C ALGORITHM 726, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 20, NO. 1, MARCH, 1994, PP. 21-62. C C Remark -- to appear cat < README This is a package of routines, called ORTHPOL, for generating orthogonal polynomials and Gauss-type quadrature rules developed by Walter Gautschi. A description of the underlying methods can be found in a companion paper published in ``ACM Transactions on Mathematical Software''. There are files of four kinds in this package: the fortran netlib programs r1mach,d1mach, generating single- and double-precision machine constants for a variety of computers (Chapter 0); driver programs in fortran, called test1.f, test2.f, ... (Chapter 1); files called test1.out, test2.out, ... containing the output of the respective drivers when run on the Cyber 205 (Chapter 1); the fortran subroutines making up the core of the package (Chapters 2 - 6). The machine constants highlighted in the netlib programs are those for the Cyber 205. They have been kindly supplied by David A. Seaman of the Purdue University Computing Center. If the package is to be run on a different computer, the Cyber 205 machine constants have to be commented out and the constants appropriate for the particular machine uncommented. Structurally, the package is one single UNIX file, which, when given a name, say ``package'', can be broken up into its individual component files by the command sh < package At the same time, this will create a Makefile which allows the user to compile and run (on a variety of computers) all test programs by typing make or the N-th test by typing make testN.out.local The output of testN in either case is placed into a file called testN.out.local. On computers which do not support UNIX, the individual files can be recovered by noting that they each start with a line of the form cat < filename and end with the line C-END-OF-FILE To see which files must be assembled to run each test, refer to the lines starting with 'TESTn = ' in Makefile. The following is a brief description of the individual files of the package. r1mach.f a netlib program generating single-precision machine constants for a variety of computers d1mach.f a netlib program generating double-precision machine constants for a variety of computers test1.f relates to Example 3.1 of the companion paper, where orthogonal polynomials are generated relative to a weight function on (-1,1) having square root singularities at 1, -1, 1/omega, -1/omega, with omega between 0 and 1 test1.out contains the output of test1.f test2.f relates to Example 3.2, where orthogonal polynomials are generated relative to a weight function on (0,1) having a logarithmic singularity at the origin as well as an algebraic singularity with exponent sigma greater than -1 test2.out contains the output of test2.f test3.f relates to Example 4.1, implementing Stieltjes's procedure and the Lanczos algorithm to generate discrete Legendre polynomials test3.out contains the output of test3.f test4.f relates to Example 4.2, where a discretization procedure is applied to generate orthogonal polynomials relative to the Chebyshev weight function plus a constant test4.out contains the output of test4.f test5.f relates to Example 4.3 illustrating the use of a discretization procedure to generate orthogonal polynomials relative to the Jacobi weight function with a mass point of given strength placed at the left end point test5.out contains the output of test5.f test6.f relates to Example 4.4 implementing a discretization procedure to generate orthogonal polynomials for the logistics density function test6.out contains the output of test6.f test7.f relates to Example 4.5 employing a general-purpose discretization procedure to generate the half-range Hermite polynomials test7.out contains the output of test7.f test8.f relates to Example 4.6, where Example 3.1 is redone by means of a discretized modified Chebyshev algorithm test8.out contains the output of test8.f test9.f relates to Example 5.1, redoing Example 3.2 for sigma=1/2, using a modification algorithm test9.out contains the output of test9.f test10.f relates to Example 5.2, generating induced Legendre polynomials test10.out contains the output of test10.f test11.f relates to Example 5.3, illustrating the performance of the routines chri.f and gchri.f (see below) in the case of the Jacobi weight function multiplied or divided by a linear and quadratic factor test11.out contains the output of test11.f recur.f a subroutine generating the recursion coefficients of classical orthogonal polynomials drecur.f a double-precision version of recur.f cheb.f a subroutine implementing the modified Chebyshev algorithm dcheb.f a double-precision version of cheb.f sti.f a subroutine generating the recursion coefficients of discrete orthogonal polynomials by Stieltjes's procedure dsti.f a double-precision version of sti.f lancz.f a subroutine generating the recursion coefficients of discrete orthogonal polynomials by Lanczos's algorithm dlancz.f a double-precision version of lancz.f mcdis.f a subroutine computing the recursion coefficients (to a given degree of approximation) of continuous and mixed-type orthogonal polynomials by means of a multi- component discretization procedure dmcdis.f a double-precision version of mcdis.f qgp.f a general-purpose quadrature routine for use in mcdis.f or in mccheb.f dqgp.f a general-purpose quadrature routine for use in dmcdis.f or in dmcheb.f mccheb.f a subroutine implementing the discretized modified Chebyshev algorithm whereby modified moments are approximated by discrete modified moments dmcheb.f a double-precision version of mccheb.f chri.f a subroutine for computing the recursion coefficients of polynomials orthogonal with respect to a weight function obtained by a linear or quadratic modification of a given weight function dchri.f a double-precision version of chri.f knum.f a subroutine which applies a backward recurrence algorithm to generate weighted integrals of orthogonal polynomials multiplied by a Cauchy kernel nu0jac.f auxiliary routines providing an estimate for the starting nu0lag.f index in the backward recurrence algorithm of knum.f for nu0her.f respectively the Jacobi, Laguerre and Hermite weights dknum.f a double-precision version of knum.f kern.f a subroutine generating the kernels in the remainder term of Gauss quadrature rules applied to analytic functions dkern.f a double-precision version of kern.f gchri.f an alternative subroutine (to chri.f) for computing the recursion coefficients of polynomials orthogonal with with respect to a weight function obtained by dividing a given weight function by a linear or quadratic factor dgchri.f a double-precision version of gchri.f gauss.f a subroutine generating Gauss quadrature rules relative to a given integration measure dgauss.f a double-precision version of gauss.f radau.f a subroutine generating Gauss-Radau quadrature rules relative to a given integration measure dradau.f a double-precision version of radau.f lob.f a subroutine generating Gauss-Lobatto quadrature rules relative to a given integration measure dlob.f a double-precision version of lob.f C-END-OF-FILE cat < Makefile ####################################################################### # # # Makefile for ORTHPOL # # # # Usage: # # # # Type make to compile and run all test programs # # Type make testN.out.local to compile and run the test program # # number N # # Type make clean to remove all but the generated output # # # ####################################################################### #---------------------------------------------------------------------- # This section specifies the name of the linker and compilation options # for various systems. All but one are commented out. #---------------------------------------------------------------------- # ... For the Sun LD = f77 FFLAGS = #Do not use -O2; it may introduce errors # ... For the Cray #LD = cf77 #FFLAGS = # ... For the Convex #LD = fc #FFLAGS = -O2 # ... For the RS/6000 #LD = xlf #FFLAGS = -O # ... For the HP 9000 series #LD = f77 #FFLAGS = -O -K -w # ... For Silicon Graphics #LD = f77 #FFLAGS = -O2 #------------------------------------------------------------------- # This section specifies which object files are needed for each test # program. #------------------------------------------------------------------- TEST1 = test1.o r1mach.o d1mach.o recur.o drecur.o cheb.o dcheb.o TEST2 = test2.o r1mach.o d1mach.o recur.o drecur.o cheb.o dcheb.o TEST3 = test3.o r1mach.o sti.o lancz.o TEST4 = test4.o r1mach.o mcdis.o qgp.o sti.o lancz.o recur.o gauss.o TEST5 = test5.o r1mach.o d1mach.o recur.o drecur.o mcdis.o qgp.o sti.o lancz.o gauss.o TEST6 = test6.o r1mach.o d1mach.o mcdis.o dmcdis.o qgp.o dqgp.o sti.o dsti.o lancz.o dlancz.o recur.o drecur.o gauss.o dgauss.o TEST7 = test7.o r1mach.o d1mach.o mcdis.o dmcdis.o qgp.o dqgp.o sti.o dsti.o lancz.o dlancz.o TEST8 = test8.o r1mach.o recur.o mccheb.o qgp.o cheb.o TEST9 = test9.o r1mach.o d1mach.o recur.o drecur.o cheb.o dcheb.o chri.o dchri.o TEST10= test10.o r1mach.o d1mach.o recur.o drecur.o gauss.o dgauss.o chri.o dchri.o TEST11= test11.o r1mach.o d1mach.o recur.o drecur.o knum.o nu0jac.o dknum.o gchri.o dgchri.o cheb.o dcheb.o chri.o dchri.o #-------------------------------------------------------------- # This is the default target. It will cause all the tests to be # generated and run, saving their outputs in files. #-------------------------------------------------------------- all : test1.out.local test2.out.local test3.out.local test4.out.local test5.out.local test6.out.local test7.out.local test8.out.local test9.out.local test10.out.local test11.out.local #---------------------------------------------------------------------- # This section shows how to run each test program. The output for testN # is put in testN.out.local. #---------------------------------------------------------------------- test1.out.local : test1 ; test1 > \$@ test2.out.local : test2 ; test2 > \$@ test3.out.local : test3 ; test3 > \$@ test4.out.local : test4 ; test4 > \$@ test5.out.local : test5 ; test5 > \$@ test6.out.local : test6 ; test6 > \$@ test7.out.local : test7 ; test7 > \$@ test8.out.local : test8 ; test8 > \$@ test9.out.local : test9 ; test9 > \$@ test10.out.local : test10 ; test10 > \$@ test11.out.local : test11 ; test11 > \$@ #-------------------------------------------------- # This section shows how to link each test program. #-------------------------------------------------- test1 : $(TEST1) ; $(LD) -o \$@ $(TEST1) test2 : $(TEST2) ; $(LD) -o \$@ $(TEST2) test3 : $(TEST3) ; $(LD) -o \$@ $(TEST3) test4 : $(TEST4) ; $(LD) -o \$@ $(TEST4) test5 : $(TEST5) ; $(LD) -o \$@ $(TEST5) test6 : $(TEST6) ; $(LD) -o \$@ $(TEST6) test7 : $(TEST7) ; $(LD) -o \$@ $(TEST7) test8 : $(TEST8) ; $(LD) -o \$@ $(TEST8) test9 : $(TEST9) ; $(LD) -o \$@ $(TEST9) test10 : $(TEST10) ; $(LD) -o \$@ $(TEST10) test11 : $(TEST11) ; $(LD) -o \$@ $(TEST11) #---------------------------------------------- # This section shows how to clean up afterward. #---------------------------------------------- clean : rm -f core test1 test2 test3 test4 test5 test6 test7 test8 test9 test10 test11 *.o C-END-OF-FILE ######################### # # # 0. MACHINE CONSTANTS # # # ######################### cat < r1mach.f c c real function r1mach(i) c c Single-precision machine constants c c r1mach(1) = b**(emin-1), the smallest positive magnitude. c c r1mach(2) = b**emax*(1 - b**(-t)), the largest magnitude. c c r1mach(3) = b**(-t), the smallest relative spacing. c c r1mach(4) = b**(1-t), the largest relative spacing. c c r1mach(5) = log10(b) c c To alter this function for a particular environment, c the desired set of data statements should be activated by c removing the c from column 1. c On rare machines a static statement may need to be added. c (But probably more systems prohibit it than require it.) c c For IEEE-arithmetic machines (binary standard), the second c set of constants below should be appropriate. c c Where possible, decimal, octal or hexadecimal constants are used c to specify the constants exactly. Sometimes this requires using c equivalent integer arrays. If your compiler uses half-word c integers by default (sometimes called integer*2), you may need to c change integer to integer*4 or otherwise instruct your compiler c to use full-word integers in the next 5 declarations. c integer small(2) integer large(2) integer right(2) integer diver(2) integer log10(2) integer sc c real rmach(5) c equivalence (rmach(1),small(1)) equivalence (rmach(2),large(1)) equivalence (rmach(3),right(1)) equivalence (rmach(4),diver(1)) equivalence (rmach(5),log10(1)) c c machine constants for cdc cyber 205 and eta-10. c data small(1) / x'9000400000000000' / data