DGET39
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
DGET39 tests DLAQTR, a routine for solving the real or
special complex quasi upper triangular system
op(T)*p = scale*c,
or
op(T + iB)*(p+iq) = scale*(c+id),
in real arithmetic. T is upper quasi-triangular.
If it is complex, then the first diagonal block of T must be
1 by 1, B has the special structure
B = [ b(1) b(2) ... b(n) ]
[ w ]
[ w ]
[ . ]
[ w ]
op(A) = A or A', where A' denotes the conjugate transpose of
the matrix A.
On input, X = [ c ]. On output, X = [ p ].
[ d ] [ q ]
Scale is an output less than or equal to 1, chosen to avoid
overflow in X.
This subroutine is specially designed for the condition number
estimation in the eigenproblem routine DTRSNA.
The test code verifies that the following residual is order 1:
||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)||
max(ulp*(||T||+||B||)*(||x1||+||x2||),
(||T||+||B||)*smlnum/ulp,
smlnum)
(The (||T||+||B||)*smlnum/ulp term accounts for possible
(gradual or nongradual) underflow in x1 and x2.)
special complex quasi upper triangular system
op(T)*p = scale*c,
or
op(T + iB)*(p+iq) = scale*(c+id),
in real arithmetic. T is upper quasi-triangular.
If it is complex, then the first diagonal block of T must be
1 by 1, B has the special structure
B = [ b(1) b(2) ... b(n) ]
[ w ]
[ w ]
[ . ]
[ w ]
op(A) = A or A', where A' denotes the conjugate transpose of
the matrix A.
On input, X = [ c ]. On output, X = [ p ].
[ d ] [ q ]
Scale is an output less than or equal to 1, chosen to avoid
overflow in X.
This subroutine is specially designed for the condition number
estimation in the eigenproblem routine DTRSNA.
The test code verifies that the following residual is order 1:
||(T+i*B)*(x1+i*x2) - scale*(d1+i*d2)||
max(ulp*(||T||+||B||)*(||x1||+||x2||),
(||T||+||B||)*smlnum/ulp,
smlnum)
(The (||T||+||B||)*smlnum/ulp term accounts for possible
(gradual or nongradual) underflow in x1 and x2.)
Arguments
| RMAX |
(output) DOUBLE PRECISION
Value of the largest test ratio.
|
| LMAX |
(output) INTEGER
Example number where largest test ratio achieved.
|
| NINFO |
(output) INTEGER
Number of examples where INFO is nonzero.
|
| KNT |
(output) INTEGER
Total number of examples tested.
|