table of contents
| ungtsqr_row(3) | LAPACK | ungtsqr_row(3) |
NAME¶
ungtsqr_row - {un,or}gtsqr_row: generate Q from latsqr
SYNOPSIS¶
Functions¶
subroutine cungtsqr_row (m, n, mb, nb, a, lda, t, ldt,
work, lwork, info)
CUNGTSQR_ROW subroutine dorgtsqr_row (m, n, mb, nb, a, lda, t,
ldt, work, lwork, info)
DORGTSQR_ROW subroutine sorgtsqr_row (m, n, mb, nb, a, lda, t,
ldt, work, lwork, info)
SORGTSQR_ROW subroutine zungtsqr_row (m, n, mb, nb, a, lda, t,
ldt, work, lwork, info)
ZUNGTSQR_ROW
Detailed Description¶
Function Documentation¶
subroutine cungtsqr_row (integer m, integer n, integer mb, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer lwork, integer info)¶
CUNGTSQR_ROW
Purpose:
CUNGTSQR_ROW generates an M-by-N complex matrix Q_out with
orthonormal columns from the output of CLATSQR. These N orthonormal
columns are the first N columns of a product of complex unitary
matrices Q(k)_in of order M, which are returned by CLATSQR in
a special format.
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
The input matrices Q(k)_in are stored in row and column blocks in A.
See the documentation of CLATSQR for more details on the format of
Q(k)_in, where each Q(k)_in is represented by block Householder
transformations. This routine calls an auxiliary routine CLARFB_GETT,
where the computation is performed on each individual block. The
algorithm first sweeps NB-sized column blocks from the right to left
starting in the bottom row block and continues to the top row block
(hence _ROW in the routine name). This sweep is in reverse order of
the order in which CLATSQR generates the output blocks.
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.
MB
MB is INTEGER
The row block size used by CLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).
NB
NB is INTEGER
The column block size used by CLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).
A
A is COMPLEX array, dimension (LDA,N)
On entry:
The elements on and above the diagonal are not used as
input. The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by CLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored). See CLATSQR for more details.
On exit:
The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)
The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of the NIRB block reflector
sequences is stored in a larger NB-by-N column block of T
and consists of NICB smaller NB-by-NB upper-triangular
column blocks. See CLATSQR for more details on the format
of T.
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB,N)).
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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
where NBLOCAL=MIN(NB,N).
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 dorgtsqr_row (integer m, integer n, integer mb, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer lwork, integer info)¶
DORGTSQR_ROW
Purpose:
DORGTSQR_ROW generates an M-by-N real matrix Q_out with
orthonormal columns from the output of DLATSQR. These N orthonormal
columns are the first N columns of a product of complex unitary
matrices Q(k)_in of order M, which are returned by DLATSQR in
a special format.
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
The input matrices Q(k)_in are stored in row and column blocks in A.
See the documentation of DLATSQR for more details on the format of
Q(k)_in, where each Q(k)_in is represented by block Householder
transformations. This routine calls an auxiliary routine DLARFB_GETT,
where the computation is performed on each individual block. The
algorithm first sweeps NB-sized column blocks from the right to left
starting in the bottom row block and continues to the top row block
(hence _ROW in the routine name). This sweep is in reverse order of
the order in which DLATSQR generates the output blocks.
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.
MB
MB is INTEGER
The row block size used by DLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).
NB
NB is INTEGER
The column block size used by DLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry:
The elements on and above the diagonal are not used as
input. The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by DLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored). See DLATSQR for more details.
On exit:
The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is DOUBLE PRECISION array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)
The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of the NIRB block reflector
sequences is stored in a larger NB-by-N column block of T
and consists of NICB smaller NB-by-NB upper-triangular
column blocks. See DLATSQR for more details on the format
of T.
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB,N)).
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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
where NBLOCAL=MIN(NB,N).
