Fortran 77 interface
The Fortran 77 wrappers provide a very similar interface to the
einspline library as in C, with a few exceptions:
- The fortran routine names are the C names, prefixed by an "f".
- The spline object pointers are passed as INTEGER*8 arguments,
to ensure proper functioning on 64-bit platforms.
- Since F77 has no concept of structures, uniform grid objects
have been replaced by extra parameters to the
create_UBspline_x routines.
- For 2D and 3D splines, data is assumed to be stored in
contiguous, row-order format (C-style). If the data is statically
allocated in F77, care must be take to ensure all element data is
contiguous in memory.
| Boundary condition type | Code | Meaning |
| PERIODIC | 0 | Use periodic boundary conditions. The value, first
derivative and second derivative at the left boundary match
those at the right boundary. |
| DERIV1 | 1 | The value of the first derivative is specified in lVal or rVal. |
| DERIV2 | 2 | The value of the second derivative is specified in lVal or rVal. |
| FLAT | 3 | The value of the first derivative is set to zero at the boundary. |
| NATURAL | 4 | The value of the second derivative is set to zero at the boundary. |
| ANTIPERIODIC | 5 | Use anti-periodic boundary conditions. The value, first derivative
and second derivative at the left boundary are the negative of those
at the right boundary. |
Please see the documentation for the C routines for more information.
The subroutine names and parameters are given below:
Uniform spline creation routines
One-dimensional:
Single-precision real
SUBROUTINE FCREATE_UBSPLINE_1D_S (x0, x1, num_x, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First grid point |
| x1 | IN | REAL*8 | Last grid point |
| num_x | IN | INTEGER | # of grid points |
| x0_code | IN | INTEGER | Left BC type |
| x0_val | IN | REAL*4 | Left BC value |
| x1_code | IN | INTEGER | Right BC type |
| x1_val | IN | REAL*4 | Right BC value |
| data | IN | REAL*4 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Double-precision real
SUBROUTINE FCREATE_UBSPLINE_1D_D (x0, x1, num_x, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First grid point |
| x1 | IN | REAL*8 | Last grid point |
| num_x | IN | INTEGER | # of grid points |
| x0_code | IN | INTEGER | Left BC type |
| x0_val | IN | REAL*8 | Left BC value |
| x1_code | IN | INTEGER | Right BC type |
| x1_val | IN | REAL*8 | Right BC value |
| data | IN | REAL*8 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Single-precision complex
SUBROUTINE FCREATE_UBSPLINE_1D_C (x0, x1, num_x, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First grid point |
| x1 | IN | REAL*8 | Last grid point |
| num_x | IN | INTEGER | # of grid points |
| x0_code | IN | INTEGER | Left BC type |
| x0_val | IN | COMPLEX*8 | Left BC value |
| x1_code | IN | INTEGER | Right BC type |
| x1_val | IN | COMPLEX*8 | Right BC value |
| data | IN | COMPLEX*8 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Double-precision complex
SUBROUTINE FCREATE_UBSPLINE_1D_Z (x0, x1, num_x, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First grid point |
| x1 | IN | REAL*8 | Last grid point |
| num_x | IN | INTEGER | # of grid points |
| x0_code | IN | INTEGER | Left BC type |
| x0_val | IN | COMPLEX*16 | Left BC value |
| x1_code | IN | INTEGER | Right BC type |
| x1_val | IN | COMPLEX*16 | Right BC value |
| data | IN | COMPLEX*16 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Two-dimensional:
Single-precision real
SUBROUTINE FCREATE_UBSPLINE_2D_S (x0, x1, num_x, y0, y1, num_y,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | REAL*4 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | REAL*4 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | REAL*4 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | REAL*4 | Right y BC value |
| data | IN | REAL*4 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Double-precision real
SUBROUTINE FCREATE_UBSPLINE_2D_D (x0, x1, num_x, y0, y1, num_y,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | REAL*8 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | REAL*8 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | REAL*8 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | REAL*8 | Right y BC value |
| data | IN | REAL*8 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Single-precision complex
SUBROUTINE FCREATE_UBSPLINE_2D_C (x0, x1, num_x, y0, y1, num_y,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | COMPLEX*8 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | COMPLEX*8 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | COMPLEX*8 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | COMPLEX*8 | Right y BC value |
