# ?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)

## Description

This routine 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)

  INTEGER. REAL for slamsh

  DOUBLE PRECISION for dlamsh

  Array, DIMENSION (lds,*).

  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 leading dimension of S; unchanged on exit.

h

  (local) INTEGER.

  REAL for slamsh

  DOUBLE PRECISION for dlamsh

  Array, DIMENSION (lds, 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

  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.

Parent topic: Auxiliary Routines