SGEQRT computes a blocked QR factorization of a real M-by-N matrix A


 using the compact WY representation of Q.  

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.  N >= 0.

NB

          NB is INTEGER


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

A

          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

          LDA is INTEGER


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

T

          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

          LDT is INTEGER


          The leading dimension of the array T.  LDT >= NB.

WORK

          WORK is REAL array, dimension (NB*N)

INFO

          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

  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).