For input of a complex number, Z = X + iY, the complex number can be rewritten as Z = R exp(iq), where R = abs(Z) and q = atan(y,x). The complex log base 10 is then given by,
alog10(Z) = alog10(R) + i q/alog(10)
In the above formula, the use of the two-argument arctangent separates the solutions at Y = 0 and takes into account the branch-cut discontinuity along the real axis from -∞ to 0, and ensures that 10^(alog10(Z)) is equal to Z 1.
Find the base 10 logarithm of 100 and print the result by entering:
See the ATAN function for an example of visualizing the complex logarithm.
Result = ALOG10(X)
Returns the logarithm to the base 10 of X.
The value for which the base 10 log is desired. For real input, X should be greater than or equal to zero. If X is double-precision floating or complex, the result is of the same type. All other types are converted to single-precision floating-point and yield floating-point results. If X is an array, the result has the same structure, with each element containing the base 10 log of the corresponding element of X.
Thread Pool Keywords
This routine is written to make use of IDL’s thread pool, which can increase execution speed on systems with multiple CPUs. The values stored in the !CPU system variable control whether IDL uses the thread pool for a given computation. In addition, you can use the thread pool keywords TPOOL_MAX_ELTS, TPOOL_MIN_ELTS, and TPOOL_NOTHREAD to override the defaults established by !CPU for a single invocation of this routine. See Thread Pool Keywords for details.
1. See formulas 4.4.1-3 in Abramowitz, M. and Stegun, I.A., 1964: Handbook of Mathematical Functions (Washington: National Bureau of Standards).
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