Annotation of rpl/lapack/lapack/dopmtr.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DOPMTR
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DOPMTR + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dopmtr.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dopmtr.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dopmtr.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
! 22: * INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER SIDE, TRANS, UPLO
! 26: * INTEGER INFO, LDC, M, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> DOPMTR 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 of order nq, with nq = m if
! 45: *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
! 46: *> nq-1 elementary reflectors, as returned by DSPTRD using packed
! 47: *> storage:
! 48: *>
! 49: *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
! 50: *>
! 51: *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
! 52: *> \endverbatim
! 53: *
! 54: * Arguments:
! 55: * ==========
! 56: *
! 57: *> \param[in] SIDE
! 58: *> \verbatim
! 59: *> SIDE is CHARACTER*1
! 60: *> = 'L': apply Q or Q**T from the Left;
! 61: *> = 'R': apply Q or Q**T from the Right.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in] UPLO
! 65: *> \verbatim
! 66: *> UPLO is CHARACTER*1
! 67: *> = 'U': Upper triangular packed storage used in previous
! 68: *> call to DSPTRD;
! 69: *> = 'L': Lower triangular packed storage used in previous
! 70: *> call to DSPTRD.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] TRANS
! 74: *> \verbatim
! 75: *> TRANS is CHARACTER*1
! 76: *> = 'N': No transpose, apply Q;
! 77: *> = 'T': Transpose, apply Q**T.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] M
! 81: *> \verbatim
! 82: *> M is INTEGER
! 83: *> The number of rows of the matrix C. M >= 0.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] N
! 87: *> \verbatim
! 88: *> N is INTEGER
! 89: *> The number of columns of the matrix C. N >= 0.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] AP
! 93: *> \verbatim
! 94: *> AP is DOUBLE PRECISION array, dimension
! 95: *> (M*(M+1)/2) if SIDE = 'L'
! 96: *> (N*(N+1)/2) if SIDE = 'R'
! 97: *> The vectors which define the elementary reflectors, as
! 98: *> returned by DSPTRD. AP is modified by the routine but
! 99: *> restored on exit.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in] TAU
! 103: *> \verbatim
! 104: *> TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
! 105: *> or (N-1) if SIDE = 'R'
! 106: *> TAU(i) must contain the scalar factor of the elementary
! 107: *> reflector H(i), as returned by DSPTRD.
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[in,out] C
! 111: *> \verbatim
! 112: *> C is DOUBLE PRECISION array, dimension (LDC,N)
! 113: *> On entry, the M-by-N matrix C.
! 114: *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] LDC
! 118: *> \verbatim
! 119: *> LDC is INTEGER
! 120: *> The leading dimension of the array C. LDC >= max(1,M).
! 121: *> \endverbatim
! 122: *>
! 123: *> \param[out] WORK
! 124: *> \verbatim
! 125: *> WORK is DOUBLE PRECISION array, dimension
! 126: *> (N) if SIDE = 'L'
! 127: *> (M) if SIDE = 'R'
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[out] INFO
! 131: *> \verbatim
! 132: *> INFO is INTEGER
! 133: *> = 0: successful exit
! 134: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 135: *> \endverbatim
! 136: *
! 137: * Authors:
! 138: * ========
! 139: *
! 140: *> \author Univ. of Tennessee
! 141: *> \author Univ. of California Berkeley
! 142: *> \author Univ. of Colorado Denver
! 143: *> \author NAG Ltd.
! 144: *
! 145: *> \date November 2011
! 146: *
! 147: *> \ingroup doubleOTHERcomputational
! 148: *
! 149: * =====================================================================
1.1 bertrand 150: SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
151: $ INFO )
152: *
1.8 ! bertrand 153: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 154: * -- LAPACK is a software package provided by Univ. of Tennessee, --
155: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 156: * November 2011
1.1 bertrand 157: *
158: * .. Scalar Arguments ..
159: CHARACTER SIDE, TRANS, UPLO
160: INTEGER INFO, LDC, M, N
161: * ..
162: * .. Array Arguments ..
163: DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * )
164: * ..
165: *
166: * =====================================================================
167: *
168: * .. Parameters ..
169: DOUBLE PRECISION ONE
170: PARAMETER ( ONE = 1.0D+0 )
171: * ..
172: * .. Local Scalars ..
173: LOGICAL FORWRD, LEFT, NOTRAN, UPPER
174: INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
175: DOUBLE PRECISION AII
176: * ..
