Test Matrices for the Singular Value Decomposition Routines

Six different types of test matrices may be generated for the singular value decomposition routines. Table 2 shows the types available, along with the numbers used to refer to the matrix types. Except as noted, all matrix types other than the random bidiagonal matrices have $O(1)$ entries. The expression $U D V$ means a real diagonal matrix $D$ with $O(1)$ entries multiplied by unitary (or real orthogonal) matrices on the left and right.

Table 2: Test matrices for the singular value decomposition

	Singular Value Distribution
Type	Arithmetic	Other
Zero		1
Identity		2
Diagonal	3
$U D V$	4, 5, 6
- matrix entries are $O(\sqrt{\mbox{overflow}})$
- matrix entries are $O(\sqrt{\mbox{underflow}})$