General Introduction. Most of the programs provided in GQOPT require the user to write a MAIN program that reads in the data and calls the appropriate subroutine(s). This is time-consuming and error prone, because the user always has to check that he/she has the calling sequence of the subroutine right, that arrays are properly dimensioned, etc. The shell provided in this version of GQOPT eases many of these tasks.

In general, GQOPT permits users to name input data files anything they want, and (with very minor exceptions) also permits the user to name user-defined function and subroutines in arbitrary manner. By restricting the naming conventions and by requiring that data input conform to certain conventions, the SHELL permits many of these burdens to be avoided. Thus, for example, if the user wishes to solve the simultanous (nonlinear) equations

f(x)=0, g(x)=0, h(x)=0

by minimizingf(x)**2+g(x)**2+h(x)**2,

the input file must be called MINRES.IN. If the user wishes to perform the Kolmogorov one-sample test (which requires the computation of the "theoretical" cumulative probabilities from a posited distribution function, the name of this function must be KOLSMIR.FOR. All the naming conventions and the order in which input has to be arranged is spelled out in the tables that follow.

Navigating between the part of the Handbook that describes the SHELL and the substantive parts of the Handbook is easy. Tables 1A, 2A, 3A, and 4A have clickable links to the other parts of the Handbook; each substantive section of the Handbook has clickable links back to the appropriate part of the SHELL description.

The SHELL subdirectory that is created when GQOPT is installed contains (1) both the source code (SHELL.FOR) and the object code (SHELL.OBJ), (2) sample input files for every SHELL function, (3) sample subroutines or function subprograms for every SHELL function that requires one. These subprograms are all contained in a single file and a subprogram must be present for every SHELL function that requires one, even if that function is not the one being executed. This is the reason that all these subroutines and functions are in a single file called SHELLFUN.FOR. The user would simply change that subprogram which pertains to his/her particular computation, compile the entire SHELLFUN.FOR (including all the subprograms that the user is not currently interested in, which therefore act as dummies), and then link SHELL.OBJ with SHELLFUN.OBJ and the appropriate library, i.e., .LIB file. SHELLFUN.FOR does not have to be recompiled unless the user wants to change it and improve on it. The presence in the SHELL subdirectory of all the functions and subroutines that might be needed, along with all the illustrative input files and output files (corresponding to the sample input files and functions provided) provides an excellent tutorial for the user. Once the user has provided the appropriate input file (and additional function/subroutine, if needed), the SHELL may be executed by invoking a generic command of the type

linkcommand SHELL.OBJ SHELLFUN.OBJ mylib

For the LF95 compiler, it would be

lf95 shell.obj shellfun.obj -lib c:\gqopt710\lib\gqlf9571.lib

For the Digital Visual Fortran compiler,

df shell.obj shellfun.obj c:\gqopt710\lib\gqdvf710.lib

For the WATCOM compiler, it would be

wlink FILE shell,shellfun LIBRARY c:\gqopt710\lib\gqwat710.lib

assuming, of course, that the paths of the library are correct.

The SHELL is then invoked by typing

shell

(in the Unix environment, the program is called gqshell and must first be made executable by executing chmod u+x gqshell).

GQ-SHELL presents the user with a menu consisting of the following options:

1. Optimize 2. Equation solving 3. Statistical Routines 4. Utility Routines 5. Exit

You select an option by entering the number of the option and pressing ENTER. That will bring up another menu, depending on which option was selected, from which the user may further select the particular procedure desired.

The basic restrictions are the following:

- Input and output files must have fixed names (shown in the tables below)
- The input must be arranged in a certain format. Input in any event is unformatted: integers or decimal numbers (as the case may be) should be separated by one or more blanks. For the meaning of each input quantity, please consult the relevant section of the Handbook.
- If the procedure requires a user-supplied function, the name of the function must agree with the built-in name (shown in the tables below)

Selecting a procedure immediately starts execution; the SHELL expects to find the input as described below.

