SLAMSH − send multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through

SUBROUTINE SLAMSH |
( S, LDS, NBULGE, JBLK, H, LDH, N, ULP ) |
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INTEGER |
LDS, NBULGE, JBLK, LDH, N |
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REAL |
ULP |
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REAL |
S(LDS,*), H(LDH,*) |

SLAMSH sends multiple shifts through a small (single node) matrix to

see how consecutive small subdiagonal elements are modified by

subsequent shifts in an effort to maximize the number of bulges

that can be sent through. SLAMSH 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 consecutive small

subdiagonal elements.

S (local input/output) REAL array, (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). On exit, the data is rearranged in the best order for applying.

LDS (local input) INTEGER

On entry, the leading dimension of S. Unchanged on exit. 1 < NBULGE <= JBLK <= LDS/2

NBULGE (local input/output) 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 On exit, the maximum number of bulges that can be sent through.

JBLK (local input) INTEGER

On entry, the number of shifts determined for S. Unchanged on exit.

H (local input/output) REAL array (LDH,N)

On entry, the local matrix to apply the shifts on. H should be aligned so that the starting row is 2. On exit, the data is destroyed.

LDS (local input) INTEGER

On entry, the leading dimension of S. Unchanged on exit.

N (local input) INTEGER

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

ULP (local input) REAL

On entry, machine precision Unchanged on exit.

Implemented by: G. Henry, May 1, 1997