Annotation of rpl/lapack/lapack/zunmrz.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZUNMRZ
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZUNMRZ + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunmrz.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunmrz.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunmrz.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
! 22: * WORK, LWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER SIDE, TRANS
! 26: * INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZUNMRZ overwrites the general complex M-by-N matrix C with
! 39: *>
! 40: *> SIDE = 'L' SIDE = 'R'
! 41: *> TRANS = 'N': Q * C C * Q
! 42: *> TRANS = 'C': Q**H * C C * Q**H
! 43: *>
! 44: *> where Q is a complex unitary matrix defined as the product of k
! 45: *> elementary reflectors
! 46: *>
! 47: *> Q = H(1) H(2) . . . H(k)
! 48: *>
! 49: *> as returned by ZTZRZF. Q is of order M if SIDE = 'L' and of order N
! 50: *> if SIDE = 'R'.
! 51: *> \endverbatim
! 52: *
! 53: * Arguments:
! 54: * ==========
! 55: *
! 56: *> \param[in] SIDE
! 57: *> \verbatim
! 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.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] TRANS
! 64: *> \verbatim
! 65: *> TRANS is CHARACTER*1
! 66: *> = 'N': No transpose, apply Q;
! 67: *> = 'C': Conjugate transpose, apply Q**H.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] M
! 71: *> \verbatim
! 72: *> M is INTEGER
! 73: *> The number of rows of the matrix C. M >= 0.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] N
! 77: *> \verbatim
! 78: *> N is INTEGER
! 79: *> The number of columns of the matrix C. N >= 0.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] K
! 83: *> \verbatim
! 84: *> K is INTEGER
! 85: *> The number of elementary reflectors whose product defines
! 86: *> the matrix Q.
! 87: *> If SIDE = 'L', M >= K >= 0;
! 88: *> if SIDE = 'R', N >= K >= 0.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[in] L
! 92: *> \verbatim
! 93: *> L is INTEGER
! 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.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] A
! 100: *> \verbatim
! 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.
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[in] LDA
! 111: *> \verbatim
! 112: *> LDA is INTEGER
! 113: *> The leading dimension of the array A. LDA >= max(1,K).
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[in] TAU
! 117: *> \verbatim
! 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.
! 121: *> \endverbatim
! 122: *>
! 123: *> \param[in,out] C
! 124: *> \verbatim
! 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.
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[in] LDC
! 131: *> \verbatim
! 132: *> LDC is INTEGER
! 133: *> The leading dimension of the array C. LDC >= max(1,M).
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[out] WORK
! 137: *> \verbatim
! 138: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 139: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 140: *> \endverbatim
! 141: *>
! 142: *> \param[in] LWORK
! 143: *> \verbatim
! 144: *> LWORK is INTEGER
! 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 optimum performance LWORK >= N*NB if SIDE = 'L', and
! 149: *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
! 150: *> blocksize.
! 151: *>
! 152: *> If LWORK = -1, then a workspace query is assumed; the routine
! 153: *> only calculates the optimal size of the WORK array, returns
! 154: *> this value as the first entry of the WORK array, and no error
! 155: *> message related to LWORK is issued by XERBLA.
! 156: *> \endverbatim
! 157: *>
! 158: *> \param[out] INFO
! 159: *> \verbatim
! 160: *> INFO is INTEGER
! 161: *> = 0: successful exit
! 162: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 163: *> \endverbatim
! 164: *
! 165: * Authors:
! 166: * ========
! 167: *
! 168: *> \author Univ. of Tennessee
! 169: *> \author Univ. of California Berkeley
! 170: *> \author Univ. of Colorado Denver
! 171: *> \author NAG Ltd.
! 172: *
! 173: *> \date November 2011
! 174: *
! 175: *> \ingroup complex16OTHERcomputational
! 176: *
! 177: *> \par Contributors:
! 178: * ==================
! 179: *>
! 180: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 181: *
! 182: *> \par Further Details:
! 183: * =====================
! 184: *>
! 185: *> \verbatim
! 186: *> \endverbatim
! 187: *>
! 188: * =====================================================================
1.1 bertrand 189: SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
190: $ WORK, LWORK, INFO )
191: *
1.9 ! bertrand 192: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 193: * -- LAPACK is a software package provided by Univ. of Tennessee, --
194: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 195: * November 2011
1.1 bertrand 196: *
197: * .. Scalar Arguments ..
198: CHARACTER SIDE, TRANS
199: INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
200: * ..
201: * .. Array Arguments ..
202: COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
203: * ..
204: *
205: * =====================================================================
206: *
207: * .. Parameters ..
208: INTEGER NBMAX, LDT
209: PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
210: * ..
211: * .. Local Scalars ..
212: LOGICAL LEFT, LQUERY, NOTRAN
213: CHARACTER TRANST
214: INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC,
215: $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW
216: * ..
217: * .. Local Arrays ..