Selecting item 1.If the user selects 1 from the initial menu, the following secondary menu will appear:

1. General optimization using GRADX, DFP, POWELL, PATERN, RNSRCH,NMSIMP, MUKAI, or SSVM 2. Global optimization using simulated annealing 3. Global optimization using genetic algorithm 4. Linear programming when slacks provide a basic feasible solution 5. Linear programming when slacks do not provide a basic feasible solution') 6. Integer programming: Knapsack problem 7. Integer programming: Traveling salesman problem 8. Random genetic algorithm 9. Go to previous MENU') 10. Exit SHELL

The following table indicates the required input files and the function or subroutine names for which the user will have to prepare and compile programs:

Sub-Choice | Input file | Output file | Function name | Handbook Reference |
---|---|---|---|---|

1 |
optimize.in | optimize.out | optfunc | GRADX, DFP, POWELL , NMSIMP, PATERN, RNSRCH , MUKAI, SSVM |

2 |
global1.in | global1.out | simafunc | Simulated Annealing |

3 |
global2.in | global2.out | galgfunc | Genetic Algorithm |

4 |
linprog1.in | linprog1.out | LP when BFS available | |

5 |
linprog2.in | linprog2.out | LP when BFS not available | |

6 |
knapsack.in | knapsack.out | Knapsack | |

7 |
travsal.in | travsal.out | Traveling salesman | |

8 |
global3.in | global3.out | granfunc | Random genetic algorithm |

We next present the arrangement of data values in the input files for the cases depicted in Table 1-B. In Tables 1-B, 2-B, 3-B, and 4-B input "lines" are described. These "lines" refer to the types of input, and not necessarily to actual lines. For example, in Table 1-B, sub-choice 6, three lines are described. Line 1 is an actual line that should contain two integers, n and b. "Line 2" describes the input of a vector c, which may take more than one actual line. "Line 3" describes the input of a vector a, which may also take more than one actual line.

Sub-choice 1 requires a further explanation. Optimization typically involves a function that requires data. Since the form in which the data are to be read in cannot be anticipated by the GQSHELL in a general way, the reader is reponsible for reading in the data in the OPTFUNC subroutine. An example of this is provided in the source code of SHELLFUN.FOR, which ensures that the data are read in only once, not every time the function subroutine is evaluated. The user must make sure that the appropriate compile flag is set so that local variables in subroutines are remembered.

Sub-Choice | Line No. | Data Input and Explanation |
---|---|---|

1 | 1 |
mx np iterl iread !iread should=0 if default values of parameters are to be used, =1 if user wants to reset parameters |

2 | method !This should be either gradx or dfp or powell or patern or rnsrch or ssvm | |

3 | acc !if iread=0 or method=mukai or method=nmsimp | |

iver lt ifp isp nloop ist iloop !if iread=1 and method=gradx or =dfp or =ssvm | ||

step1 stpacc nlnsr !if iread=1 and method=powell | ||

stpsiz shrink !if iread=1 and method=patern | ||

deltaz sdelta rho !if iread=1 and method=rnsrch | ||

4 |
fdfrac fdmin !if iread=1 and method=gradx or =dfp or =ssvm | |

x !on this and subsequent lines, the values of the starting point, if iread=1 and method=patern or rnsrch or powell or if iread=0 | ||

5 |
step1 stpacc nlnsr !if iread=1 and method= gradx or= dfp | |

thetaa phii shrip1 shrip2 epss !if iread=1 and method =ssvm | ||

6 |
rtm eig rtmult !if iread=1 and method= gradx | |

stpmin fopt ! if iread=1 and method=dfp | ||

x !on this and subsequent lines, the values of the starting point, if iread=1 and method=ssvm | ||

7 |
ispd !if iread=1 and method= gradx | |

inflg !if iread=1 and method= dfp | ||

8 |
acti actw zful betm !if iread=1 and method= gradx | |

x !on this and subsequent lines, the values of the starting point, if iread=1 and method= dfp | ||

9 |
thetaa phii shrip1 shrip2 epss !if iread=1 and method= gradx | |

10 |
x !on this and subsequent lines, the values of the starting point, if iread=1 and method=gradx | |

2 | 1 | np neps ns nt max maxevl |

2 | eps rt t | |

3 | x !read in as many lines as necessary | |

4 | c !read in as many lines as necessary | |

5 | lb !read in as many lines as necessary | |

6 | ub !read in as many lines as necessary | |

7 | vm !read in as many lines as necessary | |

3 | 1 | np nipop npop ngood max |

2 | nc initgen ipair imate | |

3 | kterl imute itest ihowman | |

4 | xmute bacc shrink1 expand alph1 bet1 | |

5 | xl !read in as many lines as necessary | |

6 | xh !read in as many lines as necessary | |

4 | 1 | m n ifr kpiv |

2 | a !read in by rows; each row must begin on a new line; read m+1 rows of n+1 elements each---see Sect. 17.1.1 | |