large(1) / x'6FFF7FFFFFFFFFFF' / data right(1) / x'FFA3400000000000' / data diver(1) / x'FFA4400000000000' / data log10(1) / x'FFD04D104D427DE8' /, sc/987/ c c machine constants for ieee arithmetic machines, such as the at&t c 3b series, motorola 68000 based machines (e.g. sun 3 and at&t c pc 7300), and 8087 based micros (e.g. ibm pc and at&t 6300). c c data small(1) / 8388608 / c data large(1) / 2139095039 / c data right(1) / 864026624 / c data diver(1) / 872415232 / c data log10(1) / 1050288283 /, sc/987/ c c machine constants for amdahl machines. c c data small(1) / 1048576 / c data large(1) / 2147483647 / c data right(1) / 990904320 / c data diver(1) / 1007681536 / c data log10(1) / 1091781651 /, sc/987/ c c machine constants for the burroughs 1700 system. c c data rmach(1) / z400800000 / c data rmach(2) / z5ffffffff / c data rmach(3) / z4e9800000 / c data rmach(4) / z4ea800000 / c data rmach(5) / z500e730e8 /, sc/987/ c c machine constants for the burroughs 5700/6700/7700 systems. c c data rmach(1) / o1771000000000000 / c data rmach(2) / o0777777777777777 / c data rmach(3) / o1311000000000000 / c data rmach(4) / o1301000000000000 / c data rmach(5) / o1157163034761675 /, sc/987/ c c machine constants for ftn4 on the cdc 6000/7000 series. c c data rmach(1) / 00564000000000000000b / c data rmach(2) / 37767777777777777776b / c data rmach(3) / 16414000000000000000b / c data rmach(4) / 16424000000000000000b / c data rmach(5) / 17164642023241175720b /, sc/987/ c c machine constants for ftn5 on the cdc 6000/7000 series. c c data rmach(1) / o"00564000000000000000" / c data rmach(2) / o"37767777777777777776" / c data rmach(3) / o"16414000000000000000" / c data rmach(4) / o"16424000000000000000" / c data rmach(5) / o"17164642023241175720" /, sc/987/ c c machine constants for convex c-1. c c data rmach(1) / '00800000'x / c data rmach(2) / '7fffffff'x / c data rmach(3) / '34800000'x / c data rmach(4) / '35000000'x / c data rmach(5) / '3f9a209b'x /, sc/987/ c c machine constants for the cray 1, xmp, 2, and 3. c c data rmach(1) / 200034000000000000000b / c data rmach(2) / 577767777777777777776b / c data rmach(3) / 377224000000000000000b / c data rmach(4) / 377234000000000000000b / c data rmach(5) / 377774642023241175720b /, sc/987/ c c machine constants for the data general eclipse s/200. c c note - it may be appropriate to include the following line - c static rmach(5) c c data small/20k,0/,large/77777k,177777k/ c data right/35420k,0/,diver/36020k,0/ c data log10/40423k,42023k/, sc/987/ c c machine constants for the harris slash 6 and slash 7. c c data small(1),small(2) / '20000000, '00000201 / c data large(1),large(2) / '37777777, '00000177 / c data right(1),right(2) / '20000000, '00000352 / c data diver(1),diver(2) / '20000000, '00000353 / c data log10(1),log10(2) / '23210115, '00000377 /, sc/987/ c c machine constants for the honeywell dps 8/70 series. c c data rmach(1) / o402400000000 / c data rmach(2) / o376777777777 / c data rmach(3) / o714400000000 / c data rmach(4) / o716400000000 / c data rmach(5) / o776464202324 /, sc/987/ c c machine constants for the ibm 360/370 series, c the xerox sigma 5/7/9 and the sel systems 85/86. c c data rmach(1) / z00100000 / c data rmach(2) / z7fffffff / c data rmach(3) / z3b100000 / c data rmach(4) / z3c100000 / c data rmach(5) / z41134413 /, sc/987/ c c machine constants for the interdata 8/32 c with the unix system fortran 77 compiler. c c for the interdata fortran vii compiler replace c the z's specifying hex constants with y's. c c data rmach(1) / z'00100000' / c data rmach(2) / z'7effffff' / c data rmach(3) / z'3b100000' / c data rmach(4) / z'3c100000' / c data rmach(5) / z'41134413' /, sc/987/ c c machine constants for the pdp-10 (ka or ki processor). c c data rmach(1) / "000400000000 / c data rmach(2) / "377777777777 / c data rmach(3) / "146400000000 / c data rmach(4) / "147400000000 / c data rmach(5) / "177464202324 /, sc/987/ c c machine constants for pdp-11 fortrans supporting c 32-bit integers (expressed in integer and octal). c c data small(1) / 8388608 / c data large(1) / 2147483647 / c data right(1) / 880803840 / c data diver(1) / 889192448 / c data log10(1) / 1067065499 /, sc/987/ c c data rmach(1) / o00040000000 / c data rmach(2) / o17777777777 / c data rmach(3) / o06440000000 / c data rmach(4) / o06500000000 / c data rmach(5) / o07746420233 /, sc/987/ c c machine constants for pdp-11 fortrans supporting c 16-bit integers (expressed in integer and octal). c c data small(1),small(2) / 128, 0 / c data large(1),large(2) / 32767, -1 / c data right(1),right(2) / 13440, 0 / c data diver(1),diver(2) / 13568, 0 / c data log10(1),log10(2) / 16282, 8347 /, sc/987/ c c data small(1),small(2) / o000200, o000000 / c data large(1),large(2) / o077777, o177777 / c data right(1),right(2) / o032200, o000000 / c data diver(1),diver(2) / o032400, o000000 / c data log10(1),log10(2) / o037632, o020233 /, sc/987/ c c machine constants for the sequent balance 8000. c c data small(1) / $00800000 / c data large(1) / $7f7fffff / c data right(1) / $33800000 / c data diver(1) / $34000000 / c data log10(1) / $3e9a209b /, sc/987/ c c machine constants for the univac 1100 series. c c data rmach(1) / o000400000000 / c data rmach(2) / o377777777777 / c data rmach(3) / o146400000000 / c data rmach(4) / o147400000000 / c data rmach(5) / o177464202324 /, sc/987/ c c machine constants for the vax unix f77 compiler. c c data small(1) / 128 / c data large(1) / -32769 / c data right(1) / 13440 / c data diver(1) / 13568 / c data log10(1) / 547045274 /, sc/987/ c c machine constants for the vax-11 with c fortran iv-plus compiler. c c data rmach(1) / z00000080 / c data rmach(2) / zffff7fff / c data rmach(3) / z00003480 / c data rmach(4) / z00003500 / c data rmach(5) / z209b3f9a /, sc/987/ c c machine constants for vax/vms version 2.2. c c data rmach(1) / '80'x / c data rmach(2) / 'ffff7fff'x / c data rmach(3) / '3480'x / c data rmach(4) / '3500'x / c data rmach(5) / '209b3f9a'x /, sc/987/ c c *** issue stop 778 if all data statements are commented... if (sc .ne. 987) stop 778 if (i .lt. 1 .or. i .gt. 5) goto 999 r1mach = rmach(i) return 999 write(*,1999) i 1999 format(' r1mach - i out of bounds',i10) stop end C-END-OF-FILE cat < d1mach.f c c double precision function d1mach(i) c c Double-precision machine constants c c d1mach( 1) = b**(emin-1), the smallest positive magnitude. c c d1mach( 2) = b**emax*(1 - b**(-t)), the largest magnitude. c c d1mach( 3) = b**(-t), the smallest relative spacing. c c d1mach( 4) = b**(1-t), the largest relative spacing. c c d1mach( 5) = log10(b) c c To alter this function for a particular environment, c the desired set of data statements should be activated by c removing the c from column 1. c On rare machines a static statement may need to be added. c (But probably more systems prohibit it than require it.) c c For IEEE-arithmetic machines (binary standard), one of the second c two sets of constants below should be appropriate. c c Where possible, decimal, octal or hexadecimal constants are used c to specify the constants exactly. Sometimes this requires using c equivalent integer arrays. If your compiler uses half-word c integers by default (sometimes called integer*2), you may need to c change integer to integer*4 or otherwise instruct your compiler c to use full-word integers in the next 5 declarations. c integer small(2) integer large(2) integer right(2) integer diver(2) integer log10(2) integer sc c double precision dmach(5) c equivalence (dmach(1),small(1)) equivalence (dmach(2),large(1)) equivalence (dmach(3),right(1)) equivalence (dmach(4),diver(1)) equivalence (dmach(5),log10(1)) c c machine constants for cdc cyber 205 and eta-10. c data small(1) / x'9000400000000000' / data small(2) / x'8000000000000000' / data large(1) / x'6FFF7FFFFFFFFFFF' / data large(2) / x'6FD07FFFFFFFFFFF' / data right(1) / x'FF74400000000000' / data right(2) / x'8000000000000000' / data diver(1) / x'FF75400000000000' / data diver(2) / x'8000000000000000' / data log10(1) / x'FFD04D104D427DE7' / data log10(2) / x'FFA17DE623E2566B' /, sc/987/ c c machine constants for ieee arithmetic machines, such as the at&t c 3b series and motorola 68000 based machines (e.g. sun 3 and at&t c pc 7300), in which the most significant byte is stored first. c c data small(1),small(2) / 1048576, 0 / c data large(1),large(2) / 2146435071, -1 / c data right(1),right(2) / 1017118720, 0 / c data diver(1),diver(2) / 1018167296, 0 / c data log10(1),log10(2) / 1070810131, 1352628735 /, sc/987/ c c machine constants for ieee arithmetic machines and 8087-based c micros, such as the ibm pc and at&t 6300, in which the least c significant byte is stored first. c c data small(1),small(2) / 0, 1048576 / c data large(1),large(2) / -1, 2146435071 / c data right(1),right(2) / 0, 1017118720 / c data diver(1),diver(2) / 0, 1018167296 / c data log10(1),log10(2) / 1352628735, 1070810131 /, sc/987/ c c machine constants for amdahl machines. c c data small(1),small(2) / 1048576, 0 / c data large(1),large(2) / 2147483647, -1 / c data right(1),right(2) / 856686592, 0 / c data diver(1),diver(2) / 873463808, 0 / c data log10(1),log10(2) / 1091781651, 1352628735 /, sc/987/ c c machine constants for the burroughs 1700 system. c c data small(1) / zc00800000 / c data small(2) / z000000000 / c c data large(1) / zdffffffff / c data large(2) / zfffffffff / c c data right(1) / zcc5800000 / c data right(2) / z000000000 / c c data diver(1) / zcc6800000 / c data diver(2) / z000000000 / c c data log10(1) / zd00e730e7 / c data log10(2) / zc77800dc0 /, sc/987/ c c machine constants for the burroughs 5700 system. c c data small(1) / o1771000000000000 / c data small(2) / o0000000000000000 / c c data large(1) / o0777777777777777 / c data large(2) / o0007777777777777 / c c data right(1) / o1461000000000000 / c data right(2) / o0000000000000000 / c c data diver(1) / o1451000000000000 / c data diver(2) / o0000000000000000 / c c data log10(1) / o1157163034761674 / c data log10(2) / o0006677466732724 /, sc/987/ c c machine constants for the burroughs 6700/7700 systems. c c data small(1) / o1771000000000000 / c data small(2) / o7770000000000000 / c c data large(1) / o0777777777777777 / c data large(2) / o7777777777777777 / c c data right(1) / o1461000000000000 / c data right(2) / o0000000000000000 / c c data diver(1) / o1451000000000000 / c data diver(2) / o0000000000000000 / c c data log10(1) / o1157163034761674 / c data log10(2) / o0006677466732724 /, sc/987/ c c machine constants for ftn4 on the cdc 6000/7000 series. c c data small(1) / 00564000000000000000b / c data small(2) / 00000000000000000000b / c c data large(1) / 37757777777777777777b / c data large(2) / 37157777777777777774b / c c data right(1) / 15624000000000000000b / c data right(2) / 00000000000000000000b / c c data diver(1) / 15634000000000000000b / c data diver(2) / 00000000000000000000b / c c data log10(1) / 17164642023241175717b / c data log10(2) / 16367571421742254654b /, sc/987/ c c machine constants for ftn5 on the cdc 6000/7000 series. c c data small(1) / o"00564000000000000000" / c data small(2) / o"00000000000000000000" / c c data large(1) / o"37757777777777777777" / c data large(2) / o"37157777777777777774" / c c data right(1) / o"15624000000000000000" / c data right(2) / o"00000000000000000000" / c c data diver(1) / o"15634000000000000000" / c data diver(2) / o"00000000000000000000" / c c data log10(1) / o"17164642023241175717" / c data log10(2) / o"16367571421742254654" /, sc/987/ c c machine constants for convex c-1 c c data small(1),small(2) / '00100000'x, '00000000'x / c data large(1),large(2) / '7fffffff'x, 'ffffffff'x / c data right(1),right(2) / '3cc00000'x, '00000000'x / c data diver(1),diver(2) / '3cd00000'x, '00000000'x / c data log10(1),log10(2) / '3ff34413'x, '509f79ff'x /, sc/987/ c c machine constants for the cray 1, xmp, 2, and 3. c c data small(1) / 201354000000000000000b / c data small(2) / 000000000000000000000b / c c data large(1) / 577767777777777777777b / c data large(2) / 000007777777777777776b / c c data right(1) / 376434000000000000000b / c data right(2) / 000000000000000000000b / c c data diver(1) / 376444000000000000000b / c data diver(2) / 000000000000000000000b / c c data log10(1) / 377774642023241175717b / c data log10(2) / 000007571421742254654b /, sc/987/ c c machine constants for the data general eclipse s/200 c c small, large, right, diver, log10 should be declared c integer small(4), large(4), right(4), diver(4), log10(4) c c note - it may be appropriate to include the following line - c static dmach(5) c c data small/20k,3*0/,large/77777k,3*177777k/ c data right/31420k,3*0/,diver/32020k,3*0/ c data log10/40423k,42023k,50237k,74776k/, sc/987/ c c machine constants for the harris slash 6 and