putmodel2.f

131 lines · 1 definitions · on GitHub (7be4133)

Python version: putmodel2.py, 131 lines, on the right (switch to Python above the code).

Variables on this page (2)

clsun, json

Purpose

Writes a stellar model to a text file in the "MODEL2" format (LLP 4/16/03), which YREC can read back as a starting model.

How it fits

Inputs: the model and its global quantities, as arguments: the header values (model number, number of shells M, mass, $\log T_\mathrm{eff}$, $\log L$, $\log M$, age, step, inner and outer $\log m$), the physics flags and labels (EOS, atmosphere, opacity, mixture strings), the luminosities by source TLUMX, the envelope data (TRIT, TRIL, PS, TS, RS, CFENV), and the shell arrays.
Who calls it: WRTLST, for the last model.
Who reads its output: STARIN, which recognizes the leading MOD2 and calls GETMODEL2.
Output: the file on unit IWRITE; warnings to ISHORT.

The format. A header line (MOD2, the number format chosen by the age's size); a line of physics flags; a TLUMX line of seven luminosities in erg s⁻¹ (pp chains I, II, III, CNO, helium burning, neutrinos, gravitational contraction, by GETYREC7's comment); three ENV lines (negative indices if FTRI < 0); column titles; then one line per shell: shell, $\log m$, $\log r$, $L$, $\log P$, $\log T$, $\log\rho$, $\Omega$ (unlogged, a change from YREC7 files), the convection flag, and the 15 abundances.

Design

If the largest of the luminosities is at most $10^{20}$, they are taken to be in solar units and multiplied by $L_\odot$, in place: the caller's TLUMX changes too (bug 1). $L_\odot$ (CLSUN) comes from CONSTANTS_MOD. The warning for the atmosphere label ' ? ' (lines 54–58 ↗) is never written, since WRTLST, the only caller, never passes that label (settled from the code, Nov 9, 2026: wrtlst.f, lines 93–106 ↗).

Suspected bugs, checked by running the code

Each bug is marked by what running the code showed: (changes results, large) or (small), the fix moving a run clearly beyond a null change; (stops the run); (wrong output), the fix changing only what is written; (harmless in the runs), within the noise; (never occurred), the code ran but the fault did not; (not reached); (cannot be reached), a guard prevents it; (withdrawn), the suspicion was wrong.

1. (wrong output) Checked by KC (Nov 10, 2026) The caller's luminosities are left in erg s⁻¹.

(lines 90–97 ↗) The conversion to erg s⁻¹ is made in place, so after each model, when WRTOUT has called WRTLST (wrtout.f, lines 666–669 ↗), the main program's TLUMX(1..7) are in erg s⁻¹ while TLUMX(8) stays in solar units, until COEFFT recomputes them at the next model. Two readers in between expect solar units. At the start of a kind card that continues the model in memory (LFIRST(NK) false: STARIN skips reading a model, starin.f, lines 255–262 ↗), HTIMER sums TLUMX(1..4) as the hydrogen-burning luminosity "in solar units" (main.f, lines 584–586 ↗; htimer.f, lines 133–134 ↗), and once the core's hydrogen is below ATIME(1), XTIME divides by it (xtime.f, line 65 ↗; xtime.f, line 74 ↗), so the first time step of that kind card comes out about $L_\odot \approx 3.85\times10^{33}$ times too short (htimer.f, lines 171–176 ↗). And the main program's last ISNU output, with LCALS, LSNU, and LSOL, writes TLUMX(1..4) and TLUMX(7) as "energy generation fractions" (main.f, lines 1228–1229 ↗) in erg s⁻¹. Only on these paths (the default is LFIRST true for every kind card); how the near-zero step changes the following models was not traced. PUTSTORE converts in place in the same way (putstore.f, lines 243–249 ↗).

