139 SUBROUTINE sgerqf( M, N, A, LDA, TAU, WORK, LWORK, INFO )
147 INTEGER INFO, LDA, LWORK, M, N
150 REAL A( lda, * ), TAU( * ), WORK( * )
157 INTEGER I, IB, IINFO, IWS, K, KI, KK, LDWORK, LWKOPT,
158 $ mu, nb, nbmin, nu, nx
175 lquery = ( lwork.EQ.-1 )
178 ELSE IF( n.LT.0 )
THEN
180 ELSE IF( lda.LT.max( 1, m ) )
THEN
182 ELSE IF( lwork.LT.max( 1, m ) .AND. .NOT.lquery )
THEN
191 nb = ilaenv( 1,
'SGERQF',
' ', m, n, -1, -1 )
197 IF( lwork.LT.max( 1, m ) .AND. .NOT.lquery )
THEN
203 CALL xerbla(
'SGERQF', -info )
205 ELSE IF( lquery )
THEN
218 IF( nb.GT.1 .AND. nb.LT.k )
THEN
222 nx = max( 0, ilaenv( 3,
'SGERQF',
' ', m, n, -1, -1 ) )
229 IF( lwork.LT.iws )
THEN
235 nbmin = max( 2, ilaenv( 2,
'SGERQF',
' ', m, n, -1,
241 IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k )
THEN
246 ki = ( ( k-nx-1 ) / nb )*nb
249 DO 10 i = k - kk + ki + 1, k - kk + 1, -nb
250 ib = min( k-i+1, nb )
255 CALL sgerq2( ib, n-k+i+ib-1, a( m-k+i, 1 ), lda, tau( i ),
257 IF( m-k+i.GT.1 )
THEN
262 CALL slarft(
'Backward',
'Rowwise', n-k+i+ib-1, ib,
263 $ a( m-k+i, 1 ), lda, tau( i ), work, ldwork )
267 CALL slarfb(
'Right',
'No transpose',
'Backward',
268 $
'Rowwise', m-k+i-1, n-k+i+ib-1, ib,
269 $ a( m-k+i, 1 ), lda, work, ldwork, a, lda,
270 $ work( ib+1 ), ldwork )
273 mu = m - k + i + nb - 1
274 nu = n - k + i + nb - 1
282 IF( mu.GT.0 .AND. nu.GT.0 )
283 $
CALL sgerq2( mu, nu, a, lda, tau, work, iinfo )
subroutine xerbla(SRNAME, INFO)
XERBLA
subroutine slarft(DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
SLARFT forms the triangular factor T of a block reflector H = I - vtvH
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.
subroutine sgerq2(M, N, A, LDA, TAU, WORK, INFO)
SGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm...
subroutine sgerqf(M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGERQF