Annotation of rpl/lapack/lapack/dormqr.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DORMQR
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DORMQR + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormqr.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormqr.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormqr.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
! 22: * WORK, LWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER SIDE, TRANS
! 26: * INTEGER INFO, K, LDA, LDC, LWORK, M, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DORMQR overwrites the general real M-by-N matrix C with
! 39: *>
! 40: *> SIDE = 'L' SIDE = 'R'
! 41: *> TRANS = 'N': Q * C C * Q
! 42: *> TRANS = 'T': Q**T * C C * Q**T
! 43: *>
! 44: *> where Q is a real orthogonal matrix defined as the product of k
! 45: *> elementary reflectors
! 46: *>
! 47: *> Q = H(1) H(2) . . . H(k)
! 48: *>
! 49: *> as returned by DGEQRF. 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**T from the Left;
! 60: *> = 'R': apply Q or Q**T from the Right.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] TRANS
! 64: *> \verbatim
! 65: *> TRANS is CHARACTER*1
! 66: *> = 'N': No transpose, apply Q;
! 67: *> = 'T': Transpose, apply Q**T.
! 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] A
! 92: *> \verbatim
! 93: *> A is DOUBLE PRECISION 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: *> DGEQRF in the first k columns of its array argument A.
! 97: *> A is modified by the routine but restored on exit.
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[in] LDA
! 101: *> \verbatim
! 102: *> LDA is INTEGER
! 103: *> The leading dimension of the array A.
! 104: *> If SIDE = 'L', LDA >= max(1,M);
! 105: *> if SIDE = 'R', LDA >= max(1,N).
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in] TAU
! 109: *> \verbatim
! 110: *> TAU is DOUBLE PRECISION array, dimension (K)
! 111: *> TAU(i) must contain the scalar factor of the elementary
! 112: *> reflector H(i), as returned by DGEQRF.
! 113: *> \endverbatim
! 114: *>
! 115: *> \param[in,out] C
! 116: *> \verbatim
! 117: *> C is DOUBLE PRECISION array, dimension (LDC,N)
! 118: *> On entry, the M-by-N matrix C.
! 119: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[in] LDC
! 123: *> \verbatim
! 124: *> LDC is INTEGER
! 125: *> The leading dimension of the array C. LDC >= max(1,M).
! 126: *> \endverbatim
! 127: *>
! 128: *> \param[out] WORK
! 129: *> \verbatim
! 130: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 131: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 132: *> \endverbatim
! 133: *>
! 134: *> \param[in] LWORK
! 135: *> \verbatim
! 136: *> LWORK is INTEGER
! 137: *> The dimension of the array WORK.
! 138: *> If SIDE = 'L', LWORK >= max(1,N);
! 139: *> if SIDE = 'R', LWORK >= max(1,M).
! 140: *> For optimum performance LWORK >= N*NB if SIDE = 'L', and
! 141: *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
! 142: *> blocksize.
! 143: *>
! 144: *> If LWORK = -1, then a workspace query is assumed; the routine
! 145: *> only calculates the optimal size of the WORK array, returns
! 146: *> this value as the first entry of the WORK array, and no error
! 147: *> message related to LWORK is issued by XERBLA.
! 148: *> \endverbatim
! 149: *>
! 150: *> \param[out] INFO
! 151: *> \verbatim
! 152: *> INFO is INTEGER
! 153: *> = 0: successful exit
! 154: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 155: *> \endverbatim
! 156: *
! 157: * Authors:
! 158: * ========
! 159: *
! 160: *> \author Univ. of Tennessee
! 161: *> \author Univ. of California Berkeley
! 162: *> \author Univ. of Colorado Denver
! 163: *> \author NAG Ltd.
! 164: *
! 165: *> \date November 2011
! 166: *
! 167: *> \ingroup doubleOTHERcomputational
! 168: *
! 169: * =====================================================================
1.1 bertrand 170: SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
171: $ WORK, LWORK, INFO )
172: *
1.9 ! bertrand 173: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 174: * -- LAPACK is a software package provided by Univ. of Tennessee, --
175: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 176: * November 2011
1.1 bertrand 177: *
178: * .. Scalar Arguments ..
179: CHARACTER SIDE, TRANS
180: INTEGER INFO, K, LDA, LDC, LWORK, M, N
181: * ..
182: * .. Array Arguments ..
183: DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
184: * ..
185: *
186: * =====================================================================
187: *
188: * .. Parameters ..
