Make piecewise polynomial

`pp = mkpp(breaks,coefs)`

pp = mkpp(breaks,coefs,d)

`pp = mkpp(breaks,coefs)`

builds
a piecewise polynomial, `pp`

, from its breaks and
coefficients.

`breaks`

is a vector of length`L+1`

with strictly increasing elements which represent the start and end of each of`L`

intervals.`coefs`

is an`L`

-by-`k`

matrix with each row`coefs(i,:)`

containing the local coefficients of an order`k`

polynomial on the*i*th interval,`[breaks(i),breaks(i+1)]`

. That is, the polynomial`coefs(i,1)*(X-breaks(i))^(k-1) + coefs(i,2)*(X-breaks(i))^(k-2) + ... + coefs(i,k-1)*(X-breaks(i)) + coefs(i,k)`

. Notice that`mkpp`

shifts the polynomial in each interval down by`(X-breaks(i))`

.

`pp = mkpp(breaks,coefs,d)`

indicates
that the piecewise polynomial `pp`

is `d`

-vector
valued, i.e., the value of each of its coefficients is a vector of
length `d`

. `breaks`

is an increasing
vector of length `L+1`

. `coefs`

is
a `d`

-by-`L`

-by-`k`

array
with `coefs(r,i,:)`

containing the `k`

coefficients
of the `i`

th polynomial piece of the `r`

th
component of the piecewise polynomial.

Use `ppval`

to evaluate
the piecewise polynomial at specific points. Use `unmkpp`

to extract details of the piecewise
polynomial.

$${c}_{1}{x}^{k-1}+{c}_{2}{x}^{k-2}+\mathrm{...}+{c}_{k-1}x+{c}_{k}$$ It has |

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