SRC/stpqrt.f(3)            Library Functions Manual            SRC/stpqrt.f(3)

NAME
       SRC/stpqrt.f

SYNOPSIS
   Functions/Subroutines
       subroutine stpqrt (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
           STPQRT

Function/Subroutine Documentation
   subroutine stpqrt (integer m, integer n, integer l, integer nb, real,
       dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,
       integer ldb, real, dimension( ldt, * ) t, integer ldt, real, dimension(
       * ) work, integer info)
       STPQRT

       Purpose:


            STPQRT computes a blocked QR factorization of a real
            'triangular-pentagonal' matrix C, which is composed of a
            triangular block A and pentagonal block B, using the compact
            WY representation for Q.

       Parameters
           M

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

           N

                     N is INTEGER
                     The number of columns of the matrix B, and the order of the
                     triangular matrix A.
                     N >= 0.

           L

                     L is INTEGER
                     The number of rows of the upper trapezoidal part of B.
                     MIN(M,N) >= L >= 0.  See Further Details.

           NB

                     NB is INTEGER
                     The block size to be used in the blocked QR.  N >= NB >= 1.

           A

                     A is REAL array, dimension (LDA,N)
                     On entry, the upper triangular N-by-N matrix A.
                     On exit, the elements on and above the diagonal of the array
                     contain the upper triangular matrix R.

           LDA

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

           B

                     B is REAL array, dimension (LDB,N)
                     On entry, the pentagonal M-by-N matrix B.  The first M-L rows
                     are rectangular, and the last L rows are upper trapezoidal.
                     On exit, B contains the pentagonal matrix V.  See Further Details.

           LDB

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

           T

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

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:


             The input matrix C is a (N+M)-by-N matrix

                          C = [ A ]
                              [ B ]

             where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
             matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
             upper trapezoidal matrix B2:

                          B = [ B1 ]  <- (M-L)-by-N rectangular
                              [ B2 ]  <-     L-by-N upper trapezoidal.

             The upper trapezoidal matrix B2 consists of the first L rows of a
             N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
             B is rectangular M-by-N; if M=L=N, B is upper triangular.

             The matrix W stores the elementary reflectors H(i) in the i-th column
             below the diagonal (of A) in the (N+M)-by-N input matrix C

                          C = [ A ]  <- upper triangular N-by-N
                              [ B ]  <- M-by-N pentagonal

             so that W can be represented as

                          W = [ I ]  <- identity, N-by-N
                              [ V ]  <- M-by-N, same form as B.

             Thus, all of information needed for W is contained on exit in B, which
             we call V above.  Note that V has the same form as B; that is,

                          V = [ V1 ] <- (M-L)-by-N rectangular
                              [ V2 ] <-     L-by-N upper trapezoidal.

             The columns of V represent the vectors which define the H(i)'s.

             The number of blocks is B = ceiling(N/NB), where each
             block is of order NB except for the last block, which is of order
             IB = N - (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 187 of file stpqrt.f.

Author
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LAPACK                          Version 3.12.0                 SRC/stpqrt.f(3)