189: INTEGER NBMAX, LDT
190: PARAMETER ( NBMAX = 64, LDT = NBMAX+1 )
191: * ..
192: * .. Local Scalars ..
193: LOGICAL LEFT, LQUERY, NOTRAN
194: INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
195: $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW
196: * ..
197: * .. Local Arrays ..
198: DOUBLE PRECISION T( LDT, NBMAX )
199: * ..
200: * .. External Functions ..
201: LOGICAL LSAME
202: INTEGER ILAENV
203: EXTERNAL LSAME, ILAENV
204: * ..
205: * .. External Subroutines ..
206: EXTERNAL DLARFB, DLARFT, DORM2R, XERBLA
207: * ..
208: * .. Intrinsic Functions ..
209: INTRINSIC MAX, MIN
210: * ..
211: * .. Executable Statements ..
212: *
213: * Test the input arguments
214: *
215: INFO = 0
216: LEFT = LSAME( SIDE, 'L' )
217: NOTRAN = LSAME( TRANS, 'N' )
218: LQUERY = ( LWORK.EQ.-1 )
219: *
220: * NQ is the order of Q and NW is the minimum dimension of WORK
221: *
222: IF( LEFT ) THEN
223: NQ = M
224: NW = N
225: ELSE
226: NQ = N
227: NW = M
228: END IF
229: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
230: INFO = -1
231: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
232: INFO = -2
233: ELSE IF( M.LT.0 ) THEN
234: INFO = -3
235: ELSE IF( N.LT.0 ) THEN
236: INFO = -4
237: ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
238: INFO = -5
239: ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
240: INFO = -7
241: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
242: INFO = -10
243: ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
244: INFO = -12
245: END IF
246: *
247: IF( INFO.EQ.0 ) THEN
248: *
249: * Determine the block size. NB may be at most NBMAX, where NBMAX
250: * is used to define the local array T.
251: *
252: NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K,
253: $ -1 ) )
254: LWKOPT = MAX( 1, NW )*NB
255: WORK( 1 ) = LWKOPT
256: END IF
257: *
258: IF( INFO.NE.0 ) THEN
259: CALL XERBLA( 'DORMQR', -INFO )
260: RETURN
261: ELSE IF( LQUERY ) THEN
262: RETURN
263: END IF
264: *
265: * Quick return if possible
266: *
267: IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
268: WORK( 1 ) = 1
269: RETURN
270: END IF
271: *
272: NBMIN = 2
273: LDWORK = NW
274: IF( NB.GT.1 .AND. NB.LT.K ) THEN
275: IWS = NW*NB
276: IF( LWORK.LT.IWS ) THEN
277: NB = LWORK / LDWORK
278: NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K,
279: $ -1 ) )
280: END IF
281: ELSE
282: IWS = NW
283: END IF
284: *
285: IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
286: *
287: * Use unblocked code
288: *
289: CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
290: $ IINFO )
291: ELSE
292: *
293: * Use blocked code
294: *
295: IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
296: $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN
297: I1 = 1
298: I2 = K
299: I3 = NB
300: ELSE
301: I1 = ( ( K-1 ) / NB )*NB + 1
302: I2 = 1
303: I3 = -NB
304: END IF
305: *
306: IF( LEFT ) THEN
307: NI = N
308: JC = 1
309: ELSE
310: MI = M
311: IC = 1
312: END IF
313: *
314: DO 10 I = I1, I2, I3
315: IB = MIN( NB, K-I+1 )
316: *
317: * Form the triangular factor of the block reflector
318: * H = H(i) H(i+1) . . . H(i+ib-1)
319: *
320: CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ),
321: $ LDA, TAU( I ), T, LDT )
322: IF( LEFT ) THEN
323: *
1.8 bertrand 324: * H or H**T is applied to C(i:m,1:n)
1.1 bertrand 325: *
326: MI = M - I + 1
327: IC = I
328: ELSE
329: *
1.8 bertrand 330: * H or H**T is applied to C(1:m,i:n)
1.1 bertrand 331: *
332: NI = N - I + 1
333: JC = I
334: END IF
335: *
1.8 bertrand 336: * Apply H or H**T
1.1 bertrand 337: *
338: CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
339: $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
340: $ WORK, LDWORK )
341: 10 CONTINUE
342: END IF
343: WORK( 1 ) = LWKOPT
344: RETURN
345: *
346: * End of DORMQR
347: *
348: END
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