 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dorghr()

 subroutine dorghr ( integer N, integer ILO, integer IHI, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer LWORK, integer INFO )

DORGHR

Purpose:
``` DORGHR generates a real orthogonal matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
DGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).```
Parameters
 [in] N ``` N is INTEGER The order of the matrix Q. N >= 0.``` [in] ILO ` ILO is INTEGER` [in] IHI ``` IHI is INTEGER ILO and IHI must have the same values as in the previous call of DGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.``` [in,out] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the vectors which define the elementary reflectors, as returned by DGEHRD. On exit, the N-by-N orthogonal matrix Q.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEHRD.``` [out] WORK ``` WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.``` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK. LWORK >= IHI-ILO. For optimum performance LWORK >= (IHI-ILO)*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 125 of file dorghr.f.

126*
127* -- LAPACK computational routine --
128* -- LAPACK is a software package provided by Univ. of Tennessee, --
129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*
131* .. Scalar Arguments ..
132 INTEGER IHI, ILO, INFO, LDA, LWORK, N
133* ..
134* .. Array Arguments ..
135 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
136* ..
137*
138* =====================================================================
139*
140* .. Parameters ..
141 DOUBLE PRECISION ZERO, ONE
142 parameter( zero = 0.0d+0, one = 1.0d+0 )
143* ..
144* .. Local Scalars ..
145 LOGICAL LQUERY
146 INTEGER I, IINFO, J, LWKOPT, NB, NH
147* ..
148* .. External Subroutines ..
149 EXTERNAL dorgqr, xerbla
150* ..
151* .. External Functions ..
152 INTEGER ILAENV
153 EXTERNAL ilaenv
154* ..
155* .. Intrinsic Functions ..
156 INTRINSIC max, min
157* ..
158* .. Executable Statements ..
159*
160* Test the input arguments
161*
162 info = 0
163 nh = ihi - ilo
164 lquery = ( lwork.EQ.-1 )
165 IF( n.LT.0 ) THEN
166 info = -1
167 ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, n ) ) THEN
168 info = -2
169 ELSE IF( ihi.LT.min( ilo, n ) .OR. ihi.GT.n ) THEN
170 info = -3
171 ELSE IF( lda.LT.max( 1, n ) ) THEN
172 info = -5
173 ELSE IF( lwork.LT.max( 1, nh ) .AND. .NOT.lquery ) THEN
174 info = -8
175 END IF
176*
177 IF( info.EQ.0 ) THEN
178 nb = ilaenv( 1, 'DORGQR', ' ', nh, nh, nh, -1 )
179 lwkopt = max( 1, nh )*nb
180 work( 1 ) = lwkopt
181 END IF
182*
183 IF( info.NE.0 ) THEN
184 CALL xerbla( 'DORGHR', -info )
185 RETURN
186 ELSE IF( lquery ) THEN
187 RETURN
188 END IF
189*
190* Quick return if possible
191*
192 IF( n.EQ.0 ) THEN
193 work( 1 ) = 1
194 RETURN
195 END IF
196*
197* Shift the vectors which define the elementary reflectors one
198* column to the right, and set the first ilo and the last n-ihi
199* rows and columns to those of the unit matrix
200*
201 DO 40 j = ihi, ilo + 1, -1
202 DO 10 i = 1, j - 1
203 a( i, j ) = zero
204 10 CONTINUE
205 DO 20 i = j + 1, ihi
206 a( i, j ) = a( i, j-1 )
207 20 CONTINUE
208 DO 30 i = ihi + 1, n
209 a( i, j ) = zero
210 30 CONTINUE
211 40 CONTINUE
212 DO 60 j = 1, ilo
213 DO 50 i = 1, n
214 a( i, j ) = zero
215 50 CONTINUE
216 a( j, j ) = one
217 60 CONTINUE
218 DO 80 j = ihi + 1, n
219 DO 70 i = 1, n
220 a( i, j ) = zero
221 70 CONTINUE
222 a( j, j ) = one
223 80 CONTINUE
224*
225 IF( nh.GT.0 ) THEN
226*
227* Generate Q(ilo+1:ihi,ilo+1:ihi)
228*
229 CALL dorgqr( nh, nh, nh, a( ilo+1, ilo+1 ), lda, tau( ilo ),
230 \$ work, lwork, iinfo )
231 END IF
232 work( 1 ) = lwkopt
233 RETURN
234*
235* End of DORGHR
236*
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGQR
Definition: dorgqr.f:128
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