Man page - getsqrhrt(3)

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Manual

getsqrhrt

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, complex, dimension( lda, * ) a, integer lda, complex,dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work,integer lwork, integer info)
subroutine dgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, double precision, dimension( lda, * ) a, integer lda,double precision, dimension( ldt, * ) t, integer ldt, double precision,dimension( * ) work, integer lwork, integer info)
subroutine sgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, real, dimension( lda, * ) a, integer lda, real, dimension(ldt, * ) t, integer ldt, real, dimension( * ) work, integer lwork,integer info)
subroutine zgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, complex*16, dimension( lda, * ) a, integer lda,complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension(* ) work, integer lwork, integer info)
Author

NAME

getsqrhrt - getsqrhrt: tall-skinny QR factor, with Householder reconstruction

SYNOPSIS

Functions

subroutine cgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)
CGETSQRHRT
subroutine dgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)
DGETSQRHRT
subroutine sgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)
SGETSQRHRT
subroutine zgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info)
ZGETSQRHRT

Detailed Description

Function Documentation

subroutine cgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, complex, dimension( lda, * ) a, integer lda, complex,dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work,integer lwork, integer info)

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

LWORK is INTEGER
The dimension of the array WORK.
If MIN(M,N) = 0, LWORK >= 1, else
LWORK >= MAX( 1, 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

subroutine dgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, double precision, dimension( lda, * ) a, integer lda,double precision, dimension( ldt, * ) t, integer ldt, double precision,dimension( * ) work, integer lwork, integer info)

DGETSQRHRT

Purpose:

DGETSQRHRT computes a NB2-sized column blocked QR-factorization
of a real 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 DGEQRT
(Q is in blocked compact WY-representation). See the documentation
of DGEQRT 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If MIN(M,N) = 0, LWORK >= 1, else
LWORK >= MAX( 1, 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

subroutine sgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, real, dimension( lda, * ) a, integer lda, real, dimension(ldt, * ) t, integer ldt, real, dimension( * ) work, integer lwork,integer info)

SGETSQRHRT

Purpose:

SGETSQRHRT 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 SGEQRT
(Q is in blocked compact WY-representation). See the documentation
of SGEQRT 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 REAL 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 REAL 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) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If MIN(M,N) = 0, LWORK >= 1, else
LWORK >= MAX( 1, 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

subroutine zgetsqrhrt (integer m, integer n, integer mb1, integer nb1,integer nb2, complex*16, dimension( lda, * ) a, integer lda,complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension(* ) work, integer lwork, integer info)

ZGETSQRHRT

Purpose:

ZGETSQRHRT 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 ZGEQRT
(Q is in blocked compact WY-representation). See the documentation
of ZGEQRT 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*16 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*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If MIN(M,N) = 0, LWORK >= 1, else
LWORK >= MAX( 1, 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

Author

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