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have been replaced by extra parameters to the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. |
Please see the documentation for the C routines for more information.
The subroutine names and parameters are given below:
Nonuniform grid creation routines
The general grid is a catch-all grid type which can be constructed from any monotonic sequence of
grid points. To create it, we pass an array with the grid points, the number of points to the grid
FCREATE_GENERAL_GRID. A handle to the grid object is returned in the parameter grid.
SUBROUTINE FCREATE_GENERAL_GRID (points, num, grid)
| Argument | Intent | Type | Description |
| points | IN | REAL*8 | Monotonic set of points for grid with num elements |
| num | IN | REAL*8 | Number of elements in points array |
| grid | OUT | INTEGER*8 | Grid handle |
The center grid is a grid in which the points are clustered more closely around the center than at the
outsides. It is useful for splines representing functions which have rapid oscillations near the origin
and are more smooth further out. Atomic wave functions have this property. A create_center_grid
function takes 5 arguments, as described below. The ratio argument is the ratio of the largest spacing
to the smallest spacing. Thus with a ratio of 10, the points at the center would be spaced ten
times closer together than the points at the left and right extremes of the grid.
SUBROUTINE FCREATE_CENTER_GRID (start, end, ratio, num, grid)
| Argument | Intent | Type | Description |
| start | IN | REAL*8 | First grid point |
| end | IN | REAL*8 | Last grid point |
| ratio | IN | REAL*8 | Largest spacing divided by smallest spacing |
| num | IN | REAL*8 | Number of points in the grid |
| grid | OUT | INTEGER*8 | Grid handle |
Once the grids are created, their handles are passed to the nonuniform spline create routines documented below.
Nonuniform grid destruction routine
The grid objects must be destroyed once they are no longer needed. If they have been passed to
a spline creation routine, they should not be destroyed until after the spline has been
destroyed. The following routine can be used to destroy either of the nonuniform grids.
SUBROUTINE FDESTROY_GRID (grid)
| Argument | Intent | Type | Description |
| grid | IN | INTEGER*8 | Handle of grid object |
Nonuniform spline creation routines
One-dimensional:
Single-precision real
SUBROUTINE FCREATE_NUBSPLINE_1D_S (x_grid, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| 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_NUBSPLINE_1D_D (x_grid, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| 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_NUBSPLINE_1D_C (x_grid, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| 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_NUBSPLINE_1D_Z (x_grid, x0_code, x0_val, x1_code, x1_val, data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| 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_NUBSPLINE_2D_S (x_grid, y_grid,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| 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_NUBSPLINE_2D_D (x_grid, y_grid,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| 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_NUBSPLINE_2D_C (x_grid, y_grid,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| 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_NUBSPLINE_2D_Z (x_grid, y_grid,
x0_code, x0_val, x1_code, x1_val,
y0_code, y0_val, y1_code, y1_val,
data, spline)
| Argument | Intent | Type | Description |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| 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_NUBSPLINE_3D_S (x_grid, y_grid, z_grid,
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 |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| z_grid | IN | INTEGER*8 | Handle of z grid object |
| 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_NUBSPLINE_3D_D (x_grid, y_grid, z_grid,
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 |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| z_grid | IN | INTEGER*8 | Handle of z grid object |
| 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_NUBSPLINE_3D_C (x_grid, y_grid, z_grid,
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 |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| z_grid | IN | INTEGER*8 | Handle of z grid object |
| 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_NUBSPLINE_3D_Z (x_grid, y_grid, z_grid,
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 |
| x_grid | IN | INTEGER*8 | Handle of x grid object |
| y_grid | IN | INTEGER*8 | Handle of y grid object |
| z_grid | IN | INTEGER*8 | Handle of z grid object |
| 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 evaulation routines
One-dimensional
SUBROUTINE FEVAL_NUBSPLINE_1D_S (spline, x, val)
SUBROUTINE FEVAL_NUBSPLINE_1D_D (spline, x, val)
SUBROUTINE FEVAL_NUBSPLINE_1D_C (spline, x, val)
SUBROUTINE FEVAL_NUBSPLINE_1D_Z (spline, x, val)
SUBROUTINE FEVAL_NUBSPLINE_1D_S_VG (spline, x, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_1D_D_VG (spline, x, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_1D_C_VG (spline, x, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_1D_Z_VG (spline, x, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_1D_S_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_1D_D_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_1D_C_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_1D_Z_VGL (spline, x, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_1D_S_VGH (spline, x, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_1D_D_VGH (spline, x, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_1D_C_VGH (spline, x, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_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_NUBSPLINE_2D_S (spline, x, y, val)
SUBROUTINE FEVAL_NUBSPLINE_2D_D (spline, x, y, val)
SUBROUTINE FEVAL_NUBSPLINE_2D_C (spline, x, y, val)
SUBROUTINE FEVAL_NUBSPLINE_2D_Z (spline, x, y, val)
SUBROUTINE FEVAL_NUBSPLINE_2D_S_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_2D_D_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_2D_C_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_2D_Z_VG (spline, x, y, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_2D_S_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_2D_D_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_2D_C_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_2D_Z_VGL (spline, x, y, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_2D_S_VGH (spline, x, y, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_2D_D_VGH (spline, x, y, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_2D_C_VGH (spline, x, y, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_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_NUBSPLINE_3D_S (spline, x, y, z, val)
SUBROUTINE FEVAL_NUBSPLINE_3D_D (spline, x, y, z, val)
SUBROUTINE FEVAL_NUBSPLINE_3D_C (spline, x, y, z, val)
SUBROUTINE FEVAL_NUBSPLINE_3D_Z (spline, x, y, z, val)
SUBROUTINE FEVAL_NUBSPLINE_3D_S_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_3D_D_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_3D_C_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_3D_Z_VG (spline, x, y, z, val, grad)
SUBROUTINE FEVAL_NUBSPLINE_3D_S_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_3D_D_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_3D_C_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_3D_Z_VGL (spline, x, y, z, val, grad, lapl)
SUBROUTINE FEVAL_NUBSPLINE_3D_S_VGH (spline, x, y, z, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_3D_D_VGH (spline, x, y, z, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_3D_C_VGH (spline, x, y, z, val, grad, hess)
SUBROUTINE FEVAL_NUBSPLINE_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) |
