 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dgelqt()

 subroutine dgelqt ( integer M, integer N, integer MB, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldt, * ) T, integer LDT, double precision, dimension( * ) WORK, integer INFO )

DGELQT

Purpose:
``` DGELQT computes a blocked LQ factorization of a real 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 138 of file dgelqt.f.

139 *
140 * -- LAPACK computational routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144 * .. Scalar Arguments ..
145  INTEGER INFO, LDA, LDT, M, N, MB
146 * ..
147 * .. Array Arguments ..
148  DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * ..
154 * .. Local Scalars ..
155  INTEGER I, IB, IINFO, K
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL dgelqt3, dlarfb, xerbla
159 * ..
160 * .. Executable Statements ..
161 *
162 * Test the input arguments
163 *
164  info = 0
165  IF( m.LT.0 ) THEN
166  info = -1
167  ELSE IF( n.LT.0 ) THEN
168  info = -2
169  ELSE IF( mb.LT.1 .OR. ( mb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
170  info = -3
171  ELSE IF( lda.LT.max( 1, m ) ) THEN
172  info = -5
173  ELSE IF( ldt.LT.mb ) THEN
174  info = -7
175  END IF
176  IF( info.NE.0 ) THEN
177  CALL xerbla( 'DGELQT', -info )
178  RETURN
179  END IF
180 *
181 * Quick return if possible
182 *
183  k = min( m, n )
184  IF( k.EQ.0 ) RETURN
185 *
186 * Blocked loop of length K
187 *
188  DO i = 1, k, mb
189  ib = min( k-i+1, mb )
190 *
191 * Compute the LQ factorization of the current block A(I:M,I:I+IB-1)
192 *
193  CALL dgelqt3( ib, n-i+1, a(i,i), lda, t(1,i), ldt, iinfo )
194  IF( i+ib.LE.m ) THEN
195 *
196 * Update by applying H**T to A(I:M,I+IB:N) from the right
197 *
198  CALL dlarfb( 'R', 'N', 'F', 'R', m-i-ib+1, n-i+1, ib,
199  \$ a( i, i ), lda, t( 1, i ), ldt,
200  \$ a( i+ib, i ), lda, work , m-i-ib+1 )
201  END IF
202  END DO
203  RETURN
204 *
205 * End of DGELQT
206 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
recursive subroutine dgelqt3(M, N, A, LDA, T, LDT, INFO)
DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact...
Definition: dgelqt3.f:131
subroutine dlarfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition: dlarfb.f:197
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