stpqrt2.f(3)

NAME
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, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Function/Subroutine Documentation

  subroutine stpqrt2 (integerM, integerN, integerL, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( ldt, * )T, integerLDT, integerINFO)

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 "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 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.

Date:
    September 2012

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 174 of file stpqrt2.f.

Author

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