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21 * SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
23 * .. Scalar Arguments ..
25 * INTEGER INFO, K, LDA, LWORK, M, N
27 * .. Array Arguments ..
28 * REAL A( LDA, * ), TAU( * ), WORK( * )
37 *> SORGBR generates one of the real orthogonal matrices Q or P**T
38 *> determined by SGEBRD when reducing a real matrix A to bidiagonal
39 *> form: A = Q * B * P**T. Q and P**T are defined as products of
40 *> elementary reflectors H(i) or G(i) respectively.
42 *> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
44 *> if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
45 *> columns of Q, where m >= n >= k;
46 *> if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an
49 *> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
51 *> if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m
52 *> rows of P**T, where n >= m >= k;
53 *> if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as
62 *> VECT is CHARACTER*1
63 *> Specifies whether the matrix Q or the matrix P**T is
64 *> required, as defined in the transformation applied by SGEBRD:
66 *> = 'P': generate P**T.
72 *> The number of rows of the matrix Q or P**T to be returned.
79 *> The number of columns of the matrix Q or P**T to be returned.
81 *> If VECT = 'Q', M >= N >= min(M,K);
82 *> if VECT = 'P', N >= M >= min(N,K).
88 *> If VECT = 'Q', the number of columns in the original M-by-K
89 *> matrix reduced by SGEBRD.
90 *> If VECT = 'P', the number of rows in the original K-by-N
91 *> matrix reduced by SGEBRD.
97 *> A is REAL array, dimension (LDA,N)
98 *> On entry, the vectors which define the elementary reflectors,
99 *> as returned by SGEBRD.
100 *> On exit, the M-by-N matrix Q or P**T.
106 *> The leading dimension of the array A. LDA >= max(1,M).
111 *> TAU is REAL array, dimension
112 *> (min(M,K)) if VECT = 'Q'
113 *> (min(N,K)) if VECT = 'P'
114 *> TAU(i) must contain the scalar factor of the elementary
115 *> reflector H(i) or G(i), which determines Q or P**T, as
116 *> returned by SGEBRD in its array argument TAUQ or TAUP.
121 *> WORK is REAL array, dimension (MAX(1,LWORK))
122 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
128 *> The dimension of the array WORK. LWORK >= max(1,min(M,N)).
129 *> For optimum performance LWORK >= min(M,N)*NB, where NB
130 *> is the optimal blocksize.
132 *> If LWORK = -1, then a workspace query is assumed; the routine
133 *> only calculates the optimal size of the WORK array, returns
134 *> this value as the first entry of the WORK array, and no error
135 *> message related to LWORK is issued by XERBLA.
141 *> = 0: successful exit
142 *> < 0: if INFO = -i, the i-th argument had an illegal value
148 *> \author Univ. of Tennessee
149 *> \author Univ. of California Berkeley
150 *> \author Univ. of Colorado Denver
155 *> \ingroup realGBcomputational
157 * =====================================================================
158 SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
160 * -- LAPACK computational routine (version 3.4.1) --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 * .. Scalar Arguments ..
167 INTEGER INFO, K, LDA, LWORK, M, N
169 * .. Array Arguments ..
170 REAL A( LDA, * ), TAU( * ), WORK( * )
173 * =====================================================================
177 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
179 * .. Local Scalars ..
180 LOGICAL LQUERY, WANTQ
181 INTEGER I, IINFO, J, LWKOPT, MN
183 * .. External Functions ..
186 EXTERNAL ILAENV, LSAME
188 * .. External Subroutines ..
189 EXTERNAL SORGLQ, SORGQR, XERBLA
191 * .. Intrinsic Functions ..
194 * .. Executable Statements ..
196 * Test the input arguments
199 WANTQ = LSAME( VECT, 'Q' )
201 LQUERY = ( LWORK.EQ.-1 )
202 IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
204 ELSE IF( M.LT.0 ) THEN
206 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
207 $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
208 $ MIN( N, K ) ) ) ) THEN
210 ELSE IF( K.LT.0 ) THEN
212 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
214 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
222 CALL SORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
225 CALL SORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
231 CALL SORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
234 CALL SORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
240 LWKOPT = MAX (LWKOPT, MN)
244 CALL XERBLA( 'SORGBR', -INFO )
246 ELSE IF( LQUERY ) THEN
251 * Quick return if possible
253 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
260 * Form Q, determined by a call to SGEBRD to reduce an m-by-k
265 * If m >= k, assume m >= n >= k
267 CALL SORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
271 * If m < k, assume m = n
273 * Shift the vectors which define the elementary reflectors one
274 * column to the right, and set the first row and column of Q
275 * to those of the unit matrix
280 A( I, J ) = A( I, J-1 )
291 CALL SORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
297 * Form P**T, determined by a call to SGEBRD to reduce a k-by-n
302 * If k < n, assume k <= m <= n
304 CALL SORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
308 * If k >= n, assume m = n
310 * Shift the vectors which define the elementary reflectors one
311 * row downward, and set the first row and column of P**T to
312 * those of the unit matrix
319 DO 50 I = J - 1, 2, -1
320 A( I, J ) = A( I-1, J )
328 CALL SORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,