bm_version : print version number
bmc_matdetg : matrix determinant (Givens rotations) bmc_matdetlu : matrix determinant (LU decomposition) bmc_matinvg : matrix inverse (Givens rotations) bmc_matinvlu : matrix inverse (LU decomposition) bmc_matludecomp : matrix LU decomposition bmc_matlumsubst : LU back-substitution (multiple vectors) bmc_matlusubst : LU back-substitution bmc_matsolcg : solution of matrix equation (conjugate gradients) bmc_matsolg : solution of matrix equation (Givens rotations) bmc_matsollu : solution of matrix equation (LU decomposition) bmc_muptrisol : solution of upper triangular matrix equation (multiple vectors) bmc_orthoggs : Gram-Schmidt orthogonalisation bmc_sparsematsolcg : solution of sparse matrix equation (conjugate gradients) bmc_tridiagludecomp : LU decomposition of tridiagonal matrix equation bmc_tridiaglusubst : LU back-substitution of tridiagonal matrix equation bmc_tridiagsollu : solution of tridiagonal matrix equation bmc_uptrisol : solution of upper triangular matrix equation bmc_vanmonfitsol : solution of Vandermonde matrix equation (fitting type) bmc_vanmonmomsol : solution of Vandermonde matrix equation (moments type)
bmc_mattotel : sum of elements bmc_mattrace : trace of matrix bmc_matabstotel : sum of absolute values of elements bmc_matnorm : norm of matrix bmc_matabsbigel : find element of largest magnitude bmc_matabstinel : find element of smallest magnitude bmc_matadd : add matrices bmc_mateq : set matrices equal bmc_matfilter : set small values to zero bmc_matidentity : create identity matrix bmc_matmult : multiply matrices bmc_matmulttran : multiply matrix by transpose of matrix bmc_matmultvec : multiply vector by matrix bmc_matread : simple read of matrix elements bmc_matset : set matrix elements to a single value bmc_matshow : display matrix bmc_matsmult : multiply matrix by scalar bmc_matsub : subtract matrices bmc_mattran : transpose matrix bmc_mattranmult : multiply matrix by transpose of matrix bmc_mattranmultvec : multiply vector by transpose of matrix bmc_matstackhoriz : combine two matrices by `stacking side-by-side' bmc_matstackvert : combine two matrices by `stacking vertically'
bmc_veccross2D : cross product (2D) bmc_vecdot : inner product bmc_vecdot2D : inner product (2D) bmc_vecdot3D : inner product (3D) bmc_vectotel : sum of elements bmc_vecabstotel : sum of absolute values of elements bmc_veclen : length bmc_veclen2D : length (2D) bmc_veclen3D : length (3D) bmc_vecnorm : norm bmc_vecnorm2D : norm (2D) bmc_vecnorm3D : norm (3D) bmc_vecabsbigel : find largest absolute element bmc_vecabstinel : find smallest absolute element bmc_vecadd : add vectors bmc_vecadd2D : add vectors (2D) bmc_vecadd3D : add vectors (3D) bmc_veccross3D : cross product (3D) bmc_vecdirprod : outer product bmc_veceq : set vectors equal bmc_veceq2D : set vectors equal (2D) bmc_veceq3D : set vectors equal (3D) bmc_vecfilter : set small elements to zero bmc_vecnormalise : normalise vector bmc_vecnormalise2D : normalise vector (2D) bmc_vecnormalise3D : normalise vector (3D) bmc_vecread : read elements bmc_vecread2D : read elements (2D) bmc_vecread3D : read elements (3D) bmc_vecset : set elements to a single value bmc_vecset2D : set elements to a single value (2D) bmc_vecset3D : set elements to a single value (3D) bmc_vecshow : display vector bmc_vecshow2D : display vector (2D) bmc_vecshow3D : display vector (3D) bmc_vecsmult : multiply vector by scalar bmc_vecsmult2D : multiply vector by scalar (2D) bmc_vecsmult3D : multiply vector by scalar (3D) bmc_vecsub : subtract vectors bmc_vecsub2D : subtract vectors (2D) bmc_vecsub3D : subtract vectors (3D) bmc_wedge1 : wedge product
bm_Ggrav : gravitational constant bm_Qcharge : charge on electron bm_amu : atomic mass units bm_avogadro : Avogadro's number bm_clight : speed of light bm_e : exp(1) bm_elecmass : mass of electron bm_epsilon0 : permittivity of free space bm_eulmasch : Euler-Mascheroni constant bm_hPlanck : Planck's constant bm_kBoltzmann : Boltzmann's constant bm_mu0 : permeability of free space bm_pi : pi bm_sigmaStefBoltz : Stefan-Boltzmann constant