slash 7 c c data small(1),small(2) / '20000000, '00000201 / c data large(1),large(2) / '37777777, '37777577 / c data right(1),right(2) / '20000000, '00000333 / c data diver(1),diver(2) / '20000000, '00000334 / c data log10(1),log10(2) / '23210115, '10237777 /, sc/987/ c c machine constants for the honeywell dps 8/70 series. c c data small(1),small(2) / o402400000000, o000000000000 / c data large(1),large(2) / o376777777777, o777777777777 / c data right(1),right(2) / o604400000000, o000000000000 / c data diver(1),diver(2) / o606400000000, o000000000000 / c data log10(1),log10(2) / o776464202324, o117571775714 /, sc/987/ c c machine constants for the ibm 360/370 series, c the xerox sigma 5/7/9 and the sel systems 85/86. c c data small(1),small(2) / z00100000, z00000000 / c data large(1),large(2) / z7fffffff, zffffffff / c data right(1),right(2) / z33100000, z00000000 / c data diver(1),diver(2) / z34100000, z00000000 / c data log10(1),log10(2) / z41134413, z509f79ff /, sc/987/ c c machine constants for the interdata 8/32 c with the unix system fortran 77 compiler. c c for the interdata fortran vii compiler replace c the z's specifying hex constants with y's. c c data small(1),small(2) / z'00100000', z'00000000' / c data large(1),large(2) / z'7effffff', z'ffffffff' / c data right(1),right(2) / z'33100000', z'00000000' / c data diver(1),diver(2) / z'34100000', z'00000000' / c data log10(1),log10(2) / z'41134413', z'509f79ff' /, sc/987/ c c machine constants for the pdp-10 (ka processor). c c data small(1),small(2) / "033400000000, "000000000000 / c data large(1),large(2) / "377777777777, "344777777777 / c data right(1),right(2) / "113400000000, "000000000000 / c data diver(1),diver(2) / "114400000000, "000000000000 / c data log10(1),log10(2) / "177464202324, "144117571776 /, sc/987/ c c machine constants for the pdp-10 (ki processor). c c data small(1),small(2) / "000400000000, "000000000000 / c data large(1),large(2) / "377777777777, "377777777777 / c data right(1),right(2) / "103400000000, "000000000000 / c data diver(1),diver(2) / "104400000000, "000000000000 / c data log10(1),log10(2) / "177464202324, "047674776746 /, sc/987/ c c machine constants for pdp-11 fortrans supporting c 32-bit integers (expressed in integer and octal). c c data small(1),small(2) / 8388608, 0 / c data large(1),large(2) / 2147483647, -1 / c data right(1),right(2) / 612368384, 0 / c data diver(1),diver(2) / 620756992, 0 / c data log10(1),log10(2) / 1067065498, -2063872008 /, sc/987/ c c data small(1),small(2) / o00040000000, o00000000000 / c data large(1),large(2) / o17777777777, o37777777777 / c data right(1),right(2) / o04440000000, o00000000000 / c data diver(1),diver(2) / o04500000000, o00000000000 / c data log10(1),log10(2) / o07746420232, o20476747770 /, sc/987/ c c machine constants for pdp-11 fortrans supporting c 16-bit integers (expressed in integer and octal). c c small, large, right, diver, log10 should be declared c integer small(4), large(4), right(4), diver(4), log10(4) c c data small(1),small(2) / 128, 0 / c data small(3),small(4) / 0, 0 / c c data large(1),large(2) / 32767, -1 / c data large(3),large(4) / -1, -1 / c c data right(1),right(2) / 9344, 0 / c data right(3),right(4) / 0, 0 / c c data diver(1),diver(2) / 9472, 0 / c data diver(3),diver(4) / 0, 0 / c c data log10(1),log10(2) / 16282, 8346 / c data log10(3),log10(4) / -31493, -12296 /, sc/987/ c c data small(1),small(2) / o000200, o000000 / c data small(3),small(4) / o000000, o000000 / c c data large(1),large(2) / o077777, o177777 / c data large(3),large(4) / o177777, o177777 / c c data right(1),right(2) / o022200, o000000 / c data right(3),right(4) / o000000, o000000 / c c data diver(1),diver(2) / o022400, o000000 / c data diver(3),diver(4) / o000000, o000000 / c c data log10(1),log10(2) / o037632, o020232 / c data log10(3),log10(4) / o102373, o147770 /, sc/987/ c c machine constants for the prime 50 series systems c with 32-bit integers and 64v mode instructions, c supplied by igor bray. c c data small(1),small(2) / :10000000000, :00000100001 / c data large(1),large(2) / :17777777777, :37777677775 / c data right(1),right(2) / :10000000000, :00000000122 / c data diver(1),diver(2) / :10000000000, :00000000123 / c data log10(1),log10(2) / :11504046501, :07674600177 /, sc/987/ c c machine constants for the sequent balance 8000 c c data small(1),small(2) / $00000000, $00100000 / c data large(1),large(2) / $ffffffff, $7fefffff / c data right(1),right(2) / $00000000, $3ca00000 / c data diver(1),diver(2) / $00000000, $3cb00000 / c data log10(1),log10(2) / $509f79ff, $3fd34413 /, sc/987/ c c machine constants for the univac 1100 series. c c data small(1),small(2) / o000040000000, o000000000000 / c data large(1),large(2) / o377777777777, o777777777777 / c data right(1),right(2) / o170540000000, o000000000000 / c data diver(1),diver(2) / o170640000000, o000000000000 / c data log10(1),log10(2) / o177746420232, o411757177572 /, sc/987/ c c machine constants for the vax unix f77 compiler c c data small(1),small(2) / 128, 0 / c data large(1),large(2) / -32769, -1 / c data right(1),right(2) / 9344, 0 / c data diver(1),diver(2) / 9472, 0 / c data log10(1),log10(2) / 546979738, -805796613 /, sc/987/ c c machine constants for the vax-11 with c fortran iv-plus compiler c c data small(1),small(2) / z00000080, z00000000 / c data large(1),large(2) / zffff7fff, zffffffff / c data right(1),right(2) / z00002480, z00000000 / c data diver(1),diver(2) / z00002500, z00000000 / c data log10(1),log10(2) / z209a3f9a, zcff884fb /, sc/987/ c c machine constants for vax/vms version 2.2 c c data small(1),small(2) / '80'x, '0'x / c data large(1),large(2) / 'ffff7fff'x, 'ffffffff'x / c data right(1),right(2) / '2480'x, '0'x / c data diver(1),diver(2) / '2500'x, '0'x / c data log10(1),log10(2) / '209a3f9a'x, 'cff884fb'x /, sc/987/ c c *** issue stop 779 if all data statements are commented... if (sc .ne. 987) stop 779 c *** issue stop 778 if all data statements are obviously wrong... if (dmach(4) .ge. 1.0d0) stop 778 if (i .lt. 1 .or. i .gt. 5) goto 999 d1mach = dmach(i) return 999 write(*,1999) i 1999 format(' d1mach - i out of bounds',i10) stop end C-END-OF-FILE ############# # # # 1. TESTS # # # ############# cat < test1.f c c program test1 c c dimension fnu(160),f(80),f0(80),rr(80),a(159),b(159), *alpha(80),beta(80),s(80),s0(160),s1(160),s2(160) double precision doom2(7),deps,d1mach,dom2,dnu(160),d(80), *d0(80),drr(80),da(159),db(159),dalpha(80),dbeta(80),ds(80), *ds0(160),ds1(160),ds2(160) logical modmom data doom2/.1d0,.3d0,.5d0,.7d0,.9d0,.99d0,.999d0/ c c This test generates the first n beta-coefficients in the recurrence c relation for the orthogonal polynomials relative to the weight c function c c ((1-om2*x**2)*(1-x**2))**(-1/2) on (-1,1) c c for om2=.1(.2).9,.99,.999, both in single and double precision, c using modified moments if modmom=.true. and ordinary moments c otherwise. In the former case, n=80, in the latter, n=20. Printed c are the double-precision values of the coefficients along with the c relative errors of the single-precision values. c write(*,1) 1 format(/) modmom=.true. eps=r1mach(3) deps=d1mach(3) if(modmom) then n=80 else n=20 end if ndm1=2*n-1 do 30 iom=1,7 dom2=doom2(iom) om2=sngl(dom2) c c Compute the modified resp. ordinary moments using Eqs. (3.7) and (3.9) c of the companion paper. On machines with limited exponent range, some c of the high-order modified moments may underflow, without this having c any deteriorating effect on the accuracy. c call fmm(n,eps,modmom,om2,fnu,ierr,f,f0,rr) call dmm(n,deps,modmom,dom2,dnu,iderr,d,d0,drr) if(ierr.ne.0 .or. iderr.ne.0) then write(*,2) ierr,iderr,om2 2 format(/5x,'ierr in fmm = ',i1,' iderr in dmm = ',i1, * ' for om2 = ',f8.4/) goto 30 end if c c Generate the recursion coefficients for the polynomials defining the c modified resp. ordinary moments. c if(modmom) then call recur(ndm1,3,0.,0.,a,b,ierr) call drecur(ndm1,3,0.d0,0.d0,da,db,iderr) else do 10 k=1,ndm1 a(k)=0. b(k)=0. da(k)=0.d0 db(k)=0.d0 10 continue end if c c Compute the desired recursion coefficients by means of the modified c Chebyshev algorithm; for the latter, see, e.g., Section 2.4 of c W. Gautschi, ``On generating orthogonal polynomials'', SIAM J. Sci. c Statist. Comput. 3, 1982, 289-317. c call cheb(n,a,b,fnu,alpha,beta,s,ierr,s0,s1,s2) c c On machines with limited single-precision exponent range, the routine c cheb may generate an underflow exception, which however is harmless c and can be ignored. c call dcheb(n,da,db,dnu,dalpha,dbeta,ds,iderr,ds0,ds1,ds2) write(*,3) ierr,iderr 3 format(/5x,'ierr in cheb = ',i3,' iderr in dcheb = ',i3/) write(*,4) 4 format(/5x,'k',14x,'dbeta(k)'/) do 20 k=1,n km1=k-1 if(iderr.eq.0 .or. km1.lt.abs(iderr)) then if(ierr.eq.0 .or. km1.lt.abs(ierr)) then errb=sngl(dabs(dble(beta(k))-dbeta(k))/dbeta(k)) if(k.eq.1) then write(*,5) km1,dbeta(k),errb,om2 5 format(1x,i5,d36.28,e12.4,' om2 =',f6.3) else write(*,6) km1,dbeta(k),errb 6 format(1x,i5,d36.28,e12.4) end if else write(*,7) km1,dbeta(k) 7 format(1x,i5,d36.28) end if end if 20 continue write(*,1) 30 continue stop end subroutine fmm(n,eps,modmom,om2,fnu,ierr,f,f0,rr) c c This routine generates the modified (Chebyshev) resp. ordinary c moments of the weight function c c ((1-om2*x**2)*(1-x**2))**(-1/2) on (-1,1) c c using Eqs. (3.7) resp. (3.9) of the companion paper. c dimension fnu(*),f(n),f0(n),rr(n) logical modmom c c The array fnu is assumed to have dimension 2*n. c ierr=0 nd=2*n ndm1=nd-1 pi=4.*atan(1.) c c Compute the Fourier coefficients of ((1-om2*sin(theta)**2))**(-1/2) c as minimal solution of a three-term recurrence relation as described c on pp.310-311 of W. Gautschi,``On generating orthogonal polynomials'', c SIAM J. Sci. Statist. Comput. 3, 1982, 289-317. c q=om2/(2.-om2+2.*sqrt(1.-om2)) q1=(1.+q*q)/q do 10 k=1,n f(k)=0. 10 continue nu=nd 20 nu=nu+10 do 30 k=1,n f0(k)=f(k) 30 continue if(nu.gt.500) then ierr=1 return end if r=0. s=0. do 40 k=1,nu n1=nu-k+1 fn1=real(n1) r=-(fn1-.5)/(fn1*q1+(fn1+.5)*r) s=r*(2.+s) if(n1.le.n) rr(n1)=r 40 continue c0=1./(1.+s) f(1)=rr(1)*c0 if(n.gt.1) then do 50 k=2,n f(k)=rr(k)*f(k-1) 50 continue end if do 60 k=1,n if(abs(f(k)-f0(k)).gt.eps*abs(f(k))) goto 20 60 continue c c Compute the desired modified resp. ordinary moments in term of c the above Fourier coefficients. c fnu(1)=pi*c0 if(n.eq.1) return fnu(2)=0. if(n.eq.2) return if(modmom) then c=2.*pi do 70 k=3,ndm1,2 k1=(k-1)/2 c=-.25*c fnu(k)=c*f(k1) fnu(k+1)=0. 70 continue else c=.5*pi fnu(3)=c*(c0-f(1)) fnu(4)=0. c=-c do 90 k=5,ndm1,2 k1=(k-1)/2 k1m1=k1-1 c=-.25*c c1=1. sum=f(k1) do 80 i=1,k1m1 c1=-c1*real(2*k1-i+1)/real(i) sum=sum+c1*f(k1-i) 80 continue c1=-c1*real(k1+1)/real(2*k1) sum=sum+c1*c0 fnu(k)=c*sum fnu(k+1)=0. 90 continue end if end subroutine dmm(n,deps,modmom,dom2,dnu,ierrd,d,d0,drr) c c This is a double-precision version of the routine fmm. c double precision deps,dom2,dnu(*),d(n),d0(n),drr(n),dpi,dq, *dq1,dr,ds,dn1,dc0,dc,dc1,dsum logical modmom c c The array dnu is assumed to have dimension 2*n. c ierrd=0 nd=2*n ndm1=nd-1 dpi=4.d0*datan(1.d0) dq=dom2/(2.d0-dom2+2.d0*dsqrt(1.d0-dom2)) dq1=(1.d0+dq*dq)/dq do 10 k=1,n d(k)=0.d0 10 continue nud=nd 20 nud=nud+10 do 30 k=1,n d0(k)=d(k) 30 continue if(nud.gt.1000) then ierrd=1 return end if dr=0.d0 ds=0.d0 do 40 k=1,nud n1=nud-k+1 dn1=dble(n1) dr=-(dn1-.5d0)/(dn1*dq1+(dn1+.5d0)*dr) ds=dr*(2.d0+ds) if(n1.le.n) drr(n1)=dr 40 continue dc0=1.d0/(1.d0+ds) d(1)=drr(1)*dc0 if(n.gt.1) then do 50 k=2,n d(k)=drr(k)*d(k-1) 50 continue end if do 60 k=1,n if(dabs(d(k)-d0(k)).gt.deps*dabs(d(k))) goto 20 60 continue dnu(1)=dpi*dc0 if(n.eq.1) return dnu(2)=0.d0 if(n.eq.2) return if(modmom) then dc=2.d0*dpi do 70 k=3,ndm1,2 k1=(k-1)/2 dc=-.25d0*dc dnu(k)=dc*d(k1) dnu(k+1)=0.d0 70 continue else dc=.5d0*dpi dnu(3)=dc*(dc0-d(1)) dnu(4)=0.d0 dc=-dc do 90 k=5,ndm1,2 k1=(k-1)/2 k1m1=k1-1 dc=-.25d0*dc dc1=1.d0 dsum=d(k1) do 80 i=1,k1m1 dc1=-dc1*dble(2*k1-i+1)/dble(i) dsum=dsum+dc1*d(k1-i) 80 continue dc1=-dc1*dble(k1+1)/dble(2*k1) dsum=dsum+dc1*dc0 dnu(k)=dc*dsum dnu(k+1)=0.d0 90 continue end if end C-END-OF-FILE cat < test1.out output of test1 with modmom=.true.: IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.3224882697440438796459832725D+01 0.1433E-13 OM2 = 0.100 1 0.5065840806382684475158495727D+00 0.1187E-13 2 0.2467293493188785576130435953D+00 0.9371E-14 3 0.2499786103248681596536302010D+00 0.5923E-14 4 0.2499997192892932646699795011D+00 0.5105E-14 5 0.2499999953890031901881028267D+00 0.1109E-13 6 0.2499999999151142217232291027D+00 0.1105E-13 7 0.2499999999983250486706790196D+00 0.2193E-13 8 0.2499999999999653681699452575D+00 0.3581E-14 9 0.2499999999999992594133250895D+00 0.1125E-13 10 0.2499999999999999837550002295D+00 0.6498E-16 11 0.2499999999999999996365048540D+00 