LAPACK  3.9.0 LAPACK: Linear Algebra PACKage

## ◆ 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```
Date
December 2016

Definition at line 116 of file sopgtr.f.

116 *
117 * -- LAPACK computational routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  CHARACTER UPLO
124  INTEGER INFO, LDQ, N
125 * ..
126 * .. Array Arguments ..
127  REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  REAL ZERO, ONE
134  parameter( zero = 0.0e+0, one = 1.0e+0 )
135 * ..
136 * .. Local Scalars ..
137  LOGICAL UPPER
138  INTEGER I, IINFO, IJ, J
139 * ..
140 * .. External Functions ..
141  LOGICAL LSAME
142  EXTERNAL lsame
143 * ..
144 * .. External Subroutines ..
145  EXTERNAL sorg2l, sorg2r, xerbla
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC max
149 * ..
150 * .. Executable Statements ..
151 *
152 * Test the input arguments
153 *
154  info = 0
155  upper = lsame( uplo, 'U' )
156  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
157  info = -1
158  ELSE IF( n.LT.0 ) THEN
159  info = -2
160  ELSE IF( ldq.LT.max( 1, n ) ) THEN
161  info = -6
162  END IF
163  IF( info.NE.0 ) THEN
164  CALL xerbla( 'SOPGTR', -info )
165  RETURN
166  END IF
167 *
168 * Quick return if possible
169 *
170  IF( n.EQ.0 )
171  \$ RETURN
172 *
173  IF( upper ) THEN
174 *
175 * Q was determined by a call to SSPTRD with UPLO = 'U'
176 *
177 * Unpack the vectors which define the elementary reflectors and
178 * set the last row and column of Q equal to those of the unit
179 * matrix
180 *
181  ij = 2
182  DO 20 j = 1, n - 1
183  DO 10 i = 1, j - 1
184  q( i, j ) = ap( ij )
185  ij = ij + 1
186  10 CONTINUE
187  ij = ij + 2
188  q( n, j ) = zero
189  20 CONTINUE
190  DO 30 i = 1, n - 1
191  q( i, n ) = zero
192  30 CONTINUE
193  q( n, n ) = one
194 *
195 * Generate Q(1:n-1,1:n-1)
196 *
197  CALL sorg2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
198 *
199  ELSE
200 *
201 * Q was determined by a call to SSPTRD with UPLO = 'L'.
202 *
203 * Unpack the vectors which define the elementary reflectors and
204 * set the first row and column of Q equal to those of the unit
205 * matrix
206 *
207  q( 1, 1 ) = one
208  DO 40 i = 2, n
209  q( i, 1 ) = zero
210  40 CONTINUE
211  ij = 3
212  DO 60 j = 2, n
213  q( 1, j ) = zero
214  DO 50 i = j + 1, n
215  q( i, j ) = ap( ij )
216  ij = ij + 1
217  50 CONTINUE
218  ij = ij + 2
219  60 CONTINUE
220  IF( n.GT.1 ) THEN
221 *
222 * Generate Q(2:n,2:n)
223 *
224  CALL sorg2r( n-1, n-1, n-1, q( 2, 2 ), ldq, tau, work,
225  \$ iinfo )
226  END IF
227  END IF
228  RETURN
229 *
230 * End of SOPGTR
231 *
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sorg2l
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:116
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
sorg2r
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:116