?lamsh

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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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

void slamsh (float *s, const MKL_INT *lds, MKL_INT *nbulge, const MKL_INT *jblk, float *h, const MKL_INT *ldh, const MKL_INT *n, const float *ulp );

void dlamsh (double *s, const MKL_INT *lds, MKL_INT *nbulge, const MKL_INT *jblk, double *h, const MKL_INT *ldh, const MKL_INT *n, const double *ulp );

void clamsh (MKL_Complex8 *s , const MKL_INT *lds , MKL_INT *nbulge , const MKL_INT *jblk , MKL_Complex8 *h , const MKL_INT *ldh , const MKL_INT *n , const float *ulp );

void zlamsh (MKL_Complex16 *s , const MKL_INT *lds , MKL_INT *nbulge , const MKL_INT *jblk , MKL_Complex16 *h , const MKL_INT *ldh , const MKL_INT *n , const double *ulp );

Include Files

mkl_scalapack.h

Description

The ?lamshfunction 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 function 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)

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)

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

nbulge

(local)

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)

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

h

(local)

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)

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

n

(local)

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 function.

ulp

(local)

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: ScaLAPACK Auxiliary Routines

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?lamsh

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