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.

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

          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

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Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 November 2019, Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley