Date: 2026-06-01T23:13:46+00:00

Actual source code: chwirut1f.F90

      1: !  Program usage: mpiexec -n 1 chwirut1f [-help] [all TAO options]
      2: !
      3: !  Description:  This example demonstrates use of the TAO package to solve a
      4: !  nonlinear least-squares problem on a single processor.  We minimize the
      5: !  Chwirut function:
      6: !       sum_{i=0}^{n/2-1} ( alpha*(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2)
      7: !
      8: !  The C version of this code is test_chwirut1.c
      9: !

     11: !
     12: ! ----------------------------------------------------------------------
     13: !
     14: #include <petsc/finclude/petsctao.h>
     15: module chwirut1fmodule
     16:   use petsctao
     17:   implicit none

     19:   PetscReal t(0:213)
     20:   PetscReal y(0:213)
     21:   PetscInt, parameter :: m = 214, n = 3

     23: contains

     25: ! --------------------------------------------------------------------
     26: !  FormFunction - Evaluates the function f(X) and gradient G(X)
     27: !
     28: !  Input Parameters:
     29: !  tao - the Tao context
     30: !  X   - input vector
     31: !  dummy - not used
     32: !
     33: !  Output Parameters:
     34: !  f - function vector
     35:   subroutine FormFunction(ta, x, f, dummy, ierr)

     37:     Tao ta
     38:     Vec x, f
     39:     PetscErrorCode, intent(out) :: ierr
     40:     PetscInt dummy

     42:     PetscInt i
     43:     PetscScalar, pointer, dimension(:)  :: x_v, f_v

     45:     ierr = 0

     47: !   Get pointers to vector data
     48:     PetscCall(VecGetArray(x, x_v, ierr))
     49:     PetscCall(VecGetArray(f, f_v, ierr))

     51: !   Compute F(X)
     52:     do i = 0, m - 1
     53:       f_v(i + 1) = y(i) - exp(-x_v(1)*t(i))/(x_v(2) + x_v(3)*t(i))
     54:     end do

     56: !   Restore vectors
     57:     PetscCall(VecRestoreArray(X, x_v, ierr))
     58:     PetscCall(VecRestoreArray(F, f_v, ierr))

     60:   end

     62:   subroutine FormStartingPoint(x)
     63:     Vec x
     64:     PetscScalar, pointer, dimension(:)  :: x_v
     65:     PetscErrorCode ierr

     67:     PetscCall(VecGetArray(x, x_v, ierr))
     68:     x_v(1) = 0.15_PETSC_REAL_KIND
     69:     x_v(2) = 0.008_PETSC_REAL_KIND
     70:     x_v(3) = 0.01_PETSC_REAL_KIND
     71:     PetscCall(VecRestoreArray(x, x_v, ierr))
     72:   end

     74:   subroutine InitializeData()
     75:     integer i
     76:     i = 0
     77:     y(i) = 92.9000_PETSC_REAL_KIND; t(i) = 0.5000_PETSC_REAL_KIND; i = i + 1
     78:     y(i) = 78.7000_PETSC_REAL_KIND; t(i) = 0.6250_PETSC_REAL_KIND; i = i + 1
     79:     y(i) = 64.2000_PETSC_REAL_KIND; t(i) = 0.7500_PETSC_REAL_KIND; i = i + 1
     80:     y(i) = 64.9000_PETSC_REAL_KIND; t(i) = 0.8750_PETSC_REAL_KIND; i = i + 1
     81:     y(i) = 57.1000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
     82:     y(i) = 43.3000_PETSC_REAL_KIND; t(i) = 1.2500_PETSC_REAL_KIND; i = i + 1
     83:     y(i) = 31.1000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
     84:     y(i) = 23.6000_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
     85:     y(i) = 31.0500_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
     86:     y(i) = 23.7750_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
     87:     y(i) = 17.7375_PETSC_REAL_KIND; t(i) = 2.7500_PETSC_REAL_KIND; i = i + 1
     88:     y(i) = 13.8000_PETSC_REAL_KIND; t(i) = 3.2500_PETSC_REAL_KIND; i = i + 1
     89:     y(i) = 11.5875_PETSC_REAL_KIND; t(i) = 3.7500_PETSC_REAL_KIND; i = i + 1
     90:     y(i) = 9.4125_PETSC_REAL_KIND; t(i) = 4.2500_PETSC_REAL_KIND; i = i + 1
     91:     y(i) = 7.7250_PETSC_REAL_KIND; t(i) = 4.7500_PETSC_REAL_KIND; i = i + 1
     92:     y(i) = 7.3500_PETSC_REAL_KIND; t(i) = 5.2500_PETSC_REAL_KIND; i = i + 1
     93:     y(i) = 8.0250_PETSC_REAL_KIND; t(i) = 5.7500_PETSC_REAL_KIND; i = i + 1
     94:     y(i) = 90.6000_PETSC_REAL_KIND; t(i) = 0.5000_PETSC_REAL_KIND; i = i + 1
     95:     y(i) = 76.9000_PETSC_REAL_KIND; t(i) = 0.6250_PETSC_REAL_KIND; i = i + 1
     96:     y(i) = 71.6000_PETSC_REAL_KIND; t(i) = 0.7500_PETSC_REAL_KIND; i = i + 1
     97:     y(i) = 63.6000_PETSC_REAL_KIND; t(i) = 0.8750_PETSC_REAL_KIND; i = i + 1
     98:     y(i) = 54.0000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
     99:     y(i) = 39.2000_PETSC_REAL_KIND; t(i) = 1.2500_PETSC_REAL_KIND; i = i + 1
    100:     y(i) = 29.3000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    101:     y(i) = 21.4000_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    102:     y(i) = 29.1750_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    103:     y(i) = 22.1250_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    104:     y(i) = 17.5125_PETSC_REAL_KIND; t(i) = 2.7500_PETSC_REAL_KIND; i = i + 1
    105:     y(i) = 14.2500_PETSC_REAL_KIND; t(i) = 3.2500_PETSC_REAL_KIND; i = i + 1
    106:     y(i) = 9.4500_PETSC_REAL_KIND; t(i) = 3.7500_PETSC_REAL_KIND; i = i + 1
    107:     y(i) = 9.1500_PETSC_REAL_KIND; t(i) = 4.2500_PETSC_REAL_KIND; i = i + 1
    108:     y(i) = 7.9125_PETSC_REAL_KIND; t(i) = 4.7500_PETSC_REAL_KIND; i = i + 1
    109:     y(i) = 8.4750_PETSC_REAL_KIND; t(i) = 5.2500_PETSC_REAL_KIND; i = i + 1
    110:     y(i) = 6.1125_PETSC_REAL_KIND; t(i) = 5.7500_PETSC_REAL_KIND; i = i + 1
    111:     y(i) = 80.0000_PETSC_REAL_KIND; t(i) = 0.5000_PETSC_REAL_KIND; i = i + 1
    112:     y(i) = 79.0000_PETSC_REAL_KIND; t(i) = 0.6250_PETSC_REAL_KIND; i = i + 1
    113:     y(i) = 63.8000_PETSC_REAL_KIND; t(i) = 0.7500_PETSC_REAL_KIND; i = i + 1
    114:     y(i) = 57.2000_PETSC_REAL_KIND; t(i) = 0.8750_PETSC_REAL_KIND; i = i + 1
    115:     y(i) = 53.2000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    116:     y(i) = 42.5000_PETSC_REAL_KIND; t(i) = 1.2500_PETSC_REAL_KIND; i = i + 1
    117:     y(i) = 26.8000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    118:     y(i) = 20.4000_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    119:     y(i) = 26.8500_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    120:     y(i) = 21.0000_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    121:     y(i) = 16.4625_PETSC_REAL_KIND; t(i) = 2.7500_PETSC_REAL_KIND; i = i + 1
    122:     y(i) = 12.5250_PETSC_REAL_KIND; t(i) = 3.2500_PETSC_REAL_KIND; i = i + 1
    123:     y(i) = 10.5375_PETSC_REAL_KIND; t(i) = 3.7500_PETSC_REAL_KIND; i = i + 1
    124:     y(i) = 8.5875_PETSC_REAL_KIND; t(i) = 4.2500_PETSC_REAL_KIND; i = i + 1
    125:     y(i) = 7.1250_PETSC_REAL_KIND; t(i) = 4.7500_PETSC_REAL_KIND; i = i + 1
    126:     y(i) = 6.1125_PETSC_REAL_KIND; t(i) = 5.2500_PETSC_REAL_KIND; i = i + 1
    127:     y(i) = 5.9625_PETSC_REAL_KIND; t(i) = 5.7500_PETSC_REAL_KIND; i = i + 1
    128:     y(i) = 74.1000_PETSC_REAL_KIND; t(i) = 0.5000_PETSC_REAL_KIND; i = i + 1
