Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/31/2023
Public

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?lamsh

Sends multiple shifts through a small (single node) matrix to maximize the number of bulges that can be sent through.

Syntax

call slamsh(s, lds, nbulge, jblk, h, ldh, n, ulp)

call dlamsh(s, lds, nbulge, jblk, h, ldh, n, ulp)

call clamsh(s, lds, nbulge, jblk, h, ldh, n, ulp)

call zlamsh(s, lds, nbulge, jblk, h, ldh, n, ulp)

Description

The ?lamshroutine sends multiple shifts through a small (single node) matrix to see how small consecutive subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through. The subroutine should only be called when there are multiple shifts/bulges (nbulge > 1) and the first shift is starting in the middle of an unreduced Hessenberg matrix because of two or more small consecutive subdiagonal elements.

Input Parameters
s

(local)

REAL for slamsh

DOUBLE PRECISION for dlamsh

COMPLEX for clamsh

DOUBLE COMPLEX for zlamsh

Array of size (lds, 2*jblk).

On entry, the matrix of shifts. Only the 2x2 diagonal of s is referenced. It is assumed that s has jblk double shifts (size 2).

lds

(local) INTEGER.

On entry, the leading dimension of S; unchanged on exit. 1<nbulge jblk lds/2.

nbulge

(local) INTEGER.

On entry, the number of bulges to send through h (>1). nbulge should be less than the maximum determined (jblk). 1<nbulge jblk lds/2.

jblk

(local) INTEGER.

On entry, the number of double shifts determined for S; unchanged on exit.

h

(local)

REAL for slamsh

DOUBLE PRECISION for dlamsh

COMPLEX for clamsh

DOUBLE COMPLEX for zlamsh

Array of size (ldh, n).

On entry, the local matrix to apply the shifts on.

h should be aligned so that the starting row is 2.

ldh

(local)

INTEGER.

On entry, the leading dimension of H; unchanged on exit.

n

(local) INTEGER.

On entry, the size of H. If all the bulges are expected to go through, n should be at least 4nbulge+2. Otherwise, nbulge may be reduced by this routine.

ulp

(local)

REAL for slamsh

DOUBLE PRECISION for dlamsh

REAL for clamsh

DOUBLE PRECISION for zlamsh

On entry, machine precision. Unchanged on exit.

Output Parameters
s

On exit, the data is rearranged in the best order for applying.

nbulge

On exit, the maximum number of bulges that can be sent through.

h

On exit, the data is destroyed.

See Also