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

 subroutine sopgtr ( character UPLO, integer N, real, dimension( * ) AP, real, dimension( * ) TAU, real, dimension( ldq, * ) Q, integer LDQ, real, dimension( * ) WORK, integer INFO )

SOPGTR

Purpose:
``` SOPGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
SSPTRD using packed storage:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangular packed storage used in previous call to SSPTRD; = 'L': Lower triangular packed storage used in previous call to SSPTRD.``` [in] N ``` N is INTEGER The order of the matrix Q. N >= 0.``` [in] AP ``` AP is REAL array, dimension (N*(N+1)/2) The vectors which define the elementary reflectors, as returned by SSPTRD.``` [in] TAU ``` TAU is REAL array, dimension (N-1) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSPTRD.``` [out] Q ``` Q is REAL array, dimension (LDQ,N) The N-by-N orthogonal matrix Q.``` [in] LDQ ``` LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).``` [out] WORK ` WORK is REAL array, dimension (N-1)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 113 of file sopgtr.f.

114*
115* -- LAPACK computational routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 CHARACTER UPLO
121 INTEGER INFO, LDQ, N
122* ..
123* .. Array Arguments ..
124 REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
125* ..
126*
127* =====================================================================
128*
129* .. Parameters ..
130 REAL ZERO, ONE
131 parameter( zero = 0.0e+0, one = 1.0e+0 )
132* ..
133* .. Local Scalars ..
134 LOGICAL UPPER
135 INTEGER I, IINFO, IJ, J
136* ..
137* .. External Functions ..
138 LOGICAL LSAME
139 EXTERNAL lsame
140* ..
141* .. External Subroutines ..
142 EXTERNAL sorg2l, sorg2r, xerbla
143* ..
144* .. Intrinsic Functions ..
145 INTRINSIC max
146* ..
147* .. Executable Statements ..
148*
149* Test the input arguments
150*
151 info = 0
152 upper = lsame( uplo, 'U' )
153 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
154 info = -1
155 ELSE IF( n.LT.0 ) THEN
156 info = -2
157 ELSE IF( ldq.LT.max( 1, n ) ) THEN
158 info = -6
159 END IF
160 IF( info.NE.0 ) THEN
161 CALL xerbla( 'SOPGTR', -info )
162 RETURN
163 END IF
164*
165* Quick return if possible
166*
167 IF( n.EQ.0 )
168 \$ RETURN
169*
170 IF( upper ) THEN
171*
172* Q was determined by a call to SSPTRD with UPLO = 'U'
173*
174* Unpack the vectors which define the elementary reflectors and
175* set the last row and column of Q equal to those of the unit
176* matrix
177*
178 ij = 2
179 DO 20 j = 1, n - 1
180 DO 10 i = 1, j - 1
181 q( i, j ) = ap( ij )
182 ij = ij + 1
183 10 CONTINUE
184 ij = ij + 2
185 q( n, j ) = zero
186 20 CONTINUE
187 DO 30 i = 1, n - 1
188 q( i, n ) = zero
189 30 CONTINUE
190 q( n, n ) = one
191*
192* Generate Q(1:n-1,1:n-1)
193*
194 CALL sorg2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
195*
196 ELSE
197*
198* Q was determined by a call to SSPTRD with UPLO = 'L'.
199*
200* Unpack the vectors which define the elementary reflectors and
201* set the first row and column of Q equal to those of the unit
202* matrix
203*
204 q( 1, 1 ) = one
205 DO 40 i = 2, n
206 q( i, 1 ) = zero
207 40 CONTINUE
208 ij = 3
209 DO 60 j = 2, n
210 q( 1, j ) = zero
211 DO 50 i = j + 1, n
212 q( i, j ) = ap( ij )
213 ij = ij + 1
214 50 CONTINUE
215 ij = ij + 2
216 60 CONTINUE
217 IF( n.GT.1 ) THEN
218*
219* Generate Q(2:n,2:n)
220*
221 CALL sorg2r( n-1, n-1, n-1, q( 2, 2 ), ldq, tau, work,
222 \$ iinfo )
223 END IF
224 END IF
225 RETURN
226*
227* End of SOPGTR
228*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sorg2l(M, N, K, A, LDA, TAU, WORK, INFO)
SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf ...
Definition: sorg2l.f:114
subroutine sorg2r(M, N, K, A, LDA, TAU, WORK, INFO)
SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf ...
Definition: sorg2r.f:114
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