cgetsqrhrt.f(3) LAPACK cgetsqrhrt.f(3)

cgetsqrhrt.f


subroutine cgetsqrhrt (M, N, MB1, NB1, NB2, A, LDA, T, LDT, WORK, LWORK, INFO)
CGETSQRHRT

CGETSQRHRT

Purpose:

CGETSQRHRT computes a NB2-sized column blocked QR-factorization
of a complex M-by-N matrix A with M >= N,
   A = Q * R.
The routine uses internally a NB1-sized column blocked and MB1-sized
row blocked TSQR-factorization and perfors the reconstruction
of the Householder vectors from the TSQR output. The routine also
converts the R_tsqr factor from the TSQR-factorization output into
the R factor that corresponds to the Householder QR-factorization,
   A = Q_tsqr * R_tsqr = Q * R.
The output Q and R factors are stored in the same format as in CGEQRT
(Q is in blocked compact WY-representation). See the documentation
of CGEQRT for more details on the format.

Parameters

M
M is INTEGER
The number of rows of the matrix A.  M >= 0.

N

N is INTEGER
The number of columns of the matrix A. M >= N >= 0.

MB1

MB1 is INTEGER
The row block size to be used in the blocked TSQR.
MB1 > N.

NB1

NB1 is INTEGER
The column block size to be used in the blocked TSQR.
N >= NB1 >= 1.

NB2

NB2 is INTEGER
The block size to be used in the blocked QR that is
output. NB2 >= 1.

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry: an M-by-N matrix A.
On exit:
 a) the elements on and above the diagonal
    of the array contain the N-by-N upper-triangular
    matrix R corresponding to the Householder QR;
 b) the elements below the diagonal represent Q by
    the columns of blocked V (compact WY-representation).

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).

T

T is COMPLEX array, dimension (LDT,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks.

LDT

LDT is INTEGER
The leading dimension of the array T.  LDT >= NB2.

WORK

(workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

The dimension of the array WORK.
LWORK >= MAX( LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ),
where
   NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)),
   NB1LOCAL = MIN(NB1,N).
   LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL,
   LW1 = NB1LOCAL * N,
   LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ),
If LWORK = -1, then a workspace query is assumed.
The routine only calculates the optimal size of the WORK
array, returns this value as the first entry of the WORK
array, and no error message related to LWORK is issued
by XERBLA.

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2020, Igor Kozachenko,
               Computer Science Division,
               University of California, Berkeley

Definition at line 177 of file cgetsqrhrt.f.

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