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

Definition at line 174 of file cungtsqr.f.

  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

Definition at line 174 of file dorgtsqr.f.

  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

Definition at line 174 of file sorgtsqr.f.

  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

Definition at line 174 of file zungtsqr.f.

Author

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