A possible fix (and the same in PUTSTORE):

putmodel2.f

@@ lines 23–28 @@
       REAL*8 BL,CCCMAX,CFENV,CMIXL,DAGE,DDAGE,FTRI,HCOMP,HD,HL,HP,HR,HS,
      *       HSTOT,HT,OMEGA,PDISK,PS,RS,SMASS,TDISK,TEFFL,TLUMX,TRIL,
      *       TRIT,TS,WMAX
+C 11/09/26 KC via Claude
+C code changed to convert a copy of TLUMX, so that the caller's
+C luminosities stay in solar units.
+      REAL*8 TLUMXO(7)
       INTEGER I,I0,ISHORT,IWRITE,J,JCORE,JENV,M,MODEL
       LOGICAL*4 LC,LDIFY,LDIFZ,LDISK,LEXCOM,LINSTB,LJDOT0,LOVSTC,LOVSTE,
      *       LOVSTM,LPUREZ,LROT,LSEMIC
@@ lines 89–100 @@

       CCCMAX = DMAX1(TLUMX(1),TLUMX(2),TLUMX(3),TLUMX(4),TLUMX(5),
      *     DABS(TLUMX(6)),TLUMX(7))
+      DO J = 1,7
+         TLUMXO(J) = TLUMX(J)
+      ENDDO
       IF(CCCMAX.LE.1.0D20) THEN
        DO J = 1,7
-          TLUMX(J) = TLUMX(J) * CLSUN
+          TLUMXO(J) = TLUMX(J) * CLSUN
          ENDDO
       ENDIF
-      WRITE(IWRITE,40) (TLUMX(J),J=1,7)
+      WRITE(IWRITE,40) (TLUMXO(J),J=1,7)
    40 FORMAT('TLUMX',5X,1P7E17.9)

 C write ENVELOPE DATA

How the outputs show it. In examples/run_standard_solar_model/Test_solarcal_noGS_norot, the .snu file's last line, the "energy generation fractions" of the final model 449 (main.f, line 1229 ↗), reads 3.440E+33, 3.686E+32, 2.371E+29, 1.958E+31, and -7.673E+29, the numbers of the .last file's TLUMX line (line 97 ↗), which is meant to be in erg s⁻¹. The .track line of model 449 (wrtout.f, line 558 ↗) gives the same five terms (ppI_lsun, ppII_lsun, ppIII_lsun, CNO_lsun, and Egrav_lsun) in solar units: 8.98735537E-001, 9.62952015E-002, 6.19428809E-005, 5.11441212E-003, and -2.00444567E-004. The .snu values are these times 3.828×10³³, the case's CLSUN.

Checked by running YREC (Nov 9, 2026, the counts of testsuite/Test_m1p0feh+0p0GS98_base_HeIgnite repeated on Nov 10 with a private start model; a line added at each suspected path counted how often it was taken, the outputs otherwise unchanged): Of 34 runs (26 of YREC's cases, from a 0.04 $M_\odot$ brown dwarf and the solar models to 9 $M_\odot$, rotation, and helium burning, and 8 made-up ones), 33 took the in-place conversion, after every model: from 10 times in examples/run_from_seed_to_start/m10000gs98z001000_prems to 8,571 in testsuite/Test_m1p0feh+0p0GS98_base_HeIgnite. Two lines, counted together, tested the two readers that expect solar units: HTIMER's hydrogen-burning luminosity, and the ISNU energy fractions. Values above $10^{20}$, so in erg s⁻¹, reached them in 27 runs, once in most, twice in testsuite/Test_m0p95feh+0p0_GN93_TAHB, in examples/run_from_zahb_to_tahb/ZAHB_m0p8feh+0p0_TAHB, and in YREC's 1 $M_\odot$ helium-burning case run with the AAG21 table, and 7 times in examples/run_standard_solar_model/Test_solarcal_noGS_norot, from $5.2\times10^{26}$ to $3.7\times10^{37}$. With the fix, testsuite/Test_m0p3feh+0p0GS98_scv_ZAMS gives an identical track, and Test_solarcal_noGS_norot differs exactly as for the null change ($\log L$ by up to 0.000322 dex for both): within the noise. In testsuite/Test_m0p95feh+0p0_GN93_TAHB, which runs past the core's hydrogen exhaustion to the end of helium burning and where the condition held twice, the track with the fix is identical, models and end age included (the null change moves $\log L$ by up to 1.67e-7 dex); only the .short file differs beyond 2%. So the erg luminosity did not change the evolution there. Why (rechecked on Nov 10, 2026, with lines counting HTIMER's reading and the step it gives): Both hits of this case came at the start of a kind card (the second and third), with central $X$ = 0, and each gave a step of about $1.1\times10^{-28}$ yr, through XTIME's shell criterion (xtime.f, line 74 ↗). Neither step was used: The second kind card is a rescaling, which does not age the model (main.f, line 712 ↗), and the third starts from the model numbered −3 that the rescalings left, so its first three models are relaxed without aging too (MODEL.GE.0, main.f, line 712 ↗; the step is then made negative, main.f, line 825 ↗), and HTIMER's next call (main.f, line 1055 ↗), after the luminosities are recomputed in solar units, sets the step the evolution takes. With the fix, HTIMER no longer reads an erg luminosity, and the track is identical again. In examples/class_exercises/exercise_4/Grid_m4p0feh+0p0GS98_std25_TAMS, also rerun, the one hit came at the second kind card, whose starting model still burns hydrogen in its core, with central $X$ = 0.72, above ATIME(1) ($10^{-3}$); XTIME's core criterion then takes the step from the core's mass and luminosity (xtime.f, lines 65–69 ↗), and the hydrogen-burning luminosity only decides whether XTIME is called, which it is in either unit; the other cases were not rerun. The erg step would be used only at a kind card that continues the model in memory, ages its first model, and starts with central $X$ below ATIME(1); none of the runs did. What the runs show is wrong output (the .short file; the ISNU energy fractions, a file not compared). Intent: The comment "If TLUMX are in solar units, convert to ergs" (lines 87–88 ↗) expects either unit on entry; nothing says the caller's array is meant to change.