5 | 1 | m n |

2 | a !read in by rows; each row must begin on a new line; read m+1 rows of n+1 elements each---see Sect. 17.1.1 | |

6 | 1 | n b |

2 | c !read in as many lines as necessary | |

3 | a !read in as many lines as necessary | |

7 | 1 | np nipop npop ngood |

2 | jnitgen jpair jterl jtest | |

3 | ymute bcc | |

4 | c !read by rows, as many lines as necessary, with each row beginning on a new line | |

8 | 1 | np n isur imod max |

2 | xl !read as many lines as necessary, with each row beginning on a new line | |

3 | xh !read as many lines as necessary, with each row beginning on a new line |

Selecting item 2.If the user selects 2 from the initial menu, the following secondary menu will appear:

1. For equations fi(x)=0, i=1,...,m, minimize sum of [fi(x)]-squared 2. Newton-Raphson 3. One equation, when unique root is in (a,b) interval: Regula falsi 4. Solve polynomial 5. Gauss-Seidel 6. Go to previous MENU 7. Exit GQ-SHELL

The following table indicates the required input files and the function or subroutine names for which the user will have to prepare and compile programs:

Sub-Choice | Input file | Output file | Function name | Handbook Reference |
---|---|---|---|---|

1 | minres.in | minres.out | SLVMIN | |

2 |
newraph.in | newraph.out | nwrpfunc | NEWRAP |

3 |
regfal.in | regfal.out | regffunc | REGFAL |

4 | polyroot.in | polyroot.out | PROOTS | |

5 | gausseid.in | gausseid.out | Gauss-Seidel |

We next present the arrangement of data values in the input files for the cases depicted in Table 2-A.

Sub-Choice | Line No. | Data Input and Explanation |
---|---|---|

1 | 1 |
np iterl iread !iread should=0 if default values of parameters are to be used, =1 if user wants to reset parameters |

2 | method !This should be either gradx or dfp or powell or patern or rnsrch or ssvm | |

3 | acc !if iread=0 | |

iver lt ifp isp nloop ist iloop !if iread=1 and method=gradx or =dfp or =ssvm | ||

step1 stpacc nlnsr !if iread=1 and method=powell | ||

stpsiz shrink !if iread=1 and method=patern | ||

deltaz sdelta rho !if iread=1 and method=rnsrch | ||

4 |
fdfrac fdmin !if iread=1 and method=gradx or =dfp or =ssvm | |

x !on this and subsequent lines, the values of the starting point, if iread=1 and method=patern or rnsrch or powell | ||

5 |
step1 stpacc nlnsr !if iread=1 and method= gradx or dfp | |

thetaa phii shrip1 shrip2 epss !if iread=1 and method =ssvm | ||

6 |
rtm eig rtmult !if iread=1 and method= gradx | |

stpmin fopt ! if iread=1 and method=dfp | ||

x !on this and subsequent lines, the values of the starting point, if iread=1 and method=ssvm | ||

7 |
ispd !if iread=1 and method= gradx | |

inflg !if iread=1 and method= dfp | ||

8 |
acti actw zful betm !if iread=1 and method= gradx | |

x !on this and subsequent lines, the values of the starting point, if iread=1 and method= dfp | ||

9 |
thetaa phii shrip1 shrip2 epss !if iread=1 and method=gradx | |

10 |
x !on this and subsequent lines, the values of the starting point, if iread=1 and method=gradx | |

2 | 1 | n iterl iread !iread should be set =0 if user does not want to read in new values for the variables in COMMON blocks BNWRP1 and BNWRP2 |

