Computes trapezoidal integration weights for a functional variable X1 on grid xind.

1 2 3 | ```
integrationWeights(X1, xind, id = NULL)
integrationWeightsLeft(X1, xind, leftWeight = c("first", "mean", "zero"))
``` |

`X1` |
matrix of functional variable |

`xind` |
index of functional variable |

`id` |
defaults to NULL if |

`leftWeight` |
one of |

The function `integrationWeights()`

computes trapezoidal integration weights,
that are symmetric. Per default those weights are used in the `bsignal`

-base-learner.
In the special case of regular xind with equal distances all integration weights are equal.

The function `integrationWeightsLeft()`

computes weights,
that take into account only the distance to the prior observation point.
Thus one has to decide what to do with the first observation.
The left weights are adequate for historical effects like in `bhist`

.

`bsignal`

and `bhist`

for the base-learners.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | ```
## Example for trapezoidal integration weights
xind0 <- seq(0,1,l=5)
xind <- c(0, 0.1, 0.3, 0.7, 1)
X1 <- matrix(xind^2, ncol=length(xind0), nrow=2)
# Regualar observation points
integrationWeights(X1, xind0)
# Irregular observation points
integrationWeights(X1, xind)
# with missing value
X1[1,2] <- NA
integrationWeights(X1, xind0)
integrationWeights(X1, xind)
## Example for left integration weights
xind0 <- seq(0,1,l=5)
xind <- c(0, 0.1, 0.3, 0.7, 1)
X1 <- matrix(xind^2, ncol=length(xind0), nrow=2)
# Regular observation points
integrationWeightsLeft(X1, xind0, leftWeight="mean")
integrationWeightsLeft(X1, xind0, leftWeight="first")
integrationWeightsLeft(X1, xind0, leftWeight="zero")
# Irregular observation points
integrationWeightsLeft(X1, xind, leftWeight="mean")
integrationWeightsLeft(X1, xind, leftWeight="first")
integrationWeightsLeft(X1, xind, leftWeight="zero")
# obervation points that do not start with 0
xind2 <- xind + 0.5
integrationWeightsLeft(X1, xind2, leftWeight="zero")
``` |

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