Matrix Scaling

Matrix scaling = {char_string}

Description / Usage

This optional card selects a scaling for the linear matrix system solution step.Valid options for {char_string} are listed below.

none

No scaling is performed. This is the default if no Matrix Scaling card is present.

Jacobi

Point Jacobi scaling is performed.

BJacobi

Block Jacobi scaling is performed if the underlying matrix format is VBR. If the MSR matrix format is used, the scaling reverts to point Jacobi.

row_sum

Scale each row so the sum of the magnitudes of the nonzero elements is 1.

sym_diag

Symmetric scaling so that diagonal elements are 1.

sym_row_sum

Symmetric scaling using the matrix row sums.

If the Matrix Scaling card is omitted, the default selection is none.

Examples

Following is a sample card:

Matrix scaling = sym_diag

Technical Discussion

All of these scalings are supplied via the Aztec library and thus will not affect the linear systems that are solved by other means (using front, for example). In an odd twist of fate, the linear system always undergoes a row sum scaling (equivalent to the row_sum option) before these other scalings are applied. Note that when a nontrivial scaling is selected, the matrix is overwritten with a rescaled system.