ungtsqr(3)

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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