Annotation of rpl/lapack/lapack/dlarzb.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLARZB
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLARZB + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarzb.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarzb.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarzb.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
! 22: * LDV, T, LDT, C, LDC, WORK, LDWORK )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER DIRECT, SIDE, STOREV, TRANS
! 26: * INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
! 30: * $ WORK( LDWORK, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> DLARZB applies a real block reflector H or its transpose H**T to
! 40: *> a real distributed M-by-N C from the left or the right.
! 41: *>
! 42: *> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
! 43: *> \endverbatim
! 44: *
! 45: * Arguments:
! 46: * ==========
! 47: *
! 48: *> \param[in] SIDE
! 49: *> \verbatim
! 50: *> SIDE is CHARACTER*1
! 51: *> = 'L': apply H or H**T from the Left
! 52: *> = 'R': apply H or H**T from the Right
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in] TRANS
! 56: *> \verbatim
! 57: *> TRANS is CHARACTER*1
! 58: *> = 'N': apply H (No transpose)
! 59: *> = 'C': apply H**T (Transpose)
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] DIRECT
! 63: *> \verbatim
! 64: *> DIRECT is CHARACTER*1
! 65: *> Indicates how H is formed from a product of elementary
! 66: *> reflectors
! 67: *> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
! 68: *> = 'B': H = H(k) . . . H(2) H(1) (Backward)
! 69: *> \endverbatim
! 70: *>
! 71: *> \param[in] STOREV
! 72: *> \verbatim
! 73: *> STOREV is CHARACTER*1
! 74: *> Indicates how the vectors which define the elementary
! 75: *> reflectors are stored:
! 76: *> = 'C': Columnwise (not supported yet)
! 77: *> = 'R': Rowwise
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] M
! 81: *> \verbatim
! 82: *> M is INTEGER
! 83: *> The number of rows of the matrix C.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] N
! 87: *> \verbatim
! 88: *> N is INTEGER
! 89: *> The number of columns of the matrix C.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] K
! 93: *> \verbatim
! 94: *> K is INTEGER
! 95: *> The order of the matrix T (= the number of elementary
! 96: *> reflectors whose product defines the block reflector).
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] L
! 100: *> \verbatim
! 101: *> L is INTEGER
! 102: *> The number of columns of the matrix V containing the
! 103: *> meaningful part of the Householder reflectors.
! 104: *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[in] V
! 108: *> \verbatim
! 109: *> V is DOUBLE PRECISION array, dimension (LDV,NV).
! 110: *> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in] LDV
! 114: *> \verbatim
! 115: *> LDV is INTEGER
! 116: *> The leading dimension of the array V.
! 117: *> If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[in] T
! 121: *> \verbatim
! 122: *> T is DOUBLE PRECISION array, dimension (LDT,K)
! 123: *> The triangular K-by-K matrix T in the representation of the
! 124: *> block reflector.
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[in] LDT
! 128: *> \verbatim
! 129: *> LDT is INTEGER
! 130: *> The leading dimension of the array T. LDT >= K.
! 131: *> \endverbatim
! 132: *>
! 133: *> \param[in,out] C
! 134: *> \verbatim
! 135: *> C is DOUBLE PRECISION array, dimension (LDC,N)
! 136: *> On entry, the M-by-N matrix C.
! 137: *> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
! 138: *> \endverbatim
! 139: *>
! 140: *> \param[in] LDC
! 141: *> \verbatim
! 142: *> LDC is INTEGER
! 143: *> The leading dimension of the array C. LDC >= max(1,M).
! 144: *> \endverbatim
! 145: *>
! 146: *> \param[out] WORK
! 147: *> \verbatim
! 148: *> WORK is DOUBLE PRECISION array, dimension (LDWORK,K)
! 149: *> \endverbatim
! 150: *>
! 151: *> \param[in] LDWORK
! 152: *> \verbatim
! 153: *> LDWORK is INTEGER
! 154: *> The leading dimension of the array WORK.
! 155: *> If SIDE = 'L', LDWORK >= max(1,N);
! 156: *> if SIDE = 'R', LDWORK >= max(1,M).
! 157: *> \endverbatim
! 158: *
! 159: * Authors:
! 160: * ========
! 161: *
! 162: *> \author Univ. of Tennessee
! 163: *> \author Univ. of California Berkeley
! 164: *> \author Univ. of Colorado Denver
! 165: *> \author NAG Ltd.