2 | acc !if iread=0 | |

ivflim invlim !if iread=1 | ||

3 | x !if iread=0, this and subsequent lines should contain starting point | |

epcor epsvrt !if iread=1 | ||

4 | acc !if iread=1 | |

5 | x !if iread=0, this and subsequent lines should contain starting point | |

3 | 1 | a b acc |

2 | iterl | |

4 | 1 | m iterl |

2 | xcof !xcof(i) to contain the coefficient of x**(i-1) | |

5 | 1 | np iterl max |

2 | x !x to contain the starting point;read as many lines as necessary |

1. Kolmogorov Smirnov 1-sample test 2. Kolmogorov Smirnov 2-sample test 3. Wilcoxon-Mann-Whitney test 4. Spearman Rho 5. Kendall Tau 6. Kendall Partial Tau 7. Kendall Concordance W 8. Cumulative Sample Distribibution 9. Contingency Table 10. Autocovariance Function 11. Periodogram 12. Spectrum 13. Density Plots 14. Countour Plot 15. Density Estimation 16. Kernel Regression 17. Least Squares Regression 18. Friedman Analysis of Variance 19. Test Equality of Means 20. Wald-Wolfowitz test 21. Continuous Convolution 22. Discrete Convolution 23. Cochran Q-test 24. Wilcoxon test 25. Go to previous MENU 26. Exit GQ-SHELL

The following tables indicate the (prescribed) names of input and output files (and of auxiliary function or subroutine names if needed) and gives directions for how the input is to be prepared.

The following table indicates the required input files and the function or subroutine names for which the user will have to prepare and compile programs:

Sub-Choice | Input file | Output file | Function name | Handbook Reference |
---|---|---|---|---|

1 | klsm1.in | klsm1.out | kolsmir | KOL-SMIR 1-sample |

2 | klsm2.in | klsm2.out | KOL-SMIR 2-sample | |

3 | wmw.in | wmw.out | Wilcoxon-Mann-Whitney | |

4 | spear.in | spear.out | Spearman Rho | |

5 | kend-tau.in | kend-tau.out | Kendall Tau | |

6 | part-tau.in | part-tau.out | Kendall Partial Tau | |

7 | kw-conc.in | kw-conc.out | Kendall W | |

8 | cumdis.in | cumdis.out | Cumul. Sample Dist. | |

9 | conting.in | conting.out | Contingency tables | |

10 | autocov.in | autocov.out | Autocovariance function | |

11 | pergram.in | pergram.out | Periodogram | |

12 | spectrum.in | spectrum.out | Spectrum | |

13 | densplot.in | densplot.out | Density plots | |

14 | contour.in | contour.out | cntrfunc | Contour plots |

15 | density.in | density | Nonparametric density estimation | |

16 | kerreg.in | kerreg.out | Kernel regression | |

17 | regress.in | regress.out | Regression estimation (OLS) | |

18 | friedman.in | friedman.out | Friedman analysis of variance | |

19 | testmean.in | testmean.out | Test equality of means | |

20 | waldwolf.in | waldwolf.out | Wald-Wolfowitz test | |

21 | convolve.in | convolve.out convol.pr | convolut | Continuous convolution |

22 | discconv.in | discconv.out | funcf, funcg | Discrete convolution |

23 | cochranq.in | cochranq.out | Cochran Q test | |

24 | wilcoxon.in | wilcoxon.out | Wilcoxon test |

The arrangement of the input that is required is shown in the following table:

Sub-Choice | Line No. | Data Input and Explanation |
---|---|---|

1 | 1 | n |

2 | sig | |

3 | x !and subsequent lines, if necessary | |

2 | 1 | n m |

2 | sig | |

3 | x !and subsequent lines, if necessary | |

4 | y !and subsequent lines, if necessary. The line(s) for the y-observations follow after all the x-observations | |

3 | 1 | n1 n2 |

2 | rt | |

3 | a !and subsequent lines, if necessary | |

4 | b !and subsequent lines, if necessary. The line(s) for the b-observations follow after all the a-observations | |

4 | 1 | n |

2 | x !and subsequent lines, if necessary. | |

3 | y !and subsequent lines, if necessary.The line(s) for the y-observations follow after all the a-observations | |

5 | 1 | n |

2 | x !and subsequent lines, if necessary. | |

3 | y !and subsequent lines, if necessary.The line(s) for the y-observations follow after all the x-observations | |

6 | 1 | n |

2 | x !and subsequent lines, if necessary. | |

3 | y !and subsequent lines, if necessary.The line(s) for the y-observations follow after all the x-observations | |

4 | z !and subsequent lines, if necessary.The line(s) for the z-observations follow after all the y-observations | |