bm_deg2rad : degrees to radians bm_rad2deg : radians to degrees bm_rt2xy : 2D polar to Cartesian bm_rtp2xyz : 3D spherical to Cartesian bm_xy2rt : 2D Cartesian to polar bm_xyz2rtp : 3D Cartesian to spherical
bm_gncfit : Gauss-Newton with second derivatives bm_gncfitmem : Gauss-Newton with second derivatives (stores Jacobian) bm_gnfit : Gauss-Newton bm_gnfitmem : Gauss-Newton (stores Jacobian) bm_linfit : general linear functions bm_lmfit : Levenberg-Mardquart bm_lmfitmem : Levenberg-Mardquart (stores Jacobian) bm_lsqline : linear least squares bm_polyfitg : polynomial (Givens rotations) bm_polyfitn : polynomial (normal equation)
bm_evechesshqr : solve in Hessenberg form bm_evechqr : solve bm_evecsymmhql : solve symmetric bm_evecsymmtridiagql : solve symmetric tridiagonal bm_genhessh : convert general matrix to Hessenberg form bm_matqlh : QL decomposition bm_matqrh : QR decomposition bm_symmtridiagh : convert symmetric to tridiagonal
bm_charval : convert character expression to numerical value bm_parse : parse an expression into a series of operations bm_operate : perform a series of operations on an array of numbers
average
: average of nodal values
convect
: map node value to centre according to a direction vector
curl
: curl
div
: divergence
grad
: gradient
integral
: integral over cell
laplace
: Laplacian
volume
: cell volume
arb
: arbitrary
rec
: 2D rectangular
cub
: 3D cuboidal
bm_average1D bm_averagearbcell2D bm_averagearbcell3D bm_averagearbcellND bm_averagecub3D bm_averagerec2D bm_convectarbcell2D bm_convectarbcell3D bm_convectarbcellND bm_curlarbcell2D bm_curlarbcell3D bm_curlcub3D bm_curlrec2D bm_div1D bm_divarbcell2D bm_divarbcell3D bm_divarbcellND bm_divcub3D bm_divrec2D bm_grad1D bm_gradarbcell2D bm_gradarbcell3D bm_gradarbcellND bm_gradcub3D bm_gradrec2D bm_integral1D bm_integralcub3D bm_integralrec2D bm_laplac1D bm_laplaccub3D bm_laplacrec2D bm_volume1D bm_volumecub3D bm_volumerec2D
average
: average of nodal values
convect
: map node value to centre according to a direction vector
curl
: curl
div
: divergence
grad
: gradient
integral
: integral over cell
laplace
: Laplacian
volume
: cell volume
cen
: calculate quantity using definitions at cell centres
(result will be defined at the nodes)
node
: calculate quantity using definitions at nodes
(result will be defined at the cell centres)
arb
: arbitrary
rec
: 2D rectangular
cub
: 3D cuboidal
bm_averagearb2D bm_averagearb3D bm_averagearbND bm_averagecen1D bm_averagecencub3D bm_averagecenrec2D bm_averagenode1D bm_averagenodecub3D bm_averagenoderec2D bm_convectarb2D bm_convectarb3D bm_convectarbND bm_curlarb2D bm_curlarb3D bm_curlcencub3D bm_curlcenrec2D bm_curlnodecub3D bm_curlnoderec2D bm_divarb2D bm_divarb3D bm_divarbND bm_divcen1D bm_divcencub3D bm_divcenrec2D bm_divnode1D bm_divnodecub3D bm_divnoderec2D bm_gradarb2D bm_gradarb3D bm_gradarbND bm_gradcen1D bm_gradcencub3D bm_gradcenrec2D bm_gradnode1D bm_gradnodecub3D bm_gradnoderec2D bm_integralcen1D bm_integralcencub3D bm_integralcenrec2D bm_integralnode1D bm_integralnodecub3D bm_integralnoderec2D bm_laplaccen1D bm_laplaccencub3D bm_laplaccenrec2D bm_laplacnode1D bm_laplacnodecub3D bm_laplacnoderec2D bm_volumecen1D bm_volumecencub3D bm_volumecenrec2D bm_volumenode1D bm_volumenodecub3D bm_volumenoderec2D
bm_alegpoly : associated Legendre polynomial bm_bessj0 : Bessel J0 function bm_bessj1 : Bessel J1 function bm_bessy0 : Bessel Y0 function bm_bessy1 : Bessel Y1 function bm_beta : beta function bm_binco : binomial coefficient bm_ellipe : elliptic E function bm_ellipk : elliptic K function bm_erfapprox : error function (approximation) bm_erfcapprox : complementary error function (approximation) bm_factorial : factorial bm_fresnelc : Fresnel C function bm_fresnels : Fresnel S function bm_gamma : gamma function bm_lnfactorial : ln of factorial bm_lngamma : ln of gamma function bm_polynom : polynomial bm_bessel : Bessel function bm_bezier : Bezier function bm_bezier2D : Bezier curve (2D) bm_bezier3D : Bezier curve (3D) bm_beziersurf : Bezier hyper surface bm_erf : error function bm_erfc : complementary error function bm_spherharm : spherical harmonics