! 166: *
! 167: *> \date November 2011
! 168: *
! 169: *> \ingroup doubleOTHERcomputational
! 170: *
! 171: *> \par Contributors:
! 172: * ==================
! 173: *>
! 174: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 175: *
! 176: *> \par Further Details:
! 177: * =====================
! 178: *>
! 179: *> \verbatim
! 180: *> \endverbatim
! 181: *>
! 182: * =====================================================================
1.1 bertrand 183: SUBROUTINE DLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
184: $ LDV, T, LDT, C, LDC, WORK, LDWORK )
185: *
1.9 ! bertrand 186: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 187: * -- LAPACK is a software package provided by Univ. of Tennessee, --
188: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 189: * November 2011
1.1 bertrand 190: *
191: * .. Scalar Arguments ..
192: CHARACTER DIRECT, SIDE, STOREV, TRANS
193: INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
194: * ..
195: * .. Array Arguments ..
196: DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
197: $ WORK( LDWORK, * )
198: * ..
199: *
200: * =====================================================================
201: *
202: * .. Parameters ..
203: DOUBLE PRECISION ONE
204: PARAMETER ( ONE = 1.0D+0 )
205: * ..
206: * .. Local Scalars ..
207: CHARACTER TRANST
208: INTEGER I, INFO, J
209: * ..
210: * .. External Functions ..
211: LOGICAL LSAME
212: EXTERNAL LSAME
213: * ..
214: * .. External Subroutines ..
215: EXTERNAL DCOPY, DGEMM, DTRMM, XERBLA
216: * ..
217: * .. Executable Statements ..
218: *
219: * Quick return if possible
220: *
221: IF( M.LE.0 .OR. N.LE.0 )
222: $ RETURN
223: *
224: * Check for currently supported options
225: *
226: INFO = 0
227: IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
228: INFO = -3
229: ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
230: INFO = -4
231: END IF
232: IF( INFO.NE.0 ) THEN
233: CALL XERBLA( 'DLARZB', -INFO )
234: RETURN
235: END IF
236: *
237: IF( LSAME( TRANS, 'N' ) ) THEN
238: TRANST = 'T'
239: ELSE
240: TRANST = 'N'
241: END IF
242: *
243: IF( LSAME( SIDE, 'L' ) ) THEN
244: *
1.8 bertrand 245: * Form H * C or H**T * C
1.1 bertrand 246: *
1.8 bertrand 247: * W( 1:n, 1:k ) = C( 1:k, 1:n )**T
1.1 bertrand 248: *
249: DO 10 J = 1, K
250: CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
251: 10 CONTINUE
252: *
253: * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
1.8 bertrand 254: * C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
1.1 bertrand 255: *
256: IF( L.GT.0 )
257: $ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
258: $ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
259: *
1.8 bertrand 260: * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
1.1 bertrand 261: *
262: CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
263: $ LDT, WORK, LDWORK )
264: *
1.8 bertrand 265: * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
1.1 bertrand 266: *
267: DO 30 J = 1, N
268: DO 20 I = 1, K
269: C( I, J ) = C( I, J ) - WORK( J, I )
270: 20 CONTINUE
271: 30 CONTINUE
272: *
273: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
1.8 bertrand 274: * V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
1.1 bertrand 275: *
276: IF( L.GT.0 )
277: $ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
278: $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
279: *
280: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
281: *
1.8 bertrand 282: * Form C * H or C * H**T
1.1 bertrand 283: *
284: * W( 1:m, 1:k ) = C( 1:m, 1:k )
285: *
286: DO 40 J = 1, K
287: CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
288: 40 CONTINUE
289: *
290: * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
1.8 bertrand 291: * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
1.1 bertrand 292: *
293: IF( L.GT.0 )
294: $ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
295: $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
296: *
1.8 bertrand 297: * W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
1.1 bertrand 298: *
299: CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
300: $ LDT, WORK, LDWORK )
301: *
302: * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
303: *
304: DO 60 J = 1, K
305: DO 50 I = 1, M
306: C( I, J ) = C( I, J ) - WORK( I, J )
307: 50 CONTINUE
308: 60 CONTINUE
309: *
310: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
311: * W( 1:m, 1:k ) * V( 1:k, 1:l )
312: *
313: IF( L.GT.0 )
314: $ CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
315: $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
316: *
317: END IF
318: *
319: RETURN
320: *
321: * End of DLARZB
322: *
323: END
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