7 | 1 | m n |

2 | rk !by rows; row 1 first, row 2 beginning on a new line next, etc. | |

8 | 1 | n |

2 | a !and subsequent lines, if necessary. | |

9 | 1 | m n |

2 | a !by rows; row 1 first, row 2 beginning on a new line next, etc.. | |

10 | 1 | n m |

2 | x !and subsequent lines, if necessary. | |

11 | 1 | m |

2 | x !and subsequent lines, if necessary. | |

12 | 1 | n |

2 | window !The letter "p" or "w" or "h" or the number "4" or "6" to replace "window". | |

3 | x !and subsequent lines, if necessary. | |

13 | 1 | n |

2 | x !and subsequent lines, if necessary. | |

3 | y !and subsequent lines, if necessary.The line(s) for the y-observations follow after all the x-observations | |

14 | 1 | np i1 i2 |

2 | iopt(1) iopt(2) iopt(3) | |

3 | xmin xmax ymin ymax zmin zmax zint !The last three only if iopt(1)=1 | |

4 | xlabel ylabel !enclosed in ' ' and separated by at least one blank | |

15 | 1 | n nval kernel ih |

2 | eps h
!if ih=0 eps !if ih=1 | |

3 | x !and subsequent lines, if necessary. | |

16 | 1 | n m kernel igh ihw |

2 | h | |

3 | conf | |

4 | x !and subsequent lines, if necessary. | |

5 | y !and subsequent lines, if necessary. | |

17 | 1 | n k |

2 | x !and subsequent lines, if necessary. Read in by observations, i.e., by rows of x. Each new observation (vector) to start on a new line. | |

3 | ||

18 | 1 | m n |

2 | rk !by rows, i.e., by judges; row 1 first, row 2 beginning on a new line next, etc. | |

19 | 1 | n1 n2 |

2 | a1 !first sample; as many rows as necessary | |

3 | a2 !second sample; as many rows as necessary | |

20 | 1 | n1 n2 |

2 | a1 !first sample; as many rows as necessary | |

3 | a2 !second sample; as many rows as necessary | |

21 | 1 | n npoint yl yh ax bx |

22 | 1 | n m |

23 | 1 | n k |

2 | jresp !and subsequent lines, if necessary. Read in by individuals, i.e., by rows of jresp. Each new individual to start on a new line. | |

24 | 1 | n |

2 | a1 !first set of measurements; as many rows as necessary | |

3 | a2 !second setof measurements; as many rows as necessary |

1. Eigenvalues/eigenvectors for symmetric matrices 2. Invert symmetric matrix (GJR) 3. Invert arbitrary matrix using VERS 4. Invert arbitrary matrix using MATVRT 5. Solve system of linear equations using GAJORE 6. Compute determinant 7. Numeric integration 8. Generate random variables from selected distributions 9. Plot a time series 10. Inverse of the cumulative normal 11. Go to previous MENU 12. Exit SHELL

Selecting options 7 or 8 from this menu will result in sub-menus being presented. The following table indicates the required input files and the function or subroutine names for which the user will have to prepare and compile programs, both for this menu and the sub-menus:

Sub-Choice | Sub-Sub-Choice | Input file | Output file | Function name | Handbook Reference |
---|---|---|---|---|---|

1 |
matev2.in | matev2.out | Eigenvalues of symmetric matrices | ||

2 | invert1.in | invert1.out | Invert symmetric matrix (GJR) | ||

3 | invert2.in | invert2.out | Invert arbitrary square matrix (VERS) | ||

4 |
invert3.in | invert3.out | Invert arbitrary square matrix (MATVRT) | ||

5 | gajore.in | gajore.out | Solve linear equations (GAJORE) | ||

6 | determ.in | determ.out | Compute determinant (DTRM) | ||

7 |
1 |
normal2.in | normal2.out | Integrate normal density | |

7 |
2 |
normal3.in | normal3.out | Integrate normal density | |

7 |
3 |
newtcot.in | newtcot.out | nwct1 or nwct2 or nwct3 | Newton Cotes integration |

7 |
4 |
weddle.in | weddle.out | wdd | Weddle integration |

7 |
5 |
romberg.in | romberg.out | rmbb | Romberg integration |

7 |
6 |
gausleg.in | gausleg.out | gale1 or gale2 or gale3 | Gauss-Legendre integration |

