SRC/stpqrt2.f(3)           Library Functions Manual           SRC/stpqrt2.f(3)

NAME
       SRC/stpqrt2.f

SYNOPSIS
   Functions/Subroutines
       subroutine stpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
           STPQRT2 computes a QR factorization of a real or complex
           triangular-pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.

Function/Subroutine Documentation
   subroutine stpqrt2 (integer m, integer n, integer l, real, dimension( lda,
       * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real,
       dimension( ldt, * ) t, integer ldt, integer info)
       STPQRT2 computes a QR factorization of a real or complex "triangular-
       pentagonal" matrix, which is composed of a triangular block and a
       pentagonal block, using the compact WY representation for Q.

       Purpose:


           !>
           !> STPQRT2 computes a QR factorization of a real
           !> 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 total 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.
           !>

           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 N-by-N upper triangular factor T of the block reflector.
           !>          See Further Details.
           !>

           LDT

           !>          LDT is INTEGER
           !>          The leading dimension of the array T.  LDT >= max(1,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 (M+N)-by-(M+N) block reflector H is then given by
           !>
           !>               H = I - W * T * W^H
           !>
           !>  where W^H is the conjugate transpose of W and T is the upper triangular
           !>  factor of the block reflector.
           !>

       Definition at line 172 of file stpqrt2.f.

Author
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LAPACK                          Version 3.12.0                SRC/stpqrt2.f(3)