stpqrt.f man page

subroutine stpqrt (M, N, L, NB, A, LDA, B, LDB, T, LDT, WORK, INFO)
STPQRT

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.

Date:

December 2016

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 191 of file stpqrt.f.