0.1454E-17 12 0.2499999999999999999917355164D+00 0.3306E-19 13 0.2499999999999999999998096161D+00 0.1421E-13 14 0.2499999999999999999999955659D+00 0.1774E-22 15 0.2499999999999999999999998957D+00 0.4170E-24 16 0.2499999999999999999999999975D+00 0.9996E-26 17 0.2499999999999999999999999999D+00 0.3029E-27 18 0.2500000000000000000000000000D+00 0.0000E+00 19 0.2499999999999999999999999999D+00 0.2019E-27 20 0.2500000000000000000000000000D+00 0.0000E+00 21 0.2500000000000000000000000000D+00 0.0000E+00 22 0.2500000000000000000000000000D+00 0.0000E+00 23 0.2500000000000000000000000000D+00 0.0000E+00 24 0.2500000000000000000000000000D+00 0.0000E+00 25 0.2500000000000000000000000000D+00 0.0000E+00 26 0.2500000000000000000000000000D+00 0.0000E+00 27 0.2500000000000000000000000000D+00 0.0000E+00 28 0.2500000000000000000000000000D+00 0.0000E+00 29 0.2500000000000000000000000000D+00 0.0000E+00 30 0.2500000000000000000000000000D+00 0.0000E+00 31 0.2500000000000000000000000000D+00 0.0000E+00 32 0.2500000000000000000000000000D+00 0.0000E+00 33 0.2500000000000000000000000000D+00 0.0000E+00 34 0.2500000000000000000000000000D+00 0.0000E+00 35 0.2500000000000000000000000000D+00 0.0000E+00 36 0.2500000000000000000000000000D+00 0.0000E+00 37 0.2500000000000000000000000000D+00 0.0000E+00 38 0.2500000000000000000000000000D+00 0.0000E+00 39 0.2500000000000000000000000000D+00 0.0000E+00 40 0.2500000000000000000000000000D+00 0.0000E+00 41 0.2500000000000000000000000000D+00 0.0000E+00 42 0.2500000000000000000000000000D+00 0.0000E+00 43 0.2500000000000000000000000000D+00 0.0000E+00 44 0.2500000000000000000000000000D+00 0.0000E+00 45 0.2500000000000000000000000000D+00 0.0000E+00 46 0.2500000000000000000000000000D+00 0.0000E+00 47 0.2500000000000000000000000000D+00 0.0000E+00 48 0.2500000000000000000000000000D+00 0.0000E+00 49 0.2500000000000000000000000000D+00 0.0000E+00 50 0.2500000000000000000000000000D+00 0.0000E+00 51 0.2500000000000000000000000000D+00 0.0000E+00 52 0.2500000000000000000000000000D+00 0.0000E+00 53 0.2500000000000000000000000000D+00 0.0000E+00 54 0.2500000000000000000000000000D+00 0.0000E+00 55 0.2500000000000000000000000000D+00 0.0000E+00 56 0.2500000000000000000000000000D+00 0.0000E+00 57 0.2500000000000000000000000000D+00 0.0000E+00 58 0.2500000000000000000000000000D+00 0.0000E+00 59 0.2500000000000000000000000000D+00 0.0000E+00 60 0.2500000000000000000000000000D+00 0.0000E+00 61 0.2500000000000000000000000000D+00 0.0000E+00 62 0.2500000000000000000000000000D+00 0.0000E+00 63 0.2500000000000000000000000000D+00 0.0000E+00 64 0.2500000000000000000000000000D+00 0.0000E+00 65 0.2500000000000000000000000000D+00 0.0000E+00 66 0.2500000000000000000000000000D+00 0.0000E+00 67 0.2500000000000000000000000000D+00 0.0000E+00 68 0.2500000000000000000000000000D+00 0.0000E+00 69 0.2500000000000000000000000000D+00 0.0000E+00 70 0.2500000000000000000000000000D+00 0.0000E+00 71 0.2500000000000000000000000000D+00 0.0000E+00 72 0.2500000000000000000000000000D+00 0.0000E+00 73 0.2500000000000000000000000000D+00 0.0000E+00 74 0.2500000000000000000000000000D+00 0.0000E+00 75 0.2500000000000000000000000000D+00 0.0000E+00 76 0.2500000000000000000000000000D+00 0.0000E+00 77 0.2500000000000000000000000000D+00 0.0000E+00 78 0.2500000000000000000000000000D+00 0.0000E+00 79 0.2500000000000000000000000000D+00 0.0000E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.3427778896357582124077869689D+01 0.8867E-14 OM2 = 0.300 1 0.5222553571575005169932901811D+00 0.5370E-14 2 0.2391089484344383143284396275D+00 0.1443E-13 3 0.2497633566075743756040256623D+00 0.1802E-13 4 0.2499895949326480950578823133D+00 0.6392E-14 5 0.2499994255652457252517512062D+00 0.1306E-13 6 0.2499999644019888681144230020D+00 0.9176E-14 7 0.2499999976333568222970480036D+00 0.2369E-14 8 0.2499999998350340290206394715D+00 0.1715E-13 9 0.2499999999881026637164417901D+00 0.2807E-14 10 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0.2499999999999999999999998496D+00 0.6014E-24 30 0.2499999999999999999999999755D+00 0.9784E-25 31 0.2499999999999999999999999960D+00 0.1595E-25 32 0.2499999999999999999999999993D+00 0.2726E-26 33 0.2499999999999999999999999999D+00 0.5049E-27 34 0.2499999999999999999999999999D+00 0.2019E-27 35 0.2500000000000000000000000000D+00 0.0000E+00 36 0.2500000000000000000000000000D+00 0.0000E+00 37 0.2500000000000000000000000000D+00 0.0000E+00 38 0.2499999999999999999999999999D+00 0.2019E-27 39 0.2500000000000000000000000000D+00 0.0000E+00 40 0.2500000000000000000000000000D+00 0.0000E+00 41 0.2500000000000000000000000000D+00 0.0000E+00 42 0.2500000000000000000000000000D+00 0.0000E+00 43 0.2500000000000000000000000000D+00 0.0000E+00 44 0.2500000000000000000000000000D+00 0.0000E+00 45 0.2500000000000000000000000000D+00 0.0000E+00 46 0.2500000000000000000000000000D+00 0.0000E+00 47 0.2500000000000000000000000000D+00 0.0000E+00 48 0.2500000000000000000000000000D+00 0.0000E+00 49 0.2500000000000000000000000000D+00 0.0000E+00 50 0.2500000000000000000000000000D+00 0.0000E+00 51 0.2500000000000000000000000000D+00 0.0000E+00 52 0.2500000000000000000000000000D+00 0.0000E+00 53 0.2500000000000000000000000000D+00 0.0000E+00 54 0.2500000000000000000000000000D+00 0.0000E+00 55 0.2500000000000000000000000000D+00 0.0000E+00 56 0.2500000000000000000000000000D+00 0.0000E+00 57 0.2500000000000000000000000000D+00 0.0000E+00 58 0.2500000000000000000000000000D+00 0.0000E+00 59 0.2500000000000000000000000000D+00 0.0000E+00 60 0.2500000000000000000000000000D+00 0.0000E+00 61 0.2500000000000000000000000000D+00 0.0000E+00 62 0.2500000000000000000000000000D+00 0.0000E+00 63 0.2500000000000000000000000000D+00 0.0000E+00 64 0.2500000000000000000000000000D+00 0.0000E+00 65 0.2500000000000000000000000000D+00 0.0000E+00 66 0.2500000000000000000000000000D+00 0.0000E+00 67 0.2500000000000000000000000000D+00 0.0000E+00 68 0.2500000000000000000000000000D+00 0.0000E+00 69 0.2500000000000000000000000000D+00 0.0000E+00 70 0.2500000000000000000000000000D+00 0.0000E+00 71 0.2500000000000000000000000000D+00 0.0000E+00 72 0.2500000000000000000000000000D+00 0.0000E+00 73 0.2500000000000000000000000000D+00 0.0000E+00 74 0.2500000000000000000000000000D+00 0.0000E+00 75 0.2500000000000000000000000000D+00 0.0000E+00 76 0.2500000000000000000000000000D+00 0.0000E+00 77 0.2500000000000000000000000000D+00 0.0000E+00 78 0.2500000000000000000000000000D+00 0.0000E+00 79 0.2500000000000000000000000000D+00 0.0000E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.4150726270584938287706881112D+01 0.1672E-13 OM2 = 0.700 1 0.5738703563104107993176728175D+00 0.4583E-14 2 0.2153897141137676357945737410D+00 0.9884E-14 3 0.2476685096417081797797802723D+00 0.9911E-14 4 0.2496725302864942073704319339D+00 0.2151E-13 5 0.2499416058341949060862675826D+00 0.1383E-13 6 0.2499882473788614073598289098D+00 0.1031E-13 7 0.2499974543472129489781179846D+00 0.7304E-15 8 0.2499994207099762060333848693D+00 0.1483E-13 9 0.2499998634212174019156802858D+00 0.4960E-14 10 0.2499999669283869369933461353D+00 0.6868E-14 11 0.2499999918236198036754648399D+00 0.8166E-14 12 0.2499999979445508187833392438D+00 0.6957E-14 13 0.2499999994761779763827889382D+00 0.2957E-14 14 0.2499999998649768487726623512D+00 0.1935E-13 15 0.2499999999648583658538018813D+00 0.7238E-14 16 0.2499999999907779333282521984D+00 0.1732E-13 17 0.2499999999975624737716154063D+00 0.1275E-13 18 0.2499999999993516694822329789D+00 0.2148E-13 19 0.2499999999998265998368342322D+00 0.1694E-13 20 0.2499999999999533940488517558D+00 0.1683E-14 21 0.2499999999999874180743147633D+00 0.6516E-14 22 0.2499999999999965898347165282D+00 0.5702E-15 23 0.2499999999999990723966615358D+00 0.1050E-13 24 0.2499999999999997468569199482D+00 0.1013E-14 25 0.2499999999999999307111298251D+00 0.2772E-15 26 0.2499999999999999809827931412D+00 0.7607E-16 27 0.2499999999999999947673593529D+00 0.2093E-16 28 0.2499999999999999985568812753D+00 0.1421E-13 29 0.2499999999999999996011445311D+00 0.1595E-17 30 0.2499999999999999998895426194D+00 0.4418E-18 31 0.2499999999999999999693535707D+00 0.1226E-18 32 0.2499999999999999999914824007D+00 0.3407E-19 33 0.2499999999999999999976288548D+00 0.9485E-20 34 0.2499999999999999999993389129D+00 0.2644E-20 35 0.2499999999999999999998154225D+00 0.7383E-21 36 0.2499999999999999999999483962D+00 0.2064E-21 37 0.2499999999999999999999855544D+00 0.5778E-22 38 0.2499999999999999999999959514D+00 0.1619E-22 39 0.2499999999999999999999988640D+00 0.4544E-23 40 0.2499999999999999999999996809D+00 0.1276E-23 41 0.2499999999999999999999999102D+00 0.3591E-24 42 0.2499999999999999999999999747D+00 0.1012E-24 43 0.2499999999999999999999999929D+00 0.2847E-25 44 0.2499999999999999999999999980D+00 0.7977E-26 45 0.2499999999999999999999999994D+00 0.2423E-26 46 0.2499999999999999999999999998D+00 0.6058E-27 47 0.2499999999999999999999999999D+00 0.2019E-27 48 0.2500000000000000000000000000D+00 0.0000E+00 49 0.2499999999999999999999999999D+00 0.2019E-27 50 0.2500000000000000000000000000D+00 0.0000E+00 51 0.2500000000000000000000000000D+00 0.0000E+00 52 0.2500000000000000000000000000D+00 0.0000E+00 53 0.2500000000000000000000000000D+00 0.0000E+00 54 0.2500000000000000000000000000D+00 0.0000E+00 55 0.2500000000000000000000000000D+00 0.0000E+00 56 0.2500000000000000000000000000D+00 0.0000E+00 57 0.2500000000000000000000000000D+00 0.0000E+00 58 0.2500000000000000000000000000D+00 0.0000E+00 59 0.2500000000000000000000000000D+00 0.0000E+00 60 0.2500000000000000000000000000D+00 0.0000E+00 61 0.2500000000000000000000000000D+00 0.0000E+00 62 0.2500000000000000000000000000D+00 0.0000E+00 63 0.2500000000000000000000000000D+00 0.0000E+00 64 0.2500000000000000000000000000D+00 0.0000E+00 65 0.2500000000000000000000000000D+00 0.0000E+00 66 0.2499999999999999999999999999D+00 0.2019E-27 67 0.2500000000000000000000000000D+00 0.0000E+00 68 0.2500000000000000000000000000D+00 0.0000E+00 69 0.2500000000000000000000000000D+00 0.0000E+00 70 0.2500000000000000000000000000D+00 0.0000E+00 71 0.2500000000000000000000000000D+00 0.0000E+00 72 0.2500000000000000000000000000D+00 0.0000E+00 73 0.2500000000000000000000000000D+00 0.0000E+00 74 0.2500000000000000000000000000D+00 0.0000E+00 75 0.2500000000000000000000000000D+00 0.0000E+00 76 0.2500000000000000000000000000D+00 0.0000E+00 77 0.2500000000000000000000000000D+00 0.0000E+00 78 0.2500000000000000000000000000D+00 0.0000E+00 79 0.2500000000000000000000000000D+00 0.0000E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.5156184226696346376405141543D+01 0.6950E-14 OM2 = 0.900 1 0.6349731661452458711622492613D+00 0.7920E-14 2 0.1891491669986443569648158304D+00 0.2635E-13 3 0.2432300686739866681706961181D+00 0.9595E-14 4 0.2483762717470556873851235676D+00 0.9362E-15 5 0.2494981460742502273663466823D+00 0.6144E-14 6 0.2498235644120523880139606501D+00 0.7324E-14 7 0.2499329382129533954826949121D+00 0.1677E-14 8 0.2499731424622582194182122673D+00 0.8908E-14 9 0.2499888334872043976714436883D+00 0.1305E-13 10 0.2499952249211056861613516018D+00 0.6132E-14 11 0.2499979128874325556448624208D+00 0.9750E-14 12 0.2499990716489163159016030807D+00 0.4842E-14 13 0.2499995811151635493941187088D+00 0.5906E-14 14 0.2499998087271980386357542646D+00 0.7426E-14 15 0.2499999117758036441126071161D+00 0.5477E-14 16 0.2499999589541522526410519238D+00 0.1366E-13 17 0.2499999807604575559920393991D+00 0.3391E-14 18 0.2499999909227213910332412691D+00 0.3055E-14 19 0.2499999956925950094629502830D+00 0.1820E-13 20 0.2499999979455537253194077366D+00 0.1112E-13 21 0.2499999990156325924494555230D+00 0.2940E-14 22 0.2499999995264096544210033399D+00 0.2395E-14 23 0.2499999997713031459436158817D+00 0.7934E-14 24 0.2499999998891893925703582342D+00 0.8340E-14 25 0.2499999999461435478414324485D+00 0.1075E-13 26 0.2499999999737507419372027660D+00 0.6973E-14 27 0.2499999999871731384434618607D+00 0.7950E-14 28 0.2499999999937170944072024856D+00 0.7380E-14 29 0.2499999999969156770212988098D+00 0.1194E-13 30 0.2499999999984827779114949453D+00 0.1336E-13 31 0.2499999999992522327046396607D+00 0.7421E-14 32 0.2499999999996308048115304536D+00 0.1148E-14 33 0.2499999999998174139724912390D+00 0.8620E-14 34 0.2499999999999095610678960703D+00 0.7726E-14 35 0.2499999999999551380343851472D+00 0.5293E-14 36 0.2499999999999777157283138547D+00 0.3872E-14 37 0.2499999999999889163856012029D+00 0.1251E-13 38 0.2499999999999944805522803535D+00 0.6344E-14 39 0.2499999999999972482301653080D+00 0.3204E-14 40 0.2499999999999986265774586242D+00 0.8717E-14 41 0.2499999999999993138055421201D+00 0.2745E-14 42 0.2499999999999996568227766539D+00 0.1284E-13 43 0.2499999999999998282104100896D+00 0.6872E-15 44 0.2499999999999999139278194531D+00 0.3443E-15 45 0.2499999999999999568383382626D+00 0.1726E-15 46 0.2499999999999999783386280898D+00 0.8665E-16 47 0.2499999999999999891204630578D+00 