| data | IN | COMPLEX*8 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Double-precision complex
SUBROUTINE FCREATE_UBSPLINE_2D_Z (x0, x1, num_x, y0, y1, num_y,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | COMPLEX*16 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | COMPLEX*16 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | COMPLEX*16 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | COMPLEX*16 | Right y BC value |
| data | IN | COMPLEX*16 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Three-dimensional:
Single-precision real
SUBROUTINE FCREATE_UBSPLINE_3D_S (x0, x1, num_x, y0, y1, num_y, z0, z1, num_z,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
z0_code, z0_val, z1_code, z1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| z0 | IN | REAL*8 | First z grid point |
| z1 | IN | REAL*8 | Last z grid point |
| num_z | IN | INTEGER | # of z grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | REAL*4 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | REAL*4 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | REAL*4 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | REAL*4 | Right y BC value |
| z0_code | IN | INTEGER | Left z BC type |
| z0_val | IN | REAL*4 | Left z BC value |
| z1_code | IN | INTEGER | Right z BC type |
| z1_val | IN | REAL*4 | Right z BC value |
| data | IN | REAL*4 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Double-precision real
SUBROUTINE FCREATE_UBSPLINE_3D_D (x0, x1, num_x, y0, y1, num_y, z0, z1, num_z,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
z0_code, z0_val, z1_code, z1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| z0 | IN | REAL*8 | First z grid point |
| z1 | IN | REAL*8 | Last z grid point |
| num_z | IN | INTEGER | # of z grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | REAL*8 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | REAL*8 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | REAL*8 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | REAL*8 | Right y BC value |
| z0_code | IN | INTEGER | Left z BC type |
| z0_val | IN | REAL*8 | Left z BC value |
| z1_code | IN | INTEGER | Right z BC type |
| z1_val | IN | REAL*8 | Right z BC value |
| data | IN | REAL*8 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Single-precision complex
SUBROUTINE FCREATE_UBSPLINE_3D_C (x0, x1, num_x, y0, y1, num_y, z0, z1, num_z,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
z0_code, z0_val, z1_code, z1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| z0 | IN | REAL*8 | First z grid point |
| z1 | IN | REAL*8 | Last z grid point |
| num_z | IN | INTEGER | # of z grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | COMPLEX*8 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | COMPLEX*8 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | COMPLEX*8 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | COMPLEX*8 | Right y BC value |
| z0_code | IN | INTEGER | Left z BC type |
| z0_val | IN | COMPLEX*8 | Left z BC value |
| z1_code | IN | INTEGER | Right z BC type |
| z1_val | IN | COMPLEX*8 | Right z BC value |
| data | IN | COMPLEX*8 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Double-precision complex
SUBROUTINE FCREATE_UBSPLINE_3D_Z (x0, x1, num_x, y0, y1, num_y, z0, z1, num_z,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
z0_code, z0_val, z1_code, z1_val,
data, spline)
| Argument | Intent | Type | Description |
| x0 | IN | REAL*8 | First x grid point |
| x1 | IN | REAL*8 | Last x grid point |
| num_x | IN | INTEGER | # of x grid points |
| y0 | IN | REAL*8 | First y grid point |
| y1 | IN | REAL*8 | Last y grid point |
| num_y | IN | INTEGER | # of y grid points |
| z0 | IN | REAL*8 | First z grid point |
| z1 | IN | REAL*8 | Last z grid point |
| num_z | IN | INTEGER | # of z grid points |
| x0_code | IN | INTEGER | Left x BC type |
| x0_val | IN | COMPLEX*16 | Left x BC value |
| x1_code | IN | INTEGER | Right x BC type |
| x1_val | IN | COMPLEX*16 | Right x BC value |
| y0_code | IN | INTEGER | Left y BC type |
| y0_val | IN | COMPLEX*16 | Left y BC value |
| y1_code | IN | INTEGER | Right y BC type |
| y1_val | IN | COMPLEX*16 | Right y BC value |
| z0_code | IN | INTEGER | Left z BC type |
| z0_val | IN | COMPLEX*16 | Left z BC value |
| z1_code | IN | INTEGER | Right z BC type |
| z1_val | IN | COMPLEX*16 | Right z BC value |
| data | IN | COMPLEX*16 | Data to interpolate |
| spline | OUT | INTEGER*8 | Handle for spline object |
Spline destruction routine
The following subroutine can be used to deallocate the memory for any Bspline object.
Note that in the nonuniform case, the grid objects must be destroyed after the splines that
refer to them.
