Annotation of rpl/lapack/lapack/iparmq.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b IPARMQ
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download IPARMQ + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER IHI, ILO, ISPEC, LWORK, N
! 25: * CHARACTER NAME*( * ), OPTS*( * )
! 26: *
! 27: *
! 28: *> \par Purpose:
! 29: * =============
! 30: *>
! 31: *> \verbatim
! 32: *>
! 33: *> This program sets problem and machine dependent parameters
! 34: *> useful for xHSEQR and its subroutines. It is called whenever
! 35: *> ILAENV is called with 12 <= ISPEC <= 16
! 36: *> \endverbatim
! 37: *
! 38: * Arguments:
! 39: * ==========
! 40: *
! 41: *> \param[in] ISPEC
! 42: *> \verbatim
! 43: *> ISPEC is integer scalar
! 44: *> ISPEC specifies which tunable parameter IPARMQ should
! 45: *> return.
! 46: *>
! 47: *> ISPEC=12: (INMIN) Matrices of order nmin or less
! 48: *> are sent directly to xLAHQR, the implicit
! 49: *> double shift QR algorithm. NMIN must be
! 50: *> at least 11.
! 51: *>
! 52: *> ISPEC=13: (INWIN) Size of the deflation window.
! 53: *> This is best set greater than or equal to
! 54: *> the number of simultaneous shifts NS.
! 55: *> Larger matrices benefit from larger deflation
! 56: *> windows.
! 57: *>
! 58: *> ISPEC=14: (INIBL) Determines when to stop nibbling and
! 59: *> invest in an (expensive) multi-shift QR sweep.
! 60: *> If the aggressive early deflation subroutine
! 61: *> finds LD converged eigenvalues from an order
! 62: *> NW deflation window and LD.GT.(NW*NIBBLE)/100,
! 63: *> then the next QR sweep is skipped and early
! 64: *> deflation is applied immediately to the
! 65: *> remaining active diagonal block. Setting
! 66: *> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
! 67: *> multi-shift QR sweep whenever early deflation
! 68: *> finds a converged eigenvalue. Setting
! 69: *> IPARMQ(ISPEC=14) greater than or equal to 100
! 70: *> prevents TTQRE from skipping a multi-shift
! 71: *> QR sweep.
! 72: *>
! 73: *> ISPEC=15: (NSHFTS) The number of simultaneous shifts in
! 74: *> a multi-shift QR iteration.
! 75: *>
! 76: *> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
! 77: *> following meanings.
! 78: *> 0: During the multi-shift QR sweep,
! 79: *> xLAQR5 does not accumulate reflections and
! 80: *> does not use matrix-matrix multiply to
! 81: *> update the far-from-diagonal matrix
! 82: *> entries.
! 83: *> 1: During the multi-shift QR sweep,
! 84: *> xLAQR5 and/or xLAQRaccumulates reflections and uses
! 85: *> matrix-matrix multiply to update the
! 86: *> far-from-diagonal matrix entries.
! 87: *> 2: During the multi-shift QR sweep.
! 88: *> xLAQR5 accumulates reflections and takes
! 89: *> advantage of 2-by-2 block structure during
! 90: *> matrix-matrix multiplies.
! 91: *> (If xTRMM is slower than xGEMM, then
! 92: *> IPARMQ(ISPEC=16)=1 may be more efficient than
! 93: *> IPARMQ(ISPEC=16)=2 despite the greater level of
! 94: *> arithmetic work implied by the latter choice.)
! 95: *> \endverbatim
! 96: *>
! 97: *> \param[in] NAME
! 98: *> \verbatim
! 99: *> NAME is character string
! 100: *> Name of the calling subroutine
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] OPTS
! 104: *> \verbatim
! 105: *> OPTS is character string
! 106: *> This is a concatenation of the string arguments to
! 107: *> TTQRE.
! 108: *> \endverbatim
! 109: *>
! 110: *> \param[in] N
! 111: *> \verbatim
! 112: *> N is integer scalar
! 113: *> N is the order of the Hessenberg matrix H.
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[in] ILO
! 117: *> \verbatim
! 118: *> ILO is INTEGER
! 119: *> \endverbatim
! 120: *>
! 121: *> \param[in] IHI
! 122: *> \verbatim
! 123: *> IHI is INTEGER
! 124: *> It is assumed that H is already upper triangular
! 125: *> in rows and columns 1:ILO-1 and IHI+1:N.
! 126: *> \endverbatim
! 127: *>
! 128: *> \param[in] LWORK
! 129: *> \verbatim
! 130: *> LWORK is integer scalar
! 131: *> The amount of workspace available.
! 132: *> \endverbatim
! 133: *
! 134: * Authors:
! 135: * ========
! 136: *
! 137: *> \author Univ. of Tennessee
! 138: *> \author Univ. of California Berkeley
! 139: *> \author Univ. of Colorado Denver
! 140: *> \author NAG Ltd.
! 141: *
! 142: *> \date November 2011
! 143: *
! 144: *> \ingroup auxOTHERauxiliary
! 145: *
! 146: *> \par Further Details:
! 147: * =====================
! 148: *>
! 149: *> \verbatim
! 150: *>
! 151: *> Little is known about how best to choose these parameters.
! 152: *> It is possible to use different values of the parameters
! 153: *> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
! 154: *>
! 155: *> It is probably best to choose different parameters for
! 156: *> different matrices and different parameters at different
! 157: *> times during the iteration, but this has not been
! 158: *> implemented --- yet.
! 159: *>
! 160: *>
! 161: *> The best choices of most of the parameters depend
! 162: *> in an ill-understood way on the relative execution
! 163: *> rate of xLAQR3 and xLAQR5 and on the nature of each
! 164: *> particular eigenvalue problem. Experiment may be the
! 165: *> only practical way to determine which choices are most
! 166: *> effective.
