Contents

Function Syntax
Examples
Related Topics

Warning: This MADlib method is still in early stage development. There may be some issues that will be addressed in a future version. Interface and implementation is subject to change.

This function uses the iterative conjugate gradient method [1] to find a solution to the function:

$\boldsymbol Ax = \boldsymbol b$

where $\boldsymbol A$ is a symmetric, positive definite matrix and $x$ and $\boldsymbol b$ are vectors.

Function Syntax: Conjugate gradient returns x as an array. It has the following syntax.

conjugate_gradient( table_name,
                    name_of_row_values_col,
                    name_of_row_number_col,
                    aray_of_b_values,
                    desired_precision
                  )

Matrix $\boldsymbol A$ is assumed to be stored in a table where each row consists of at least two columns: array containing values of a given row, row number:

{TABLE|VIEW} matrix_A (
    row_number FLOAT,
    row_values FLOAT[],
)

The number of elements in each row should be the same.

$\boldsymbol b$ is passed as a FLOAT[] to the function.

Examples

Construct matrix A according to structure.

SELECT * FROM data;

Result:

 row_num | row_val
 --------+---------
       1 | {2,1}
       2 | {1,4}
(2 rows)

Call the conjugate gradient function.

SELECT conjugate_gradient( 'data',
                           'row_val',
                           'row_num',
                           '{2,1}',
                           1E-6,1
                         );

INFO:  COMPUTE RESIDUAL ERROR 14.5655661859659
INFO:  ERROR 0.144934004246004
INFO:  ERROR 3.12963615962926e-31
INFO:  TEST FINAL ERROR 2.90029642185163e-29
    conjugate_gradient
 --------------------------
 {1,-1.31838984174237e-15}
(1 row)

Literature: [1] "Conjugate gradient method" Wikipedia - http://en.wikipedia.org/wiki/Conjugate_gradient_method

Related Topics: File conjugate_gradient.sql_in documenting the SQL function.