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ungtsqr_row(3) Library Functions Manual 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
!>
!>

Definition at line 186 of file cungtsqr_row.f.

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
!>
!>

Definition at line 186 of file dorgtsqr_row.f.

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
!>
!>

Definition at line 186 of file sorgtsqr_row.f.

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
!>
!>

Definition at line 186 of file zungtsqr_row.f.

Author

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