 LAPACK  3.10.0 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 )

CGELQT

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```
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 123 of file cgelqt.f.

124 *
125 * -- LAPACK computational routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  INTEGER INFO, LDA, LDT, M, N, MB
131 * ..
132 * .. Array Arguments ..
133  COMPLEX A( LDA, * ), T( LDT, * ), WORK( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * ..
139 * .. Local Scalars ..
140  INTEGER I, IB, IINFO, K
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL cgelqt3, clarfb, xerbla
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input arguments
148 *
149  info = 0
150  IF( m.LT.0 ) THEN
151  info = -1
152  ELSE IF( n.LT.0 ) THEN
153  info = -2
154  ELSE IF( mb.LT.1 .OR. (mb.GT.min(m,n) .AND. min(m,n).GT.0 ))THEN
155  info = -3
156  ELSE IF( lda.LT.max( 1, m ) ) THEN
157  info = -5
158  ELSE IF( ldt.LT.mb ) THEN
159  info = -7
160  END IF
161  IF( info.NE.0 ) THEN
162  CALL xerbla( 'CGELQT', -info )
163  RETURN
164  END IF
165 *
166 * Quick return if possible
167 *
168  k = min( m, n )
169  IF( k.EQ.0 ) RETURN
170 *
171 * Blocked loop of length K
172 *
173  DO i = 1, k, mb
174  ib = min( k-i+1, mb )
175 *
176 * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
177 *
178  CALL cgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
179  IF( i+ib.LE.m ) THEN
180 *
181 * Update by applying H**T to A(I:M,I+IB:N) from the right
182 *
183  CALL clarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
184  \$ a( i, i ), lda, t( 1, i ), ldt,
185  \$ a( i+ib, i ), lda, work , m-i-ib+1 )
186  END IF
187  END DO
188  RETURN
189 *
190 * End of CGELQT
191 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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
recursive subroutine cgelqt3(M, N, A, LDA, T, LDT, INFO)
CGELQT3
Definition: cgelqt3.f:116
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