MPSolve - A multiprecision polynomial rootfinder
mpsolve [-a alg] [-b] [-c] [-G goal] [-o digits] [-i digits] [-j
n] [-t type] [-S set] [-D detect] [-O format] [-l filename] [-x] [-d] [-v]
[-r] [infile | -p poly]
- -a alg
- Select the algorithm used to solve the polynomial/secular equation:
- u: Classic unisolve algorithm (Aberth iterations and dynamic precision)
s: Secular algorithm, using regeneration of increasingly
better-conditioned
- secular equations with the same roots of the polynomial
- -b
- Perform Aberth iterations in Jacobi-style instead of Gauss-Seidel
- -c
- Enable crude approximation mode
- -G goal
- Select the goal to reach. Possible values are:
- a: Approximate the roots
i: Isolate the roots
c: Count the roots in the search set
- -o digits
- Number of guaranteed digits of the roots
- -i digits
- Digits of precision of the input coefficients
- -j n
- Number of threads to spawn as workers
- -t type
- Type can be 'f' for floating point or 'd' for DPE
- -S set
- Restrict the search set for the roots set can be one of:
- u: upper half-plane { x | Im(x) > 0 }
d: lower half-plane { x | Im(x) < 0 }
l: left half-plane { x | Re(x) < 0 }
r: right half-plane { x | Re(x) > 0 }
i: inside the unit circle: { x | |x| < 1 }
o: outside the unit circle { x | |x| > 1 }
R: real axis { x | Im(x) = 0 }
I: imaginary axis { x | Re(x) = 0 }
- -D detect
- Detect properties of the roots:
- r: real roots
i: imaginary roots
b: both
- -O format
- Select format for output:
- f: full output
b: bare output
c: compact output
v: verbose output
g: gnuplot-ready output
gf: gnuplot-full mode, can be piped to gnuplot and display error bars.
gp: The same as gf but only with points (suitable for high degree
polynomials)
- For example:
- mpsolve -as -Ogf myfile.pol | gnuplot
-l filename Set filename as the output for the log,
instead of the tty. Use this option with
- -d[domains] to activate the desired debug domains.
- -x
- Enable graphic visualization of convergence
-d[domains] Activate debug on selected domains, that can
be one of:
- t: trace
a: approximation
c: cluster
i: improvement
w: timings
o: input/Output
m: memory management
f: function calls
p: debug stop condition and development of iteration packets
r: regeneration Example: -dfi for function calls and improvement
- -p poly
- Solve the polynomial specified on the command line.
- For example: mpsolve -p "x^4-6*x^9+6/7*x + 5"
- -r
- Use a recursive strategy to dispose the initial approximations.
This option is available only for monomial polynomials.
Note: this option is considered experimental.
- -v
- Print the version and exit
The full documentation for MPSolve is maintained as a
Texinfo manual. If the info and MPSolve programs are properly
installed at your site, the command
- info MPSolve
should give you access to the complete manual.