bm_angsub2D : angle subtended (2D) bm_angsub3D : solid angle subtended (3D) bm_lineconeint : intersection between line and (hyper)cone bm_linecylint : intersection between line and (hyper)cylinder bm_linedist : distance between lines bm_linedist3D : distance between lines (3D) bm_lineellipsoidint : intersection between line and (hyper)ellipsoid bm_linegenconeint : intersection between line and general (hyper)cone bm_linegenellipsoidint : intersection between line and general (hyper)ellipsoid bm_lineint : intersection between lines bm_lineint2D : intersection between lines (2D) bm_lineint3D : intersection between lines (3D) bm_lineplaneint : intersection between line and (hyper)plane bm_lineplaneint3D : intersection between line and plane (3D) bm_linesphereint : intersection between line and (hyper)sphere bm_rotate2D : rotate a vector (2D) bm_rotate3D : rotate a vector (3D) bm_comtgtquad : common tangent of quadratic curves
bm_rombint : Romberg bm_simpint : Simpson's rule bm_trapint : trapezoidal
bm_interplin : linear bm_interppoly : polynomial bm_interpspline : spline bm_setinterpspline : calculate coefficients in interpolating spline bm_tabpos : find position in monotonic table
bm_matdetg : matrix determinant (Givens rotations) bm_matdetlu : matrix determinant (LU decomposition) bm_matinvg : matrix inverse (Givens rotations) bm_matinvlu : matrix inverse (LU decomposition) bm_matludecomp : matrix LU decomposition bm_matlumsubst : LU back-substitution (multiple vectors) bm_matlusubst : LU back-substitution bm_matsolcg : solution of matrix equation (conjugate gradients) bm_matsolg : solution of matrix equation (Givens rotations) bm_matsollu : solution of matrix equation (LU decomposition) bm_muptrisol : solution of upper triangular matrix equation (multiple vectors) bm_orthoggs : Gram-Schmidt orthogonalisation bm_sparsematsolcg : solution of sparse matrix equation (conjugate gradients) bm_tridiagludecomp : LU decomposition of tridiagonal matrix equation bm_tridiaglusubst : LU back-substitution of tridiagonal matrix equation bm_tridiagsollu : solution of tridiagonal matrix equation bm_uptrisol : solution of upper triangular matrix equation bm_vanmonfitsol : solution of Vandermonde matrix equation (fitting type) bm_vanmonmomsol : solution of Vandermonde matrix equation (moments type)
bm_mattotel : sum of elements bm_mattrace : trace of matrix bm_matabstotel : sum of absolute values of elements bm_matnorm : norm of matrix bm_matabsbigel : find element of largest magnitude bm_matabstinel : find element of smallest magnitude bm_matadd : add matrices bm_mateq : set matrices equal bm_matfilter : set small values to zero bm_matidentity : create identity matrix bm_matmult : multiply matrices bm_matmulttran : multiply matrix by transpose of matrix bm_matmultvec : multiply vector by matrix bm_matread : simple read of matrix elements bm_matset : set matrix elements to a single value bm_matshow : display matrix bm_matsmult : multiply matrix by scalar bm_matsub : subtract matrices bm_mattran : transpose matrix bm_mattranmult : multiply matrix by transpose of matrix bm_mattranmultvec : multiply vector by transpose of matrix bm_matblockprod : block (Kronecker) product of two matrices bm_matstackhoriz : combine two matrices by `stacking side-by-side' bm_matstackvert : combine two matrices by `stacking vertically'
bm_minbis1D : 1D bisection bm_minbisND : ND bisection bm_minbisd1D : 1D bisection (derivatives only) bm_minbrack1D : 1D bracketing bm_minbrackND : ND bracketing bm_mincgND : ND conjugate gradient bm_mincgnumND : ND conjugate gradient, numerical derivatives bm_mindumbND : ND `dumb' method bm_minnr1D : 1D Newton-Raphson bm_minnrND : ND Newton-Raphson bm_mintr1D : 1D trust region bm_mintrND : ND trust region
