tzeg6@T+ f,c>o⌻wRW/ ‹KgMzPny\F7nXoāKJg EB? Cez>^^$/fЁ1. ?c6ir;*{4N;@a-ɉ53j`?<:A0׶,)ՈGsB =- lN i|E2ZyCFa)oB"_X hTP{;*! -6;B(G Ǧ#)rN9ʈPr9.4—Ñ⑗Mo|شR'IRe\a}1OlO'rFuo,?9e^):gVmA3S9Wd U, Y!xqYW@6dNDK 1`={izqv0H[!REa^=T"XUe!B'~atN@dFovYࢨ"hk2-aœwѲ4]i W߱n6ŇXɸAQN$sGzƨNƨ羇)EG2q8f]59s4ve1mn^=T4ݝo$v27#7ύ֕09jr|,%Ea^=T"XUe!B'~atN@dF[!)Aĵ ov-Ea^=T"XUe!B'~atN@dF޽őYr;-y9'%*> =S]+93-ctwT8ևڲ)ςCuKYtz|V2ǐ#C5*_ţ.`jcc\TmUcJ˛;.HՓ9=SS43ݑսuEʻ+q_e[o9OvY*(%RbUX%txB(:.{Sůn^rabHLXjk4^YwU_6Npݑ& :iWM "k]\B,rox8^ފ[IE{us<KW9$$lqp'Q N ZG Zh]^S|'[r57BzgcwV v^)qfm yҽ57)9\{WD>il\)EV_,=/sIwDﰊ+73_htK6}\g0jSx)!tZRE}©\Yr7 {*18nn&,`\f8nn&,`\f+>/n on@q]q´u:ONs14 7W}ɆLVK+x _A!v,'G1Púߦ.7] w=#3O\EWm"U< 団=kvKˬ~>ܞ^Ewez83Vak8 z,`0mY͸Zgi4^M^)Ъ 3 ӔAADw;vGLR^W>L}|>SI@y(B[6}5(-d&fԘ-_b}.I_6k@V.\炑0LO@?#QJ >w's-{KM謶 [ U|  ˽0ԙʹZyt$;-J#=t?ʳg`ʓ||}ü.1n-ѻJ;;^!(P<4NG\Xę 7ѓKςd؄6j.LŅuBo*BT.}=38&5`|LRSD,)o&?52k@˓W50*70 ˠ_u1GDD4Ŀʾ@>q$H37J0nYH|& ϞŢY Ɗ`hh#N!1y 3LX91T,sq b%)Ƌe'Pu*<LҀ6d8q j$ B i{]^̋U5gLZ^B[6}5(-d&fԘ-_b}.:%>;#1}dE%FjжwePyꞲL~=eȠJ\ӅH!N({DkhtWQSb;KC#5hcl}9#wE[:/d_C1,x ::cDtb I%+piKo3jqk)Ap yό(k)#o\TLjtX eCR*N]1]SݽWSN Vv/U+/f:3_Y*Gs …~6ȿna?#N Dޜh^ 3Q59xb2E҃ƿQtIƺ(:VTǃNw36:/H3qrN,~!zoӅ{ ؆/}Cn_f=m-~ְ%{⿁`( Bj;Yfj8C0l'HoSqIàMˡ@/6Ody􅞒3H;\lu^a)@x1|0S@*5r2ѵF~Uu " #1}dE%FjжwePyꞘ{;Q#0 SgBx~Yt=e$YV6mW]Ew.I(̬3,o4 '%S.rL0!ȱEr[޻`N9 hjd/א;r\`Ӣf5wP:;< tJn ^q9/3f-+LF8ev,sq b%)Ƌe'Puo3?Tɗr5S_elRI8,!L:f mxLL[gkiO)ۮfmcGWh;܍)^ʓj&vA.[Zw'~pp֟3}NC_$7nWVKPb3ҙȊڍn!\2B gn`] 2rJ;$;:STE~0r-open"> JAMA For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n orthogonal matrix V so that A = U*S*V'
  •  JAMA Pythagorean Theorem: a = 3 b = 4 r = sqrt(square(a) + square(b)) r = 5 r = sqrt(a^2 + b^2) without under/overflow
  •  PHPExcel
    • Back to top  

    package JAMA Cholesky decomposition class For a symmetric, positive definite matrix A, the Cholesky decomposition is an lower triangular matrix L so that A = L*L'. If the matrix is not symmetric or positive definite, the constructor returns a partial decomposition and sets an internal flag that may be queried by the isSPD() method.
    author Paul Meagher
    author Michael Bommarito
    version 1.2

     Methods

    CholeskyDecomposition

    __construct(mixed $A) 

    Class constructor - decomposes symmetric positive definite matrix

    Parameters

    $A

    mixed

    Matrix square symmetric positive definite matrix

    getL

    getL() : \Matrix

    Return triangular factor.

    Returns

    \MatrixLower triangular matrix

    Is the matrix symmetric and positive definite?

    isSPD() : boolean

    Returns

    boolean

    Solve A*X = B

    solve($B) : \Matrix

    Parameters

    $B

    Row-equal matrix

    Returns

    \MatrixL * L' * X = B

     Properties

     

    $L : array
    access private
     

    $isspd : boolean
    access private
     

    $m : int
    access private