Annotation of rpl/lapack/lapack/dlarzt.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLARZT
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLARZT + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarzt.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarzt.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarzt.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER DIRECT, STOREV
! 25: * INTEGER K, LDT, LDV, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DLARZT forms the triangular factor T of a real block reflector
! 38: *> H of order > n, which is defined as a product of k elementary
! 39: *> reflectors.
! 40: *>
! 41: *> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
! 42: *>
! 43: *> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
! 44: *>
! 45: *> If STOREV = 'C', the vector which defines the elementary reflector
! 46: *> H(i) is stored in the i-th column of the array V, and
! 47: *>
! 48: *> H = I - V * T * V**T
! 49: *>
! 50: *> If STOREV = 'R', the vector which defines the elementary reflector
! 51: *> H(i) is stored in the i-th row of the array V, and
! 52: *>
! 53: *> H = I - V**T * T * V
! 54: *>
! 55: *> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
! 56: *> \endverbatim
! 57: *
! 58: * Arguments:
! 59: * ==========
! 60: *
! 61: *> \param[in] DIRECT
! 62: *> \verbatim
! 63: *> DIRECT is CHARACTER*1
! 64: *> Specifies the order in which the elementary reflectors are
! 65: *> multiplied to form the block reflector:
! 66: *> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
! 67: *> = 'B': H = H(k) . . . H(2) H(1) (Backward)
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] STOREV
! 71: *> \verbatim
! 72: *> STOREV is CHARACTER*1
! 73: *> Specifies how the vectors which define the elementary
! 74: *> reflectors are stored (see also Further Details):
! 75: *> = 'C': columnwise (not supported yet)
! 76: *> = 'R': rowwise
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in] N
! 80: *> \verbatim
! 81: *> N is INTEGER
! 82: *> The order of the block reflector H. N >= 0.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] K
! 86: *> \verbatim
! 87: *> K is INTEGER
! 88: *> The order of the triangular factor T (= the number of
! 89: *> elementary reflectors). K >= 1.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in,out] V
! 93: *> \verbatim
! 94: *> V is DOUBLE PRECISION array, dimension
! 95: *> (LDV,K) if STOREV = 'C'
! 96: *> (LDV,N) if STOREV = 'R'
! 97: *> The matrix V. See further details.
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[in] LDV
! 101: *> \verbatim
! 102: *> LDV is INTEGER
! 103: *> The leading dimension of the array V.
! 104: *> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[in] TAU
! 108: *> \verbatim
! 109: *> TAU is DOUBLE PRECISION array, dimension (K)
! 110: *> TAU(i) must contain the scalar factor of the elementary
! 111: *> reflector H(i).
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[out] T
! 115: *> \verbatim
! 116: *> T is DOUBLE PRECISION array, dimension (LDT,K)
! 117: *> The k by k triangular factor T of the block reflector.
! 118: *> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
! 119: *> lower triangular. The rest of the array is not used.
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[in] LDT
! 123: *> \verbatim
! 124: *> LDT is INTEGER
! 125: *> The leading dimension of the array T. LDT >= K.
! 126: *> \endverbatim
! 127: *
! 128: * Authors:
! 129: * ========
! 130: *
! 131: *> \author Univ. of Tennessee
! 132: *> \author Univ. of California Berkeley
! 133: *> \author Univ. of Colorado Denver
! 134: *> \author NAG Ltd.
! 135: *
! 136: *> \date November 2011
! 137: *
! 138: *> \ingroup doubleOTHERcomputational
! 139: *
! 140: *> \par Contributors:
! 141: * ==================
! 142: *>
! 143: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 144: *
! 145: *> \par Further Details:
! 146: * =====================
! 147: *>
! 148: *> \verbatim
! 149: *>
! 150: *> The shape of the matrix V and the storage of the vectors which define
! 151: *> the H(i) is best illustrated by the following example with n = 5 and
! 152: *> k = 3. The elements equal to 1 are not stored; the corresponding
! 153: *> array elements are modified but restored on exit. The rest of the
! 154: *> array is not used.
! 155: *>
! 156: *> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
! 157: *>
! 158: *> ______V_____
! 159: *> ( v1 v2 v3 ) / \
! 160: *> ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
! 161: *> V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
! 162: *> ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
! 163: *> ( v1 v2 v3 )
! 164: *> . . .
! 165: *> . . .
! 166: *> 1 . .
! 167: *> 1 .
! 168: *> 1
! 169: *>
! 170: *> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
! 171: *>
! 172: *> ______V_____
! 173: *> 1 / \
! 174: *> . 1 ( 1 . . . . v1 v1 v1 v1 v1 )
! 175: *> . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
! 176: *> . . . ( . . 1 . . v3 v3 v3 v3 v3 )
! 177: *> . . .
! 178: *> ( v1 v2 v3 )
! 179: *> ( v1 v2 v3 )
! 180: *> V = ( v1 v2 v3 )
! 181: *> ( v1 v2 v3 )
! 182: *> ( v1 v2 v3 )
! 183: *> \endverbatim
! 184: *>
! 185: * =====================================================================
1.1 bertrand 186: SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
187: *
1.9 ! bertrand 188: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 189: * -- LAPACK is a software package provided by Univ. of Tennessee, --
190: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 191: * November 2011
1.1 bertrand 192: *
193: * .. Scalar Arguments ..
194: CHARACTER DIRECT, STOREV
195: INTEGER K, LDT, LDV, N
196: * ..
197: * .. Array Arguments ..
198: DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
199: * ..
200: *
201: * =====================================================================
202: *
203: * .. Parameters ..
204: DOUBLE PRECISION ZERO
205: PARAMETER ( ZERO = 0.0D+0 )
206: * ..
207: * .. Local Scalars ..
208: INTEGER I, INFO, J
209: * ..
210: * .. External Subroutines ..
211: EXTERNAL DGEMV, DTRMV, XERBLA
212: * ..
213: * .. External Functions ..
214: LOGICAL LSAME
215: EXTERNAL LSAME
216: * ..
217: * .. Executable Statements ..
218: *
219: * Check for currently supported options
220: *
221: INFO = 0
222: IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
223: INFO = -1
224: ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
225: INFO = -2
226: END IF
227: IF( INFO.NE.0 ) THEN
228: CALL XERBLA( 'DLARZT', -INFO )
229: RETURN
230: END IF
231: *
232: DO 20 I = K, 1, -1
233: IF( TAU( I ).EQ.ZERO ) THEN
234: *
235: * H(i) = I
236: *
237: DO 10 J = I, K
238: T( J, I ) = ZERO
239: 10 CONTINUE
240: ELSE
241: *
242: * general case
243: *
244: IF( I.LT.K ) THEN
245: *
1.8 bertrand 246: * T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**T
1.1 bertrand 247: *
248: CALL DGEMV( 'No transpose', K-I, N, -TAU( I ),
249: $ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
250: $ T( I+1, I ), 1 )
251: *
252: * T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
253: *
254: CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
255: $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
256: END IF
257: T( I, I ) = TAU( I )
258: END IF
259: 20 CONTINUE
260: RETURN
261: *
262: * End of DLARZT
263: *
264: END
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