"much shorter than the time scale of the autocorrelation.[PAR]",
"Option [TT]-cc[tt] plots the resemblance of set i with a cosine of",
- "i/2 periods. The formula is:[BR]"
- "[MATH]2 ([INT][FROM]0[from][TO]T[to][int] y(t) [COS]i [GRK]pi[grk] t[cos] dt)^2 / [INT][FROM]0[from][TO]T[to][int] y^2(t) dt[math][BR]",
+ "i/2 periods. The formula is::",
+ "",
+ " [MATH]2 ([INT][FROM]0[from][TO]T[to][int] y(t) [COS]i [GRK]pi[grk] t[cos] dt)^2 / [INT][FROM]0[from][TO]T[to][int] y^2(t) dt[math]",
+ "",
"This is useful for principal components obtained from covariance",
"analysis, since the principal components of random diffusion are",
"pure cosines.[PAR]",
"These errors are plotted as a function of the block size.",
"Also an analytical block average curve is plotted, assuming",
"that the autocorrelation is a sum of two exponentials.",
- "The analytical curve for the block average is:[BR]",
- "[MATH]f(t) = [GRK]sigma[grk][TT]*[tt][SQRT]2/T ( [GRK]alpha[grk] ([GRK]tau[grk][SUB]1[sub] (([EXP]-t/[GRK]tau[grk][SUB]1[sub][exp] - 1) [GRK]tau[grk][SUB]1[sub]/t + 1)) +[BR]",
- " (1-[GRK]alpha[grk]) ([GRK]tau[grk][SUB]2[sub] (([EXP]-t/[GRK]tau[grk][SUB]2[sub][exp] - 1) [GRK]tau[grk][SUB]2[sub]/t + 1)))[sqrt][math],[BR]"
+ "The analytical curve for the block average is::",
+ "",
+ " [MATH]f(t) = [GRK]sigma[grk][TT]*[tt][SQRT]2/T ( [GRK]alpha[grk] ([GRK]tau[grk][SUB]1[sub] (([EXP]-t/[GRK]tau[grk][SUB]1[sub][exp] - 1) [GRK]tau[grk][SUB]1[sub]/t + 1)) +",
+ " (1-[GRK]alpha[grk]) ([GRK]tau[grk][SUB]2[sub] (([EXP]-t/[GRK]tau[grk][SUB]2[sub][exp] - 1) [GRK]tau[grk][SUB]2[sub]/t + 1)))[sqrt][math],",
+ "",
"where T is the total time.",
"[GRK]alpha[grk], [GRK]tau[grk][SUB]1[sub] and [GRK]tau[grk][SUB]2[sub] are obtained by fitting f^2(t) to error^2.",
"When the actual block average is very close to the analytical curve,",