bm_rkaccint : Runge-Kutta with accuracy checking bm_rkint : Runge-Kutta bm_rksaccint : Runge-Kutta with flexible stop conditions and accuracy checking bm_rksaccinthist : Runge-Kutta with flexible stop conditions and accuracy checking, variable histories stored bm_rksstep : single Runge-Kutta step with flexible stop conditions bm_rkstep : single Runge-Kutta step
bm_dynampc1D : 1D time-dependent predictor-corrector bm_dynampcrec2D : 2D time-dependent predictor-corrector (rectangular mesh) bm_ellipconsorreg1D : 1D elliptic, constant coefficients, SOR method, regular mesh bm_ellipconsorreg2D : 2D elliptic, constant coefficients, SOR method, regular mesh bm_ellipsor1D : 1D elliptic, SOR method bm_ellipsorrec2D : 2D elliptic, SOR method, rectangular mesh bm_ellipsorreg1D : 1D elliptic, SOR method, regular mesh bm_ellipsorreg2D : 2D elliptic, SOR method, regular mesh
bm_randisexp : generate a random number (exponential distribution) bm_randisexpgen : generate a random number (general exponential distribution) bm_randisgauss : generate a random number (Gaussian distribution) bm_randisgaussgen : generate a random number (general Gaussian distribution) bm_randislorentz : generate a random number (Lorentz distribution) bm_ransub : generate a random number (uniform distribution) bm_ranoutcome : random choice between discrete outcomes with different probabilities bm_setransub : seed random number generator
bm_rootbis1D : 1D bisection bm_rootnr1D : 1D Newton-Raphson bm_rootquad : quadratic bm_rootsfuncbis : all roots of arbitrary function by bisection bm_rootspolybis : all roots of polynomial by bisection bm_synthdiv : synthetic division of polynomials
bm_index : ordering indices bm_indexheap : index using heapsort bm_indexinsert : index using insertion bm_indexrank : rank given ordering indices bm_indexshell : index using shell method bm_indexsort : sort given ordering indices bm_sort : sort bm_sortheap : heapsort bm_sortinsert : insertion sort bm_sortshell : shell sort
bm_lincor : linear correlation coefficient bm_moment : moments bm_meanabsdev : mean and absolute deviation bm_meanvarsd : mean. variance and standard deviation bm_runmeanvarsd : running mean, variance and standard deviation
bm_fftcomp1D : 1D complex fast Fourier transform bm_fftcompnd : ND complex fast Fourier transform
bm_veccross2D : cross product (2D) bm_vecdot : inner product bm_vecdot2D : inner product (2D) bm_vecdot3D : inner product (3D) bm_vectotel : sum of elements bm_vecabstotel : sum of absolute values of elements bm_veclen : length bm_veclen2D : length (2D) bm_veclen3D : length (3D) bm_vecnorm : norm bm_vecnorm2D : norm (2D) bm_vecnorm3D : norm (3D) bm_vecabsbigel : find largest absolute element bm_vecabstinel : find smallest absolute element bm_vecadd : add vectors bm_vecadd2D : add vectors (2D) bm_vecadd3D : add vectors (3D) bm_veccross3D : cross product (3D) bm_vecdirprod : outer product bm_veceq : set vectors equal bm_veceq2D : set vectors equal (2D) bm_veceq3D : set vectors equal (3D) bm_vecfilter : set small elements to zero bm_vecnormalise : normalise vector bm_vecnormalise2D : normalise vector (2D) bm_vecnormalise3D : normalise vector (3D) bm_vecread : read elements bm_vecread2D : read elements (2D) bm_vecread3D : read elements (3D) bm_vecset : set elements to a single value bm_vecset2D : set elements to a single value (2D) bm_vecset3D : set elements to a single value (3D) bm_vecshow : display vector bm_vecshow2D : display vector (2D) bm_vecshow3D : display vector (3D) bm_vecsmult : multiply vector by scalar bm_vecsmult2D : multiply vector by scalar (2D) bm_vecsmult3D : multiply vector by scalar (3D) bm_vecsub : subtract vectors bm_vecsub2D : subtract vectors (2D) bm_vecsub3D : subtract vectors (3D) bm_wedge1 : wedge product