Estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
Syntax
call slacon( n, v, x, isgn, est, kase )
call dlacon( n, v, x, isgn, est, kase )
call clacon( n, v, x, est, kase )
call zlacon( n, v, x, est, kase )
Include Files
The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).
Description
The routine estimates the 1-norm of a square, real/complex matrix A. Reverse communication is used for evaluating matrix-vector products.
Warning
The ?lacon routine is not thread-safe. It is deprecated and retained for the backward compatibility only. Use the thread-safe ?lacn2 routine instead.
Input Parameters
- n
INTEGER. The order of the matrix A (n ≥ 1).
- v, x
REAL for slacon
DOUBLE PRECISION for dlacon
COMPLEX for clacon
COMPLEX*16 for zlacon.
Arrays, DIMENSION (n) each.
v is a workspace array.
x is used as input after an intermediate return.
- isgn
INTEGER.
Workspace array, DIMENSION (n), used with real flavors only.
- est
REAL for slacon/clacon
DOUBLE PRECISION for dlacon/zlacon
An estimate that with kase=1 or 2 should be unchanged from the previous call to ?lacon.
- kase
INTEGER.
On the initial call to ?lacon, kase should be 0.
Output Parameters
- est
REAL for slacon/clacon
DOUBLE PRECISION for dlacon/zlacon
An estimate (a lower bound) for norm(A).
- kase
On an intermediate return, kase will be 1 or 2, indicating whether x should be overwritten by A*x or A'*x. On the final return from ?lacon, kase will again be 0.
- v
On the final return, v = A*w, where est = norm(v)/norm(w) (w is not returned).
- x
On an intermediate return, x should be overwritten by
A*x , if kase = 1,
A'*x , if kase = 2,
(where for complex flavors A' is the conjugate transpose of A), and ?lacon must be re-called with all the other parameters unchanged.