0.4352E-16 48 0.2499999999999999945316443720D+00 0.2187E-16 49 0.2499999999999999972495030779D+00 0.1100E-16 50 0.2499999999999999986156028244D+00 0.5538E-17 51 0.2499999999999999993027424459D+00 0.2789E-17 52 0.2499999999999999996486035894D+00 0.1406E-17 53 0.2499999999999999998228006001D+00 0.7088E-18 54 0.2499999999999999999105916887D+00 0.3576E-18 55 0.2499999999999999999548627890D+00 0.1805E-18 56 0.2499999999999999999772005837D+00 0.9120E-19 57 0.2499999999999999999884777735D+00 0.1421E-13 58 0.2499999999999999999941740774D+00 0.2330E-19 59 0.2499999999999999999970528584D+00 0.1179E-19 60 0.2499999999999999999985084491D+00 0.5966E-20 61 0.2499999999999999999992447877D+00 0.3021E-20 62 0.2499999999999999999996174507D+00 0.1530E-20 63 0.2499999999999999999998061405D+00 0.7754E-21 64 0.2499999999999999999999017207D+00 0.3931E-21 65 0.2499999999999999999999501567D+00 0.1994E-21 66 0.2499999999999999999999747119D+00 0.1012E-21 67 0.2499999999999999999999871654D+00 0.5134E-22 68 0.2499999999999999999999934836D+00 0.2607E-22 69 0.2499999999999999999999966903D+00 0.1324E-22 70 0.2499999999999999999999983185D+00 0.6726E-23 71 0.2499999999999999999999991454D+00 0.3418E-23 72 0.2499999999999999999999995656D+00 0.1738E-23 73 0.2499999999999999999999997790D+00 0.8839E-24 74 0.2499999999999999999999998876D+00 0.4495E-24 75 0.2499999999999999999999999428D+00 0.2288E-24 76 0.2499999999999999999999999709D+00 0.1165E-24 77 0.2499999999999999999999999852D+00 0.5927E-25 78 0.2499999999999999999999999925D+00 0.3019E-25 79 0.2499999999999999999999999962D+00 0.1525E-25 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.7391274725979749355619908411D+01 0.1045E-13 OM2 = 0.990 1 0.7324070684920274763522917773D+00 0.6150E-14 2 0.1479427849683386321203381374D+00 0.1693E-13 3 0.2338554949163391305861598413D+00 0.7757E-14 4 0.2443419680995167639069168716D+00 0.4833E-14 5 0.2473968641083465752633955127D+00 0.2578E-14 6 0.2486202548943184490423548756D+00 0.5089E-14 7 0.2492022455253279683751347413D+00 0.1878E-14 8 0.2495108348820873078088301188D+00 0.1998E-14 9 0.2496871092764909748169056006D+00 0.4508E-14 10 0.2497933988931581641824952669D+00 0.9977E-14 11 0.2498601662192155628188028573D+00 0.4800E-14 12 0.2499034676221020533663127869D+00 0.4993E-14 13 0.2499322763973436023483807309D+00 0.7516E-14 14 0.2499518462973810000631441302D+00 0.1116E-13 15 0.2499653717034652803781567628D+00 0.9095E-14 16 0.2499748562994608555372130536D+00 0.4613E-14 17 0.2499815900555124114558066011D+00 0.1585E-14 18 0.2499864219462821878699396706D+00 0.3972E-16 19 0.2499899213248304987952240007D+00 0.5548E-14 20 0.2499924762634408213553096362D+00 0.3241E-14 21 0.2499943550268148128757315281D+00 0.2376E-14 22 0.2499957453603629556491348547D+00 0.3563E-14 23 0.2499967800924363291651714642D+00 0.7181E-14 24 0.2499975541062351695624174479D+00 0.7214E-14 25 0.2499981357626615138937073944D+00 0.6161E-14 26 0.2499985746929869732184204492D+00 0.4224E-14 27 0.2499989071796163774140646299D+00 0.4135E-15 28 0.2499991599119596132253985826D+00 0.5645E-14 29 0.2499993526338356733305944807D+00 0.3853E-15 30 0.2499995000261038054348812260D+00 0.3023E-14 31 0.2499996130562136721643785296D+00 0.3481E-14 32 0.2499996999526959611715190320D+00 0.1188E-14 33 0.2499997669135220480693883681D+00 0.6667E-15 34 0.2499998186241540461928756938D+00 0.2234E-15 35 0.2499998586385340721352640430D+00 0.9524E-14 36 0.2499998896607161427614732529D+00 0.9180E-14 37 0.2499999137540386272816545560D+00 0.4437E-15 38 0.2499999324971599746617482378D+00 0.9606E-14 39 0.2499999471009277820247909149D+00 0.1713E-14 40 0.2499999584962413690863987514D+00 0.7021E-14 41 0.2499999674003378171871783371D+00 0.1203E-13 42 0.2499999743669626218425193136D+00 0.5698E-14 43 0.2499999798244580488717573773D+00 0.2854E-14 44 0.2499999841047608130830406578D+00 0.1307E-13 45 0.2499999874655373080101220713D+00 0.8446E-14 46 0.2499999901071224060134895954D+00 0.7242E-14 47 0.2499999921855119697236944091D+00 0.2326E-14 48 0.2499999938223503083770563002D+00 0.2798E-14 49 0.2499999951126234719328140642D+00 0.2763E-14 50 0.2499999961305968951712746287D+00 0.2115E-14 51 0.2499999969344064587277270058D+00 0.1838E-14 52 0.2499999975696145183830097519D+00 0.4308E-14 53 0.2499999980719687703044300298D+00 0.6459E-14 54 0.2499999984695459857113345277D+00 0.7220E-14 55 0.2499999987844202263239335276D+00 0.4100E-14 56 0.2499999990339628386423312347D+00 0.1013E-13 57 0.2499999992318568529288242945D+00 0.1058E-14 58 0.2499999993888895322448466702D+00 0.9881E-14 59 0.2499999995135723375482205565D+00 0.3055E-14 60 0.2499999996126264482272000195D+00 0.5476E-15 61 0.2499999996913634107650925333D+00 0.7436E-14 62 0.2499999997539838804755978987D+00 0.5422E-14 63 0.2499999998038123156394446866D+00 0.1082E-14 64 0.2499999998434815319179873900D+00 0.4570E-15 65 0.2499999998750779619152275177D+00 0.8132E-14 66 0.2499999999002560868961616900D+00 0.5906E-14 67 0.2499999999203286590618025439D+00 0.7264E-14 68 0.2499999999363378936760955455D+00 0.4120E-14 69 0.2499999999491116885705258465D+00 0.3037E-14 70 0.2499999999593080530588459338D+00 0.3342E-14 71 0.2499999999674502441989476076D+00 0.8277E-15 72 0.2499999999739545731922478200D+00 0.1228E-13 73 0.2499999999791524256276846235D+00 0.1002E-14 74 0.2499999999833077107440717755D+00 0.7649E-14 75 0.2499999999866306970794232838D+00 0.1765E-14 76 0.2499999999892889893786483428D+00 0.1684E-14 77 0.2499999999914162424302140780D+00 0.1605E-14 78 0.2499999999931190822302459653D+00 0.2755E-14 79 0.2499999999944826062146632982D+00 0.1178E-15 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.9682265121100594060678208257D+01 0.1194E-12 OM2 = 0.999 1 0.7937821421385176965531719571D+00 0.6311E-13 2 0.1198676724605760566508984706D+00 0.2427E-12 3 0.2270401183698990236478358431D+00 0.1423E-13 4 0.2410608787266061460471631497D+00 0.3900E-14 5 0.2454285325203698010528098865D+00 0.8229E-14 6 0.2473016530297635082320973535D+00 0.5952E-14 7 0.2482587060199244993507069567D+00 0.2247E-14 8 0.2488056563182398337702848786D+00 0.5436E-15 9 0.2491436516500235662300446611D+00 0.2490E-14 10 0.2493649425541732785713756724D+00 0.7264E-16 11 0.2495164122910211102422347642D+00 0.5588E-14 12 0.2496238132093984309100496946D+00 0.8068E-14 13 0.2497021807830055845646993234D+00 0.6956E-14 14 0.2497607367186780964244373358D+00 0.2874E-14 15 0.2498053715523733403244514780D+00 0.7799E-15 16 0.2498399785559649451745447768D+00 0.3896E-15 17 0.2498672067961906948509922813D+00 0.7928E-14 18 0.2498889044665883526357482704D+00 0.9971E-14 19 0.2499063894398209200047452537D+00 0.1026E-13 20 0.2499206196165231602203909115D+00 0.8154E-14 21 0.2499323031609509319254796296D+00 0.1026E-13 22 0.2499419715850828499756137364D+00 0.5133E-14 23 0.2499500292585915038956821595D+00 0.2426E-14 24 0.2499567876037903691881455655D+00 0.4016E-14 25 0.2499624891284640857487168428D+00 0.4566E-15 26 0.2499673245856652663185916277D+00 0.1703E-14 27 0.2499714454036620578074169345D+00 0.2906E-14 28 0.2499749728090034183731376502D+00 0.1479E-14 29 0.2499780046038181465987326795D+00 0.4098E-15 30 0.2499806202568039236144397457D+00 0.1100E-13 31 0.2499828847669805689657726897D+00 0.6512E-14 32 0.2499848516240893440607962480D+00 0.9325E-14 33 0.2499865650969887674775692795D+00 0.2794E-14 34 0.2499880620172148980355969873D+00 0.5809E-14 35 0.2499893731797995851944555752D+00 0.8241E-14 36 0.2499905244514168246823682605D+00 0.3269E-14 37 0.2499915376529289251735965670D+00 0.3577E-14 38 0.2499924312667191276936114929D+00 0.1368E-13 39 0.2499932210069768852202778652D+00 0.4305E-14 40 0.2499939202820711464146962184D+00 0.8080E-14 41 0.2499945405714167280803653189D+00 0.4689E-14 42 0.2499950917341830713499801678D+00 0.6968E-14 43 0.2499955822633680825859750068D+00 0.8282E-14 44 0.2499960194958428135558206496D+00 0.8424E-15 45 0.2499964097867341326951169655D+00 0.5632E-14 46 0.2499967586547834795590916777D+00 0.4708E-14 47 0.2499970709039761326045421868D+00 0.1440E-14 48 0.2499973507256851779307102268D+00 0.9192E-15 49 0.2499976017847489179996389014D+00 0.7753E-15 50 0.2499978272922482594570085372D+00 0.2555E-14 51 0.2499980300672327043443863432D+00 0.2898E-14 52 0.2499982125892303062464575832D+00 0.1097E-13 53 0.2499983770430456739044282726D+00 0.1118E-14 54 0.2499985253570833720508446261D+00 0.8731E-14 55 0.2499986592362183971966761407D+00 0.1135E-13 56 0.2499987801900603121699346698D+00 0.5188E-14 57 0.2499988895573149187786363157D+00 0.1112E-14 58 0.2499989885268306062507010812D+00 0.2863E-14 59 0.2499990781558206671129154805D+00 0.1299E-14 60 0.2499991593856739095826996477D+00 0.1221E-13 61 0.2499992330557006258053604460D+00 0.2775E-14 62 0.2499992999151068510107986487D+00 0.7683E-16 63 0.2499993606334448281130268345D+00 0.3220E-14 64 0.2499994158097500327434601393D+00 0.5863E-16 65 0.2499994659805436887853955976D+00 0.4013E-15 66 0.2499995116268533393828096318D+00 0.1171E-14 67 0.2499995531803818592965610137D+00 0.8669E-14 68 0.2499995910289365885902790955D+00 0.6408E-14 69 0.2499996255212144516896407709D+00 0.6265E-14 70 0.2499996569710255211441431787D+00 0.5649E-14 71 0.2499996856610260978327166803D+00 0.5093E-14 72 0.2499997118460226835351908954D+00 0.7707E-15 73 0.2499997357558999483848558192D+00 0.1308E-14 74 0.2499997575982187211295314401D+00 0.1052E-13 75 0.2499997775605239682686717749D+00 0.9442E-14 76 0.2499997958123975237310978975D+00 0.9260E-14 77 0.2499998125072858539381665907D+00 0.4941E-14 78 0.2499998277841292849705531175D+00 0.2824E-14 79 0.2499998417688157876153069211D+00 0.1548E-14 output of test1 with modmom=.false.: IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.3224882697440438796459832725D+01 0.1433E-13 OM2 = 0.100 1 0.5065840806382684475158495728D+00 0.1187E-13 2 0.2467293493188785576130435954D+00 0.1943E-13 3 0.2499786103248681596536302022D+00 0.2783E-12 4 0.2499997192892932646699794933D+00 0.2293E-11 5 0.2499999953890031901881028629D+00 0.1065E-10 6 0.2499999999151142217232289544D+00 0.4684E-10 7 0.2499999999983250486706797234D+00 0.2603E-09 8 0.2499999999999653681699413492D+00 0.1572E-08 9 0.2499999999999992594133473805D+00 0.8875E-08 10 0.2499999999999999837548811949D+00 0.4803E-07 11 0.2499999999999999996370863573D+00 0.2684E-06 12 0.2499999999999999999890015809D+00 0.1583E-05 13 0.2500000000000000000137988065D+00 0.9663E-05 14 0.2499999999999999999144912203D+00 0.5969E-04 15 0.2500000000000000005892766820D+00 0.3669E-03 16 0.2499999999999999959164770184D+00 0.2206E-02 17 0.2500000000000000267067176355D+00 0.1288E-01 18 0.2499999999999998379720071920D+00 0.7204E-01 19 0.2500000000000009150882591094D+00 0.4251E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.3427778896357582124077869689D+01 0.8867E-14 OM2 = 0.300 1 0.5222553571575005169932901811D+00 0.5370E-14 2 0.2391089484344383143284396276D+00 0.1529E-13 3 0.2497633566075743756040256634D+00 0.1384E-12 4 0.2499895949326480950578823039D+00 0.1342E-11 5 0.2499994255652457252517512732D+00 0.1092E-10 6 0.2499999644019888681144226174D+00 0.7698E-10 7 0.2499999976333568222970499346D+00 0.4435E-09 8 0.2499999998350340290206302342D+00 0.2222E-08 9 0.2499999999881026637164869565D+00 0.1038E-07 10 0.2499999999991196293284908519D+00 0.4833E-07 11 0.2499999999999335336360523052D+00 0.2409E-06 12 0.2499999999999949003387521603D+00 0.1353E-05 13 0.2499999999999996035487949242D+00 0.8517E-05 14 0.2499999999999999686781356360D+00 0.5630E-04 15 0.2499999999999999982227496019D+00 0.3650E-03 16 0.2499999999999999963194029494D+00 0.2242E-02 17 0.2500000000000000207021909718D+00 0.1307E-01 18 0.2499999999999998610645975228D+00 0.7226E-01 19 0.2500000000000009477819455726D+00 0.4208E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.3708149354602743836867700694D+01 0.9005E-14 OM2 = 0.500 1 0.5430534189555363746250333773D+00 0.2431E-13 2 0.2293202676904703911217264152D+00 0.6115E-13 3 0.2491525790663757991195108389D+00 0.9973E-13 4 0.2499288948105138848163926139D+00 0.2308E-11 5 0.2499924766475489607913894033D+00 0.1822E-10 6 0.2499991045593934697881801862D+00 0.1051E-09 7 0.2499998855221811249212852887D+00 0.5571E-09 8 0.2499999846431723296083659240D+00 0.2909E-08 9 0.2499999978674175371387411867D+00 0.1459E-07 10 0.2499999996960280038005323741D+00 0.6945E-07 11 0.2499999999557817675323460669D+00 0.3275E-06 12 0.2499999999934617441423514997D+00 0.1649E-05 13 0.2499999999990201961894103441D+00 0.9307E-05 14 0.2499999999998515182568170078D+00 0.5788E-04 15 0.2499999999999772849906577539D+00 0.3757E-03 16 0.2499999999999964933063576359D+00 0.2429E-02 17 0.2499999999999994773784998165D+00 0.1529E-01 18 0.2499999999999997775408626986D+00 0.9137E-01 19 0.2500000000000007883792341279D+00 0.5798E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.4150726270584938287706881112D+01 0.1672E-13 OM2 = 0.700 1 0.5738703563104107993176728175D+00 0.4583E-14 