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21 * SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS
26 * INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
28 * .. Array Arguments ..
29 * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
38 *> ZUNMRZ 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 ZTZRZF. 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.
94 *> The number of columns of the matrix A containing
95 *> the meaningful part of the Householder reflectors.
96 *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
101 *> A is COMPLEX*16 array, dimension
102 *> (LDA,M) if SIDE = 'L',
103 *> (LDA,N) if SIDE = 'R'
104 *> The i-th row must contain the vector which defines the
105 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
106 *> ZTZRZF in the last k rows of its array argument A.
107 *> A is modified by the routine but restored on exit.
113 *> The leading dimension of the array A. LDA >= max(1,K).
118 *> TAU is COMPLEX*16 array, dimension (K)
119 *> TAU(i) must contain the scalar factor of the elementary
120 *> reflector H(i), as returned by ZTZRZF.
125 *> C is COMPLEX*16 array, dimension (LDC,N)
126 *> On entry, the M-by-N matrix C.
127 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
133 *> The leading dimension of the array C. LDC >= max(1,M).
138 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
139 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
145 *> The dimension of the array WORK.
146 *> If SIDE = 'L', LWORK >= max(1,N);
147 *> if SIDE = 'R', LWORK >= max(1,M).
148 *> For good performance, LWORK should generally be larger.
150 *> If LWORK = -1, then a workspace query is assumed; the routine
151 *> only calculates the optimal size of the WORK array, returns
152 *> this value as the first entry of the WORK array, and no error
153 *> message related to LWORK is issued by XERBLA.
159 *> = 0: successful exit
160 *> < 0: if INFO = -i, the i-th argument had an illegal value
166 *> \author Univ. of Tennessee
167 *> \author Univ. of California Berkeley
168 *> \author Univ. of Colorado Denver
171 *> \date November 2015
173 *> \ingroup complex16OTHERcomputational
175 *> \par Contributors:
178 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
180 *> \par Further Details:
181 * =====================
186 * =====================================================================
187 SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
188 $ WORK, LWORK, INFO )
190 * -- LAPACK computational routine (version 3.6.0) --
191 * -- LAPACK is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195 * .. Scalar Arguments ..
196 CHARACTER SIDE, TRANS
197 INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
199 * .. Array Arguments ..
200 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
203 * =====================================================================
206 INTEGER NBMAX, LDT, TSIZE
207 PARAMETER ( NBMAX = 64, LDT = NBMAX+1,
208 $ TSIZE = LDT*NBMAX )
210 * .. Local Scalars ..
211 LOGICAL LEFT, LQUERY, NOTRAN
213 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JA, JC,
214 $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
216 * .. External Functions ..
219 EXTERNAL LSAME, ILAENV
221 * .. External Subroutines ..
222 EXTERNAL XERBLA, ZLARZB, ZLARZT, ZUNMR3
224 * .. Intrinsic Functions ..
227 * .. Executable Statements ..
229 * Test the input arguments
232 LEFT = LSAME( SIDE, 'L' )
233 NOTRAN = LSAME( TRANS, 'N' )
234 LQUERY = ( LWORK.EQ.-1 )
236 * NQ is the order of Q and NW is the minimum dimension of WORK
245 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
247 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
249 ELSE IF( M.LT.0 ) THEN
251 ELSE IF( N.LT.0 ) THEN
253 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
255 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
256 $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
258 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
260 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
262 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
268 * Compute the workspace requirements
270 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
273 NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N,
275 LWKOPT = NW*NB + TSIZE
281 CALL XERBLA( 'ZUNMRZ', -INFO )
283 ELSE IF( LQUERY ) THEN
287 * Quick return if possible
289 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
293 * Determine the block size. NB may be at most NBMAX, where NBMAX
294 * is used to define the local array T.
296 NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N, K,
300 IF( NB.GT.1 .AND. NB.LT.K ) THEN
301 IF( LWORK.LT.NW*NB+TSIZE ) THEN
302 NB = (LWORK-TSIZE) / LDWORK
303 NBMIN = MAX( 2, ILAENV( 2, 'ZUNMRQ', SIDE // TRANS, M, N, K,
308 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
312 CALL ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
319 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
320 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
325 I1 = ( ( K-1 ) / NB )*NB + 1
347 IB = MIN( NB, K-I+1 )
349 * Form the triangular factor of the block reflector
350 * H = H(i+ib-1) . . . H(i+1) H(i)
352 CALL ZLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
353 $ TAU( I ), WORK( IWT ), LDT )
357 * H or H**H is applied to C(i:m,1:n)
363 * H or H**H is applied to C(1:m,i:n)
371 CALL ZLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
372 $ IB, L, A( I, JA ), LDA, WORK( IWT ), LDT,
373 $ C( IC, JC ), LDC, WORK, LDWORK )