next up previous contents
Next: Tests for Triangular Matrices Up: The Linear Equation Test Previous: The Linear Equation Test   Contents

Tests for General and Symmetric Matrices

For each LAPACK test path specified in the input file, the test program generates test matrices, calls the LAPACK routines in that path, and computes a number of test ratios to verify that each operation has performed correctly. The test matrices used in the test paths for general and symmetric matrices are shown in Table 1. Both the computational routines and the driver routines are tested with the same set of matrix types. In this context, 9#9 is the machine epsilon and 15#15 is the condition number of the matrix 16#16. Matrix types with one or more columns set to zero (or rows and columns, if the matrix is symmetric) are used to test the error return codes. For band matrices, all combinations of the values 0, 1, 17#17, 18#18, and 19#19 are used for 20#20 and 21#21 in the GB path, and for 22#22 in the PB path. For the tridiagonal test paths xGT and xPT, types 1-6 use matrices of predetermined condition number, while types 7-12 use random tridiagonal matrices.


Table 1: Test matrices for general and symmetric linear systems
Test matrix type GE GB GT PO, PP PB PT SY, SP, HE, HP
Diagonal 1   1 1   1 1
Upper triangular 2            
Lower triangular 3            
Random, 23#23 4 1 2 2 1 2 2
Random, 24#24 8 5 3 6 5 3 7
Random, 25#25 9 6 4 7 6 4 8
First column zero 5 2 8 3 2 8 3
Last column zero 6 3 9 4 3 9 4
Middle column zero       5 4 10 5
Last 4#4/2 columns zero 7 4 10       6
Scaled near underflow 10 7 5, 11 8 7 5, 11 9
Scaled near overflow 11 8 6, 12 9 8 6, 12 10
Random, unspecified 15#15     7     7  
Block diagonal             1126#26
26#26- complex symmetric test paths only


For the LAPACK test paths shown in Table 1, each test matrix is subjected to the following tests:

The solve and iterative refinement steps are also tested with 16#16 replaced by 44#44 or 45#45 where applicable. The test ratios computed for the general and symmetric test paths are listed in Table 2. Here we use 46#46 to describe the difference in the recomputed matrix, even though it is actually 47#47 or some other form for other paths.


Table 2: Tests performed for general and symmetric linear systems
  GE, PO, PP, SY, SP GB, GT, PB, PT
Test ratio routines drivers routines drivers
27#27 1 1 1 1
33#33 2      
35#35 3 2 2 2
36#36 4   3  
36#36, refined 5 3 4 3
(backward error)38#38 6 4 5 4
48#48 7 5 6 5
49#49 8 6 7 6



next up previous contents
Next: Tests for Triangular Matrices Up: The Linear Equation Test Previous: The Linear Equation Test   Contents
Susan Blackford 2001-08-13