Search for minimum and maximum for periodic timeseries when only intermediate values are known.

For each couple of value with an increasing or decreasing segment of
the sinusoid function, it is possible to estimate a minimum and maximum
values using analytical algebra.

Then the average and standard deviations of all minima and maxima are evaluated.

It should be noted that any extremum can be estimated at least twice, one by
increasing segment and one by decreasing segment. Both are used here to produce SD.

`time.minmax.daily`

should be used when the time at which maximum and minimum indices are regular and
`time.minmax`

permits to define this time day by day.

1 2 3 4 |

`time.minmax.daily` |
A named vector with Min and Max being the time in the day with minimum and maximum indices (temperature or level) |

`time.minmax` |
A named vector daily with time in the day at which minimum and maximum indices are observed |

`progressbar` |
Tell if a progression bar must be shown |

`observed` |
A dataframe with at least two columns: time and temperatures. A third column SD can indicate the know error in index |

`period` |
The unit of day period (24 for hours, 24*60 for minutes) |

`colname.time` |
The name of the column for time in observed |

`colname.index` |
The name of the column for indices in observed |

`colname.SD` |
The name of the column for SD in observed |

`plot` |
If TRUE, show a plot with the different estimates |

minmax.periodic search for minimum and maximum indices (temperatures or levels) in periodic timeseries

A data.frame with a column time, a column index and a column SD

Marc Girondot

Other Periodic patterns of indices: `index.periodic`

,
`moon.info`

, `sun.info`

,
`tide.info`

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 | ```
## Not run:
library("HelpersMG")
# Generate a timeserie of time
time.obs <- NULL
for (i in 0:9) time.obs <- c(time.obs, c(0, 6, 12, 18)+i*24)
# For these time, generate a timeseries of temperatures
temp.obs <- rep(NA, length(time.obs))
temp.obs[3+(0:9)*4] <- rnorm(10, 25, 3)
temp.obs[1+(0:9)*4] <- rnorm(10, 10, 3)
for (i in 1:(length(time.obs)-1))
if (is.na(temp.obs[i]))
temp.obs[i] <- mean(c(temp.obs[i-1], temp.obs[i+1]))
if (is.na(temp.obs[length(time.obs)]))
temp.obs[length(time.obs)] <- temp.obs[length(time.obs)-1]/2
observed <- data.frame(time=time.obs, temperature=temp.obs)
# Search for the minimum and maximum values
r <- minmax.periodic(time.minmax.daily=c(Min=2, Max=15),
observed=observed, period=24, colname.index="temperature")
# Estimate all the temperatures for these values
t <- index.periodic(minmax=r)
plot_errbar(x=t[,"time"], y=t[,"index"],
errbar.y=ifelse(is.na(t[,"sd"]), 0, 2*t[,"sd"]),
type="l", las=1, bty="n", errbar.y.polygon = TRUE,
xlab="hours", ylab="Temperatures", ylim=c(0, 35),
errbar.y.polygon.list = list(col="grey"))
plot_add(x=t[,"time"], y=t[,"index"], type="l")
plot_add(observed$time, observed$temperature, pch=19, cex=0.5)
## End(Not run)
``` |

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