LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ dorgtsqr()

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

Download DORGTSQR + dependencies [TGZ] [ZIP] [TXT]

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
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A. M >= N >= 0.
[in]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).
[in]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).
[in,out]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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in]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).
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.
          LDT >= max(1,min(NB1,N)).
[out]WORK
          (workspace) DOUBLE PRECISION array, dimension (MAX(2,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]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.
[out]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