218: COMPLEX*16 T( LDT, NBMAX )
219: * ..
220: * .. External Functions ..
221: LOGICAL LSAME
222: INTEGER ILAENV
223: EXTERNAL LSAME, ILAENV
224: * ..
225: * .. External Subroutines ..
226: EXTERNAL XERBLA, ZLARZB, ZLARZT, ZUNMR3
227: * ..
228: * .. Intrinsic Functions ..
229: INTRINSIC MAX, MIN
230: * ..
231: * .. Executable Statements ..
232: *
233: * Test the input arguments
234: *
235: INFO = 0
236: LEFT = LSAME( SIDE, 'L' )
237: NOTRAN = LSAME( TRANS, 'N' )
238: LQUERY = ( LWORK.EQ.-1 )
239: *
240: * NQ is the order of Q and NW is the minimum dimension of WORK
241: *
242: IF( LEFT ) THEN
243: NQ = M
244: NW = MAX( 1, N )
245: ELSE
246: NQ = N
247: NW = MAX( 1, M )
248: END IF
249: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
250: INFO = -1
251: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
252: INFO = -2
253: ELSE IF( M.LT.0 ) THEN
254: INFO = -3
255: ELSE IF( N.LT.0 ) THEN
256: INFO = -4
257: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
258: INFO = -5
259: ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR.
260: $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN
261: INFO = -6
262: ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
263: INFO = -8
264: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
265: INFO = -11
266: END IF
267: *
268: IF( INFO.EQ.0 ) THEN
269: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
270: LWKOPT = 1
271: ELSE
272: *
273: * Determine the block size. NB may be at most NBMAX, where
274: * NBMAX is used to define the local array T.
275: *
276: NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N,
277: $ K, -1 ) )
278: LWKOPT = NW*NB
279: END IF
280: WORK( 1 ) = LWKOPT
281: *
282: IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
283: INFO = -13
284: END IF
285: END IF
286: *
287: IF( INFO.NE.0 ) THEN
288: CALL XERBLA( 'ZUNMRZ', -INFO )
289: RETURN
290: ELSE IF( LQUERY ) THEN
291: RETURN
292: END IF
293: *
294: * Quick return if possible
295: *
296: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
297: RETURN
298: END IF
299: *
300: * Determine the block size. NB may be at most NBMAX, where NBMAX
301: * is used to define the local array T.
302: *
303: NB = MIN( NBMAX, ILAENV( 1, 'ZUNMRQ', SIDE // TRANS, M, N, K,
304: $ -1 ) )
305: NBMIN = 2
306: LDWORK = NW
307: IF( NB.GT.1 .AND. NB.LT.K ) THEN
308: IWS = NW*NB
309: IF( LWORK.LT.IWS ) THEN
310: NB = LWORK / LDWORK
311: NBMIN = MAX( 2, ILAENV( 2, 'ZUNMRQ', SIDE // TRANS, M, N, K,
312: $ -1 ) )
313: END IF
314: ELSE
315: IWS = NW
316: END IF
317: *
318: IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
319: *
320: * Use unblocked code
321: *
322: CALL ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
323: $ WORK, IINFO )
324: ELSE
325: *
326: * Use blocked code
327: *
328: IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
329: $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
330: I1 = 1
331: I2 = K
332: I3 = NB
333: ELSE
334: I1 = ( ( K-1 ) / NB )*NB + 1
335: I2 = 1
336: I3 = -NB
337: END IF
338: *
339: IF( LEFT ) THEN
340: NI = N
341: JC = 1
342: JA = M - L + 1
343: ELSE
344: MI = M
345: IC = 1
346: JA = N - L + 1
347: END IF
348: *
349: IF( NOTRAN ) THEN
350: TRANST = 'C'
351: ELSE
352: TRANST = 'N'
353: END IF
354: *
355: DO 10 I = I1, I2, I3
356: IB = MIN( NB, K-I+1 )
357: *
358: * Form the triangular factor of the block reflector
359: * H = H(i+ib-1) . . . H(i+1) H(i)
360: *
361: CALL ZLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA,
362: $ TAU( I ), T, LDT )
363: *
364: IF( LEFT ) THEN
365: *
1.8 bertrand 366: * H or H**H is applied to C(i:m,1:n)
1.1 bertrand 367: *
368: MI = M - I + 1
369: IC = I
370: ELSE
371: *
1.8 bertrand 372: * H or H**H is applied to C(1:m,i:n)
1.1 bertrand 373: *
374: NI = N - I + 1
375: JC = I
376: END IF
377: *
1.8 bertrand 378: * Apply H or H**H
1.1 bertrand 379: *
380: CALL ZLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
381: $ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
382: $ LDC, WORK, LDWORK )
383: 10 CONTINUE
384: *
385: END IF
386: *
387: WORK( 1 ) = LWKOPT
388: *
389: RETURN
390: *
391: * End of ZUNMRZ
392: *
393: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zunmrz.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack