Estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
call slacn2( n, v, x, isgn, est, kase, isave )
call dlacn2( n, v, x, isgn, est, kase, isave )
call clacn2( n, v, x, est, kase, isave )
call zlacn2( n, v, x, est, kase, isave )
The routine estimates the 1-norm of a square, real or complex matrix A. Reverse communication is used for evaluating matrix-vector products.
INTEGER. The order of the matrix A (
n ≥ 1).
- v, x
REAL for slacn2
DOUBLE PRECISION for dlacn2
COMPLEX for clacn2
DOUBLE COMPLEX for zlacn2.
Arrays, DIMENSION (n) each.
v is a workspace array.
x is used as input after an intermediate return.
Workspace array, DIMENSION (n), used with real flavors only.
REAL for slacn2/clacn2
DOUBLE PRECISION for dlacn2/zlacn2
On entry with kase set to 1 or 2, and
isave(1) = 1, est must be unchanged from the previous call to the routine.
On the initial call to the routine, kase must be set to 0.
INTEGER. Array, DIMENSION (3).
Contains variables from the previous call to the routine.
An estimate (a lower bound) for norm(A).
On an intermediate return, kase is set to 1 or 2, indicating whether x is overwritten by A*x or AT*x for real flavors and A*x or AH*x for complex flavors.
On the final return, kase is set to 0.
On the final return,
v = A*w, where
est = norm(v)/norm(w)(w is not returned).
On an intermediate return, x is overwritten by
kase = 1,
kase = 2(for real flavors),
kase = 2(for complex flavors),
and the routine must be re-called with all the other parameters unchanged.
This parameter is used to save variables between calls to the routine.