Definitions

subroutinePUTMODEL2

lines 7–131 · GitHub

Uses modules CONSTANTS_MOD, DIMENSIONS_MOD

Called by WRTLST

Change log

The changes since rp_1

Changed since rp_1. Declarations only: /CONST/ to CONSTANTS_MOD, JSON from DIMENSIONS_MOD, IMPLICIT NONE.

1C 2C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 3C PUTMMODEL2 - Write out a stallar model in MODEL2 format 4C 5C llp 4/16/03 6C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 7 SUBROUTINE PUTMODEL2(BL,CFENV,CMIXL,DAGE,DDAGE,FTRI,HCOMP,HD,HL, 8 * * HP,HR,HS,HSTOT,HT,IWRITE,ISHORT,JCORE,JENV,LC,LEXCOM,LROT,M, 9 * * MODEL,OMEGA,PS,RS,SMASS,TEFFL,TLUMX,TRIL,TRIT,TS, 10 & & ATM,EOS,HIK,LDIFY,LDIFZ,LDISK,LINSTB,LJDOT0,ALOK, 11 & & LOVSTC,LOVSTE,LOVSTM,LPUREZ,LSEMIC,COMPMIX,PDISK,TDISK,WMAX) 12C 10/15/26 MHP via Claude 13C code changed to take JSON from DIMENSIONS_MOD instead of declaring 14C PARAMETER(JSON=5000) here. 15 USE DIMENSIONS_MOD 16C 10/14/26 MHP via Claude 17C code changed to convert COMMON/CONSTANTS/ into CONSTANTS_MOD. 18 USE CONSTANTS_MOD 19C 10/20/26 MHP via Claude 20C code changed to replace implicit typing with IMPLICIT NONE and 21C explicit declarations. 22 IMPLICIT NONE 23 REAL*8 BL,CCCMAX,CFENV,CMIXL,DAGE,DDAGE,FTRI,HCOMP,HD,HL,HP,HR,HS, 24 * * HSTOT,HT,OMEGA,PDISK,PS,RS,SMASS,TDISK,TEFFL,TLUMX,TRIL, 25 * * TRIT,TS,WMAX 26 INTEGER I,I0,ISHORT,IWRITE,J,JCORE,JENV,M,MODEL 27 LOGICAL*4 LC,LDIFY,LDIFZ,LDISK,LEXCOM,LINSTB,LJDOT0,LOVSTC,LOVSTE, 28 * * LOVSTM,LPUREZ,LROT,LSEMIC 29C First three lines above are YREC7 inputs 30C Last two lines are MODEL2 add-ons 31 32C Write output model in MODEL2 format 33 34 35 CHARACTER*6 EOS 36c CHARACTER*4 ATM, LOK, HIK, COMPMIX 37c MHP 4/25 changed LOK name to make it unique, used elsewhere 38 CHARACTER*4 ATM, ALOK, HIK, COMPMIX 39 40C 9/25/26 MHP via Claude 41C code changed to merge COMMON/CONST/, COMMON/CONST1/, COMMON/CONST2/, 42C and COMMON/CONST3/ into a single COMMON/CONSTANTS/ 43 44 45 DIMENSION HCOMP(15,JSON),HD(JSON),HL(JSON),HP(JSON),HR(JSON), 46 & & HS(JSON),HT(JSON),LC(JSON),TRIT(3),TRIL(3),PS(3),TS(3),RS(3), 47 & & CFENV(9),TLUMX(8),OMEGA(JSON) 48 49 save 50 51C PUTYMODEL2 writes the model provided to it out to the LU IWRITE file. 52C Any error messages go to LU ISHORT. 