LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ dgelqt()

subroutine dgelqt ( integer  M,
integer  N,
integer  MB,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldt, * )  T,
integer  LDT,
double precision, dimension( * )  WORK,
integer  INFO 
)

DGELQT

Download DGELQT + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
 using the compact WY representation of Q.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]MB
          MB is INTEGER
          The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
          lower triangular if M <= N); the elements above the diagonal
          are the rows of V.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]T
          T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
          The upper triangular block reflectors stored in compact form
          as a sequence of upper triangular blocks.  See below
          for further details.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.  LDT >= MB.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MB*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.
Further Details:
  The matrix V stores the elementary reflectors H(i) in the i-th row
  above the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1  v1 v1 v1 v1 )
                   (     1  v2 v2 v2 )
                   (         1 v3 v3 )


  where the vi's represent the vectors which define H(i), which are returned
  in the matrix A.  The 1's along the diagonal of V are not stored in A.
  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
  block is of order MB except for the last block, which is of order
  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
  for the last block) T's are stored in the MB-by-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 138 of file dgelqt.f.

139 *
140 * -- LAPACK computational routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144 * .. Scalar Arguments ..
145  INTEGER INFO, LDA, LDT, M, N, MB
146 * ..
147 * .. Array Arguments ..
148  DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * ..
154 * .. Local Scalars ..
155  INTEGER I, IB, IINFO, K
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL dgelqt3, dlarfb, xerbla
159 * ..
160 * .. Executable Statements ..
161 *
162 * Test the input arguments
163 *
164  info = 0
165  IF( m.LT.0 ) THEN
166  info = -1
167  ELSE IF( n.LT.0 ) THEN
168  info = -2
169  ELSE IF( mb.LT.1 .OR. ( mb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
170  info = -3
171  ELSE IF( lda.LT.max( 1, m ) ) THEN
172  info = -5
173  ELSE IF( ldt.LT.mb ) THEN
174  info = -7
175  END IF
176  IF( info.NE.0 ) THEN
177  CALL xerbla( 'DGELQT', -info )
178  RETURN
179  END IF
180 *
181 * Quick return if possible
182 *
183  k = min( m, n )
184  IF( k.EQ.0 ) RETURN
185 *
186 * Blocked loop of length K
187 *
188  DO i = 1, k, mb
189  ib = min( k-i+1, mb )
190 *
191 * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
192 *
193  CALL dgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
194  IF( i+ib.LE.m ) THEN
195 *
196 * Update by applying H**T to A(I:M,I+IB:N) from the right
197 *
198  CALL dlarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
199  $ a( i, i ), lda, t( 1, i ), ldt,
200  $ a( i+ib, i ), lda, work , m-i-ib+1 )
201  END IF
202  END DO
203  RETURN
204 *
205 * End of DGELQT
206 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
recursive subroutine dgelqt3(M, N, A, LDA, T, LDT, INFO)
DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact...
Definition: dgelqt3.f:131
subroutine dlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: dlarfb.f:197
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