CheckIfReasonablyMonotonic

Test whether a gridded density profile is monotonic enough for stretched coordinates.

Developer documentation: this item describes internal implementation details.

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Declaration

 [flag,dTotalVariation,rho_zCheb,rho_zLobatto,rhoz_zCheb,rhoz_zLobatto] = CheckIfReasonablyMonotonic(zLobatto,rho_zCheb,rho_zLobatto,rhoz_zCheb,rhoz_zLobatto)

Parameters

• zLobatto Lobatto depth grid
• rho_zCheb Chebyshev coefficients of density
• rho_zLobatto density sampled on zLobatto
• rhoz_zCheb Chebyshev coefficients of \(\partial_z \rho\)
• rhoz_zLobatto \(\partial_z \rho\) sampled on zLobatto

Returns

• flag monotonicity status flag
• dTotalVariation fractional change in total variation after coercion
• rho_zCheb possibly corrected Chebyshev coefficients of density
• rho_zLobatto possibly corrected density on zLobatto
• rhoz_zCheb possibly corrected Chebyshev coefficients of \(\partial_z \rho\)
• rhoz_zLobatto possibly corrected \(\partial_z \rho\) on zLobatto

Discussion

                          We want to know if the density function is decreasing as z   increases. If it's not, are the discrepencies small enough   that we can just force them?

flag is 0 if the function is not reasonably monotonic, 1 if it is, and 2 if we were able to to coerce it to be, without too much change