SUBROUTINE FDESTROY_BSPLINE (spline)
| Argument | Intent | Type | Description |
| spline | IN | INTEGER*8 | Spline object handle |
Uniform spline evalulation routines
One-dimensional
SUBROUTINE FEVAL_UBSPLINE_1D_S (spline, x, val)
SUBROUTINE FEVAL_UBSPLINE_1D_D (spline, x, val)
SUBROUTINE FEVAL_UBSPLINE_1D_C (spline, x, val)
SUBROUTINE FEVAL_UBSPLINE_1D_Z (spline, x, val)
SUBROUTINE FEVAL_UBSPLINE_1D_S_VG (spline, x, val, grad)
SUBROUTINE FEVAL_UBSPLINE_1D_D_VG (spline, x, val, grad)
SUBROUTINE FEVAL_UBSPLINE_1D_C_VG (spline, x, val, grad)
SUBROUTINE FEVAL_UBSPLINE_1D_Z_VG (spline, x, val, grad)
SUBROUTINE FEVAL_UBSPLINE_1D_S_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_1D_D_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_1D_C_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_1D_Z_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_1D_S_VGH (spline, x, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_1D_D_VGH (spline, x, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_1D_C_VGH (spline, x, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_1D_Z_VGH (spline, x, val, grad, hess)
| Argument | Intent | _S Type | _D Type | _C Type | _Z Type | Description |
| spline | IN | INTEGER*8 | INTEGER*8 | INTEGER*8 | INTEGER*8 | Spline handle |
| x | IN | REAL*8 | REAL*8 | REAL*8 | REAL*8 | Interpolation position |
| val | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated value |
| grad | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated first derivative |
| lapl | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated second derivative |
| hess | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated second derivative |
Two-dimensional
SUBROUTINE FEVAL_UBSPLINE_2D_S (spline, x, y, val)
SUBROUTINE FEVAL_UBSPLINE_2D_D (spline, x, y, val)
SUBROUTINE FEVAL_UBSPLINE_2D_C (spline, x, y, val)
SUBROUTINE FEVAL_UBSPLINE_2D_Z (spline, x, y, val)
SUBROUTINE FEVAL_UBSPLINE_2D_S_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_UBSPLINE_2D_D_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_UBSPLINE_2D_C_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_UBSPLINE_2D_Z_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_UBSPLINE_2D_S_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_2D_D_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_2D_C_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_2D_Z_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_2D_S_VGH (spline, x, y, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_2D_D_VGH (spline, x, y, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_2D_C_VGH (spline, x, y, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_2D_Z_VGH (spline, x, y, val, grad, hess)
| Argument | Intent | _S Type | _D Type | _C Type | _Z Type | Description |
| spline | IN | INTEGER*8 | INTEGER*8 | INTEGER*8 | INTEGER*8 | Spline handle |
| x | IN | REAL*8 | REAL*8 | REAL*8 | REAL*8 | x coordinate for interpolation |
| y | IN | REAL*8 | REAL*8 | REAL*8 | REAL*8 | y coordinate for interpolation |
| val | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated value |
| grad | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated gradient (2 elements) |
| lapl | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated Laplacian |
| hess | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated Hessian (4 elements) |
Three-dimensional
SUBROUTINE FEVAL_UBSPLINE_3D_S (spline, x, y, z, val)
SUBROUTINE FEVAL_UBSPLINE_3D_D (spline, x, y, z, val)
SUBROUTINE FEVAL_UBSPLINE_3D_C (spline, x, y, z, val)
SUBROUTINE FEVAL_UBSPLINE_3D_Z (spline, x, y, z, val)
SUBROUTINE FEVAL_UBSPLINE_3D_S_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_UBSPLINE_3D_D_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_UBSPLINE_3D_C_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_UBSPLINE_3D_Z_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_UBSPLINE_3D_S_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_3D_D_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_3D_C_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_3D_Z_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_UBSPLINE_3D_S_VGH (spline, x, y, z, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_3D_D_VGH (spline, x, y, z, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_3D_C_VGH (spline, x, y, z, val, grad, hess)
SUBROUTINE FEVAL_UBSPLINE_3D_Z_VGH (spline, x, y, z, val, grad, hess)
| Argument | Intent | _S Type | _D Type | _C Type | _Z Type | Description |
| spline | IN | INTEGER*8 | INTEGER*8 | INTEGER*8 | INTEGER*8 | Spline handle |
| x | IN | REAL*8 | REAL*8 | REAL*8 | REAL*8 | x coordinate for interpolation |
| y | IN | REAL*8 | REAL*8 | REAL*8 | REAL*8 | y coordinate for interpolation |
| z | IN | REAL*8 | REAL*8 | REAL*8 | REAL*8 | z coordinate for interpolation |
| val | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated value |
| grad | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated gradient (3 elements) |
| lapl | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated Laplacian |
| hess | OUT | REAL*4 | REAL*8 | COMPLEX*8 | COMPLEX*16 | Interpolated Hessian (9 elements) |
