LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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ctpqrt2.f File Reference

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Functions/Subroutines

subroutine ctpqrt2 (M, N, L, A, LDA, B, LDB, T, LDT, INFO)
 CTPQRT2 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 ctpqrt2 ( integer  M,
integer  N,
integer  L,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( ldt, * )  T,
integer  LDT,
integer  INFO 
)

CTPQRT2 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.

Download CTPQRT2 + dependencies [TGZ] [ZIP] [TXT]
Purpose:
 CTPQRT2 computes a QR factorization of a complex "triangular-pentagonal"
 matrix C, which is composed of a triangular block A and pentagonal block B, 
 using the compact WY representation for Q.
Parameters:
[in]M
          M is INTEGER
          The total number of rows of the matrix B.  
          M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix B, and the order of
          the triangular matrix A.
          N >= 0.
[in]L
          L is INTEGER
          The number of rows of the upper trapezoidal part of B.  
          MIN(M,N) >= L >= 0.  See Further Details.
[in,out]A
          A is COMPLEX 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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]B
          B is COMPLEX 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.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,M).
[out]T
          T is COMPLEX array, dimension (LDT,N)
          The N-by-N upper triangular factor T of the block reflector.
          See Further Details.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= max(1,N)
[out]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 ctpqrt2.f.

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