    129:     y(i) = 67.3000_PETSC_REAL_KIND; t(i) = 0.6250_PETSC_REAL_KIND; i = i + 1
    130:     y(i) = 60.8000_PETSC_REAL_KIND; t(i) = 0.7500_PETSC_REAL_KIND; i = i + 1
    131:     y(i) = 55.5000_PETSC_REAL_KIND; t(i) = 0.8750_PETSC_REAL_KIND; i = i + 1
    132:     y(i) = 50.3000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    133:     y(i) = 41.0000_PETSC_REAL_KIND; t(i) = 1.2500_PETSC_REAL_KIND; i = i + 1
    134:     y(i) = 29.4000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    135:     y(i) = 20.4000_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    136:     y(i) = 29.3625_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    137:     y(i) = 21.1500_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    138:     y(i) = 16.7625_PETSC_REAL_KIND; t(i) = 2.7500_PETSC_REAL_KIND; i = i + 1
    139:     y(i) = 13.2000_PETSC_REAL_KIND; t(i) = 3.2500_PETSC_REAL_KIND; i = i + 1
    140:     y(i) = 10.8750_PETSC_REAL_KIND; t(i) = 3.7500_PETSC_REAL_KIND; i = i + 1
    141:     y(i) = 8.1750_PETSC_REAL_KIND; t(i) = 4.2500_PETSC_REAL_KIND; i = i + 1
    142:     y(i) = 7.3500_PETSC_REAL_KIND; t(i) = 4.7500_PETSC_REAL_KIND; i = i + 1
    143:     y(i) = 5.9625_PETSC_REAL_KIND; t(i) = 5.2500_PETSC_REAL_KIND; i = i + 1
    144:     y(i) = 5.6250_PETSC_REAL_KIND; t(i) = 5.7500_PETSC_REAL_KIND; i = i + 1
    145:     y(i) = 81.5000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    146:     y(i) = 62.4000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    147:     y(i) = 32.5000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    148:     y(i) = 12.4100_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    149:     y(i) = 13.1200_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    150:     y(i) = 15.5600_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    151:     y(i) = 5.6300_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    152:     y(i) = 78.0000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    153:     y(i) = 59.9000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    154:     y(i) = 33.2000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    155:     y(i) = 13.8400_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    156:     y(i) = 12.7500_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    157:     y(i) = 14.6200_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    158:     y(i) = 3.9400_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    159:     y(i) = 76.8000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    160:     y(i) = 61.0000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    161:     y(i) = 32.9000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    162:     y(i) = 13.8700_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    163:     y(i) = 11.8100_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    164:     y(i) = 13.3100_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    165:     y(i) = 5.4400_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    166:     y(i) = 78.0000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    167:     y(i) = 63.5000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    168:     y(i) = 33.8000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    169:     y(i) = 12.5600_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    170:     y(i) = 5.6300_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    171:     y(i) = 12.7500_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    172:     y(i) = 13.1200_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    173:     y(i) = 5.4400_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    174:     y(i) = 76.8000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    175:     y(i) = 60.0000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    176:     y(i) = 47.8000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    177:     y(i) = 32.0000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    178:     y(i) = 22.2000_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    179:     y(i) = 22.5700_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    180:     y(i) = 18.8200_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    181:     y(i) = 13.9500_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    182:     y(i) = 11.2500_PETSC_REAL_KIND; t(i) = 4.0000_PETSC_REAL_KIND; i = i + 1
