LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sgelqt()

subroutine sgelqt ( integer  m,
integer  n,
integer  mb,
real, dimension( lda, * )  a,
integer  lda,
real, dimension( ldt, * )  t,
integer  ldt,
real, dimension( * )  work,
integer  info 
)

SGELQT

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 REAL 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 REAL 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 REAL 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.
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 sgelqt.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 REAL 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 sgeqrt2, sgeqrt3, sgelqt3, slarfb, 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( 'SGELQT', -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 sgelqt3( 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 slarfb( '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 SGELQT
191*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
recursive subroutine sgelqt3(m, n, a, lda, t, ldt, info)
SGELQT3
Definition sgelqt3.f:116
subroutine sgeqrt2(m, n, a, lda, t, ldt, info)
SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY represen...
Definition sgeqrt2.f:127
recursive subroutine sgeqrt3(m, n, a, lda, t, ldt, info)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact...
Definition sgeqrt3.f:132
subroutine slarfb(side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
SLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition slarfb.f:197
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