LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgeqrt()

subroutine sgeqrt ( integer  M,
integer  N,
integer  NB,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldt, * )  T,
integer  LDT,
real, dimension( * )  WORK,
integer  INFO 
)

SGEQRT

Download SGEQRT + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SGEQRT computes a blocked QR 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]NB
          NB is INTEGER
          The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 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 above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
          upper triangular if M >= N); the elements below the diagonal
          are the columns 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 >= NB.
[out]WORK
          WORK is REAL array, dimension (NB*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 column
  below the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 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/NB), where each
  block is of order NB except for the last block, which is of order
  IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
  reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
  for the last block) T's are stored in the NB-by-K matrix T as

               T = (T1 T2 ... TB).

Definition at line 140 of file sgeqrt.f.

141 *
142 * -- LAPACK computational routine --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 *
146 * .. Scalar Arguments ..
147  INTEGER INFO, LDA, LDT, M, N, NB
148 * ..
149 * .. Array Arguments ..
150  REAL A( LDA, * ), T( LDT, * ), WORK( * )
151 * ..
152 *
153 * =====================================================================
154 *
155 * ..
156 * .. Local Scalars ..
157  INTEGER I, IB, IINFO, K
158  LOGICAL USE_RECURSIVE_QR
159  parameter( use_recursive_qr=.true. )
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL sgeqrt2, sgeqrt3, slarfb, xerbla
163 * ..
164 * .. Executable Statements ..
165 *
166 * Test the input arguments
167 *
168  info = 0
169  IF( m.LT.0 ) THEN
170  info = -1
171  ELSE IF( n.LT.0 ) THEN
172  info = -2
173  ELSE IF( nb.LT.1 .OR. ( nb.GT.min(m,n) .AND. min(m,n).GT.0 ) )THEN
174  info = -3
175  ELSE IF( lda.LT.max( 1, m ) ) THEN
176  info = -5
177  ELSE IF( ldt.LT.nb ) THEN
178  info = -7
179  END IF
180  IF( info.NE.0 ) THEN
181  CALL xerbla( 'SGEQRT', -info )
182  RETURN
183  END IF
184 *
185 * Quick return if possible
186 *
187  k = min( m, n )
188  IF( k.EQ.0 ) RETURN
189 *
190 * Blocked loop of length K
191 *
192  DO i = 1, k, nb
193  ib = min( k-i+1, nb )
194 *
195 * Compute the QR factorization of the current block A(I:M,I:I+IB-1)
196 *
197  IF( use_recursive_qr ) THEN
198  CALL sgeqrt3( m-i+1, ib, a(i,i), lda, t(1,i), ldt, iinfo )
199  ELSE
200  CALL sgeqrt2( m-i+1, ib, a(i,i), lda, t(1,i), ldt, iinfo )
201  END IF
202  IF( i+ib.LE.n ) THEN
203 *
204 * Update by applying H**T to A(I:M,I+IB:N) from the left
205 *
206  CALL slarfb( 'L', 'T', 'F', 'C', m-i+1, n-i-ib+1, ib,
207  $ a( i, i ), lda, t( 1, i ), ldt,
208  $ a( i, i+ib ), lda, work , n-i-ib+1 )
209  END IF
210  END DO
211  RETURN
212 *
213 * End of SGEQRT
214 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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 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
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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