    183:     y(i) = 9.0000_PETSC_REAL_KIND; t(i) = 5.0000_PETSC_REAL_KIND; i = i + 1
    184:     y(i) = 6.6700_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    185:     y(i) = 75.8000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    186:     y(i) = 62.0000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    187:     y(i) = 48.8000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    188:     y(i) = 35.2000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    189:     y(i) = 20.0000_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    190:     y(i) = 20.3200_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    191:     y(i) = 19.3100_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    192:     y(i) = 12.7500_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    193:     y(i) = 10.4200_PETSC_REAL_KIND; t(i) = 4.0000_PETSC_REAL_KIND; i = i + 1
    194:     y(i) = 7.3100_PETSC_REAL_KIND; t(i) = 5.0000_PETSC_REAL_KIND; i = i + 1
    195:     y(i) = 7.4200_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    196:     y(i) = 70.5000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    197:     y(i) = 59.5000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    198:     y(i) = 48.5000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    199:     y(i) = 35.8000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    200:     y(i) = 21.0000_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    201:     y(i) = 21.6700_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    202:     y(i) = 21.0000_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    203:     y(i) = 15.6400_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    204:     y(i) = 8.1700_PETSC_REAL_KIND; t(i) = 4.0000_PETSC_REAL_KIND; i = i + 1
    205:     y(i) = 8.5500_PETSC_REAL_KIND; t(i) = 5.0000_PETSC_REAL_KIND; i = i + 1
    206:     y(i) = 10.1200_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    207:     y(i) = 78.0000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    208:     y(i) = 66.0000_PETSC_REAL_KIND; t(i) = .6250_PETSC_REAL_KIND; i = i + 1
    209:     y(i) = 62.0000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    210:     y(i) = 58.0000_PETSC_REAL_KIND; t(i) = .8750_PETSC_REAL_KIND; i = i + 1
    211:     y(i) = 47.7000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    212:     y(i) = 37.8000_PETSC_REAL_KIND; t(i) = 1.2500_PETSC_REAL_KIND; i = i + 1
    213:     y(i) = 20.2000_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    214:     y(i) = 21.0700_PETSC_REAL_KIND; t(i) = 2.2500_PETSC_REAL_KIND; i = i + 1
    215:     y(i) = 13.8700_PETSC_REAL_KIND; t(i) = 2.7500_PETSC_REAL_KIND; i = i + 1
    216:     y(i) = 9.6700_PETSC_REAL_KIND; t(i) = 3.2500_PETSC_REAL_KIND; i = i + 1
    217:     y(i) = 7.7600_PETSC_REAL_KIND; t(i) = 3.7500_PETSC_REAL_KIND; i = i + 1
    218:     y(i) = 5.4400_PETSC_REAL_KIND; t(i) = 4.2500_PETSC_REAL_KIND; i = i + 1
    219:     y(i) = 4.8700_PETSC_REAL_KIND; t(i) = 4.7500_PETSC_REAL_KIND; i = i + 1
    220:     y(i) = 4.0100_PETSC_REAL_KIND; t(i) = 5.2500_PETSC_REAL_KIND; i = i + 1
    221:     y(i) = 3.7500_PETSC_REAL_KIND; t(i) = 5.7500_PETSC_REAL_KIND; i = i + 1
    222:     y(i) = 24.1900_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    223:     y(i) = 25.7600_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    224:     y(i) = 18.0700_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    225:     y(i) = 11.8100_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    226:     y(i) = 12.0700_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    227:     y(i) = 16.1200_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    228:     y(i) = 70.8000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    229:     y(i) = 54.7000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    230:     y(i) = 48.0000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    231:     y(i) = 39.8000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    232:     y(i) = 29.8000_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    233:     y(i) = 23.7000_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    234:     y(i) = 29.6200_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    235:     y(i) = 23.8100_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    236:     y(i) = 17.7000_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    237:     y(i) = 11.5500_PETSC_REAL_KIND; t(i) = 4.0000_PETSC_REAL_KIND; i = i + 1
