Provided by: liblapack-doc_3.12.0-3build1.1_all 
NAME
ungtsqr - {un,or}gtsqr: generate Q from latsqr
SYNOPSIS
Functions
subroutine cungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
CUNGTSQR
subroutine dorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
DORGTSQR
subroutine sorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
SORGTSQR
subroutine zungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
ZUNGTSQR
Detailed Description
Function Documentation
subroutine cungtsqr (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
Purpose:
CUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal
columns, which are the first N columns of a product of comlpex unitary
matrices of order M which are returned by CLATSQR
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
See the documentation for CLATSQR.
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 accessed.
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) (same format as the output A
below the diagonal in CLATSQR).
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 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.
(same format as the output T in CLATSQR).
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).
WORK
(workspace) COMPLEX array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= (M+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 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley
subroutine dorgtsqr (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
Purpose:
DORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,
which are the first N columns of a product of real orthogonal
matrices of order M which are returned by DLATSQR
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
See the documentation for DLATSQR.
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 accessed.
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) (same format as the output A
below the diagonal in DLATSQR).
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 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.
(same format as the output T in DLATSQR).
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).
WORK
(workspace) DOUBLE PRECISION array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= (M+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 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley
subroutine sorgtsqr (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
Purpose:
SORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,
which are the first N columns of a product of real orthogonal
matrices of order M which are returned by SLATSQR
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
See the documentation for SLATSQR.
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 accessed.
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) (same format as the output A
below the diagonal in SLATSQR).
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 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.
(same format as the output T in SLATSQR).
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).
WORK
(workspace) REAL array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= (M+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 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley
subroutine zungtsqr (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
Purpose:
ZUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal
columns, which are the first N columns of a product of comlpex unitary
matrices of order M which are returned by ZLATSQR
Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
See the documentation for ZLATSQR.
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 accessed.
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) (same format as the output A
below the diagonal in ZLATSQR).
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 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.
(same format as the output T in ZLATSQR).
LDT
LDT is INTEGER
The leading dimension of the array T.
LDT >= max(1,min(NB1,N)).
WORK
(workspace) COMPLEX*16 array, dimension (MAX(2,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= (M+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 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley
Author
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