2 0.2153897141137676357945737410D+00 0.6610E-14 3 0.2476685096417081797797802732D+00 0.2770E-12 4 0.2496725302864942073704319279D+00 0.2611E-11 5 0.2499416058341949060862676210D+00 0.1662E-10 6 0.2499882473788614073598286910D+00 0.8420E-10 7 0.2499974543472129489781191466D+00 0.3955E-09 8 0.2499994207099762060333787059D+00 0.2054E-08 9 0.2499998634212174019157153457D+00 0.1191E-07 10 0.2499999669283869369931336326D+00 0.6859E-07 11 0.2499999918236198036767635788D+00 0.3752E-06 12 0.2499999979445508187755237032D+00 0.2010E-05 13 0.2499999994761779764297706701D+00 0.1094E-04 14 0.2499999998649768484863554421D+00 0.6139E-04 15 0.2499999999648583676029974411D+00 0.3537E-03 16 0.2499999999907779229177544153D+00 0.2066E-02 17 0.2499999999975625327726883868D+00 0.1210E-01 18 0.2499999999993513521496281053D+00 0.6952E-01 19 0.2499999999998282456694568532D+00 0.4266E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.5156184226696346376405141543D+01 0.6950E-14 OM2 = 0.900 1 0.6349731661452458711622492613D+00 0.3270E-14 2 0.1891491669986443569648158305D+00 0.6756E-13 3 0.2432300686739866681706961195D+00 0.1803E-12 4 0.2483762717470556873851235558D+00 0.2876E-11 5 0.2494981460742502273663467504D+00 0.1765E-10 6 0.2498235644120523880139602570D+00 0.9118E-10 7 0.2499329382129533954826972643D+00 0.4819E-09 8 0.2499731424622582194181989122D+00 0.2747E-08 9 0.2499888334872043976715148711D+00 0.1658E-07 10 0.2499952249211056861609814486D+00 0.1006E-06 11 0.2499979128874325556467785523D+00 0.5896E-06 12 0.2499990716489163158917293162D+00 0.3322E-05 13 0.2499995811151635494455745425D+00 0.1841E-04 14 0.2499998087271980383558568830D+00 0.1032E-03 15 0.2499999117758036457198140400D+00 0.5923E-03 16 0.2499999589541522431052312623D+00 0.3427E-02 17 0.2499999807604576127479385412D+00 0.1962E-01 18 0.2499999909227210587021774835D+00 0.1068E+00 19 0.2499999956925969055814911116D+00 0.6272E+00 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.7391274725979749355619908411D+01 0.1045E-13 OM2 = 0.990 1 0.7324070684920274763522917773D+00 0.6150E-14 2 0.1479427849683386321203381376D+00 0.4924E-14 3 0.2338554949163391305861598433D+00 0.7066E-12 4 0.2443419680995167639069168498D+00 0.5646E-11 5 0.2473968641083465752633956528D+00 0.3728E-10 6 0.2486202548943184490423540952D+00 0.2296E-09 7 0.2492022455253279683751388324D+00 0.1385E-08 8 0.2495108348820873078088079048D+00 0.8281E-08 9 0.2496871092764909748170361959D+00 0.4868E-07 10 0.2497933988931581641816946797D+00 0.2816E-06 11 0.2498601662192155628236710135D+00 0.1627E-05 12 0.2499034676221020533377108253D+00 0.9435E-05 13 0.2499322763973436025090379204D+00 0.5404E-04 14 0.2499518462973809992025803817D+00 0.2982E-03 15 0.2499653717034652847973611384D+00 0.1563E-02 16 0.2499748562994608334747028380D+00 0.7786E-02 17 0.2499815900555125209913830588D+00 0.3822E-01 18 0.2499864219462816313468050505D+00 0.1855E+00 19 0.2499899213248334657189498256D+00 0.1198E+01 IERR IN CHEB = 0 IDERR IN DCHEB = 0 K DBETA(K) 0 0.9682265121100594060678208257D+01 0.1194E-12 OM2 = 0.999 1 0.7937821421385176965531719571D+00 0.6311E-13 2 0.1198676724605760566508984707D+00 0.1537E-12 3 0.2270401183698990236478358456D+00 0.3457E-12 4 0.2410608787266061460471631230D+00 0.6481E-11 5 0.2454285325203698010528100587D+00 0.5193E-10 6 0.2473016530297635082320965795D+00 0.3123E-09 7 0.2482587060199244993507094034D+00 0.1745E-08 8 0.2488056563182398337702789697D+00 0.1037E-07 9 0.2491436516500235662300695460D+00 0.6669E-07 10 0.2493649425541732785711189445D+00 0.4316E-06 11 0.2495164122910211102447012714D+00 0.2663E-05 12 0.2496238132093984308907807478D+00 0.1549E-04 13 0.2497021807830055846970659779D+00 0.8589E-04 14 0.2497607367186780955693561744D+00 0.4658E-03 15 0.2498053715523733457073782618D+00 0.2548E-02 16 0.2498399785559649120090823862D+00 0.1433E-01 17 0.2498672067961908924975572273D+00 0.8448E-01 18 0.2498889044665872234788367299D+00 0.4663E+00 19 0.2499063894398271240566500550D+00 0.4808E+01 C-END-OF-FILE cat < test2.f c c program test2 c c dimension a(199),b(199),fnu(200),alpha(100),beta(100),s(100), *s0(200),s1(200),s2(200) double precision dsigma,da(199),db(199),dnu(200),dalpha(100), *dbeta(100),ds(100),ds0(200),ds1(200),ds2(200) logical modmom,intexp c c This test generates the first n recursion coefficients for the c orthogonal polynomials relative to the weight function c c (x**sigma)*ln(1/x) on (0,1], sigma = -.5, 0, .5, c c where n=100 when using modified (Legendre) moments, and n=12 when c using ordinary moments. It prints the double-precision values of the c coefficients as well as the relative errors of the respective single- c precision values and the maximum relative errors. c modmom=.true. c c Generate the recursion coefficients for the polynomials defining the c modified resp. ordinary moments. c if(modmom) then n=100 ndm1=2*n-1 call recur(ndm1,2,0.,0.,a,b,ierr) call drecur(ndm1,2,0.d0,0.d0,da,db,iderr) else n=12 ndm1=2*n-1 do 10 k=1,ndm1 a(k)=0. b(k)=0. da(k)=0.d0 db(k)=0.d0 10 continue end if do 30 is=1,3 dsigma=-.5d0+.5d0*dble(is-1) sigma=sngl(dsigma) if(is.eq.2) then intexp=.true. else intexp=.false. end if c c Compute the modified resp. ordinary moments using Eqs. (3.12) and c (3.11) of the companion paper. On machines with limited exponent c range, some of the high-order modified moments may underflow, without c this having any deteriorating effect on the accuracy. c call fmm(n,modmom,intexp,sigma,fnu) call dmm(n,modmom,intexp,dsigma,dnu) c c Compute the desired recursion coefficients by means of the modified c Chebyshev algorithm; for the latter, see, e.g., Section 2.4 of c W. Gautschi, ``On generating orthogonal polynomials'', SIAM J. Sci. c Statist. Comput. 3, 1982, 289-317. c call cheb(n,a,b,fnu,alpha,beta,s,ierr,s0,s1,s2) c c On machines with limited single-precision exponent range, the routine c cheb may generate an underflow exception, which however is harmless c and can be ignored. c call dcheb(n,da,db,dnu,dalpha,dbeta,ds,iderr,ds0,ds1,ds2) write(*,1) ierr,iderr 1 format(/6x,'ierr in cheb = ',i4,' iderr in dcheb = ',i4/) c c Compute and print the relative errors and their maxima. c eamax=0. ebmax=0. write(*,2) sigma 2 format(/32x,'sigma =',f5.1) write(*,3) 3 format(/3x,'k',13x,'dalpha(k)',25x,'dbeta(k)'/) do 20 k=1,n km1=k-1 if(iderr.eq.0 .or. km1.lt.abs(iderr)) then write(*,4) km1,dalpha(k),dbeta(k) 4 format(1x,i3,2d33.25) if(ierr.eq.0 .or. km1.lt.abs(ierr)) then erra=sngl(dabs(dble(alpha(k))-dalpha(k))/dalpha(k)) errb=sngl(dabs(dble(beta(k))-dbeta(k))/dbeta(k)) write(*,5) erra,errb 5 format(4x,e12.4,21x,e12.4) if(erra.gt.eamax) then eamax=erra kamax=km1 end if if(errb.gt.ebmax) then ebmax=errb kbmax=km1 end if end if end if 20 continue write(*,6) eamax,kamax,ebmax,kbmax 6 format(/6x,'eamax =',e11.4,' at',i3,9x,'ebmax =',e11.4, * ' at',i3//) 30 continue stop end subroutine fmm(n,modmom,intexp,sigma,fnu) c c This generates the first 2*n modified moments (if modmom=.true.) c relative to shifted monic Legendre polynomials, using Eq. (3.12) of c the companion paper, and the first 2*n ordinary moments (if modmom c =.false.) by Eq. (3.11), of the weight function c c (x**sigma)*ln(1/x) on (0,1], sigma > -1, c c for sigma an integer (if intexp=.true.) or a real number (if intexp c =.false.). In either case, the input variable sigma is of type real. c dimension fnu(*) logical modmom,intexp c c The array fnu is assumed to have dimension 2*n. c nd=2*n sigp1=sigma+1. if(modmom) then isigma=int(sigma) isigp1=isigma+1 isigp2=isigma+2 isigp3=isigma+3 if(intexp .and. isigp1.lt.nd) then kmax=isigp1 else kmax=nd end if c=1. do 20 k=1,kmax km1=k-1 fk=real(k) p=1. s=1./sigp1 if(kmax.gt.1) then do 10 i=1,km1 fi=real(i) p=(sigp1-fi)*p/(sigp1+fi) s=s+1./(sigp1+fi)-1./(sigp1-fi) 10 continue end if fnu(k)=c*s*p/sigp1 c=fk*c/(4.*fk-2.) 20 continue if(.not.intexp .or. isigp1.ge.nd) return q=-.5 if(isigma.gt.0) then do 30 iq=1,isigma fiq=real(iq) q=fiq*fiq*q/((2.*fiq+1.)*(2.*fiq+2.)) 30 continue end if fnu(isigp2)=c*q if(isigp2.eq.nd) return do 40 k=isigp3,nd km1=k-1 fkm1=real(km1) fnu(k)=-fkm1*(fkm1-sigp1)*fnu(km1)/((4.*fkm1-2.)* * (fkm1+sigp1)) 40 continue return else do 50 k=1,nd fkm1=real(k-1) fnu(k)=(1./(sigp1+fkm1))**2 50 continue end if end subroutine dmm(n,modmom,intexp,dsigma,dnu) c c This is a double-precision version of the routine fmm. c double precision dsigma,dnu(*),dsigp1,dc,dk,dp,ds,di,dq,diq,dkm1 logical modmom,intexp c c The array dnu is assumed to have dimension 2*n. c nd=2*n dsigp1=dsigma+1.d0 if(modmom) then isigma=idint(dsigma) isigp1=isigma+1 isigp2=isigma+2 isigp3=isigma+3 if(intexp .and. isigp1.lt.nd) then kmax=isigp1 else kmax=nd end if dc=1.d0 do 20 k=1,kmax km1=k-1 dk=dble(k) dp=1.d0 ds=1.d0/dsigp1 if(kmax.gt.1) then do 10 i=1,km1 di=dble(i) dp=(dsigp1-di)*dp/(dsigp1+di) ds=ds+1.d0/(dsigp1+di)-1.d0/(dsigp1-di) 10 continue end if dnu(k)=dc*ds*dp/dsigp1 dc=dk*dc/(4.d0*dk-2.d0) 20 continue if(.not.intexp .or. isigp1.ge.nd) return dq=-.5d0 if(isigma.gt.0) then do 30 iq=1,isigma diq=dble(iq) dq=diq*diq*dq/((2.d0*diq+1.d0)*(2.d0*diq+2.d0)) 30 continue end if dnu(isigp2)=dc*dq if(isigp2.eq.nd) return do 40 k=isigp3,nd km1=k-1 dkm1=dble(km1) dnu(k)=-dkm1*(dkm1-dsigp1)*dnu(km1)/((4.d0*dkm1-2.d0)* * (dkm1+dsigp1)) 40 continue return else do 50 k=1,nd dkm1=dble(k-1) dnu(k)=(1.d0/(dsigp1+dkm1))**2 50 continue end if end C-END-OF-FILE cat < test2.out output of test2 with modmom=.true.: IERR IN CHEB = 0 IDERR IN DCHEB = 0 SIGMA = -0.5 K DALPHA(K) DBETA(K) 0 0.1111111111111111111111111D+00 0.4000000000000000000000000D+01 0.2842E-13 0.0000E+00 1 0.4661483641075477810171688D+00 0.2765432098765432098765432D-01 0.1784E-12 0.1292E-12 2 0.4880690581976426561739654D+00 0.5534292684170711183265476D-01 0.4460E-12 0.6611E-12 3 0.4938743419208057331274822D+00 0.5940526298488865183067045D-01 0.7147E-12 0.1102E-11 4 0.4962639578613459263700277D+00 0.6077714606674732893827287D-01 0.8756E-12 0.1657E-11 5 0.4974805136345470499404327D+00 0.6140371143126410746951299D-01 0.1038E-11 0.1904E-11 6 0.4981846424539394712819088D+00 0.6174167659202270796881379D-01 0.1291E-11 0.2342E-11 7 0.4986290336259843770529448D+00 0.6194453627914717711328688D-01 0.1602E-11 0.2873E-11 8 0.4989276082849235415546195D+00 0.6207576580933626144340940D-01 0.1966E-11 0.3595E-11 9 0.4991379564664850047980802D+00 0.6216550244588411861001341D-01 0.2280E-11 0.4255E-11 10 0.4992917697449965925976574D+00 0.6222955193630939853437094D-01 0.2669E-11 0.4938E-11 11 0.4994076708859089483520375D+00 0.6227685326078544899112281D-01 0.2975E-11 0.5692E-11 12 0.4994971916094638566242202D+00 0.6231277082877488477563886D-01 0.3285E-11 0.6235E-11 13 0.4995677851751364266156599D+00 0.6234068199929453251339864D-01 0.3624E-11 0.6929E-11 14 0.4996244439462620957645566D+00 0.6236279899520571298076283D-01 0.3872E-11 0.7554E-11 15 0.4996706145979840808548842D+00 0.6238061988995864213325718D-01 0.4229E-11 0.8110E-11 16 0.4997087392464561491728915D+00 0.6239518834725249753338138D-01 0.4618E-11 0.8834E-11 17 0.4997405876531736626190872D+00 0.6240724948356001710689111D-01 0.4981E-11 0.9630E-11 18 0.4997674679010946606417245D+00 0.6241734675384434899468191D-01 0.5361E-11 0.1033E-10 19 0.4997903638440694047466612D+00 0.6242588405027882485913615D-01 0.5713E-11 0.1110E-10 20 0.4998100270509691381859106D+00 0.6243316658846858305615025D-01 0.6055E-11 0.1182E-10 21 0.4998270396901901811053116D+00 0.6243942847487754986053115D-01 0.6457E-11 0.1247E-10 22 0.4998418584011269547061628D+00 0.6244485169209210663968073D-01 0.6910E-11 0.1343E-10 23 0.4998548454525784424706020D+00 0.6244957942452422353437694D-01 0.7300E-11 0.1421E-10 24 0.4998662912324218943801592D+00 0.6245372557342242600457226D-01 0.7747E-11 0.1501E-10 25 0.4998764307204424397405948D+00 0.6245738165737186124658778D-01 0.8148E-11 0.1599E-10 26 0.4998854557169246669449019D+00 0.6246062188808478979166957D-01 0.8564E-11 0.1667E-10 27 0.4998935240328226886591572D+00 0.6246350695269707453479568D-01 0.9086E-11 0.1769E-10 28 0.4999007664750365107918077D+00 0.6246608686595204798542240D-01 0.9580E-11 0.1864E-10 29 0.4999072922115382430628671D+00 0.6246840314472866468672816D-01 0.1016E-10 0.1970E-10 30 0.4999131929321822564939469D+00 0.6247049048282836967879567D-01 0.1067E-10 0.2085E-10 31 0.4999185461046623069180692D+00 0.6247237805306714282029063D-01 0.1125E-10 0.2190E-10 32 0.4999234175438090965764987D+00 0.6247409052851061161429977D-01 0.1178E-10 0.2307E-10 33 0.4999278634549460876866086D+00 0.6247564888999735836355421D-01 0.1219E-10 0.2399E-10 34 0.4999319320708932838633869D+00 0.6247707106956441823595053D-01 0.1266E-10 0.2480E-10 35 0.4999356649724540623274387D+00 0.6247837246679940094973984D-01 0.1320E-10 0.2592E-10 36 0.4999390981604717422591136D+00 0.6247956636600570708844247D-01 0.1371E-10 0.2689E-10 37 0.4999422629314923704886477D+00 0.6248066427536794284683246D-01 