p?laqr2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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p?laqr2

Performs the orthogonal/unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).

Syntax

void pslaqr2(MKL_INT* wantt, MKL_INT* wantz, MKL_INT* n, MKL_INT* ktop, MKL_INT* kbot, MKL_INT* nw, float* a, MKL_INT* desca, MKL_INT* iloz, MKL_INT* ihiz, float* z, MKL_INT* descz, MKL_INT* ns, MKL_INT* nd, float* sr, float* si, float* t, MKL_INT* ldt, float* v, MKL_INT* ldv, float* wr, float* wi, float* work, MKL_INT* lwork);

void pdlaqr2(MKL_INT* wantt, MKL_INT* wantz, MKL_INT* n, MKL_INT* ktop, MKL_INT* kbot, MKL_INT* nw, double* a, MKL_INT* desca, MKL_INT* iloz, MKL_INT* ihiz, double* z, MKL_INT* descz, MKL_INT* ns, MKL_INT* nd, double* sr, double* si, double* t, MKL_INT* ldt, double* v, MKL_INT* ldv, double* wr, double* wi, double* work, MKL_INT* lwork);

Include Files

mkl_scalapack.h

Description

p?laqr2 accepts as input an upper Hessenberg matrix A and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output Ais overwritten by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of A. It is to be hoped that the final version of A has many zero subdiagonal entries.

This function handles small deflation windows which is affordable by one processor. Normally, it is called by p?laqr1. All the inputs are assumed to be valid without checking.

Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

Input Parameters

wantt

(global )

If wantt is non-zero, then the Hessenberg matrix A is fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the calling function).

If wantt equals zero, then only enough of A is updated to preserve the eigenvalues.

wantz

(global )

If wantz is non-zero, then the orthogonal matrix Z is updated so that the orthogonal Schur factor may be computed (in cooperation with the calling function).

If wantz equals zero, then z is not referenced.

n

(global )

The order of the matrix A and (if wantz is non-zero) the order of the orthogonal matrix Z.

ktop, kbot

(global )

It is assumed without a check that either kbot = n or A(kbot+1,kbot)=0. kbot and ktop together determine an isolated block along the diagonal of the Hessenberg matrix. However, A(ktop,ktop-1)=0 is not essentially necessary if wantt is non-zero .

nw

(global )

Deflation window size. 1 ≤nw≤ (kbot-ktop+1). Normally nw≥ 3 if p?laqr2 is called by p?laqr1.

a

(local ) array of size lld_a * LOC_c(n)

The initial n-by-n section of a stores the Hessenberg matrix undergoing aggressive early deflation.

desca

(global and local) array of size dlen_.

The array descriptor for the distributed matrix A.

iloz, ihiz

(global )

Specify the rows of the matrix Zto which transformations must be applied if wantz is non-zero. 1 ≤iloz≤ihiz≤n.

z

Array of size lld_z * LOC_c(n)

If wantz is non-zero, then on output, the orthogonal similarity transformation mentioned above has been accumulated into the matrix Z(iloz:ihiz,

kbot:ktop), stored in z, from the right.

If wantz is zero, then z is unreferenced.

descz

(global and local) array of size dlen_.

The array descriptor for the distributed matrix Z.

t

(local workspace) array of size ldt * nw.

ldt

(local )

The leading dimension of the array t. ldt≥nw.

v

(local workspace) array of size ldv * nw.

ldv

(local )

The leading dimension of the array v. ldv≥nw.

wr, wi

(local workspace) array of size kbot.

work

(local workspace) array of size lwork.

lwork

(local )

work(lwork) is a local array and lwork is assumed big enough so that lwork≥nw*nw.

OUTPUT Parameters

a

On output a has been transformed by an orthogonal similarity transformation, perturbed, and returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries.

z

ns

(global )

The number of unconverged (that is, approximate) eigenvalues returned in sr and si that may be used as shifts by the calling function.

nd

(global )

The number of converged eigenvalues uncovered by this function.

sr, si

(global ) array of size kbot

On output, the real and imaginary parts of approximate eigenvalues that may be used for shifts are stored in sr[kbot-nd-ns] through sr[kbot-nd-1] and si[kbot-nd-ns] through si[kbot-nd-1], respectively.

On processor #0, the real and imaginary parts of converged eigenvalues are stored in sr[kbot-nd] through sr[kbot-1] and si[kbot-nd] through si[kbot-1], respectively. On other processors, these entries are set to zero.

Parent topic: ScaLAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?laqr2

Syntax

Include Files

Description

Input Parameters

OUTPUT Parameters

See Also