7 |
7 |
igausleg.in | igausleg.out | gale1 or gale2 or gale3 or gale4 | Gauss-Legendre integration |

7 |
8 |
bivar2.in | bivar2.out | ax(x), ay(x),bvr2(x,y) | Variable limit bivariate integration |

7 |
9 |
gauslag.in | gauslag.out | glg | Gauss-Laguerre integration |

7 |
10 |
moncarl.in | moncarl.out | Monte Carlo integration | |

8 |
1 |
randvar.in | randvar.out | Uniform random variables | |

8 |
2 |
normalbm.in | normalbm.out | Normal variates (Box-Muller) | |

8 |
3 |
normalmb.in | normalmb.out | Normal variates (Marsaglia-Bray) | |

8 |
4 |
normalsu.in | normalsu.out | Normal variates (summing uniforms) | |

8 |
5 |
expon.in | expon.out | Exponential variates | |

8 |
6 |
cauchy.in | cauchy.out | Cauchy variates | |

8 |
7 |
raylei.in | raylei.out | Rayleigh variates | |

8 |
8 |
pareto.in | pareto.out | Pareto variates | |

8 |
9 |
logistic.in | logistic.out | Logistic variates | |

9 |
plotcurv.in | plotcurv.out | Plot a time series (PLOTCURV) | ||

10 |
invgaus.in | invgaus.out | Invert the cumulative normal (INVGAUS) |

The arrangement of the input that is required is shown in the following table:

Sub-Choice | Sub-Sub-Choice | Line No. | Data Input and Explanation |
---|---|---|---|

1 | 1 | n isw | |

2 | a !on this and subsequent lines as necessary; since a is symmetric, you may list values by rows or columns; each new row (column) to start on a new line | ||

2 | 1 | n | |

2 | a !on this and subsequent lines as necessary; since a is symmetric, you may list values by rows or columns | ||

3 | 1 | n | |

2 | a !on this and subsequent lines as necessary; list matrix elements by rows; each row should start on a new line and use as many lines for each matrix row as necessary | ||

4 | 1 | n | |

2 | a !on this and subsequent lines as necessary; list matrix elements by rows; each row should start on a new line and use as many lines for each matrix row as necessary | ||

5 | 1 | n | |

2 | b !the vector of "right hand sides" on this and subsequent lines as needed | ||

3 | a !on this and subsequent lines as necessary; list matrix elements by rows; each row should start on a new line and use as many lines for each matrix row as necessary | ||

6 | 1 | n | |

2 | |||

7 | 1 | 1 | ax ay r12 |

2 | method !where method should be one of biv2 or dutt or clark | ||

2 | 1 | ax ay az r12 r13 r23 | |

2 | method !where method should be one of dutt or clark | ||

3 | 1 | idim | |

2 | ax bx nx
!if idim=1 ax bx ay by nx ny !if idim=2 ax bx ay by az bz nx ny nz !if idim=3 | ||

4 | 1 | ax bx n | |

5 | 1 | ax bx | |

6 | 1 | idim | |

2 | ax bx nx
!if idim=1 ax bx ay by nx ny !if idim=2 ax bx ay by az bz nx ny nz !if idim=3 | ||

7 | 1 | idim n | |

2 | ax bx nx
!if idim=1 ax bx ay by nx ny !if idim=2 ax bx ay by az bz nx ny nz !if idim=3 ax bx ay by az bz aw bw nx ny nz nw !if idim=4 | ||

8 | 1 | ax bx | |

9 | 1 | ax n | |

10 | 1 | nrep ndim indep iconst | |

2 | a !read by rows starting with a(1,0); each row to start on a new line | ||

3 | xmu !as many lines as necessary | ||

4 | sig !if indep=.TRUE., as many lines as necessary cov !if indep=.FALSE.; by rows, with each row starting on a new line; as many lines as necessary | ||

8 | 1 | 1 | n |

2 | 1 | n | |

3 | 1 | n | |

4 | 1 | n m | |

5 | 1 | n a | |

6 | 1 | n s | |

7 | 1 | n s | |

8 | 1 | n a b | |

9 | 1 | n | |

9 | 1 | n | |

2 | x !the variable plotted on the horizontal axis; on this and subsequent lines as needed | ||

3 | y !the variable plotted on the vertical axis; on this and subsequent lines as necessary; | ||

10 | 1 | xmu var y acc iterl |

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