    238:     y(i) = 12.0700_PETSC_REAL_KIND; t(i) = 5.0000_PETSC_REAL_KIND; i = i + 1
    239:     y(i) = 8.7400_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    240:     y(i) = 80.7000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    241:     y(i) = 61.3000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    242:     y(i) = 47.5000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    243:     y(i) = 29.0000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    244:     y(i) = 24.0000_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    245:     y(i) = 17.7000_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    246:     y(i) = 24.5600_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    247:     y(i) = 18.6700_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    248:     y(i) = 16.2400_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    249:     y(i) = 8.7400_PETSC_REAL_KIND; t(i) = 4.0000_PETSC_REAL_KIND; i = i + 1
    250:     y(i) = 7.8700_PETSC_REAL_KIND; t(i) = 5.0000_PETSC_REAL_KIND; i = i + 1
    251:     y(i) = 8.5100_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    252:     y(i) = 66.7000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    253:     y(i) = 59.2000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    254:     y(i) = 40.8000_PETSC_REAL_KIND; t(i) = 1.0000_PETSC_REAL_KIND; i = i + 1
    255:     y(i) = 30.7000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    256:     y(i) = 25.7000_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    257:     y(i) = 16.3000_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    258:     y(i) = 25.9900_PETSC_REAL_KIND; t(i) = 2.0000_PETSC_REAL_KIND; i = i + 1
    259:     y(i) = 16.9500_PETSC_REAL_KIND; t(i) = 2.5000_PETSC_REAL_KIND; i = i + 1
    260:     y(i) = 13.3500_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    261:     y(i) = 8.6200_PETSC_REAL_KIND; t(i) = 4.0000_PETSC_REAL_KIND; i = i + 1
    262:     y(i) = 7.2000_PETSC_REAL_KIND; t(i) = 5.0000_PETSC_REAL_KIND; i = i + 1
    263:     y(i) = 6.6400_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    264:     y(i) = 13.6900_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    265:     y(i) = 81.0000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    266:     y(i) = 64.5000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    267:     y(i) = 35.5000_PETSC_REAL_KIND; t(i) = 1.5000_PETSC_REAL_KIND; i = i + 1
    268:     y(i) = 13.3100_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    269:     y(i) = 4.8700_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    270:     y(i) = 12.9400_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    271:     y(i) = 5.0600_PETSC_REAL_KIND; t(i) = 6.0000_PETSC_REAL_KIND; i = i + 1
    272:     y(i) = 15.1900_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    273:     y(i) = 14.6200_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    274:     y(i) = 15.6400_PETSC_REAL_KIND; t(i) = 3.0000_PETSC_REAL_KIND; i = i + 1
    275:     y(i) = 25.5000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    276:     y(i) = 25.9500_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    277:     y(i) = 81.7000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    278:     y(i) = 61.6000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    279:     y(i) = 29.8000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    280:     y(i) = 29.8100_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    281:     y(i) = 17.1700_PETSC_REAL_KIND; t(i) = 2.7500_PETSC_REAL_KIND; i = i + 1
    282:     y(i) = 10.3900_PETSC_REAL_KIND; t(i) = 3.7500_PETSC_REAL_KIND; i = i + 1
    283:     y(i) = 28.4000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    284:     y(i) = 28.6900_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    285:     y(i) = 81.3000_PETSC_REAL_KIND; t(i) = .5000_PETSC_REAL_KIND; i = i + 1
    286:     y(i) = 60.9000_PETSC_REAL_KIND; t(i) = .7500_PETSC_REAL_KIND; i = i + 1
    287:     y(i) = 16.6500_PETSC_REAL_KIND; t(i) = 2.7500_PETSC_REAL_KIND; i = i + 1
    288:     y(i) = 10.0500_PETSC_REAL_KIND; t(i) = 3.7500_PETSC_REAL_KIND; i = i + 1
    289:     y(i) = 28.9000_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    290:     y(i) = 28.9500_PETSC_REAL_KIND; t(i) = 1.7500_PETSC_REAL_KIND; i = i + 1
    291:   end
    292: end module chwirut1fmodule

