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21 * SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS
26 * INTEGER INFO, K, LDA, LDC, LWORK, M, N
28 * .. Array Arguments ..
29 * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
38 *> ZUNMQR overwrites the general complex M-by-N matrix C with
40 *> SIDE = 'L' SIDE = 'R'
41 *> TRANS = 'N': Q * C C * Q
42 *> TRANS = 'C': Q**H * C C * Q**H
44 *> where Q is a complex unitary matrix defined as the product of k
45 *> elementary reflectors
47 *> Q = H(1) H(2) . . . H(k)
49 *> as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N
58 *> SIDE is CHARACTER*1
59 *> = 'L': apply Q or Q**H from the Left;
60 *> = 'R': apply Q or Q**H from the Right.
65 *> TRANS is CHARACTER*1
66 *> = 'N': No transpose, apply Q;
67 *> = 'C': Conjugate transpose, apply Q**H.
73 *> The number of rows of the matrix C. M >= 0.
79 *> The number of columns of the matrix C. N >= 0.
85 *> The number of elementary reflectors whose product defines
87 *> If SIDE = 'L', M >= K >= 0;
88 *> if SIDE = 'R', N >= K >= 0.
93 *> A is COMPLEX*16 array, dimension (LDA,K)
94 *> The i-th column must contain the vector which defines the
95 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
96 *> ZGEQRF in the first k columns of its array argument A.
102 *> The leading dimension of the array A.
103 *> If SIDE = 'L', LDA >= max(1,M);
104 *> if SIDE = 'R', LDA >= max(1,N).
109 *> TAU is COMPLEX*16 array, dimension (K)
110 *> TAU(i) must contain the scalar factor of the elementary
111 *> reflector H(i), as returned by ZGEQRF.
116 *> C is COMPLEX*16 array, dimension (LDC,N)
117 *> On entry, the M-by-N matrix C.
118 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
124 *> The leading dimension of the array C. LDC >= max(1,M).
129 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
130 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
136 *> The dimension of the array WORK.
137 *> If SIDE = 'L', LWORK >= max(1,N);
138 *> if SIDE = 'R', LWORK >= max(1,M).
139 *> For good performance, LWORK should generally be larger.
141 *> If LWORK = -1, then a workspace query is assumed; the routine
142 *> only calculates the optimal size of the WORK array, returns
143 *> this value as the first entry of the WORK array, and no error
144 *> message related to LWORK is issued by XERBLA.
150 *> = 0: successful exit
151 *> < 0: if INFO = -i, the i-th argument had an illegal value
157 *> \author Univ. of Tennessee
158 *> \author Univ. of California Berkeley
159 *> \author Univ. of Colorado Denver
162 *> \date November 2015
164 *> \ingroup complex16OTHERcomputational
166 * =====================================================================
167 SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
168 $ WORK, LWORK, INFO )
170 * -- LAPACK computational routine (version 3.6.0) --
171 * -- LAPACK is a software package provided by Univ. of Tennessee, --
172 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 * .. Scalar Arguments ..
176 CHARACTER SIDE, TRANS
177 INTEGER INFO, K, LDA, LDC, LWORK, M, N
179 * .. Array Arguments ..
180 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
183 * =====================================================================
186 INTEGER NBMAX, LDT, TSIZE
187 PARAMETER ( NBMAX = 64, LDT = NBMAX+1,
188 $ TSIZE = LDT*NBMAX )
190 * .. Local Scalars ..
191 LOGICAL LEFT, LQUERY, NOTRAN
192 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
193 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW
195 * .. External Functions ..
198 EXTERNAL LSAME, ILAENV
200 * .. External Subroutines ..
201 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNM2R
203 * .. Intrinsic Functions ..
206 * .. Executable Statements ..
208 * Test the input arguments
211 LEFT = LSAME( SIDE, 'L' )
212 NOTRAN = LSAME( TRANS, 'N' )
213 LQUERY = ( LWORK.EQ.-1 )
215 * NQ is the order of Q and NW is the minimum dimension of WORK
224 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
226 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
228 ELSE IF( M.LT.0 ) THEN
230 ELSE IF( N.LT.0 ) THEN
232 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
234 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
236 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
238 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
244 * Compute the workspace requirements
246 NB = MIN( NBMAX, ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N, K,
248 LWKOPT = MAX( 1, NW )*NB + TSIZE
253 CALL XERBLA( 'ZUNMQR', -INFO )
255 ELSE IF( LQUERY ) THEN
259 * Quick return if possible
261 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
268 IF( NB.GT.1 .AND. NB.LT.K ) THEN
269 IF( LWORK.LT.NW*NB+TSIZE ) THEN
270 NB = (LWORK-TSIZE) / LDWORK
271 NBMIN = MAX( 2, ILAENV( 2, 'ZUNMQR', SIDE // TRANS, M, N, K,
276 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
280 CALL ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
287 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
288 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
293 I1 = ( ( K-1 ) / NB )*NB + 1
307 IB = MIN( NB, K-I+1 )
309 * Form the triangular factor of the block reflector
310 * H = H(i) H(i+1) . . . H(i+ib-1)
312 CALL ZLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ),
313 $ LDA, TAU( I ), WORK( IWT ), LDT )
316 * H or H**H is applied to C(i:m,1:n)
322 * H or H**H is applied to C(1:m,i:n)
330 CALL ZLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
331 $ IB, A( I, I ), LDA, WORK( IWT ), LDT,
332 $ C( IC, JC ), LDC, WORK, LDWORK )