added a comparison with linear interpolation

comparing k=2 spline with linear interpolation from finterp library
See #88

fpm.toml

@@ -14,6 +14,7 @@ auto-tests = true
 
 [dev-dependencies]
 pyplot-fortran = { git = "https://github.com/jacobwilliams/pyplot-fortran", tag = "3.3.0" }
+finterp = { git = "https://github.com/jacobwilliams/finterp", tag = "1.3.0" }
 
 [library]
 source-dir = "src"

test/bspline_linear_test.f90

@@ -0,0 +1,107 @@
+!*****************************************************************************************
+!>
+!  Linear interpolation test
+
+    program bspline_linear_test
+
+    use bspline_module
+    use bspline_kinds_module, only: wp, ip
+    use pyplot_module
+    use linear_interpolation_module
+
+    implicit none
+
+    integer(ip),parameter :: nx    = 10    !! number of points in x
+    integer(ip),parameter :: nxv   = 111 !100   !! number of points to evaluate interpolant
+
+    integer(ip),parameter :: kx    = 2    !! order in x [linear]
+    !integer(ip),parameter :: kx    = bspline_order_cubic    !! order in x [cubic]
+    !integer(ip),parameter :: kx    = bspline_order_quartic
+    integer(ip),parameter :: iknot = 0    !! automatically select the knots
+
+    real(wp) :: x(nx)
+    real(wp) :: xval(nxv),fval(nxv),fval_linear(nxv)
+    real(wp) :: tx(nx+kx)
+    real(wp) :: fcn_1d(nx)
+    real(wp) :: val,tru,err,errmax
+    integer(ip) :: i,idx,iflag,inbvx,iloy
+    type(pyplot) :: plt
+    integer :: istat  !! pyplot-fortran status flag
+    real(wp),dimension(3*kx) :: w1_1d !! work array
+    type(linear_interp_1d) :: s1
+
+    idx = 0
+
+    x = huge(1.0_wp)
+    xval = huge(1.0_wp)
+
+    do i=1,nx
+        x(i) = real(i-1,wp) * 10.0_wp
+        fcn_1d(i) = f1(x(i))
+    end do
+    do i=1,nxv
+        xval(i) = real(i-1,wp) - 10
+    end do
+
+    !have to set these before the first evaluate call:
+    inbvx = 1
+    iloy  = 1
+
+    ! initialize
+    call db1ink(x,nx,fcn_1d,kx,iknot,tx,fcn_1d,iflag)
+    if (iflag/=0) then
+        write(*,*) 'Error initializing 1D spline: '//get_status_message(iflag)
+    end if
+    call s1%initialize(x,fcn_1d,iflag)
+    if (iflag/=0) then
+        write(*,*) 'Error initializing 1D linear interpolator: ', iflag
+    end if
+
+    !initialize the plot:
+    call plt%initialize(grid=.true.,xlabel='x (deg)',ylabel='f(x)',&
+                        title='Linear Test',legend=.true.)
+    call plt%add_plot(x,fcn_1d,&
+                        label='Function $f(x) = \sin(x)$',&
+                        linestyle='ko',markersize=5,linewidth=2,istat=istat)
+
+    errmax = 0.0_wp
+    do i=1,nxv
+        call db1val(xval(i),idx,tx,nx,kx,fcn_1d,val,iflag,inbvx,w1_1d,extrap=.true.)
+        fval(i) = val  ! save it for plot
+        if (iflag/=0) error stop 'error calling db1val: '//get_status_message(iflag)
+
+        tru    = f1(xval(i))
+        err    = abs(tru-val)
+        errmax = max(err,errmax)
+        !write(*,*) xval(i), val, tru, err, iflag
+
+        ! also compute linear interpolation:
+        call s1%evaluate(xval(i),val)
+        fval_linear(i) = val ! linear vector for plot
+        write(*,*) "error : ", xval(i), fval(i) - fval_linear(i)
+
+    end do
+
+    ! check max error against tolerance
+    write(*,*) ''
+    write(*,*) '1D: max error:', errmax
+    write(*,*) ''
+
+    call plt%add_plot(xval,fval,&
+            label='k=2 Spline Interpolated',&
+            linestyle='g.-',linewidth=1,istat=istat)
+    call plt%add_plot(xval,fval_linear,&
+            label='Linear Interpolated',&
+            linestyle='r.-',linewidth=1,istat=istat)
+    call plt%savefig('bspline_linear_test.png',istat=istat)
+
+    contains
+
+        real(wp) function f1(x) !! 1d test function
+        implicit none
+        real(wp) :: x
+        real(wp),parameter :: a = acos(-1.0_wp)/18.0_wp
+        f1 = sin(a*x)
+        end function f1
+
+    end program bspline_linear_test