0.1419E-10 0.2788E-10 38 0.4999451865971175754297572D+00 0.6248167620434672378022245D-01 0.1467E-10 0.2883E-10 39 0.4999478930781540114073128D+00 0.6248261089183034006005443D-01 0.1521E-10 0.2990E-10 40 0.4999504033978688392463883D+00 0.6248347599478382249321287D-01 0.1585E-10 0.3105E-10 41 0.4999527360934751182615016D+00 0.6248427824502116118751316D-01 0.1646E-10 0.3228E-10 42 0.4999549075609863005157917D+00 0.6248502358010969536816872D-01 0.1713E-10 0.3363E-10 43 0.4999569323454961738619833D+00 0.6248571725317097460386049D-01 0.1778E-10 0.3491E-10 44 0.4999588233865400022085640D+00 0.6248636392537765834044482D-01 0.1846E-10 0.3620E-10 45 0.4999605922263117426170317D+00 0.6248696774419352905015697D-01 0.1915E-10 0.3762E-10 46 0.4999622491870299058307070D+00 0.6248753240981319504469108D-01 0.1976E-10 0.3892E-10 47 0.4999638035225698808616725D+00 0.6248806123179200596514721D-01 0.2038E-10 0.4014E-10 48 0.4999652635485445800661969D+00 0.6248855717748684742433618D-01 0.2106E-10 0.4147E-10 49 0.4999666367542657434951760D+00 0.6248902291363342497098043D-01 0.2164E-10 0.4275E-10 50 0.4999679298994151058697458D+00 0.6248946084214908332126385D-01 0.2220E-10 0.4381E-10 51 0.4999691490977670252895535D+00 0.6248987313105962943007473D-01 0.2280E-10 0.4499E-10 52 0.4999702998899082096191760D+00 0.6249026174129439284484898D-01 0.2345E-10 0.4626E-10 53 0.4999713873065772549159492D+00 0.6249062844996838433907695D-01 0.2401E-10 0.4749E-10 54 0.4999724159239822749292820D+00 0.6249097487066807275398101D-01 0.2462E-10 0.4858E-10 55 0.4999733899122375046656649D+00 0.6249130247117342087934171D-01 0.2533E-10 0.4995E-10 56 0.4999743130778803590509506D+00 0.6249161258897980601024295D-01 0.2613E-10 0.5145E-10 57 0.4999751889012818397363903D+00 0.6249190644492645302489131D-01 0.2690E-10 0.5302E-10 58 0.4999760205696396844641164D+00 0.6249218515519076536316924D-01 0.2773E-10 0.5465E-10 59 0.4999768110061406606236640D+00 0.6249244974186864670497903D-01 0.2849E-10 0.5624E-10 60 0.4999775628957922328764516D+00 0.6249270114232811644774819D-01 0.2922E-10 0.5768E-10 61 0.4999782787083515100262005D+00 0.6249294021749607086844031D-01 0.3009E-10 0.5926E-10 62 0.4999789607187184893133688D+00 0.6249316775921498850954361D-01 0.3093E-10 0.6109E-10 63 0.4999796110251092079375052D+00 0.6249338449678696015999789D-01 0.3172E-10 0.6263E-10 64 0.4999802315652808832931335D+00 0.6249359110280602015518800D-01 0.3259E-10 0.6430E-10 65 0.4999808241310441662847610D+00 0.6249378819836585975999630D-01 0.3343E-10 0.6600E-10 66 0.4999813903812661709776500D+00 0.6249397635771819984114799D-01 0.3428E-10 0.6774E-10 67 0.4999819318535410926892670D+00 0.6249415611244704749850511D-01 0.3519E-10 0.6946E-10 68 0.4999824499746822529848128D+00 0.6249432795521547829357329D-01 0.3603E-10 0.7128E-10 69 0.4999829460701697066273291D+00 0.6249449234313423932856532D-01 0.3689E-10 0.7289E-10 70 0.4999834213726706073831202D+00 0.6249464970079516550903630D-01 0.3781E-10 0.7471E-10 71 0.4999838770297349356284461D+00 0.6249480042300698114169577D-01 0.3858E-10 0.7647E-10 72 0.4999843141107565888762889D+00 0.6249494487726638748190090D-01 0.3937E-10 0.7793E-10 73 0.4999847336132789314898946D+00 0.6249508340599330177430745D-01 0.4024E-10 0.7963E-10 74 0.4999851364687144438985805D+00 0.6249521632855562063538541D-01 0.4104E-10 0.8128E-10 75 0.4999855235475398955558700D+00 0.6249534394310585118905246D-01 0.4183E-10 0.8288E-10 76 0.4999858956640213131307627D+00 0.6249546652824932049195603D-01 0.4267E-10 0.8451E-10 77 0.4999862535805167765288282D+00 0.6249558434456138111659899D-01 0.4343E-10 0.8611E-10 78 0.4999865980113996234652464D+00 0.6249569763596903056671454D-01 0.4423E-10 0.8765E-10 79 0.4999869296266398705890535D+00 0.6249580663101061396102569D-01 0.4507E-10 0.8930E-10 80 0.4999872490550774736510815D+00 0.6249591154398574866660388D-01 0.4589E-10 0.9095E-10 81 0.4999875568874173723953749D+00 0.6249601257600626690066199D-01 0.4677E-10 0.9266E-10 82 0.4999878536789730305318126D+00 0.6249610991595779263883088D-01 0.4762E-10 0.9446E-10 83 0.4999881399521823296847290D+00 0.6249620374138053097068321D-01 0.4851E-10 0.9610E-10 84 0.4999884161989171590890288D+00 0.6249629421927693288786306D-01 0.4941E-10 0.9793E-10 85 0.4999886828826058173914092D+00 0.6249638150685309052629655D-01 0.5027E-10 0.9971E-10 86 0.4999889404401853724423155D+00 0.6249646575220000346266932D-01 0.5112E-10 0.1014E-09 87 0.4999891892838993776656731D+00 0.6249654709492022401174982D-01 0.5201E-10 0.1032E-09 88 0.4999894298029547919706245D+00 0.6249662566670482840875654D-01 0.5293E-10 0.1050E-09 89 0.4999896623650505703804859D+00 0.6249670159186516247938763D-01 0.5376E-10 0.1067E-09 90 0.4999898873177891638918130D+00 0.6249677498782336725853075D-01 0.5463E-10 0.1084E-09 91 0.4999901049899810715268292D+00 0.6249684596556529537947903D-01 0.5550E-10 0.1102E-09 92 0.4999903156928516094091928D+00 0.6249691463005907714323314D-01 0.5633E-10 0.1119E-09 93 0.4999905197211581872778771D+00 0.6249698108064228095881834D-01 0.5716E-10 0.1135E-09 94 0.4999907173542256001838438D+00 0.6249704541138033192705537D-01 0.5802E-10 0.1152E-09 95 0.4999909088569061417086197D+00 0.6249710771139860088117153D-01 0.5890E-10 0.1169E-09 96 0.4999910944804707157151021D+00 0.6249716806519035083547535D-01 0.5976E-10 0.1187E-09 97 0.4999912744634365583230272D+00 0.6249722655290252557984422D-01 0.6057E-10 0.1203E-09 98 0.4999914490323366734035746D+00 0.6249728325060118350439252D-01 0.6141E-10 0.1220E-09 99 0.4999916184024356271670789D+00 0.6249733823051821636937156D-01 0.6211E-10 0.1235E-09 EAMAX = 0.6211E-10 AT 99 EBMAX = 0.1235E-09 AT 99 IERR IN CHEB = 0 IDERR IN DCHEB = 0 SIGMA = 0.0 K DALPHA(K) DBETA(K) 0 0.2500000000000000000000000D+00 0.1000000000000000000000000D+01 0.0000E+00 0.0000E+00 1 0.4642857142857142857142857D+00 0.4861111111111111111111111D-01 0.1312E-13 0.2639E-13 2 0.4854824464561713402517112D+00 0.5868480725623582766439909D-01 0.2288E-13 0.4939E-13 3 0.4921030818713608586050337D+00 0.6072858391891785822637763D-01 0.4578E-13 0.7445E-13 4 0.4950284987583539049494567D+00 0.6148202019693696071375070D-01 0.6221E-13 0.1250E-12 5 0.4965795116435580984519746D+00 0.6184080953188484218106730D-01 0.8189E-13 0.1379E-12 6 0.4975013013049582411838083D+00 0.6203906295445598496037138D-01 0.8694E-13 0.1672E-12 7 0.4980940182042518540907413D+00 0.6215991915828943043448013D-01 0.9170E-13 0.1873E-12 8 0.4984978019782527493617411D+00 0.6223893767166674441228095D-01 0.1133E-12 0.2065E-12 9 0.4987853226556929738980263D+00 0.6229338867990748308084260D-01 0.1226E-12 0.2595E-12 10 0.4989973531671536624227043D+00 0.6233247750665634201166525D-01 0.1535E-12 0.2897E-12 11 0.4991582216780129299345265D+00 0.6236147348381100858979132D-01 0.1719E-12 0.3359E-12 12 0.4992831802157361310272625D+00 0.6238356835953571123560330D-01 0.1963E-12 0.3805E-12 13 0.4993821876708659391916256D+00 0.6240078643427266552454125D-01 0.2307E-12 0.4280E-12 14 0.4994619720966186081501716D+00 0.6241446153535189814894302D-01 0.2492E-12 0.5015E-12 15 0.4995272124267306332814372D+00 0.6242550130298840435441763D-01 0.2839E-12 0.5513E-12 16 0.4995812447300375902610308D+00 0.6243454062356624546528951D-01 0.3048E-12 0.6154E-12 17 0.4996264998058222738864005D+00 0.6244203431425522665242969D-01 0.3299E-12 0.6528E-12 18 0.4996647829280136809732498D+00 0.6244831505981949444443223D-01 0.3458E-12 0.6913E-12 19 0.4996974576412242075578802D+00 0.6245363072435638507373495D-01 0.3739E-12 0.7323E-12 20 0.4997255694718122716627491D+00 0.6245816901837448725144309D-01 0.4029E-12 0.7921E-12 21 0.4997499310067592882605290D+00 0.6246207418964090992246729D-01 0.4302E-12 0.8641E-12 22 0.4997711815425514461486568D+00 0.6246545855360315677000643D-01 0.4528E-12 0.9041E-12 23 0.4997898296374528440927498D+00 0.6246841060865245759104617D-01 0.4817E-12 0.9610E-12 24 0.4998062839486146398501532D+00 0.6247100084469111001639128D-01 0.5105E-12 0.1012E-11 25 0.4998208759015741365903055D+00 0.6247328596467972262924752D-01 0.5208E-12 0.1059E-11 26 0.4998338765749831628531735D+00 0.6247531199583130438086609D-01 0.5280E-12 0.1071E-11 27 0.4998455094286890040986238D+00 0.6247711661195300995777342D-01 0.5418E-12 0.1090E-11 28 0.4998559600051912951546279D+00 0.6247873088741341491450190D-01 0.5531E-12 0.1125E-11 29 0.4998653834001782684040857D+00 0.6248018063625859555633633D-01 0.5850E-12 0.1135E-11 30 0.4998739100699455950707739D+00 0.6248148744489220418147314D-01 0.6076E-12 0.1204E-11 31 0.4998816503859023411215063D+00 0.6248266947588215845157551D-01 0.6336E-12 0.1254E-11 32 0.4998886982359269976838699D+00 0.6248374209905709477262265D-01 0.6659E-12 0.1321E-11 33 0.4998951338939793992052415D+00 0.6248471839101898767466744D-01 0.6760E-12 0.1363E-11 34 0.4999010263231367171309733D+00 0.6248560953350398750843817D-01 0.7103E-12 0.1403E-11 35 0.4999064350364226887693023D+00 0.6248642513333126814156294D-01 0.7259E-12 0.1454E-11 36 0.4999114116099006454717312D+00 0.6248717348108807027478547D-01 0.7530E-12 0.1492E-11 37 0.4999160009203821298672548D+00 0.6248786176159410118430076D-01 0.7806E-12 0.1543E-11 38 0.4999202421635933128956971D+00 0.6248849622614664564112328D-01 0.8097E-12 0.1623E-11 39 0.4999241696962148209413941D+00 0.6248908233427397182789098D-01 0.8322E-12 0.1665E-11 40 0.4999278137357828840785235D+00 0.6248962487101087697580835D-01 0.8575E-12 0.1715E-11 41 0.4999312009452334776507319D+00 0.6249012804440846928879119D-01 0.8874E-12 0.1736E-11 42 0.4999343549233237402868303D+00 0.6249059556699416397224481D-01 0.8981E-12 0.1803E-11 43 0.4999372966178657615142740D+00 0.6249103072413028142506413D-01 0.9244E-12 0.1831E-11 44 0.4999400446753546611038819D+00 0.6249143643162421195422989D-01 0.9435E-12 0.1883E-11 45 0.4999426157379416464197606D+00 0.6249181528447831946053721D-01 0.9634E-12 0.1942E-11 46 0.4999450246966260395316235D+00 0.6249216959830275591468911D-01 0.9817E-12 0.1955E-11 47 0.4999472849078921912024467D+00 0.6249250144462608285077586D-01 0.1014E-11 0.2005E-11 48 0.4999494083797023879356424D+00 0.6249281268110967462373889D-01 0.1023E-11 0.2060E-11 49 0.4999514059317026413232424D+00 0.6249310497748914279024519D-01 0.1050E-11 0.2094E-11 50 0.4999532873336489086320336D+00 0.6249337983791942691734170D-01 0.1078E-11 0.2135E-11 51 0.4999550614253738620244102D+00 0.6249363862028203608455978D-01 0.1114E-11 0.2205E-11 52 0.4999567362210554809764463D+00 0.6249388255291724800724901D-01 0.1124E-11 0.2266E-11 53 0.4999583190000925121709272D+00 0.6249411274916626210968730D-01 0.1135E-11 0.2299E-11 54 0.4999598163865178691000496D+00 0.6249433022004475714419017D-01 0.1158E-11 0.2296E-11 55 0.4999612344185733024907224D+00 0.6249453588531719892432816D-01 0.1171E-11 0.2326E-11 56 0.4999625786098144828871262D+00 0.6249473058319835429750671D-01 0.1194E-11 0.2358E-11 57 0.4999638540029049218074105D+00 0.6249491507887303231178769D-01 0.1226E-11 0.2428E-11 58 0.4999650652170818751865808D+00 0.6249509007199569220230538D-01 0.1256E-11 0.2492E-11 59 0.4999662164901310761119598D+00 0.6249525620330711203904189D-01 0.1268E-11 0.2550E-11 60 0.4999673117155846456334848D+00 0.6249541406048490493276837D-01 0.1297E-11 0.2561E-11 61 0.4999683544757536398505338D+00 0.6249556418332757968524932D-01 0.1327E-11 0.2640E-11 62 0.4999693480711200101821521D+00 0.6249570706835748627317068D-01 0.1346E-11 0.2695E-11 63 0.4999702955465395160004566D+00 0.6249584317291589031524770D-01 0.1379E-11 0.2732E-11 64 0.4999711997146450759203140D+00 0.6249597291881319941240034D-01 0.1403E-11 0.2785E-11 65 0.4999720631767873250790975D+00 0.6249609669558870323104158D-01 0.1420E-11 0.2842E-11 66 0.4999728883418042390181040D+00 0.6249621486342683043728300D-01 0.1455E-11 0.2898E-11 67 0.4999736774428733353066583D+00 0.6249632775577065693930967D-01 0.1470E-11 0.2932E-11 68 0.4999744325526671336346934D+00 0.6249643568166804635441350D-01 0.1502E-11 0.3000E-11 69 0.4999751555970043823352609D+00 0.6249653892788122038545937D-01 0.1524E-11 0.3040E-11 70 0.4999758483671653274118096D+00 0.6249663776078662370400743D-01 0.1559E-11 0.3082E-11 71 0.4999765125310184110475319D+00 0.6249673242808856498841226D-01 0.1580E-11 0.3145E-11 72 0.4999771496430877398597959D+00 0.6249682316036719949611034D-01 0.1608E-11 0.3203E-11 73 0.4999777611536750390557829D+00 0.6249691017247889912271663D-01 0.1617E-11 0.3238E-11 74 0.4999783484171362541107596D+00 0.6249699366482487472502745D-01 0.1653E-11 0.3303E-11 75 0.4999789126994011789874200D+00 0.6249707382450202327943004D-01 0.1670E-11 0.3332E-11 76 0.4999794551848142277020037D+00 0.6249715082634832765922600D-01 0.1692E-11 0.3368E-11 77 0.4999799769823655111411284D+00 0.6249722483389370432450252D-01 0.1710E-11 0.3431E-11 78 0.4999804791313735525337511D+00 0.6249729600022594427483634D-01 0.1741E-11 0.3486E-11 79 0.4999809626066741189503632D+00 0.6249736446878029995706861D-01 0.1776E-11 0.3514E-11 80 0.4999814283233636313712341D+00 