53 54 IF(ATM .EQ. ' ? ') THEN 55 WRITE(ISHORT,7) 56 7 7 FORMAT('*** YREC7 input file, flags, etc., have been ', 57 * * 'defaulted. ***') 58 ENDIF 59 60C write header records 61 IF(DAGE .lt. 1d3) THEN 62 WRITE(IWRITE,10) 'MOD2 ',MODEL,M,SMASS,TEFFL,BL,HSTOT,DAGE, 63 * * DDAGE,HS(1),HS(M) 64 10 10 FORMAT(A5,2I8,5F16.11,1PE18.10,0P2F16.12) 65 ELSE IF (DAGE .LT. 1D4) THEN 66 WRITE(IWRITE,11) 'MOD2 ',MODEL,M,SMASS,TEFFL,BL,HSTOT,DAGE, 67 * * DDAGE,HS(1),HS(M) 68 11 11 FORMAT(A5,2I8,4F16.12,F16.10,1PE18.10,0P2F16.12) 69 ELSE IF (DAGE .LT. 1D5) THEN 70 WRITE(IWRITE,12) 'MOD2 ',MODEL,M,SMASS,TEFFL,BL,HSTOT,DAGE, 71 * * DDAGE,HS(1),HS(M) 72 12 12 FORMAT(A5,2I8,4F16.12,F16.9,1PE18.10,0P2F16.12) 73 ELSE 74 WRITE(IWRITE,13) 'MOD2 ',MODEL,M,SMASS,TEFFL,BL,HSTOT,DAGE, 75 * * DDAGE,HS(1),HS(M) 76 13 13 FORMAT(A5,2I8,4F16.12,F16.8,1PE18.10,0P2F16.12) 77 ENDIF 78 79C write physics flags: 80 WRITE(IWRITE,30) JCORE,JENV,CMIXL,EOS,ATM,ALOK,HIK,LPUREZ, 81 & & COMPMIX,LEXCOM,LDIFY,LDIFZ,LSEMIC,LOVSTC,LOVSTE,LOVSTM, 82 & & LROT,LINSTB,LJDOT0,LDISK,TDISK,PDISK,WMAX 83 30 30 FORMAT(2I8,F16.10,1X,A6,1X,3(A4,1X),L1,1X,A4,1X,11(L1,1X), 84 & & 3(1PE18.10)) 85 86C write luminosities 87C If TLUMX are in solar units, convert to ergs. Decide by 88C comparing to 10**20, if smaller, multiply by CLSUN 89 90 CCCMAX = DMAX1(TLUMX(1),TLUMX(2),TLUMX(3),TLUMX(4),TLUMX(5), 91 * * DABS(TLUMX(6)),TLUMX(7)) 92 IF(CCCMAX.LE.1.0D20) THEN 93 DO J = 1,7 94 TLUMX(J) = TLUMX(J) * CLSUN 95 ENDDO 96 ENDIF 97 WRITE(IWRITE,40) (TLUMX(J),J=1,7) 98 40 40 FORMAT('TLUMX',5X,1P7E17.9) 99 100C write ENVELOPE DATA 101 DO I = 1,3 102 I0 = I 103 IF(FTRI.LT.0D0) I0 = -I 104 WRITE(IWRITE,50)I0,TRIT(I),TRIL(I),PS(I),TS(I),RS(I), 105 & & (CFENV(3*I-3+J),J=1,3) 106 ENDDO 107 50 50 FORMAT('ENV',I2,5F16.12,1P3E20.12) 108 109C write column headings for all per shell information 110 WRITE(IWRITE,*) 111 WRITE(IWRITE,55) ' SHELL','MASS ','RADIUS ', 112 * * 'LUMINOSITY ','PRESSURE ','TEMPERATURE ', 113 * * 'DENSITY ','OMEGA ',' C',' H1 ',' He4 ', 114 * * ' METALS ','He3 ','C12 ','C13 ','N14 ', 115 * * 'N15 ','O16 ','O17 ','O18 ','H2 ', 116 * * 'Li6 ','Li7 ','Be9 ' 117 55 55 FORMAT(A6,2A18,A24,3A18,A24,A2,3A12,12A16) 118 WRITE(IWRITE,*) 119 120C LLP 4/16/03 Output OMEGA rather Log10(OMEGA), a change from YREC7 files 121 122C write per shell information, one line per shell 123 DO I = 1,M 124 WRITE(IWRITE,60) I,HS(I),HR(I),HL(I),HP(I),HT(I),HD(I), 125 * * OMEGA(I),LC(I),(HCOMP(J,I),J=1,15) 126 ENDDO 127 60 60 FORMAT(I6,0P2F18.14,1PE24.16,0P3F18.14,1PE24.16,1x,L1, 128 & & 3(0PF12.9),12(0PE16.8)) 129 130 RETURN 131 END

