Annotation of rpl/lapack/lapack/iparmq.f, revision 1.1
1.1 ! bertrand 1: INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: INTEGER IHI, ILO, ISPEC, LWORK, N
! 10: CHARACTER NAME*( * ), OPTS*( * )
! 11: *
! 12: * Purpose
! 13: * =======
! 14: *
! 15: * This program sets problem and machine dependent parameters
! 16: * useful for xHSEQR and its subroutines. It is called whenever
! 17: * ILAENV is called with 12 <= ISPEC <= 16
! 18: *
! 19: * Arguments
! 20: * =========
! 21: *
! 22: * ISPEC (input) integer scalar
! 23: * ISPEC specifies which tunable parameter IPARMQ should
! 24: * return.
! 25: *
! 26: * ISPEC=12: (INMIN) Matrices of order nmin or less
! 27: * are sent directly to xLAHQR, the implicit
! 28: * double shift QR algorithm. NMIN must be
! 29: * at least 11.
! 30: *
! 31: * ISPEC=13: (INWIN) Size of the deflation window.
! 32: * This is best set greater than or equal to
! 33: * the number of simultaneous shifts NS.
! 34: * Larger matrices benefit from larger deflation
! 35: * windows.
! 36: *
! 37: * ISPEC=14: (INIBL) Determines when to stop nibbling and
! 38: * invest in an (expensive) multi-shift QR sweep.
! 39: * If the aggressive early deflation subroutine
! 40: * finds LD converged eigenvalues from an order
! 41: * NW deflation window and LD.GT.(NW*NIBBLE)/100,
! 42: * then the next QR sweep is skipped and early
! 43: * deflation is applied immediately to the
! 44: * remaining active diagonal block. Setting
! 45: * IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
! 46: * multi-shift QR sweep whenever early deflation
! 47: * finds a converged eigenvalue. Setting
! 48: * IPARMQ(ISPEC=14) greater than or equal to 100
! 49: * prevents TTQRE from skipping a multi-shift
! 50: * QR sweep.
! 51: *
! 52: * ISPEC=15: (NSHFTS) The number of simultaneous shifts in
! 53: * a multi-shift QR iteration.
! 54: *
! 55: * ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
! 56: * following meanings.
! 57: * 0: During the multi-shift QR sweep,
! 58: * xLAQR5 does not accumulate reflections and
! 59: * does not use matrix-matrix multiply to
! 60: * update the far-from-diagonal matrix
! 61: * entries.
! 62: * 1: During the multi-shift QR sweep,
! 63: * xLAQR5 and/or xLAQRaccumulates reflections and uses
! 64: * matrix-matrix multiply to update the
! 65: * far-from-diagonal matrix entries.
! 66: * 2: During the multi-shift QR sweep.
! 67: * xLAQR5 accumulates reflections and takes
! 68: * advantage of 2-by-2 block structure during
! 69: * matrix-matrix multiplies.
! 70: * (If xTRMM is slower than xGEMM, then
! 71: * IPARMQ(ISPEC=16)=1 may be more efficient than
! 72: * IPARMQ(ISPEC=16)=2 despite the greater level of
! 73: * arithmetic work implied by the latter choice.)
! 74: *
! 75: * NAME (input) character string
! 76: * Name of the calling subroutine
! 77: *
! 78: * OPTS (input) character string
! 79: * This is a concatenation of the string arguments to
! 80: * TTQRE.
! 81: *
! 82: * N (input) integer scalar
! 83: * N is the order of the Hessenberg matrix H.
! 84: *
! 85: * ILO (input) INTEGER
! 86: * IHI (input) INTEGER
! 87: * It is assumed that H is already upper triangular
! 88: * in rows and columns 1:ILO-1 and IHI+1:N.
! 89: *
! 90: * LWORK (input) integer scalar
! 91: * The amount of workspace available.
! 92: *
! 93: * Further Details
! 94: * ===============
! 95: *
! 96: * Little is known about how best to choose these parameters.
! 97: * It is possible to use different values of the parameters
! 98: * for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
! 99: *
! 100: * It is probably best to choose different parameters for
! 101: * different matrices and different parameters at different
! 102: * times during the iteration, but this has not been
! 103: * implemented --- yet.
! 104: *
! 105: *
! 106: * The best choices of most of the parameters depend
! 107: * in an ill-understood way on the relative execution
! 108: * rate of xLAQR3 and xLAQR5 and on the nature of each
! 109: * particular eigenvalue problem. Experiment may be the
! 110: * only practical way to determine which choices are most
! 111: * effective.
! 112: *
! 113: * Following is a list of default values supplied by IPARMQ.
! 114: * These defaults may be adjusted in order to attain better
! 115: * performance in any particular computational environment.
! 116: *
! 117: * IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
! 118: * Default: 75. (Must be at least 11.)
! 119: *
! 120: * IPARMQ(ISPEC=13) Recommended deflation window size.
! 121: * This depends on ILO, IHI and NS, the
! 122: * number of simultaneous shifts returned
! 123: * by IPARMQ(ISPEC=15). The default for
! 124: * (IHI-ILO+1).LE.500 is NS. The default
! 125: * for (IHI-ILO+1).GT.500 is 3*NS/2.
! 126: *
! 127: * IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
! 128: *
! 129: * IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
! 130: * a multi-shift QR iteration.
! 131: *
! 132: * If IHI-ILO+1 is ...
! 133: *
! 134: * greater than ...but less ... the
! 135: * or equal to ... than default is
! 136: *
! 137: * 0 30 NS = 2+
! 138: * 30 60 NS = 4+
! 139: * 60 150 NS = 10
! 140: * 150 590 NS = **
! 141: * 590 3000 NS = 64
! 142: * 3000 6000 NS = 128
! 143: * 6000 infinity NS = 256
! 144: *
! 145: * (+) By default matrices of this order are
! 146: * passed to the implicit double shift routine
! 147: * xLAHQR. See IPARMQ(ISPEC=12) above. These
! 148: * values of NS are used only in case of a rare
! 149: * xLAHQR failure.
! 150: *
! 151: * (**) The asterisks (**) indicate an ad-hoc
! 152: * function increasing from 10 to 64.
! 153: *
! 154: * IPARMQ(ISPEC=16) Select structured matrix multiply.
! 155: * (See ISPEC=16 above for details.)
! 156: * Default: 3.
! 157: *
! 158: * ================================================================
! 159: * .. Parameters ..
! 160: INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22
! 161: PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14,
! 162: $ ISHFTS = 15, IACC22 = 16 )
! 163: INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
! 164: PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14,
! 165: $ NIBBLE = 14, KNWSWP = 500 )
! 166: REAL TWO
! 167: PARAMETER ( TWO = 2.0 )
! 168: * ..
! 169: * .. Local Scalars ..
! 170: INTEGER NH, NS
! 171: * ..
! 172: * .. Intrinsic Functions ..
! 173: INTRINSIC LOG, MAX, MOD, NINT, REAL
! 174: * ..
! 175: * .. Executable Statements ..
! 176: IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
! 177: $ ( ISPEC.EQ.IACC22 ) ) THEN
! 178: *
! 179: * ==== Set the number simultaneous shifts ====
! 180: *
! 181: NH = IHI - ILO + 1
! 182: NS = 2
! 183: IF( NH.GE.30 )
! 184: $ NS = 4
! 185: IF( NH.GE.60 )
! 186: $ NS = 10
! 187: IF( NH.GE.150 )
! 188: $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
! 189: IF( NH.GE.590 )
! 190: $ NS = 64
! 191: IF( NH.GE.3000 )
! 192: $ NS = 128
! 193: IF( NH.GE.6000 )
! 194: $ NS = 256
! 195: NS = MAX( 2, NS-MOD( NS, 2 ) )
! 196: END IF
! 197: *
! 198: IF( ISPEC.EQ.INMIN ) THEN
! 199: *
! 200: *
! 201: * ===== Matrices of order smaller than NMIN get sent
! 202: * . to xLAHQR, the classic double shift algorithm.
! 203: * . This must be at least 11. ====
! 204: *
! 205: IPARMQ = NMIN
! 206: *
! 207: ELSE IF( ISPEC.EQ.INIBL ) THEN
! 208: *
! 209: * ==== INIBL: skip a multi-shift qr iteration and
! 210: * . whenever aggressive early deflation finds
! 211: * . at least (NIBBLE*(window size)/100) deflations. ====
! 212: *
! 213: IPARMQ = NIBBLE
! 214: *
! 215: ELSE IF( ISPEC.EQ.ISHFTS ) THEN
! 216: *
! 217: * ==== NSHFTS: The number of simultaneous shifts =====
! 218: *
! 219: IPARMQ = NS
! 220: *
! 221: ELSE IF( ISPEC.EQ.INWIN ) THEN
! 222: *
! 223: * ==== NW: deflation window size. ====
! 224: *
! 225: IF( NH.LE.KNWSWP ) THEN
! 226: IPARMQ = NS
! 227: ELSE
! 228: IPARMQ = 3*NS / 2
! 229: END IF
! 230: *
! 231: ELSE IF( ISPEC.EQ.IACC22 ) THEN
! 232: *
! 233: * ==== IACC22: Whether to accumulate reflections
! 234: * . before updating the far-from-diagonal elements
! 235: * . and whether to use 2-by-2 block structure while
! 236: * . doing it. A small amount of work could be saved
! 237: * . by making this choice dependent also upon the
! 238: * . NH=IHI-ILO+1.
! 239: *
! 240: IPARMQ = 0
! 241: IF( NS.GE.KACMIN )
! 242: $ IPARMQ = 1
! 243: IF( NS.GE.K22MIN )
! 244: $ IPARMQ = 2
! 245: *
! 246: ELSE
! 247: * ===== invalid value of ispec =====
! 248: IPARMQ = -1
! 249: *
! 250: END IF
! 251: *
! 252: * ==== End of IPARMQ ====
! 253: *
! 254: END
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