[R] How does the survfit.coxph calculate the survival value?

[Terry Therneau]

The answers to your questions consume an entire chapter of my book, so
it is difficult to write a reasonable email response.  When there are
time dependent covariates, the creation and interpretation of a survival
curve is particularly subtle.
  The survfit.coxph routine calculates the usual estimates: Breslow,
Fleming-Harrington, or Kalbfleisch-Prentice; these differ in how they
handle ties but the numerical results are usually very close.  A
treatise on the formulas, theory, and derivation of these is beyond the
scope of this message.

Terry Therneau

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I am in an urgent using R to fit the cox proportional model. My data is
a
data frame including 100 individuals which are software stress tests. 
There are time-to-failure and six covariates meaning the system resource
(every 4 minutes).
Is it possible to use R to fit the Cox model?

I used "*coxph*" to estimated the coefficients for both time-independent
and
time-dependent covariates.
And next I need to calculated the survival and hazard rate for cox model
with time-independent and that with time-dependent covariates.

I see many people use *survfit.coxph *to get the survival.
Could anybody please tell me how is the survival value calculated? For
example, what kind of procedure.