integer |
num, |
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regproc |
dist = "squared_dist_norm2" |
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This function does essentially the same as closest_column(), except that it allows to specify the number of closest columns to return. The return value is a composite value:
columns_ids INTEGER[] - The 0-based indices of the num columns of \( M \) that are closest to \( x \). In case of ties, the first such indices are returned.distances DOUBLE PRECISION[] - The distances between the columns of \( M \) with indices in columns_ids and \( x \). That is, distances[i] contains \( \operatorname{dist}(\vec{m_j}, \vec x) \), where \( j = \) columns_ids[i].
Definition at line 242 of file linalg.sql_in.
| float8 dist_angle |
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float8[] |
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float8[] |
y |
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- Parameters
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| x | Vector \( \vec x = (x_1, \dots, x_n) \) |
| y | Vector \( \vec y = (y_1, \dots, y_n) \) |
- Returns
- \( \arccos\left(\frac{\langle \vec x, \vec y \rangle} {\| \vec x \| \cdot \| \vec y \|}\right) \)
Definition at line 141 of file linalg.sql_in.
| float8 dist_norm1 |
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float8[] |
x, |
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float8[] |
y |
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- Parameters
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| x | Vector \( \vec x = (x_1, \dots, x_n) \) |
| y | Vector \( \vec y = (y_1, \dots, y_n) \) |
- Returns
- \( \| x - y \|_1 = \sum_{i=1}^n |x_i - y_i| \)
Definition at line 92 of file linalg.sql_in.
| float8 dist_norm2 |
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float8[] |
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float8[] |
y |
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- Parameters
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| x | Vector \( \vec x = (x_1, \dots, x_n) \) |
| y | Vector \( \vec y = (y_1, \dots, y_n) \) |
- Returns
- \( \| x - y \|_2 = \sqrt{\sum_{i=1}^n (x_i - y_i)^2} \)
Definition at line 108 of file linalg.sql_in.
| float8 dist_tanimoto |
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float8[] |
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float8[] |
y |
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- Parameters
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| x | Vector \( \vec x = (x_1, \dots, x_n) \) |
| y | Vector \( \vec y = (y_1, \dots, y_n) \) |
- Returns
- \( 1 - \frac{\langle \vec x, \vec y \rangle} {\| \vec x \|^2 \cdot \| \vec y \|^2 - \langle \vec x, \vec y \rangle} \)
Definition at line 159 of file linalg.sql_in.
| aggregate float8 [] matrix_agg |
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float8[] |
x) | |
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Given vectors \( \vec x_1, \dots, \vec x_n \in \mathbb R^m \), return matrix \( ( \vec x_1 \dots \vec x_n ) \in \mathbb R^{m \times n}\).
- Parameters
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- Returns
- Matrix with columns \( x_1, \dots, x_n \)
Definition at line 375 of file linalg.sql_in.
| float8 [] matrix_column |
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float8 |
matrix[][], |
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integer |
col |
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- Parameters
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| matrix | Two-dimensional matrix |
| col | Column of the matrix to return (0-based index) |
Definition at line 392 of file linalg.sql_in.
| float8 norm1 |
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float8[] |
x) | |
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- Parameters
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| x | Vector \( \vec x = (x_1, \dots, x_n) \) |
- Returns
- \( \| x \|_1 = \sum_{i=1}^n |x_i| \)
Definition at line 63 of file linalg.sql_in.
| float8 norm2 |
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float8[] |
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- Parameters
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| x | Vector \( \vec x = (x_1, \dots, x_n) \) |
- Returns
- \( \| x \|_2 = \sqrt{\sum_{i=1}^n x_i^2} \)
Definition at line 77 of file linalg.sql_in.
| aggregate float8 [] normalized_avg |
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float8[] |
x) | |
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Given vectors \( x_1, \dots, x_n \), define \( \widetilde{x} := \frac 1n \sum_{i=1}^n \frac{x_i}{\| x_i \|} \), and compute the normalized average \( \frac{\widetilde{x}}{\| \widetilde{x} \|} \).
- Parameters
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- Returns
- Normalized average \( \frac{\widetilde{x}}{\| \widetilde{x} \|} \)
Definition at line 339 of file linalg.sql_in.
| float8 squared_dist_norm2 |
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float8[] |
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float8[] |
y |
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- Parameters
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| x | Vector \( \vec x = (x_1, \dots, x_n) \) |
| y | Vector \( \vec y = (y_1, \dots, y_n) \) |
- Returns
- \( \| x - y \|_2^2 = \sum_{i=1}^n (x_i - y_i)^2 \)
Definition at line 124 of file linalg.sql_in.
1.8.4