sgelqt.f - Man Page



subroutine sgelqt (M, N, MB, A, LDA, T, LDT, WORK, INFO)

Function/Subroutine Documentation

subroutine sgelqt (integer M, integer N, integer MB, real, dimension( lda, * ) A, integer LDA, real, dimension( ldt, * ) T, integer LDT, real, dimension( * ) WORK, integer INFO)


DGELQT computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q.  



          M is INTEGER
          The number of rows of the matrix A.  M >= 0.


          N is INTEGER
          The number of columns of the matrix A.  N >= 0.


          MB is INTEGER
          The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.


          A is REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
          lower triangular if M <= N); the elements above the diagonal
          are the rows of V.


          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).


          T is REAL array, dimension (LDT,MIN(M,N))
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See below
          for further details.


          LDT is INTEGER
          The leading dimension of the array T.  LDT >= MB.


          WORK is REAL array, dimension (MB*N)


          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

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November 2017

Further Details:

The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is

V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each block is of order MB except for the last block, which is of order IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB for the last block) T's are stored in the MB-by-K matrix T as

T = (T1 T2 ... TB).  

Definition at line 124 of file sgelqt.f.


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Referenced By

The man page sgelqt(3) is an alias of sgelqt.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK