Annotation of rpl/lapack/lapack/dlarra.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLARRA
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLARRA + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarra.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarra.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarra.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
! 22: * NSPLIT, ISPLIT, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER INFO, N, NSPLIT
! 26: * DOUBLE PRECISION SPLTOL, TNRM
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER ISPLIT( * )
! 30: * DOUBLE PRECISION D( * ), E( * ), E2( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> Compute the splitting points with threshold SPLTOL.
! 40: *> DLARRA sets any "small" off-diagonal elements to zero.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] N
! 47: *> \verbatim
! 48: *> N is INTEGER
! 49: *> The order of the matrix. N > 0.
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] D
! 53: *> \verbatim
! 54: *> D is DOUBLE PRECISION array, dimension (N)
! 55: *> On entry, the N diagonal elements of the tridiagonal
! 56: *> matrix T.
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in,out] E
! 60: *> \verbatim
! 61: *> E is DOUBLE PRECISION array, dimension (N)
! 62: *> On entry, the first (N-1) entries contain the subdiagonal
! 63: *> elements of the tridiagonal matrix T; E(N) need not be set.
! 64: *> On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
! 65: *> are set to zero, the other entries of E are untouched.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in,out] E2
! 69: *> \verbatim
! 70: *> E2 is DOUBLE PRECISION array, dimension (N)
! 71: *> On entry, the first (N-1) entries contain the SQUARES of the
! 72: *> subdiagonal elements of the tridiagonal matrix T;
! 73: *> E2(N) need not be set.
! 74: *> On exit, the entries E2( ISPLIT( I ) ),
! 75: *> 1 <= I <= NSPLIT, have been set to zero
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] SPLTOL
! 79: *> \verbatim
! 80: *> SPLTOL is DOUBLE PRECISION
! 81: *> The threshold for splitting. Two criteria can be used:
! 82: *> SPLTOL<0 : criterion based on absolute off-diagonal value
! 83: *> SPLTOL>0 : criterion that preserves relative accuracy
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] TNRM
! 87: *> \verbatim
! 88: *> TNRM is DOUBLE PRECISION
! 89: *> The norm of the matrix.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[out] NSPLIT
! 93: *> \verbatim
! 94: *> NSPLIT is INTEGER
! 95: *> The number of blocks T splits into. 1 <= NSPLIT <= N.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[out] ISPLIT
! 99: *> \verbatim
! 100: *> ISPLIT is INTEGER array, dimension (N)
! 101: *> The splitting points, at which T breaks up into blocks.
! 102: *> The first block consists of rows/columns 1 to ISPLIT(1),
! 103: *> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
! 104: *> etc., and the NSPLIT-th consists of rows/columns
! 105: *> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] INFO
! 109: *> \verbatim
! 110: *> INFO is INTEGER
! 111: *> = 0: successful exit
! 112: *> \endverbatim
! 113: *
! 114: * Authors:
! 115: * ========
! 116: *
! 117: *> \author Univ. of Tennessee
! 118: *> \author Univ. of California Berkeley
! 119: *> \author Univ. of Colorado Denver
! 120: *> \author NAG Ltd.
! 121: *
! 122: *> \date November 2011
! 123: *
! 124: *> \ingroup auxOTHERauxiliary
! 125: *
! 126: *> \par Contributors:
! 127: * ==================
! 128: *>
! 129: *> Beresford Parlett, University of California, Berkeley, USA \n
! 130: *> Jim Demmel, University of California, Berkeley, USA \n
! 131: *> Inderjit Dhillon, University of Texas, Austin, USA \n
! 132: *> Osni Marques, LBNL/NERSC, USA \n
! 133: *> Christof Voemel, University of California, Berkeley, USA
! 134: *
! 135: * =====================================================================
1.1 bertrand 136: SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
137: $ NSPLIT, ISPLIT, INFO )
138: *
1.9 ! bertrand 139: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 140: * -- LAPACK is a software package provided by Univ. of Tennessee, --
141: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 142: * November 2011
1.1 bertrand 143: *
144: * .. Scalar Arguments ..
145: INTEGER INFO, N, NSPLIT
146: DOUBLE PRECISION SPLTOL, TNRM
147: * ..
148: * .. Array Arguments ..
149: INTEGER ISPLIT( * )
150: DOUBLE PRECISION D( * ), E( * ), E2( * )
151: * ..
152: *
153: * =====================================================================
154: *
155: * .. Parameters ..
156: DOUBLE PRECISION ZERO
157: PARAMETER ( ZERO = 0.0D0 )
158: * ..
159: * .. Local Scalars ..
160: INTEGER I
161: DOUBLE PRECISION EABS, TMP1
162:
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC ABS
166: * ..
167: * .. Executable Statements ..
168: *
169: INFO = 0
170:
171: * Compute splitting points
172: NSPLIT = 1
173: IF(SPLTOL.LT.ZERO) THEN
174: * Criterion based on absolute off-diagonal value
175: TMP1 = ABS(SPLTOL)* TNRM
176: DO 9 I = 1, N-1
177: EABS = ABS( E(I) )
178: IF( EABS .LE. TMP1) THEN
179: E(I) = ZERO
180: E2(I) = ZERO
181: ISPLIT( NSPLIT ) = I
182: NSPLIT = NSPLIT + 1
183: END IF
184: 9 CONTINUE
185: ELSE
186: * Criterion that guarantees relative accuracy
187: DO 10 I = 1, N-1
188: EABS = ABS( E(I) )
189: IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
190: $ THEN
191: E(I) = ZERO
192: E2(I) = ZERO
193: ISPLIT( NSPLIT ) = I
194: NSPLIT = NSPLIT + 1
195: END IF
196: 10 CONTINUE
197: ENDIF
198: ISPLIT( NSPLIT ) = N
199:
200: RETURN
201: *
202: * End of DLARRA
203: *
204: END
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