table of contents
| getsqrhrt(3) | LAPACK | getsqrhrt(3) |
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
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
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
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
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
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
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
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
Author¶
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