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---
:name: iparmq
:md5sum: 73ec37559601ded71e0b8df251efd10e
:category: :function
:type: integer
:arguments:
- ispec:
:type: integer
:intent: input
- name:
:type: char
:intent: input
- opts:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ilo:
:type: integer
:intent: input
- ihi:
:type: integer
:intent: input
- lwork:
:type: integer
:intent: input
:substitutions: {}
:fortran_help: " INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This program sets problem and machine dependent parameters\n\
* useful for xHSEQR and its subroutines. It is called whenever \n\
* ILAENV is called with 12 <= ISPEC <= 16\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* ISPEC (input) integer scalar\n\
* ISPEC specifies which tunable parameter IPARMQ should\n\
* return.\n\
*\n\
* ISPEC=12: (INMIN) Matrices of order nmin or less\n\
* are sent directly to xLAHQR, the implicit\n\
* double shift QR algorithm. NMIN must be\n\
* at least 11.\n\
*\n\
* ISPEC=13: (INWIN) Size of the deflation window.\n\
* This is best set greater than or equal to\n\
* the number of simultaneous shifts NS.\n\
* Larger matrices benefit from larger deflation\n\
* windows.\n\
*\n\
* ISPEC=14: (INIBL) Determines when to stop nibbling and\n\
* invest in an (expensive) multi-shift QR sweep.\n\
* If the aggressive early deflation subroutine\n\
* finds LD converged eigenvalues from an order\n\
* NW deflation window and LD.GT.(NW*NIBBLE)/100,\n\
* then the next QR sweep is skipped and early\n\
* deflation is applied immediately to the\n\
* remaining active diagonal block. Setting\n\
* IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a\n\
* multi-shift QR sweep whenever early deflation\n\
* finds a converged eigenvalue. Setting\n\
* IPARMQ(ISPEC=14) greater than or equal to 100\n\
* prevents TTQRE from skipping a multi-shift\n\
* QR sweep.\n\
*\n\
* ISPEC=15: (NSHFTS) The number of simultaneous shifts in\n\
* a multi-shift QR iteration.\n\
*\n\
* ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the\n\
* following meanings.\n\
* 0: During the multi-shift QR sweep,\n\
* xLAQR5 does not accumulate reflections and\n\
* does not use matrix-matrix multiply to\n\
* update the far-from-diagonal matrix\n\
* entries.\n\
* 1: During the multi-shift QR sweep,\n\
* xLAQR5 and/or xLAQRaccumulates reflections and uses\n\
* matrix-matrix multiply to update the\n\
* far-from-diagonal matrix entries.\n\
* 2: During the multi-shift QR sweep.\n\
* xLAQR5 accumulates reflections and takes\n\
* advantage of 2-by-2 block structure during\n\
* matrix-matrix multiplies.\n\
* (If xTRMM is slower than xGEMM, then\n\
* IPARMQ(ISPEC=16)=1 may be more efficient than\n\
* IPARMQ(ISPEC=16)=2 despite the greater level of\n\
* arithmetic work implied by the latter choice.)\n\
*\n\
* NAME (input) character string\n\
* Name of the calling subroutine\n\
*\n\
* OPTS (input) character string\n\
* This is a concatenation of the string arguments to\n\
* TTQRE.\n\
*\n\
* N (input) integer scalar\n\
* N is the order of the Hessenberg matrix H.\n\
*\n\
* ILO (input) INTEGER\n\
* IHI (input) INTEGER\n\
* It is assumed that H is already upper triangular\n\
* in rows and columns 1:ILO-1 and IHI+1:N.\n\
*\n\
* LWORK (input) integer scalar\n\
* The amount of workspace available.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Little is known about how best to choose these parameters.\n\
* It is possible to use different values of the parameters\n\
* for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.\n\
*\n\
* It is probably best to choose different parameters for\n\
* different matrices and different parameters at different\n\
* times during the iteration, but this has not been\n\
* implemented --- yet.\n\
*\n\
*\n\
* The best choices of most of the parameters depend\n\
* in an ill-understood way on the relative execution\n\
* rate of xLAQR3 and xLAQR5 and on the nature of each\n\
* particular eigenvalue problem. Experiment may be the\n\
* only practical way to determine which choices are most\n\
* effective.\n\
*\n\
* Following is a list of default values supplied by IPARMQ.\n\
* These defaults may be adjusted in order to attain better\n\
* performance in any particular computational environment.\n\
*\n\
* IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.\n\
* Default: 75. (Must be at least 11.)\n\
*\n\
* IPARMQ(ISPEC=13) Recommended deflation window size.\n\
* This depends on ILO, IHI and NS, the\n\
* number of simultaneous shifts returned\n\
* by IPARMQ(ISPEC=15). The default for\n\
* (IHI-ILO+1).LE.500 is NS. The default\n\
* for (IHI-ILO+1).GT.500 is 3*NS/2.\n\
*\n\
* IPARMQ(ISPEC=14) Nibble crossover point. Default: 14.\n\
*\n\
* IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.\n\
* a multi-shift QR iteration.\n\
*\n\
* If IHI-ILO+1 is ...\n\
*\n\
* greater than ...but less ... the\n\
* or equal to ... than default is\n\
*\n\
* 0 30 NS = 2+\n\
* 30 60 NS = 4+\n\
* 60 150 NS = 10\n\
* 150 590 NS = **\n\
* 590 3000 NS = 64\n\
* 3000 6000 NS = 128\n\
* 6000 infinity NS = 256\n\
*\n\
* (+) By default matrices of this order are\n\
* passed to the implicit double shift routine\n\
* xLAHQR. See IPARMQ(ISPEC=12) above. These\n\
* values of NS are used only in case of a rare\n\
* xLAHQR failure.\n\
*\n\
* (**) The asterisks (**) indicate an ad-hoc\n\
* function increasing from 10 to 64.\n\
*\n\
* IPARMQ(ISPEC=16) Select structured matrix multiply.\n\
* (See ISPEC=16 above for details.)\n\
* Default: 3.\n\
*\n\
* ================================================================\n"
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