0.6249743037406031395183483D-01 0.1807E-11 0.3594E-11 81 0.4999818771411403300686896D+00 0.6249749384229664585259313D-01 0.1830E-11 0.3642E-11 82 0.4999823098682817192391867D+00 0.6249755499204991613499568D-01 0.1845E-11 0.3692E-11 83 0.4999827272652927125951614D+00 0.6249761393476293657928818D-01 0.1880E-11 0.3736E-11 84 0.4999831300482552791471555D+00 0.6249767077526712444565527D-01 0.1894E-11 0.3798E-11 85 0.4999835188919071846647117D+00 0.6249772561224739221906045D-01 0.1914E-11 0.3826E-11 86 0.4999838944324745866588901D+00 0.6249777853866935781575845D-01 0.1939E-11 0.3862E-11 87 0.4999842572702807236773290D+00 0.6249782964217232432656308D-01 0.1975E-11 0.3922E-11 88 0.4999846079721507038432192D+00 0.6249787900543112730742584D-01 0.1994E-11 0.3986E-11 89 0.4999849470736304087258701D+00 0.6249792670648963581339862D-01 0.2009E-11 0.4019E-11 90 0.4999852750810357571085502D+00 0.6249797281906841603487619D-01 0.2028E-11 0.4036E-11 91 0.4999855924733469931771618D+00 0.6249801741284881938847791D-01 0.2046E-11 0.4081E-11 92 0.4999858997039612525659040D+00 0.6249806055373553663046258D-01 0.2067E-11 0.4129E-11 93 0.4999861972023153978985746D+00 0.6249810230409946285286466D-01 0.2090E-11 0.4183E-11 94 0.4999864853753899857627109D+00 0.6249814272300254234581504D-01 0.2108E-11 0.4229E-11 95 0.4999867646091042143925788D+00 0.6249818186640610486311477D-01 0.2131E-11 0.4263E-11 96 0.4999870352696107925132529D+00 0.6249821978736406371004936D-01 0.2158E-11 0.4292E-11 97 0.4999872977044988532172624D+00 0.6249825653620221943945057D-01 0.2165E-11 0.4327E-11 98 0.4999875522439123022113293D+00 0.6249829216068479917556125D-01 0.2211E-11 0.4379E-11 99 0.4999877992015903283047919D+00 0.6249832670616925926204896D-01 0.2237E-11 0.4446E-11 EAMAX = 0.2237E-11 AT 99 EBMAX = 0.4446E-11 AT 99 IERR IN CHEB = 0 IDERR IN DCHEB = 0 SIGMA = 0.5 K DALPHA(K) DBETA(K) 0 0.3600000000000000000000000D+00 0.4444444444444444444444444D+00 0.2132E-13 0.1954E-13 1 0.4719914117015566290928610D+00 0.5407346938775510204081633D-01 0.4742E-13 0.9773E-13 2 0.4879269724351617942679262D+00 0.5943841686774258104224939D-01 0.4411E-13 0.1109E-12 3 0.4932798327365417067423327D+00 0.6091940289441790471800011D-01 0.6024E-13 0.1224E-12 4 0.4957216320837135342773834D+00 0.6153509994700859144730978D-01 0.6915E-13 0.1376E-12 5 0.4970386426421355402433441D+00 0.6184950526468488541437227D-01 0.8700E-13 0.1593E-12 6 0.4978294203847389969822529D+00 0.6203162731630896597352813D-01 0.1126E-12 0.1952E-12 7 0.4983412074859196337520109D+00 0.6214656330041469428590224D-01 0.1170E-12 0.2164E-12 8 0.4986913480145008158357355D+00 0.6222375466280028995988519D-01 0.1301E-12 0.2589E-12 9 0.4989413835287815429850298D+00 0.6227810665498392805707788D-01 0.1514E-12 0.2910E-12 10 0.4991261249443936636915347D+00 0.6231782657996529774306834D-01 0.1650E-12 0.3382E-12 11 0.4992664682477055927182757D+00 0.6234773797508452199599062D-01 0.1737E-12 0.3418E-12 12 0.4993755732917555644203267D+00 0.6237082738280752611960887D-01 0.1877E-12 0.3756E-12 13 0.4994620627897156306981325D+00 0.6238902459454281914249312D-01 0.2163E-12 0.4120E-12 14 0.4995317778015998082616149D+00 0.6240362179255481511368181D-01 0.2197E-12 0.4527E-12 15 0.4995887889551455894238523D+00 0.6241551074437725515664532D-01 0.2449E-12 0.4717E-12 16 0.4996360033773615874569452D+00 0.6242532304911859697584015D-01 0.2495E-12 0.5028E-12 17 0.4996755420559208811991705D+00 0.6243351622682346972392998D-01 0.2612E-12 0.5263E-12 18 0.4997089817666155927613889D+00 0.6244042830417754417921846D-01 0.2684E-12 0.5553E-12 19 0.4997375143993141903485142D+00 0.6244631341888401724625467D-01 0.2849E-12 0.5663E-12 20 0.4997620544096438217950718D+00 0.6245136563006098053160644D-01 0.2850E-12 0.5875E-12 21 0.4997833128374760845597535D+00 0.6245573519842510412423656D-01 0.3063E-12 0.6032E-12 22 0.4998018492728466982272779D+00 0.6245953994072605716404695D-01 0.3151E-12 0.6345E-12 23 0.4998181089701914535760930D+00 0.6246287329138696125060280D-01 0.3395E-12 0.6712E-12 24 0.4998324497706394488722725D+00 0.6246581011945496883543089D-01 0.3545E-12 0.7165E-12 25 0.4998451619096538438402624D+00 0.6246841098796679818788527D-01 0.3688E-12 0.7332E-12 26 0.4998564827801957268954676D+00 0.6247072531490881204449373D-01 0.3626E-12 0.7533E-12 27 0.4998666080678056467977383D+00 0.6247279374805509669862980D-01 0.3853E-12 0.7634E-12 28 0.4998757002418247017210173D+00 0.6247464996949865776164874D-01 0.3942E-12 0.7973E-12 29 0.4998838950965001447988206D+00 0.6247632208123854681624580D-01 0.4149E-12 0.8423E-12 30 0.4998913068374629443080956D+00 0.6247783367943595945401558D-01 0.4284E-12 0.8658E-12 31 0.4998980320718154123236136D+00 0.6247920469481738505487917D-01 0.4336E-12 0.8832E-12 32 0.4999041529637934192289478D+00 0.6248045205566242753443320D-01 0.4404E-12 0.9007E-12 33 0.4999097397496046158651518D+00 0.6248159021493702067538866D-01 0.4553E-12 0.9183E-12 34 0.4999148527559424898122170D+00 0.6248263157248967419492307D-01 0.4757E-12 0.9541E-12 35 0.4999195440310304794672079D+00 0.6248358681553027106912242D-01 0.4838E-12 0.9743E-12 36 0.4999238586709130706291502D+00 0.6248446519498547085172373D-01 0.4942E-12 0.9996E-12 37 0.4999278359043646441993023D+00 0.6248527475117414361228339D-01 0.5095E-12 0.1020E-11 38 0.4999315099853402155579072D+00 0.6248602249915596165535206D-01 0.5168E-12 0.1049E-11 39 0.4999349109310140409691553D+00 0.6248671458178573912330464D-01 0.5334E-12 0.1055E-11 40 0.4999380651351962451100940D+00 0.6248735639674952332535790D-01 0.5314E-12 0.1096E-11 41 0.4999409958806052161048960D+00 0.6248795270251860659803352D-01 0.5651E-12 0.1123E-11 42 0.4999437237686129203082009D+00 0.6248850770712829033823226D-01 0.5611E-12 0.1142E-11 43 0.4999462670813125059807219D+00 0.6248902514289202603706833D-01 0.5674E-12 0.1130E-11 44 0.4999486420878182968971901D+00 0.6248950832954168059759670D-01 0.5738E-12 0.1156E-11 45 0.4999508633044014524286604D+00 0.6248996022779909550410346D-01 0.5739E-12 0.1169E-11 46 0.4999529437162436672219048D+00 0.6249038348500150007351923D-01 0.5940E-12 0.1194E-11 47 0.4999548949671460434946354D+00 0.6249078047410017571180685D-01 0.6175E-12 0.1226E-11 48 0.4999567275223771727791521D+00 0.6249115332711027176695932D-01 0.6246E-12 0.1245E-11 49 0.4999584508089198456948402D+00 0.6249150396389631947419380D-01 0.6350E-12 0.1284E-11 50 0.4999600733366308424902958D+00 0.6249183411702242683445893D-01 0.6540E-12 0.1326E-11 51 0.4999616028032252827289771D+00 0.6249214535327039419233590D-01 0.6685E-12 0.1348E-11 52 0.4999630461855068194929622D+00 0.6249243909232689722447384D-01 0.6833E-12 0.1353E-11 53 0.4999644098188647761106063D+00 0.6249271662305763778099856D-01 0.6881E-12 0.1394E-11 54 0.4999656994667312926320664D+00 0.6249297911771820532339798D-01 0.7250E-12 0.1435E-11 55 0.4999669203814216187436092D+00 0.6249322764439536743364059D-01 0.7394E-12 0.1487E-11 56 0.4999680773575577380887059D+00 0.6249346317792628229857515D-01 0.7605E-12 0.1537E-11 57 0.4999691747790906970560429D+00 0.6249368660950484618697944D-01 0.7849E-12 0.1558E-11 58 0.4999702166607832835623294D+00 0.6249389875515257757497028D-01 0.8002E-12 0.1587E-11 59 0.4999712066848864029133724D+00 0.6249410036320491421124313D-01 0.8028E-12 0.1620E-11 60 0.4999721482336350772391725D+00 0.6249429212094160952212189D-01 0.8178E-12 0.1633E-11 61 0.4999730444180997753474637D+00 0.6249447466047129329460356D-01 0.8343E-12 0.1668E-11 62 0.4999738981038527794413059D+00 0.6249464856396458721681804D-01 0.8517E-12 0.1695E-11 63 0.4999747119338450873618386D+00 0.6249481436831693346525225D-01 0.8597E-12 0.1721E-11 64 0.4999754883488349520402226D+00 0.6249497256931109198434623D-01 0.8824E-12 0.1744E-11 65 0.4999762296056629496953900D+00 0.6249512362533975202121856D-01 0.8994E-12 0.1781E-11 66 0.4999769377936291098983298D+00 0.6249526796074060874237548D-01 0.9227E-12 0.1829E-11 67 0.4999776148491940328687792D+00 0.6249540596878934803358105D-01 0.9325E-12 0.1860E-11 68 0.4999782625691971514359877D+00 0.6249553801439007314157062D-01 0.9452E-12 0.1897E-11 69 0.4999788826227606112748653D+00 0.6249566443649763920130830D-01 0.9476E-12 0.1913E-11 70 0.4999794765620260145278866D+00 0.6249578555030200582608385D-01 0.9682E-12 0.1913E-11 71 0.4999800458318529740903752D+00 0.6249590164920096536661457D-01 0.9844E-12 0.1949E-11 72 0.4999805917785926197341248D+00 0.6249601300658436449979864D-01 0.9974E-12 0.1986E-11 73 0.4999811156580355146816407D+00 0.6249611987745013348504999D-01 0.1004E-11 0.2012E-11 74 0.4999816186426215725898534D+00 0.6249622249987000685398710D-01 0.1023E-11 0.2040E-11 75 0.4999821018279892491294552D+00 0.6249632109632070766584596D-01 0.1038E-11 0.2049E-11 76 0.4999825662389322988704391D+00 0.6249641587489452932040333D-01 0.1041E-11 0.2084E-11 77 0.4999830128348245501653662D+00 0.6249650703040164580126188D-01 0.1051E-11 0.2112E-11 78 0.4999834425145662995407218D+00 0.6249659474537508048355780D-01 0.1067E-11 0.2132E-11 79 0.4999838561210999278064360D+00 0.6249667919098803752449566D-01 0.1091E-11 0.2186E-11 80 0.4999842544455370776022882D+00 0.6249676052789222470794015D-01 0.1096E-11 0.2212E-11 81 0.4999846382309351080952381D+00 0.6249683890698485223439219D-01 0.1110E-11 0.2213E-11 82 0.4999850081757564728418271D+00 0.6249691447011116104760201D-01 0.1103E-11 0.2225E-11 83 0.4999853649370410792162724D+00 0.6249698735070860204521348D-01 0.1126E-11 0.2252E-11 84 0.4999857091333185202026977D+00 0.6249705767439814119743096D-01 0.1142E-11 0.2259E-11 85 0.4999860413472842683019828D+00 0.6249712555952759423193690D-01 0.1158E-11 0.2315E-11 86 0.4999863621282614406895723D+00 0.6249719111767138868095742D-01 0.1172E-11 0.2357E-11 87 0.4999866719944675447181588D+00 0.6249725445409070255950143D-01 0.1195E-11 0.2380E-11 88 0.4999869714351036588750188D+00 0.6249731566815753068318073D-01 0.1217E-11 0.2411E-11 89 0.4999872609122817664443415D+00 0.6249737485374587551085453D-01 0.1224E-11 0.2431E-11 90 0.4999875408628044113852852D+00 0.6249743209959294408918089D-01 0.1237E-11 0.2457E-11 91 0.4999878116998094656880476D+00 0.6249748748963295155320773D-01 0.1256E-11 0.2484E-11 92 0.4999880738142915649907439D+00 0.6249754110330588066564603D-01 0.1275E-11 0.2518E-11 93 0.4999883275765106673134879D+00 0.6249759301584332253747359D-01 0.1287E-11 0.2561E-11 94 0.4999885733372972033418690D+00 0.6249764329853332288768545D-01 0.1299E-11 0.2604E-11 95 0.4999888114292624025921767D+00 0.6249769201896597827768467D-01 0.1316E-11 0.2640E-11 96 0.4999890421679215864606035D+00 0.6249773924126136533571248D-01 0.1342E-11 0.2654E-11 97 0.4999892658527375064523897D+00 0.6249778502628124099694122D-01 0.1338E-11 0.2677E-11 98 0.4999894827680901648832002D+00 0.6249782943182582140407308D-01 0.1358E-11 0.2713E-11 99 0.4999896931841789781887674D+00 0.6249787251281682973825635D-01 0.1370E-11 0.2724E-11 EAMAX = 0.1370E-11 AT 99 EBMAX = 0.2724E-11 AT 99 output of test2 with modmom=.false.: IERR IN CHEB = 0 IDERR IN DCHEB = 0 SIGMA = -0.5 K DALPHA(K) DBETA(K) 0 0.1111111111111111111111111D+00 0.4000000000000000000000000D+01 0.3553E-13 0.0000E+00 1 0.4661483641075477810171688D+00 0.2765432098765432098765432D-01 0.3357E-13 0.1536E-13 2 0.4880690581976426561739654D+00 0.5534292684170711183265476D-01 0.1840E-12 0.7715E-13 3 0.4938743419208057331274822D+00 0.5940526298488865183067045D-01 0.9937E-11 0.3398E-11 4 0.4962639578613459263700272D+00 0.6077714606674732893827292D-01 0.1655E-09 0.8674E-10 5 0.4974805136345470499404300D+00 0.6140371143126410746951331D-01 0.2156E-08 0.1195E-08 6 0.4981846424539394712820765D+00 0.6174167659202270796881237D-01 0.2514E-07 0.1601E-07 7 0.4986290336259843770623033D+00 0.6194453627914717711290500D-01 0.3179E-06 0.5731E-07 8 0.4989276082849235417170176D+00 0.6207576580933626143263374D-01 0.1141E-04 0.5484E-05 9 0.4991379564664850066978632D+00 0.6216550244588411847564971D-01 0.2493E-03 0.2412E-04 10 0.4992917697449966613224589D+00 0.6222955193630939619411773D-01 0.1796E-01 0.5439E-02 11 0.4994076708859141785874036D+00 0.6227685326078529901498445D-01 0.2488E+00 0.1747E+00 EAMAX = 0.2488E+00 AT 11 EBMAX = 0.1747E+00 AT 11 IERR IN CHEB = 0 IDERR IN DCHEB = 0 SIGMA = 0.0 K DALPHA(K) DBETA(K) 0 0.2500000000000000000000000D+00 0.1000000000000000000000000D+01 0.0000E+00 0.0000E+00 1 0.4642857142857142857142857D+00 0.4861111111111111111111111D-01 0.1399E-12 0.8120E-13 2 0.4854824464561713402517112D+00 0.5868480725623582766439909D-01 0.4162E-12 0.7607E-12 3 0.4921030818713608586050335D+00 0.6072858391891785822637764D-01 0.2480E-10 0.6712E-11 4 0.4950284987583539049494542D+00 0.6148202019693696071375090D-01 0.2065E-09 0.1833E-09 5 0.4965795116435580984519647D+00 0.6184080953188484218106874D-01 0.4201E-08 0.1170E-09 6 0.4975013013049582411833342D+00 0.6203906295445598496037927D-01 0.1529E-06 0.6217E-07 7 0.4980940182042518540528188D+00 0.6215991915828943043575570D-01 0.1328E-05