! 167: *>
! 168: *> Following is a list of default values supplied by IPARMQ.
! 169: *> These defaults may be adjusted in order to attain better
! 170: *> performance in any particular computational environment.
! 171: *>
! 172: *> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
! 173: *> Default: 75. (Must be at least 11.)
! 174: *>
! 175: *> IPARMQ(ISPEC=13) Recommended deflation window size.
! 176: *> This depends on ILO, IHI and NS, the
! 177: *> number of simultaneous shifts returned
! 178: *> by IPARMQ(ISPEC=15). The default for
! 179: *> (IHI-ILO+1).LE.500 is NS. The default
! 180: *> for (IHI-ILO+1).GT.500 is 3*NS/2.
! 181: *>
! 182: *> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
! 183: *>
! 184: *> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
! 185: *> a multi-shift QR iteration.
! 186: *>
! 187: *> If IHI-ILO+1 is ...
! 188: *>
! 189: *> greater than ...but less ... the
! 190: *> or equal to ... than default is
! 191: *>
! 192: *> 0 30 NS = 2+
! 193: *> 30 60 NS = 4+
! 194: *> 60 150 NS = 10
! 195: *> 150 590 NS = **
! 196: *> 590 3000 NS = 64
! 197: *> 3000 6000 NS = 128
! 198: *> 6000 infinity NS = 256
! 199: *>
! 200: *> (+) By default matrices of this order are
! 201: *> passed to the implicit double shift routine
! 202: *> xLAHQR. See IPARMQ(ISPEC=12) above. These
! 203: *> values of NS are used only in case of a rare
! 204: *> xLAHQR failure.
! 205: *>
! 206: *> (**) The asterisks (**) indicate an ad-hoc
! 207: *> function increasing from 10 to 64.
! 208: *>
! 209: *> IPARMQ(ISPEC=16) Select structured matrix multiply.
! 210: *> (See ISPEC=16 above for details.)
! 211: *> Default: 3.
! 212: *> \endverbatim
! 213: *>
! 214: * =====================================================================
1.1 bertrand 215: INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
216: *
1.9 ! bertrand 217: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 218: * -- LAPACK is a software package provided by Univ. of Tennessee, --
219: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 220: * November 2011
! 221: *
1.1 bertrand 222: * .. Scalar Arguments ..
223: INTEGER IHI, ILO, ISPEC, LWORK, N
224: CHARACTER NAME*( * ), OPTS*( * )
225: *
1.9 ! bertrand 226: * ================================================================
1.1 bertrand 227: * .. Parameters ..
228: INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22
229: PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14,
230: $ ISHFTS = 15, IACC22 = 16 )
231: INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
232: PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14,
233: $ NIBBLE = 14, KNWSWP = 500 )
234: REAL TWO
235: PARAMETER ( TWO = 2.0 )
236: * ..
237: * .. Local Scalars ..
238: INTEGER NH, NS
239: * ..
240: * .. Intrinsic Functions ..
241: INTRINSIC LOG, MAX, MOD, NINT, REAL
242: * ..
243: * .. Executable Statements ..
244: IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
245: $ ( ISPEC.EQ.IACC22 ) ) THEN
246: *
247: * ==== Set the number simultaneous shifts ====
248: *
249: NH = IHI - ILO + 1
250: NS = 2
251: IF( NH.GE.30 )
252: $ NS = 4
253: IF( NH.GE.60 )
254: $ NS = 10
255: IF( NH.GE.150 )
256: $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
257: IF( NH.GE.590 )
258: $ NS = 64
259: IF( NH.GE.3000 )
260: $ NS = 128
261: IF( NH.GE.6000 )
262: $ NS = 256
263: NS = MAX( 2, NS-MOD( NS, 2 ) )
264: END IF
265: *
266: IF( ISPEC.EQ.INMIN ) THEN
267: *
268: *
269: * ===== Matrices of order smaller than NMIN get sent
270: * . to xLAHQR, the classic double shift algorithm.
271: * . This must be at least 11. ====
272: *
273: IPARMQ = NMIN
274: *
275: ELSE IF( ISPEC.EQ.INIBL ) THEN
276: *
277: * ==== INIBL: skip a multi-shift qr iteration and
278: * . whenever aggressive early deflation finds
279: * . at least (NIBBLE*(window size)/100) deflations. ====
280: *
281: IPARMQ = NIBBLE
282: *
283: ELSE IF( ISPEC.EQ.ISHFTS ) THEN
284: *
285: * ==== NSHFTS: The number of simultaneous shifts =====
286: *
287: IPARMQ = NS
288: *
289: ELSE IF( ISPEC.EQ.INWIN ) THEN
290: *
291: * ==== NW: deflation window size. ====
292: *
293: IF( NH.LE.KNWSWP ) THEN
294: IPARMQ = NS
295: ELSE
296: IPARMQ = 3*NS / 2
297: END IF
298: *
299: ELSE IF( ISPEC.EQ.IACC22 ) THEN
300: *
301: * ==== IACC22: Whether to accumulate reflections
302: * . before updating the far-from-diagonal elements
303: * . and whether to use 2-by-2 block structure while
304: * . doing it. A small amount of work could be saved
305: * . by making this choice dependent also upon the
306: * . NH=IHI-ILO+1.
307: *
308: IPARMQ = 0
309: IF( NS.GE.KACMIN )
310: $ IPARMQ = 1
311: IF( NS.GE.K22MIN )
312: $ IPARMQ = 2
313: *
314: ELSE
315: * ===== invalid value of ispec =====
316: IPARMQ = -1
317: *
318: END IF
319: *
320: * ==== End of IPARMQ ====
321: *
322: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to iparmq.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack