--- /dev/null
+*> \brief \b IPARMQ
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download IPARMQ + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/iparmq.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/iparmq.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/iparmq.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
+*
+* .. Scalar Arguments ..
+* INTEGER IHI, ILO, ISPEC, LWORK, N
+* CHARACTER NAME*( * ), OPTS*( * )
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> This program sets problem and machine dependent parameters
+*> useful for xHSEQR and its subroutines. It is called whenever
+*> ILAENV is called with 12 <= ISPEC <= 16
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] ISPEC
+*> \verbatim
+*> ISPEC is integer scalar
+*> ISPEC specifies which tunable parameter IPARMQ should
+*> return.
+*>
+*> ISPEC=12: (INMIN) Matrices of order nmin or less
+*> are sent directly to xLAHQR, the implicit
+*> double shift QR algorithm. NMIN must be
+*> at least 11.
+*>
+*> ISPEC=13: (INWIN) Size of the deflation window.
+*> This is best set greater than or equal to
+*> the number of simultaneous shifts NS.
+*> Larger matrices benefit from larger deflation
+*> windows.
+*>
+*> ISPEC=14: (INIBL) Determines when to stop nibbling and
+*> invest in an (expensive) multi-shift QR sweep.
+*> If the aggressive early deflation subroutine
+*> finds LD converged eigenvalues from an order
+*> NW deflation window and LD.GT.(NW*NIBBLE)/100,
+*> then the next QR sweep is skipped and early
+*> deflation is applied immediately to the
+*> remaining active diagonal block. Setting
+*> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a
+*> multi-shift QR sweep whenever early deflation
+*> finds a converged eigenvalue. Setting
+*> IPARMQ(ISPEC=14) greater than or equal to 100
+*> prevents TTQRE from skipping a multi-shift
+*> QR sweep.
+*>
+*> ISPEC=15: (NSHFTS) The number of simultaneous shifts in
+*> a multi-shift QR iteration.
+*>
+*> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the
+*> following meanings.
+*> 0: During the multi-shift QR sweep,
+*> xLAQR5 does not accumulate reflections and
+*> does not use matrix-matrix multiply to
+*> update the far-from-diagonal matrix
+*> entries.
+*> 1: During the multi-shift QR sweep,
+*> xLAQR5 and/or xLAQRaccumulates reflections and uses
+*> matrix-matrix multiply to update the
+*> far-from-diagonal matrix entries.
+*> 2: During the multi-shift QR sweep.
+*> xLAQR5 accumulates reflections and takes
+*> advantage of 2-by-2 block structure during
+*> matrix-matrix multiplies.
+*> (If xTRMM is slower than xGEMM, then
+*> IPARMQ(ISPEC=16)=1 may be more efficient than
+*> IPARMQ(ISPEC=16)=2 despite the greater level of
+*> arithmetic work implied by the latter choice.)
+*> \endverbatim
+*>
+*> \param[in] NAME
+*> \verbatim
+*> NAME is character string
+*> Name of the calling subroutine
+*> \endverbatim
+*>
+*> \param[in] OPTS
+*> \verbatim
+*> OPTS is character string
+*> This is a concatenation of the string arguments to
+*> TTQRE.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is integer scalar
+*> N is the order of the Hessenberg matrix H.
+*> \endverbatim
+*>
+*> \param[in] ILO
+*> \verbatim
+*> ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHI
+*> \verbatim
+*> IHI is INTEGER
+*> It is assumed that H is already upper triangular
+*> in rows and columns 1:ILO-1 and IHI+1:N.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is integer scalar
+*> The amount of workspace available.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup auxOTHERauxiliary
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Little is known about how best to choose these parameters.
+*> It is possible to use different values of the parameters
+*> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.
+*>
+*> It is probably best to choose different parameters for
+*> different matrices and different parameters at different
+*> times during the iteration, but this has not been
+*> implemented --- yet.
+*>
+*>
+*> The best choices of most of the parameters depend
+*> in an ill-understood way on the relative execution
+*> rate of xLAQR3 and xLAQR5 and on the nature of each
+*> particular eigenvalue problem. Experiment may be the
+*> only practical way to determine which choices are most
+*> effective.
+*>
+*> Following is a list of default values supplied by IPARMQ.
+*> These defaults may be adjusted in order to attain better
+*> performance in any particular computational environment.
+*>
+*> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.
+*> Default: 75. (Must be at least 11.)
+*>
+*> IPARMQ(ISPEC=13) Recommended deflation window size.
+*> This depends on ILO, IHI and NS, the
+*> number of simultaneous shifts returned
+*> by IPARMQ(ISPEC=15). The default for
+*> (IHI-ILO+1).LE.500 is NS. The default
+*> for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>
+*> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.
+*>
+*> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.
+*> a multi-shift QR iteration.
+*>
+*> If IHI-ILO+1 is ...
+*>
+*> greater than ...but less ... the
+*> or equal to ... than default is
+*>
+*> 0 30 NS = 2+
+*> 30 60 NS = 4+
+*> 60 150 NS = 10
+*> 150 590 NS = **
+*> 590 3000 NS = 64
+*> 3000 6000 NS = 128
+*> 6000 infinity NS = 256
+*>
+*> (+) By default matrices of this order are
+*> passed to the implicit double shift routine
+*> xLAHQR. See IPARMQ(ISPEC=12) above. These
+*> values of NS are used only in case of a rare
+*> xLAHQR failure.
+*>
+*> (**) The asterisks (**) indicate an ad-hoc
+*> function increasing from 10 to 64.
+*>
+*> IPARMQ(ISPEC=16) Select structured matrix multiply.
+*> (See ISPEC=16 above for details.)
+*> Default: 3.
+*> \endverbatim
+*>
+* =====================================================================
+ INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )
+*
+* -- LAPACK auxiliary routine (version 3.4.0) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
+*
+* .. Scalar Arguments ..
+ INTEGER IHI, ILO, ISPEC, LWORK, N
+ CHARACTER NAME*( * ), OPTS*( * )
+*
+* ================================================================
+* .. Parameters ..
+ INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22
+ PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14,
+ $ ISHFTS = 15, IACC22 = 16 )
+ INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP
+ PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14,
+ $ NIBBLE = 14, KNWSWP = 500 )
+ REAL TWO
+ PARAMETER ( TWO = 2.0 )
+* ..
+* .. Local Scalars ..
+ INTEGER NH, NS
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC LOG, MAX, MOD, NINT, REAL
+* ..
+* .. Executable Statements ..
+ IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR.
+ $ ( ISPEC.EQ.IACC22 ) ) THEN
+*
+* ==== Set the number simultaneous shifts ====
+*
+ NH = IHI - ILO + 1
+ NS = 2
+ IF( NH.GE.30 )
+ $ NS = 4
+ IF( NH.GE.60 )
+ $ NS = 10
+ IF( NH.GE.150 )
+ $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) )
+ IF( NH.GE.590 )
+ $ NS = 64
+ IF( NH.GE.3000 )
+ $ NS = 128
+ IF( NH.GE.6000 )
+ $ NS = 256
+ NS = MAX( 2, NS-MOD( NS, 2 ) )
+ END IF
+*
+ IF( ISPEC.EQ.INMIN ) THEN
+*
+*
+* ===== Matrices of order smaller than NMIN get sent
+* . to xLAHQR, the classic double shift algorithm.
+* . This must be at least 11. ====
+*
+ IPARMQ = NMIN
+*
+ ELSE IF( ISPEC.EQ.INIBL ) THEN
+*
+* ==== INIBL: skip a multi-shift qr iteration and
+* . whenever aggressive early deflation finds
+* . at least (NIBBLE*(window size)/100) deflations. ====
+*
+ IPARMQ = NIBBLE
+*
+ ELSE IF( ISPEC.EQ.ISHFTS ) THEN
+*
+* ==== NSHFTS: The number of simultaneous shifts =====
+*
+ IPARMQ = NS
+*
+ ELSE IF( ISPEC.EQ.INWIN ) THEN
+*
+* ==== NW: deflation window size. ====
+*
+ IF( NH.LE.KNWSWP ) THEN
+ IPARMQ = NS
+ ELSE
+ IPARMQ = 3*NS / 2
+ END IF
+*
+ ELSE IF( ISPEC.EQ.IACC22 ) THEN
+*
+* ==== IACC22: Whether to accumulate reflections
+* . before updating the far-from-diagonal elements
+* . and whether to use 2-by-2 block structure while
+* . doing it. A small amount of work could be saved
+* . by making this choice dependent also upon the
+* . NH=IHI-ILO+1.
+*
+ IPARMQ = 0
+ IF( NS.GE.KACMIN )
+ $ IPARMQ = 1
+ IF( NS.GE.K22MIN )
+ $ IPARMQ = 2
+*
+ ELSE
+* ===== invalid value of ispec =====
+ IPARMQ = -1
+*
+ END IF
+*
+* ==== End of IPARMQ ====
+*
+ END
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