1"""Python version of putmodel2.f (YREC 7be4133): write a model in the 2MODEL2 text format.""" 3 4import math 5 6import numpy as np 7 8from pyrec import constants_mod 9from pyrec import iounits_mod 10 11 12def _l1(flag): 13 """Fortran's L1.""" 14 15 return "T" if flag else "F" 16 17 18def _e1(x, w, d): 19 """Fortran's 1PEw.d: one digit before the point, e.g. 1.2345E+05.""" 20 21 return f"{x:{w}.{d}E}" 22 23 24def _e0(x, w, d): 25 """Fortran's 0PEw.d: a mantissa in [0.1, 1), e.g. 0.12345678E+01.""" 26 27 if x == 0.0: 28 return f"{'0.' + '0' * d + 'E+00':>{w}}" 29 e = math.floor(math.log10(abs(x))) + 1 30 m = x / 10.0**e 31 if round(abs(m), d) >= 1.0: # rounding carried into the next decade 32 m /= 10.0 33 e += 1 34 s = f"{abs(m):.{d}f}"[1:] 35 sign = "-" if x < 0 else "" 36 return f"{sign + '0' + s + f'E{e:+03d}':>{w}}" 37 38 39def putmodel2(bl: float, cfenv: np.ndarray, cmixl: float, dage: float, ddage: float, ftri: float, hcomp: np.ndarray, 40 hd: np.ndarray, hl: np.ndarray, hp: np.ndarray, hr: np.ndarray, hs: np.ndarray, hstot: float, 41 ht: np.ndarray, iwrite: int, ishort: int, jcore: int, jenv: int, lc: np.ndarray, lexcom: bool, lrot: bool, 42 m: int, model: int, omega: np.ndarray, ps: np.ndarray, rs: np.ndarray, smass: float, teffl: float, 43 tlumx: np.ndarray, tril: np.ndarray, trit: np.ndarray, ts: np.ndarray, atm: str, eos: str, hik: str, 44 ldify: bool, ldifz: bool, ldisk: bool, linstb: bool, ljdot0: bool, alok: str, lovstc: bool, lovste: bool, 45 lovstm: bool, lpurez: bool, lsemic: bool, compmix: str, pdisk: float, tdisk: float, wmax: float) -> None: 46 """Write the model to unit iwrite in the MODEL2 format: a header line 47 (its age format chosen by the age's size), a line of physics flags, 48 the luminosities TLUMX(1..7) in erg/s, three ENV lines, column titles 49 and one line per shell. 50 51 Translates: putmodel2.f#PUTMODEL2 (7be4133) 52 53 Arguments: as in the Fortran (arrays with index 0 unused; trit, tril, 54 ps, ts, rs [1..3], cfenv [1..9], tlumx [1..8]). tlumx is changed in 55 place when converted from solar units. Returns nothing. 56 57 """ 58 59 w = iounits_mod.write 60 61 # Never true: WRTLST never passes ' ? ' (Fortran lines 54–58). 62 if atm == ' ? ': 63 w(ishort, "*** YREC7 input file, flags, etc., have been " 64 "defaulted. ***") 65 66 # The header line; DAGE's format by its size (formats 10-13) (Fortran 67 # lines 60–77). 