Computes a blocked QR factorization of a general real or complex matrix using the compact WY representation of Q.
The strictly lower triangular matrix
Vcontains the elementary reflectors
i) in the
ith column below the diagonal. For example, if
n=3, the matrix
represents one of the vectors that define
i). The vectors are returned in the lower triangular part of array
The 1s along the diagonal of
Vare not stored in
. The number of blocks is
, where each block is of order
nbexcept for the last block, which is of order
. For each of the
bblocks, a upper triangular block reflector factor is computed:
ibfor the last block)
ts are stored in the
- The number of rows in the matrixINTEGER.A(m≥ 0).
- The number of columns inINTEGER.A(n≥ 0).
- The block size to be used in the blocked QR (min(INTEGER.m,n) ≥nb≥ 1).
- REALforsgeqrtDOUBLE PRECISIONfordgeqrtCOMPLEXforcgeqrtCOMPLEX*16forzgeqrt.Arrays:aDIMENSION(lda,n) contains them-by-nmatrixA.workDIMENSION(nb,n) is a workspace array.