sgeqrt.f (3) - Linux Manuals


sgeqrt.f -



subroutine sgeqrt (M, N, NB, A, LDA, T, LDT, WORK, INFO)

Function/Subroutine Documentation

subroutine sgeqrt (integerM, integerN, integerNB, real, dimension( lda, * )A, integerLDA, real, dimension( ldt, * )T, integerLDT, real, dimension( * )WORK, integerINFO)



 SGEQRT computes a blocked QR 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.


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


          A is REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
          upper triangular if M >= N); the elements below the diagonal
          are the columns 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 >= NB.


          WORK is REAL array, dimension (NB*N)


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



Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


November 2011

Further Details:

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

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 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/NB), where each
  block is of order NB except for the last block, which is of order 
  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB 
  for the last block) T's are stored in the NB-by-N matrix T as

               T = (T1 T2 ... TB).


Definition at line 142 of file sgeqrt.f.


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