Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
p?laqr3
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
call pslaqr3 ( wantt , wantz , n , ktop , kbot , nw , h , desch , iloz , ihiz , z , descz , ns , nd , sr , si , v , descv , nh , t , desct , nv , wv , descw , work , lwork , iwork , liwork , reclevel )
call pdlaqr3 ( wantt , wantz , n , ktop , kbot , nw , h , desch , iloz , ihiz , z , descz , ns , nd , sr , si , v , descv , nh , t , desct , nv , wv , descw , work , lwork , iwork , liwork , reclevel )
Include Files
mkl_scalapack.h
Description
This subroutine function accepts as input an upper Hessenberg matrix H and performs an orthogonal similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output H is overwritten by a new Hessenberg matrix that is a perturbation of an orthogonal similarity transformation of H . It is to be hoped that the final version of H has many zero subdiagonal entries.
Input Parameters
- wantt
-
(global ) LOGICAL
If .TRUE. , then the Hessenberg matrix H is fully updated so that the quasi-triangular Schur factor may be computed (in cooperation with the calling subroutine ).
If .FALSE. , then only enough of H is updated to preserve the eigenvalues.
- wantz
-
(global ) LOGICAL
If .TRUE. , then the orthogonal matrix Z is updated so that the orthogonal Schur factor may be computed (in cooperation with the calling subroutine ).
If .FALSE. , then z is not referenced.
- n
-
(global ) INTEGER
The order of the matrix H and (if wantz is .TRUE. ), the order of the orthogonal matrix Z .
- ktop
-
(global ) INTEGER It is assumed that either ktop = 1 or H ( ktop , ktop -1)=0. kbot and ktop together determine an isolated block along the diagonal of the Hessenberg matrix.
- kbot
-
(global ) INTEGER It is assumed without a check that either kbot = n or H ( kbot +1, kbot )=0. kbot and ktop together determine an isolated block along the diagonal of the Hessenberg matrix.
- nw
-
(global ) INTEGER Deflation window size. 1 ≤ nw ≤ ( kbot - ktop +1).
- h
-
REAL for pslaqr3 DOUBLE PRECISION for pdlaqr3
(local ) array of size ( lld_h , LOCc ( n ))
The initial n -by- n section of H stores the Hessenberg matrix undergoing aggressive early deflation.
desch
(global and local) INTEGER array of size dlen_ .
The array descriptor for the distributed matrix H .
- iloz , ihiz
-
(global ) INTEGER
Specify the rows of the matrix Z to which transformations must be applied if wantz is .TRUE. . 1 ≤ iloz ≤ ihiz ≤ n .
- z
-
REAL for pslaqr3 DOUBLE PRECISION for pdlaqr3
Array of size ( lld_z , LOCc ( n ))
If wantz is .TRUE. , then on output, the orthogonal similarity transformation mentioned above has been accumulated into the matrix Z ( iloz : ihiz , kbot : ktop ) from the right.
If wantz is .FALSE. , then z is unreferenced.
descz
(global and local) INTEGER array of size dlen_ .
The array descriptor for the distributed matrix Z .
- v
-
REAL for pslaqr3 DOUBLE PRECISION for pdlaqr3
(global workspace) array of size ( lld_v , LOCc ( nw ))
An nw -by- nw distributed work array.
descv
(global and local) INTEGER array of size dlen_ .
The array descriptor for the distributed matrix V .
- nh
-
INTEGER scalar The number of columns of t . nh ≥ nw .
- t
-
REAL for pslaqr3 DOUBLE PRECISION for pdlaqr3
(global workspace) array of size ( lld_t , LOCc ( nh ))
desct
(global and local) INTEGER array of size dlen_ .
The array descriptor for the distributed matrix T .
- nv
-
(global ) INTEGER The number of rows of work array wv available for workspace. nv ≥ nw .
wv
(global workspace) REAL array of size ( lld_w , LOCc ( nw ) )
descw
(global and local) INTEGER array of size dlen_ .
The array descriptor for the distributed matrix wv .
- work
-
(local workspace) REAL array of size lwork .
- lwork
-
(local ) INTEGER The size of the work array work ( lwork ≥ 1). lwork = 2* nw suffices, but greater efficiency may result from larger values of lwork .
If lwork = -1, then a workspace query is assumed; p?laqr3 only estimates the optimal workspace size for the given values of n , nw , ktop and kbot . The estimate is returned in work (1) . No error message related to lwork is issued by GUID-F3536B0B-2FA0-40B4-AF9B-51A182827F73.xml . Neither h nor z are accessed.
- iwork
-
(local workspace) INTEGER array of size liwork
- liwork
-
(local ) INTEGER The length of the workspace array iwork ( liwork ≥ 1). If liwork =-1, then a workspace query is assumed.
OUTPUT Parameters
- h
-
On output h has been transformed by an orthogonal similarity transformation, perturbed, and the returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries.
z
IF wantz is .TRUE. , then on output, the orthogonal similarity transformation mentioned above has been accumulated into the matrix Z ( iloz : ihiz , kbot : ktop ) from the right.
If wantz is .FALSE. , then z is unreferenced.
- ns
-
(global ) INTEGER
The number of unconverged (that is, approximate) eigenvalues returned in sr and si that may be used as shifts by the calling subroutine .
- nd
-
(global ) INTEGER
The number of converged eigenvalues uncovered by this subroutine .
- sr , si
-
REAL for pslaqr3 DOUBLE PRECISION for pdlaqr3
(global ) array of size kbot . The real and imaginary parts of approximate eigenvalues that may be used for shifts are stored in sr ( kbot - nd - ns +1) through sr ( kbot - nd ) and si ( kbot - nd - ns +1) through si ( kbot - nd ) , respectively. The real and imaginary parts of converged eigenvalues are stored in sr ( kbot - nd +1) through sr ( kbot ) and si ( kbot - nd +1) through si ( kbot ) , respectively.
work (1) [0]
On exit, if info = 0, work (1) returns the optimal lwork
iwork (1) [0]
On exit, if info = 0, iwork (1) returns the optimal liwork