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math library for kdb+
Home Page: http://althenia.net/qml
License: Other
This project forked from zholos/qml
math library for kdb+
Home Page: http://althenia.net/qml
License: Other
Introduction ------------ qml is a library for statistics, linear algebra, and optimization in kdb+. It provides an interface between the q programming language and numerical libraries such as LAPACK. License ------- qml is free software, distributed under a BSD-style license. It is provided in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranties of MERCHANTABILITY and FITNESS FOR A PARTICULAR PURPOSE. See LICENSE.txt for more details. qml is linked against several other libraries. The copyrights and licenses for these libraries are also listed in LICENSE.txt. Installation ------------ To compile and install from source code, run ./configure make make test make install To install a precompiled binary, copy qml.q into the same directory as q.k, and copy qml.dll or qml.so into the same directory as q.exe or q. Then run test.q. Usage ----- Load with q)\l qml.q All functions are in the .qml namespace. Numerical arguments are automatically converted into floating-point. Matrixes are in the usual row-major layout (lists of row vectors). Complex numbers are represented as pairs of their real and imaginary parts. q).qml.nicdf .25 .5 .975 / normal distribution quantiles -0.6744898 0 1.959964 q).qml.mchol (1 2 1;2 5 4;1 4 6) / Cholesky factorization 1 2 1 0 1 2 0 0 1 q).qml.poly 2 -9 16 -15 / solve 2x^3-9x^2+16x-15=0 2.5 1 1.414214 1 -1.414214 q).qml.mlsq[(1 1;1 2;1 3;1 4);11 2 -3 -4] / fit line 14 -5f q).qml.conmin[{x*y+1};{1-(x*x)+y*y};0 0] / minimize x(y+1) s.t. x^2+y^2<=1 -0.8660254 0.5 Constants and functions ----------------------- pi pi e e eps smallest representable step from 1. sin[x] sine cos[x] cosine tan[x] tangent asin[x] arcsine acos[x] arccosine atan[x] arctangent atan2[x;y] atan[x%y] sinh[x] hyperbolic sine cosh[x] hyperbolic cosine tanh[x] hyperbolic tangent asinh[x] hyperbolic arcsine acosh[x] hyperbolic arccosine atanh[x] hyperbolic arctangent exp[x] exponential expm1[x] exp[x]-1 log[x] logarithm log10[x] base-10 logarithm logb[x] extract binary exponent log1p[x] log[1+x] pow[a;x] exponentiation sqrt[x] square root cbrt[x] cube root hypot[x;y] sqrt[pow[x;2]+pow[y;2]] floor[x] round downward ceil[x] round upward fabs[x] absolute value fmod[x;y] remainder of x%y erf[x] error function erfc[x] complementary error function lgamma[x] log of absolute value of gamma function gamma[x] gamma function beta[x;y] beta function pgamma[a;x] lower incomplete gamma function (a>0) pgammac[a;x] upper incomplete gamma function (a>0) pgammar[a;x] regularized lower incomplete gamma function (a>0) pgammarc[a;x] regularized upper incomplete gamma function (a>0) ipgammarc[a;p] inverse complementary regularized incomplete gamma function (a>0,p>=.5) pbeta[a;b;x] incomplete beta function (a,b>0) pbetar[a;b;x] regularized incomplete beta function (a,b>0) ipbetar[a;b;p] inverse regularized incomplete beta function (a,b>0) j0[x] order 0 Bessel function j1[x] order 1 Bessel function y0[x] order 0 Bessel function of the second kind y1[x] order 1 Bessel function of the second kind ncdf[x] CDF of normal distribution nicdf[p] its inverse c2cdf[k;x] CDF of chi-squared distribution (k>=1) c2icdf[k;p] its inverse stcdf[k;x] CDF of Student's t-distribution (natural k) sticdf[k;p] its inverse fcdf[d1;d2;x] CDF of F-distribution (d1,d2>=1,x>=0) ficdf[d1;d2;p] its inverse gcdf[k;th;x] CDF of gamma distribution gicdf[k;th;p] its inverse bncdf[k;n;p] CDF of binomial distribution bnicdf[k;n;x] its inverse for p (k<n) pscdf[k;lambda] CDF of Poisson distribution psicdf[k;p] its inverse for lambda smcdf[n;e] CDF for one-sided Kolmogorov-Smirnov test smicdf[n;e] its inverse kcdf[x] CDF for Kolmogorov distribution kicdf[p] its inverse (p>=1e-8) diag[diag] make diagonal matrix mdim[matrix] number of (rows; columns) mdiag[matrix] extract main diagonal mdet[matrix] determinant mrank[matrix] rank minv[matrix] inverse mpinv[matrix] pseudoinverse dot[a;b] dot product mm[A;B] multiply mmx[opt;A;B] mm[] with options `lflip: flip A `rflip: flip B ms[A;B] solve B=A mm X, A is triangular mev[matrix] (eigenvalues; eigenvectors) sorted by decreasing modulus mchol[matrix] Cholesky factorization upper matrix mqr[matrix] QR factorization: (Q; R) mqrp[matrix] QR factorization with column pivoting: (Q; R; P), matrix@\:P=Q mm R mlup[matrix] LUP factorization with row pivoting: (L; U; P), matrix[P]=L mm U msvd[matrix] singular value decomposition: (U; Sigma; V) mkron[A;B] Kronecker product poly[coef] roots of a polynomial (highest-degree coefficient first) mls[A;B] solve B=A mm X mlsx[opt;A;B] mls[] with options `equi: equilibrate the system (default: don't) `flip: flip A, and flip B and X unless B is a vector mlsq[A;B] solve min ||B-A mm X|| mlsqx[opt;A;B] mlsq[] with options `svd: use SVD algorithm (default: QR or LQ) `flip: flip A, and flip B and X unless B is a vector root[f;(x0;x1)] find root on interval (f(x0)f(x1)<0) rootx[opt;f;(x0;x1)] root[] with options (as dictionary or mixed list) `iter: max iterations (default: 100) `tol: numerical tolerance (default: ~1e-8) `full: full output (default: only x) `quiet: return null on failure (default: signal) solve[eqs;x0] solve nonlinear equations (given as functions) solvex[opt;eqs;x0] solve[] with options `iter: max iterations (default: 1000) `tol: numerical tolerance (default: ~1e-8) `full: full output (default: only x) `quiet: return null on failure (default: signal) `steps: RK steps per iteration (default: 1) `rk: use RK steps only (default: RK, SLP) `slp: use SLP steps only (default: RK, SLP) line[f;base;x0] line search for minimum from base linex[opt;f;base;x0] line[] with same options as rootx[] min[f;x0] find unconstrained minimum min[(f;df);x0] min[] with analytic gradient function minx[opt;f;x0] min[] with same options as solvex[], plus `nm: use Nelder–Mead method (default: CONMAX) `sbplx: use Subplex method (default: CONMAX) conmin[f;cons;x0] find constrained minimum (functions cons>=0) conmin[(f;df);flip(cons;dcons);x0] conmin[] with analytic gradient functions conminx[opt;f;cons;x0] conmin[] with same options as solvex[], plus `lincon: assume linear cons (default: nonlinear) `cobyla: use COBYLA method (default: CONMAX)
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