LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zgeqrt()

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

ZGEQRT

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

Purpose:
 ZGEQRT computes a blocked QR 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]NB
          NB is INTEGER
          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 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 above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
          upper triangular if M >= N); the elements below the diagonal
          are the columns 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 >= NB.
[out]WORK
          WORK is COMPLEX*16 array, dimension (NB*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 column
  below the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 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/NB), where each
  block is of order NB except for the last block, which is of order
  IB = K - (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-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 143 of file zgeqrt.f.

143 *
144 * -- LAPACK computational routine (version 3.7.1) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * June 2017
148 *
149 * .. Scalar Arguments ..
150  INTEGER info, lda, ldt, m, n, nb
151 * ..
152 * .. Array Arguments ..
153  COMPLEX*16 a( lda, * ), t( ldt, * ), work( * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * ..
159 * .. Local Scalars ..
160  INTEGER i, ib, iinfo, k
161  LOGICAL use_recursive_qr
162  parameter( use_recursive_qr=.true. )
163 * ..
164 * .. External Subroutines ..
165  EXTERNAL zgeqrt2, zgeqrt3, zlarfb, xerbla
166 * ..
167 * .. Executable Statements ..
168 *
169 * Test the input arguments
170 *
171  info = 0
172  IF( m.LT.0 ) THEN
173  info = -1
174  ELSE IF( n.LT.0 ) THEN
175  info = -2
176  ELSE IF( nb.LT.1 .OR. ( nb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
177  info = -3
178  ELSE IF( lda.LT.max( 1, m ) ) THEN
179  info = -5
180  ELSE IF( ldt.LT.nb ) THEN
181  info = -7
182  END IF
183  IF( info.NE.0 ) THEN
184  CALL xerbla( 'ZGEQRT', -info )
185  RETURN
186  END IF
187 *
188 * Quick return if possible
189 *
190  k = min( m, n )
191  IF( k.EQ.0 ) RETURN
192 *
193 * Blocked loop of length K
194 *
195  DO i = 1, k, nb
196  ib = min( k-i+1, nb )
197 *
198 * Compute the QR factorization of the current block A(I:M,I:I+IB-1)
199 *
200  IF( use_recursive_qr ) THEN
201  CALL zgeqrt3( m-i+1, ib, a(i,i), lda, t(1,i), ldt, iinfo )
202  ELSE
203  CALL zgeqrt2( m-i+1, ib, a(i,i), lda, t(1,i), ldt, iinfo )
204  END IF
205  IF( i+ib.LE.n ) THEN
206 *
207 * Update by applying H**H to A(I:M,I+IB:N) from the left
208 *
209  CALL zlarfb( 'L', 'C', 'F', 'C', m-i+1, n-i-ib+1, ib,
210  $ a( i, i ), lda, t( 1, i ), ldt,
211  $ a( i, i+ib ), lda, work , n-i-ib+1 )
212  END IF
213  END DO
214  RETURN
215 *
216 * End of ZGEQRT
217 *
subroutine zgeqrt2(M, N, A, LDA, T, LDT, INFO)
ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY represen...
Definition: zgeqrt2.f:129
recursive subroutine zgeqrt3(M, N, A, LDA, T, LDT, INFO)
ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact...
Definition: zgeqrt3.f:134
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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