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

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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```
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 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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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