LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cgelqt()

subroutine cgelqt ( integer  M,
integer  N,
integer  MB,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldt, * )  T,
integer  LDT,
complex, dimension( * )  WORK,
integer  INFO 
)
Purpose:

CGELQT 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 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 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 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 125 of file cgelqt.f.

125 *
126 * -- LAPACK computational routine (version 3.7.1) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * June 2017
130 *
131 * .. Scalar Arguments ..
132  INTEGER info, lda, ldt, m, n, mb
133 * ..
134 * .. Array Arguments ..
135  COMPLEX a( lda, * ), t( ldt, * ), work( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * ..
141 * .. Local Scalars ..
142  INTEGER i, ib, iinfo, k
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL cgelqt3, clarfb, xerbla
146 * ..
147 * .. Executable Statements ..
148 *
149 * Test the input arguments
150 *
151  info = 0
152  IF( m.LT.0 ) THEN
153  info = -1
154  ELSE IF( n.LT.0 ) THEN
155  info = -2
156  ELSE IF( mb.LT.1 .OR. (mb.GT.min(m,n) .AND. min(m,n).GT.0 ))THEN
157  info = -3
158  ELSE IF( lda.LT.max( 1, m ) ) THEN
159  info = -5
160  ELSE IF( ldt.LT.mb ) THEN
161  info = -7
162  END IF
163  IF( info.NE.0 ) THEN
164  CALL xerbla( 'CGELQT', -info )
165  RETURN
166  END IF
167 *
168 * Quick return if possible
169 *
170  k = min( m, n )
171  IF( k.EQ.0 ) RETURN
172 *
173 * Blocked loop of length K
174 *
175  DO i = 1, k, mb
176  ib = min( k-i+1, mb )
177 *
178 * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
179 *
180  CALL cgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
181  IF( i+ib.LE.m ) THEN
182 *
183 * Update by applying H**T to A(I:M,I+IB:N) from the right
184 *
185  CALL clarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
186  $ a( i, i ), lda, t( 1, i ), ldt,
187  $ a( i+ib, i ), lda, work , m-i-ib+1 )
188  END IF
189  END DO
190  RETURN
191 *
192 * End of CGELQT
193 *
recursive subroutine cgelqt3(M, N, A, LDA, T, LDT, INFO)
Definition: cgelqt3.f:116
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine clarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix...
Definition: clarfb.f:197
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