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

    !>          LWORK is INTEGER
    !>          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

    !>          LWORK is INTEGER
    !>          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

    !>          LWORK is INTEGER
    !>          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

    !>          LWORK is INTEGER
    !>          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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