177: * .. External Functions ..
178: LOGICAL LSAME
179: EXTERNAL LSAME
180: * ..
181: * .. External Subroutines ..
182: EXTERNAL DLARF, XERBLA
183: * ..
184: * .. Intrinsic Functions ..
185: INTRINSIC MAX
186: * ..
187: * .. Executable Statements ..
188: *
189: * Test the input arguments
190: *
191: INFO = 0
192: LEFT = LSAME( SIDE, 'L' )
193: NOTRAN = LSAME( TRANS, 'N' )
194: UPPER = LSAME( UPLO, 'U' )
195: *
196: * NQ is the order of Q
197: *
198: IF( LEFT ) THEN
199: NQ = M
200: ELSE
201: NQ = N
202: END IF
203: IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
204: INFO = -1
205: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
206: INFO = -2
207: ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
208: INFO = -3
209: ELSE IF( M.LT.0 ) THEN
210: INFO = -4
211: ELSE IF( N.LT.0 ) THEN
212: INFO = -5
213: ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
214: INFO = -9
215: END IF
216: IF( INFO.NE.0 ) THEN
217: CALL XERBLA( 'DOPMTR', -INFO )
218: RETURN
219: END IF
220: *
221: * Quick return if possible
222: *
223: IF( M.EQ.0 .OR. N.EQ.0 )
224: $ RETURN
225: *
226: IF( UPPER ) THEN
227: *
228: * Q was determined by a call to DSPTRD with UPLO = 'U'
229: *
230: FORWRD = ( LEFT .AND. NOTRAN ) .OR.
231: $ ( .NOT.LEFT .AND. .NOT.NOTRAN )
232: *
233: IF( FORWRD ) THEN
234: I1 = 1
235: I2 = NQ - 1
236: I3 = 1
237: II = 2
238: ELSE
239: I1 = NQ - 1
240: I2 = 1
241: I3 = -1
242: II = NQ*( NQ+1 ) / 2 - 1
243: END IF
244: *
245: IF( LEFT ) THEN
246: NI = N
247: ELSE
248: MI = M
249: END IF
250: *
251: DO 10 I = I1, I2, I3
252: IF( LEFT ) THEN
253: *
254: * H(i) is applied to C(1:i,1:n)
255: *
256: MI = I
257: ELSE
258: *
259: * H(i) is applied to C(1:m,1:i)
260: *
261: NI = I
262: END IF
263: *
264: * Apply H(i)
265: *
266: AII = AP( II )
267: AP( II ) = ONE
268: CALL DLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAU( I ), C, LDC,
269: $ WORK )
270: AP( II ) = AII
271: *
272: IF( FORWRD ) THEN
273: II = II + I + 2
274: ELSE
275: II = II - I - 1
276: END IF
277: 10 CONTINUE
278: ELSE
279: *
280: * Q was determined by a call to DSPTRD with UPLO = 'L'.
281: *
282: FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR.
283: $ ( .NOT.LEFT .AND. NOTRAN )
284: *
285: IF( FORWRD ) THEN
286: I1 = 1
287: I2 = NQ - 1
288: I3 = 1
289: II = 2
290: ELSE
291: I1 = NQ - 1
292: I2 = 1
293: I3 = -1
294: II = NQ*( NQ+1 ) / 2 - 1
295: END IF
296: *
297: IF( LEFT ) THEN
298: NI = N
299: JC = 1
300: ELSE
301: MI = M
302: IC = 1
303: END IF
304: *
305: DO 20 I = I1, I2, I3
306: AII = AP( II )
307: AP( II ) = ONE
308: IF( LEFT ) THEN
309: *
310: * H(i) is applied to C(i+1:m,1:n)
311: *
312: MI = M - I
313: IC = I + 1
314: ELSE
315: *
316: * H(i) is applied to C(1:m,i+1:n)
317: *
318: NI = N - I
319: JC = I + 1
320: END IF
321: *
322: * Apply H(i)
323: *
324: CALL DLARF( SIDE, MI, NI, AP( II ), 1, TAU( I ),
325: $ C( IC, JC ), LDC, WORK )
326: AP( II ) = AII
327: *
328: IF( FORWRD ) THEN
329: II = II + NQ - I + 1
330: ELSE
331: II = II - NQ + I - 2
332: END IF
333: 20 CONTINUE
334: END IF
335: RETURN
336: *
337: * End of DOPMTR
338: *
339: END
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