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Package splinef (in splinef.i) -

Index of documented functions or symbols:

splined

### splined

```DOCUMENT yp = splined(dydx, y, x, xp)
or yp = splined(x_y_dydx, xp)
returns the derivative of the piecewise cubic function specified
by DYDX, Y, X at the points XP.  Extrapolation beyond the extreme
endpoints of X is linear, so splined gives the final value of DYDX.
The return value dimensions are the same as the dimensions of XP.

In the second form, X_Y_DYDX is a 3-by-nknots array of [x,y,dydx]
values.  The values of X in either case must either increase or
decrease monotonically.
```

### splinef

```DOCUMENT yp = splinef(dydx, y, x, xp)
or yp = splinef(x_y_dydx, xp)
returns piecewise cubic function specified by DYDX, Y, X at
the points XP.  Extrapolation beyond the extreme endpoints of X
is linear, with slope equal to the final value of DYDX.  The
return value dimensions are the same as the dimensions of XP.

In the second form, X_Y_DYDX is a 3-by-nknots array of [x,y,dydx]
values.  The values of X in either case must either increase or
decrease monotonically.
```

### splinei

```DOCUMENT yp = splinei(dydx, y, x, xp)
or yp = splinei(x_y_dydx, xp)
returns the integral of the piecewise cubic function specified
by DYDX, Y, X at the points XP.  The integral is quadratic beyond
the extreme endpoints of X, and zero at X(1).  The dimensions of
the return value are the same as the dimensions of XP.
This is the cubic analog of the integ function.

In the second form, X_Y_DYDX is a 3-by-nknots array of [x,y,dydx]
values.  The values of X in either case must either increase or
decrease monotonically.
```

### splinelsq

```DOCUMENT x_y_dydx = splinelsq(y, x, xfit)
...
yp = splinef(x_y_dydx, xp)
performs a least squares fit to the data points (X, Y).  The input
XFIT are the abcissas of the piecewise cubic function with knot
points XFIT which is the least squares best fit to the data (X,Y).
The XFIT must be strictly increase or decrease.

Any points in XFIT with no data points in the intervals on
either side will be removed.

A weight= keyword of the same length as X and Y may be supplied in
order to weight the various data points differently; a typical
WEIGHT function is 1/sigma^2 where sigma are the standard deviations
associated with the Y values.

You can specify y0=, dydx0=, y1=, and dydx1= keywords to fix the
value of the function or its derivative at the first (0) or last (1)
endpoint.  Be sure there is at least one point in the final
interval so that the XFIT at the endpoint is not removed.

More generally, you can specify a constrain= keyword.  The value
of constrain is a hook function which will be called just before
the matrix solve.  Your constrain subroutine will be passed no
arguments, but it can access and modify the mat and rhs variables.
```

```DOCUMENT spline_coef