LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zgelqt()

subroutine zgelqt ( integer  M,
integer  N,
integer  MB,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldt, * )  T,
integer  LDT,
complex*16, dimension( * )  WORK,
integer  INFO 
)

ZGELQT

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

Purpose:
 ZGELQT computes a blocked LQ factorization of a complex 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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.
Date
June 2017
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 141 of file zgelqt.f.

141 *
142 * -- LAPACK computational routine (version 3.7.1) --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 * June 2017
146 *
147 * .. Scalar Arguments ..
148  INTEGER info, lda, ldt, m, n, mb
149 * ..
150 * .. Array Arguments ..
151  COMPLEX*16 a( lda, * ), t( ldt, * ), work( * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * ..
157 * .. Local Scalars ..
158  INTEGER i, ib, iinfo, k
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL zgelqt3, zlarfb, xerbla
162 * ..
163 * .. Executable Statements ..
164 *
165 * Test the input arguments
166 *
167  info = 0
168  IF( m.LT.0 ) THEN
169  info = -1
170  ELSE IF( n.LT.0 ) THEN
171  info = -2
172  ELSE IF( mb.LT.1 .OR. (mb.GT.min(m,n) .AND. min(m,n).GT.0 ))THEN
173  info = -3
174  ELSE IF( lda.LT.max( 1, m ) ) THEN
175  info = -5
176  ELSE IF( ldt.LT.mb ) THEN
177  info = -7
178  END IF
179  IF( info.NE.0 ) THEN
180  CALL xerbla( 'ZGELQT', -info )
181  RETURN
182  END IF
183 *
184 * Quick return if possible
185 *
186  k = min( m, n )
187  IF( k.EQ.0 ) RETURN
188 *
189 * Blocked loop of length K
190 *
191  DO i = 1, k, mb
192  ib = min( k-i+1, mb )
193 *
194 * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
195 *
196  CALL zgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
197  IF( i+ib.LE.m ) THEN
198 *
199 * Update by applying H**T to A(I:M,I+IB:N) from the right
200 *
201  CALL zlarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
202  $ a( i, i ), lda, t( 1, i ), ldt,
203  $ a( i+ib, i ), lda, work , m-i-ib+1 )
204  END IF
205  END DO
206  RETURN
207 *
208 * End of ZGELQT
209 *
recursive subroutine zgelqt3(M, N, A, LDA, T, LDT, INFO)
ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact...
Definition: zgelqt3.f:133
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix...
Definition: zlarfb.f:197
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