Conjugate Gradient

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

1. Construct matrix A according to structure.

   SELECT * FROM data;
   

   Result:

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

2. 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.