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 sorgtsqr_row (integer m, integer n, integer mb, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer lwork, integer info)¶
SORGTSQR_ROW
Purpose:
SORGTSQR_ROW generates an M-by-N real matrix Q_out with
orthonormal columns from the output of SLATSQR. These N orthonormal
columns are the first N columns of a product of complex unitary
matrices Q(k)_in of order M, which are returned by SLATSQR in
a special format.
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
The input matrices Q(k)_in are stored in row and column blocks in A.
See the documentation of SLATSQR for more details on the format of
Q(k)_in, where each Q(k)_in is represented by block Householder
transformations. This routine calls an auxiliary routine SLARFB_GETT,
where the computation is performed on each individual block. The
algorithm first sweeps NB-sized column blocks from the right to left
starting in the bottom row block and continues to the top row block
(hence _ROW in the routine name). This sweep is in reverse order of
the order in which SLATSQR generates the output blocks.
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.
MB
MB is INTEGER
The row block size used by SLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).
NB
NB is INTEGER
The column block size used by SLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).
A
A is REAL array, dimension (LDA,N)
On entry:
The elements on and above the diagonal are not used as
input. The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by SLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored). See SLATSQR for more details.
On exit:
The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is REAL array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)
The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of the NIRB block reflector
sequences is stored in a larger NB-by-N column block of T
and consists of NICB smaller NB-by-NB upper-triangular
column blocks. See SLATSQR for more details on the format
of T.
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB,N)).
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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
where NBLOCAL=MIN(NB,N).
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 zungtsqr_row (integer m, integer n, integer mb, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer lwork, integer info)¶
ZUNGTSQR_ROW
Purpose:
ZUNGTSQR_ROW generates an M-by-N complex matrix Q_out with
orthonormal columns from the output of ZLATSQR. These N orthonormal
columns are the first N columns of a product of complex unitary
matrices Q(k)_in of order M, which are returned by ZLATSQR in
a special format.
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
The input matrices Q(k)_in are stored in row and column blocks in A.
See the documentation of ZLATSQR for more details on the format of
Q(k)_in, where each Q(k)_in is represented by block Householder
transformations. This routine calls an auxiliary routine ZLARFB_GETT,
where the computation is performed on each individual block. The
algorithm first sweeps NB-sized column blocks from the right to left
starting in the bottom row block and continues to the top row block
(hence _ROW in the routine name). This sweep is in reverse order of
the order in which ZLATSQR generates the output blocks.
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.
MB
MB is INTEGER
The row block size used by ZLATSQR to return
arrays A and T. MB > N.
(Note that if MB > M, then M is used instead of MB
as the row block size).
NB
NB is INTEGER
The column block size used by ZLATSQR to return
arrays A and T. NB >= 1.
(Note that if NB > N, then N is used instead of NB
as the column block size).
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry:
The elements on and above the diagonal are not used as
input. The elements below the diagonal represent the unit
lower-trapezoidal blocked matrix V computed by ZLATSQR
that defines the input matrices Q_in(k) (ones on the
diagonal are not stored). See ZLATSQR for more details.
On exit:
The array A contains an M-by-N orthonormal matrix Q_out,
i.e the columns of A are orthogonal unit vectors.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX*16 array,
dimension (LDT, N * NIRB)
where NIRB = Number_of_input_row_blocks
= MAX( 1, CEIL((M-N)/(MB-N)) )
Let NICB = Number_of_input_col_blocks
= CEIL(N/NB)
The upper-triangular block reflectors used to define the
input matrices Q_in(k), k=(1:NIRB*NICB). The block
reflectors are stored in compact form in NIRB block
reflector sequences. Each of the NIRB block reflector
sequences is stored in a larger NB-by-N column block of T
and consists of NICB smaller NB-by-NB upper-triangular
column blocks. See ZLATSQR for more details on the format
of T.
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB,N)).
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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
where NBLOCAL=MIN(NB,N).
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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