    294: program main
    295:   use chwirut1fmodule
    296:   implicit none
    297: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    298: !                   Variable declarations
    299: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    300: !
    301: !  See additional variable declarations in the file chwirut1f.h

    303:   PetscErrorCode ierr    ! used to check for functions returning nonzeros
    304:   Vec x       ! solution vector
    305:   Vec f       ! vector of functions
    306:   Tao ta     ! Tao context
    307:   PetscInt nhist
    308:   PetscMPIInt size, rank    ! number of processes running
    309:   PetscReal hist(100) ! objective value history
    310:   PetscReal resid(100)! residual history
    311:   PetscReal cnorm(100)! cnorm history
    312:   PetscInt lits(100)   ! #ksp history
    313:   TaoConvergedReason reason

    315: !  Initialize TAO and PETSc
    316:   PetscCallA(PetscInitialize(ierr))

    318:   PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD, size, ierr))
    319:   PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, rank, ierr))
    320:   PetscCheckA(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, 'This is a uniprocessor example only')

    322: ! Allocate vectors for the solution and gradient
    323:   PetscCallA(VecCreateSeq(PETSC_COMM_SELF, n, x, ierr))
    324:   PetscCallA(VecCreateSeq(PETSC_COMM_SELF, m, f, ierr))

    326: !  The TAO code begins here

    328: ! Create TAO solver
    329:   PetscCallA(TaoCreate(PETSC_COMM_SELF, ta, ierr))
    330:   PetscCallA(TaoSetType(ta, TAOPOUNDERS, ierr))

    332: ! Set routines for function, gradient, and hessian evaluation
    333:   PetscCallA(TaoSetResidualRoutine(ta, f, FormFunction, 0, ierr))

    335: ! Optional: Set initial guess
    336:   call InitializeData()
    337:   call FormStartingPoint(x)
    338:   PetscCallA(TaoSetSolution(ta, x, ierr))

    340: ! Check for TAO command line options
    341:   PetscCallA(TaoSetFromOptions(ta, ierr))
    342:   PetscCallA(TaoSetConvergenceHistory(ta, hist, resid, cnorm, lits, 100_PETSC_INT_KIND, PETSC_TRUE, ierr))
    343: ! SOLVE THE APPLICATION
    344:   PetscCallA(TaoSolve(ta, ierr))
    345:   PetscCallA(TaoGetConvergenceHistory(ta, nhist, ierr))
    346:   PetscCallA(TaoGetConvergedReason(ta, reason, ierr))
    347:   if (reason%v <= 0) then
    348:     print *, 'Tao failed.'
    349:     print *, 'Try a different TAO method, adjust some parameters,'
    350:     print *, 'or check the function evaluation routines.'
    351:   end if

    353: !  Free TAO data structures
    354:   PetscCallA(TaoDestroy(ta, ierr))

    356: !  Free PETSc data structures
    357:   PetscCallA(VecDestroy(x, ierr))
    358:   PetscCallA(VecDestroy(f, ierr))

    360:   PetscCallA(PetscFinalize(ierr))

    362: end

    364: !/*TEST
    365: !
    366: !   build:
    367: !      requires: !complex
    368: !
    369: !   test:
    370: !      args: -tao_monitor_short -tao_max_it 100 -tao_type pounders -tao_gatol 1.e-5
    371: !      requires: !single
    372: !
    373: !TEST*/