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.


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


Point Jacobi scaling is performed.


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.


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


Symmetric scaling so that diagonal elements are 1.


Symmetric scaling using the matrix row sums.

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


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.