68 if dage < 1e3: 69 fages = [f"{smass:16.11f}", f"{teffl:16.11f}", f"{bl:16.11f}", 70 f"{hstot:16.11f}", f"{dage:16.11f}"] 71 else: 72 if dage < 1e4: 73 fage = f"{dage:16.10f}" 74 elif dage < 1e5: 75 fage = f"{dage:16.9f}" 76 else: 77 fage = f"{dage:16.8f}" 78 fages = [f"{smass:16.12f}", f"{teffl:16.12f}", f"{bl:16.12f}", 79 f"{hstot:16.12f}", fage] 80 w(iwrite, "MOD2 " + f"{model:8d}{m:8d}" + "".join(fages) 81 + _e1(ddage, 18, 10) + f"{hs[1]:16.12f}{hs[m]:16.12f}") 82 83 # Format 30: the physics flags (Fortran lines 79–84). 84 w(iwrite, f"{jcore:8d}{jenv:8d}{cmixl:16.10f} {eos:6.6s} " 85 f"{atm:4.4s} {alok:4.4s} {hik:4.4s} {_l1(lpurez)} {compmix:4.4s} " 86 + "".join(_l1(f) + " " for f in (lexcom, ldify, ldifz, lsemic, 87 lovstc, lovste, lovstm, lrot, 88 linstb, ljdot0, ldisk)) 89 + _e1(tdisk, 18, 10) + _e1(pdisk, 18, 10) + _e1(wmax, 18, 10)) 90 91 # Luminosities taken to be solar if all are at most 1e20, converted in 92 # place (Fortran lines 86–98). Suspected bug (see the page): the 93 # caller's TLUMX is left in erg/s. Question (see the page): TLUMX(8) is 94 # not written. 95 cccmax = max(tlumx[1], tlumx[2], tlumx[3], tlumx[4], tlumx[5], 96 abs(tlumx[6]), tlumx[7]) 97 if cccmax <= 1.0e20: 98 for j in range(1, 8): 99 tlumx[j] = tlumx[j] * constants_mod.clsun 100 w(iwrite, "TLUMX" + " " * 5 101 + "".join(_e1(tlumx[j], 17, 9) for j in range(1, 8))) 102 103 # The envelope triangle (Fortran lines 100–107). 104 for i in range(1, 4): 105 i0 = i 106 if ftri < 0.0: 107 i0 = -i 108 w(iwrite, f"ENV{i0:2d}{trit[i]:16.12f}{tril[i]:16.12f}" 109 f"{ps[i]:16.12f}{ts[i]:16.12f}{rs[i]:16.12f}" 110 + "".join(_e1(cfenv[3 * i - 3 + j], 20, 12) for j in range(1, 4))) 111 112 # Format 55: A6,2A18,A24,3A18,A24,A2,3A12,12A16 (Fortran lines 109–118). 113 w(iwrite, "") 114 titles = [' SHELL', 'MASS ', 'RADIUS ', 'LUMINOSITY ', 115 'PRESSURE ', 'TEMPERATURE ', 'DENSITY ', 116 'OMEGA ', ' C', ' H1 ', ' He4 ', 117 ' METALS ', 'He3 ', 'C12 ', 'C13 ', 118 'N14 ', 'N15 ', 'O16 ', 'O17 ', 119 'O18 ', 'H2 ', 'Li6 ', 'Li7 ', 120 'Be9 '] 121 widths = [6, 18, 18, 24, 18, 18, 18, 24, 2] + [12] * 3 + [16] * 12 122 w(iwrite, "".join(f"{t:>{n}}" for t, n in zip(titles, widths))) 123 w(iwrite, "") 124 125 # Format 60: one line per shell (Fortran lines 120–128). 126 for i in range(1, m + 1): 127 w(iwrite, f"{i:6d}{hs[i]:18.14f}{hr[i]:18.14f}" + _e1(hl[i], 24, 16) 128 + f"{hp[i]:18.14f}{ht[i]:18.14f}{hd[i]:18.14f}" 129 + _e1(omega[i], 24, 16) + " " + _l1(lc[i]) 130 + "".join(f"{hcomp[j, i]:12.9f}" for j in range(1, 4)) 131 + "".join(_e0(hcomp[j, i], 16, 8) for j in range(4, 16)))