Q Math Library
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.
The current version of the library is 0.4 (track updates). This is a development branch. For precompiled binaries see version 0.2.1.
News
- 2013-05-12
Welcome qml 0.4. Development continues on GitHub.
- 2013-04-11
I am working on a new version of QML.
The interface will be the same as in version 0.3, including the recently added mm, ms, mls and mlsq functions, while the configuration will be more like version 0.2, with BLAS used by default and precompiled binaries provided.
It will be compatible with kdb+ 3.0, testing will be more thorough than ever, and there will be an option to link against a different implementation of BLAS, such as ATLAS.
In the mean time, check out this patch from Kim Tang for kdb+ 3.0 support.
Also, if you want to build QML 0.3.10, the particular development snapshot of ATLAS that it uses is no longer available for download, so I'm hosting it here.
atlas-3.9.46.tar.bz2 (5.31 MB)
Just verified that it still builds on 32-bit Debian.
- 2012-12-10
QML 0.2.1 is still the stable version. It does not have the matrix performance of ATLAS, but it is easier to compile and includes binaries for 32-bit platforms.
Since it was released some of the files on the Netlib site changed, and QML 0.2.1 no longer compiles with them. I'm hosting the original files here. Place them in the download subdirectory before running make.
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 in the distribution for more details.
qml is linked against several other libraries. The copyrights and licenses for these libraries are also listed in LICENSE.txt.
Download
|
Development version:
Legacy versions:
|
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 decomposition 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
There are more examples here and in my directory at code.kx.com.
Constants and functions
Constants
| pi | pi |
| e | e |
| eps | smallest representable step from 1. |
Trigonometric functions
| 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 |
Other libm functions
| 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 |
Hypergeometric functions
| 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≥0.5) |
| 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 |
Probability distributions
| 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;x] | its inverse |
| bncdf[k;n;p] | CDF of binomial distribution |
| bnicdf[k;n;x] | its inverse for p parameter (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;x] | its inverse |
| kcdf[x] | CDF for Kolmogorov distribution |
| kicdf[p] | its inverse (p≥1e-8) |
Matrix operations
| 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 |
| mm[A;B] | multiply |
| 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) |
Polynomial roots
| poly[coef] | roots of a polynomial (highest-degree coefficient first, can be complex) |
Linear equation solving
| mls[A;B] | solve B=A mm X | |||
| mlsx[opt;A;B] | mls[] with options
| |||
| mlsq[A;B] | solve min ||B-A mm X|| | |||
| mlsqx[opt;A;B] | mlsq[] with options
|
Nonlinear equation solving and optimization
| root[f;(x0;x1)] | find root on interval (f(x0)f(x1)<1) | |||||||||||||||||||||
| rootx[opt;f;(x0;x1)] | root[] with options (as dictionary or mixed list)
| |||||||||||||||||||||
| solve[eqs;x0] | solve nonlinear equations (given as functions) | |||||||||||||||||||||
| solvex[opt;eqs;x0] | solve[] with options
| |||||||||||||||||||||
| 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 | |||||||||||||||||||||
| minx[opt;f;x0] | min[] with same options as solvex[] | |||||||||||||||||||||
| conmin[f;cons;x0] | find constrained minimum (functions cons≥0) | |||||||||||||||||||||
| conminx[opt;f;cons;x0] | min[] with same options as solvex[], plus
|