tzeg6@T+ f,c>o⌻wRW/ ‹KgMzPny\F7nXoāKJg EB? Cez>^^$/fЁ1. ?c6ir;*{4N;@a-ɉ53j`?<:A0׶,)ՈGsB =- lN i|E2ZyCFaj^{?vyև=M\H3ERIJ<3<ݪPń)< H%:ECrQ-?b1?ցK0GV+UVtPhofzR,BCCBqHW k#.~i4O<J@Z<<{I}e #!7nF!`g\ +5Hd`;R0ƭYD,\; ?DK 1`={lOԚZMDӓ[:>}ib|J/n\j&rJ%+j[,xl2O& _ݺ.e]ịI" ,*ze[%^k^t\І+2F{Gug>#.~؍sCBd'KRxە\І+2F{Gug>#.~!e.yBc@?9SYa5& mN2:v3ζ4CѨm];Ob "PJy-=`J`w 6 ݑ& :iWM QٷCobcIE{us<KWrQziQ҉wEʧck=<1I F &y29?r57S'ddRb|AWE/`le)0Mx?(DA)2 ׷ 6@…Jap$<.SU=NVBHl)KQGh7hbFreGmrHM7&<9d].v(5yPPN*RkGp/Ylm3sb$8s6P2O==8nn&,`\fsr& G6?5=j]JN7)vF=/g*àe{Lɲlj6l[*B]<u֘5[0+{ ؆/}Cn_f=m/ۗld Um#+5e.c3B[cyK\U{˩b*;~n!8pái.7] w=8$#Z0gg@t=e$YV6mW]Ewe4vE kZ/:,!1Qe4o tLWʃwt؟D6%8X}Ey9׺};ZB /L;Cϕ].p;bK+[.J}]LD6q> <ɷdL $gJüشC IUwc [ɏo+cp~Lw6IAR ~k1+nv-ȇMa֘n TS*js LݴKٍ ͔`]< 団=kvKˬx+ےoO@rhIz _h <1d[]feir{_/p7uTQz +ZM vJQ-?? CZPvgAba'Dy …~6ȿp!K}CoP,drh Ln.7] w="<5%4đHs5}o[LZ@-1B83ks1T^_cFR{]$@! F'-xs\dRnH,|hr-)iG@F-ߒ,w(}&~ ;|E~s WsE~T?1ϸ } k0!dw0ә.^cOKOTU&h."iM"ȎaT5 ap㑹`"ㆲ.w1*]wiC. %NDk1+nv-|ۗ0 _.Egv&Nx%wYs LFZ` j "**`q$((.$waWX5ۍ['5 -/V6J2¾!G L#mGVrvdej"w:`jg;:STE~0GJİ KQ>.Ww>̓hmj) 6|@.EzZh_~,?wPCtgFnyTM*wGtQ79Z`>$3-z.LG0V:Nun#2yѺtr>h)ӆ>Lw[yuV-6tl*IھaϿ v.m@AwP3>_') +ؓVyPDjhe? NPw9(Թ~=;>,sq b%)Ƌe'PuЖP'966rFL?Ʉx5JoB i{]^̋U5g]n#eGe!+TǎcPܮc=oΗ' Ov&Nx%wYs LFZ`Cx i?-QybU[vA ꖿ5 :@쨕 Gs͑K*ClW[G sIGiRD?rQ֥WmȩMVBRt!ѓeDinqp'm xg*:fɣpj*xRHrFLoZ).yI0Ei,+݂0G]w0??a V˩E?ңnZte WsE~T?1ϸ } k0!dw0ә.^cOKOTU&h."i'.GOϴ·N=s v;pCHc" (пPfs[0Pe)+cXC[4)eVBPݏ6L_>%Ieޣ|\ӆRԉ޵i'g"^?Hbv­2Adϱ)Im7|w$͚'DgKQJ >w's-folder-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
  •  Methods

    Polymorphic constructor

    __construct() 

    As PHP has no support for polymorphic constructors, we hack our own sort of polymorphism using func_num_args, func_get_arg, and gettype. In essence, we're just implementing a simple RTTI filter and calling the appropriate constructor.

    arrayLeftDivide

    arrayLeftDivide() : \Matrix

    Element-by-element Left division A / B

    Returns

    \MatrixDivision result

    arrayLeftDivideEquals

    arrayLeftDivideEquals() : \Matrix

    Element-by-element Left division Aij = Aij / Bij

    Returns

    \MatrixMatrix Aij

    arrayRightDivide

    arrayRightDivide() : \Matrix

    Element-by-element right division A / B

    Returns

    \MatrixDivision result

    arrayRightDivideEquals

    arrayRightDivideEquals() : \Matrix

    Element-by-element right division Aij = Aij / Bij

    Returns

    \MatrixMatrix Aij

    arrayTimes

    arrayTimes() : \Matrix

    Element-by-element multiplication Cij = Aij * Bij

    Returns

    \MatrixMatrix Cij

    arrayTimesEquals

    arrayTimesEquals() : \Matrix

    Element-by-element multiplication Aij = Aij * Bij

    Returns

    \MatrixMatrix Aij

    checkMatrixDimensions

    checkMatrixDimensions(\Matrix $B) : boolean

    Is matrix B the same size?

    Parameters

    $B

    \Matrix

    Matrix B

    Returns

    boolean

    concat

    concat() : \Matrix

    A = A & B

    Returns

    \MatrixSum

    det

    det() : float

    Calculate determinant

    Returns

    floatDeterminant

    diagonal

    diagonal(int $m, int $n, mixed $c) : \Matrix

    Generate a diagonal matrix

    Parameters

    $m

    int

    Row dimension

    $n

    int

    Column dimension

    $c

    mixed

    Diagonal value

    Returns

    \MatrixDiagonal matrix

    get

    get(int $i, int $j) : mixed

    Get the i,j-th element of the matrix.

    Parameters

    $i

    int

    Row position

    $j

    int

    Column position

    Returns

    mixedElement (int/float/double)

    getArray

    getArray() : array

    Returns

    arrayMatrix array

    getColumnDimension

    getColumnDimension() : int

    Returns

    intColumn dimension

    getMatrix

    getMatrix() : \Matrix

    Get a submatrix

    Returns

    \MatrixSubmatrix

    getMatrixByCol

    getMatrixByCol($j0, $jF) : \Matrix

    Get a submatrix by column index/range

    Parameters

    $j0

    $jF

    Returns

    \MatrixSubmatrix

    getMatrixByRow

    getMatrixByRow(int $i0, int $iF) : \Matrix

    Get a submatrix by row index/range

    Parameters

    $i0

    int

    Initial row index

    $iF

    int

    Final row index

    Returns

    \MatrixSubmatrix

    getRowDimension

    getRowDimension() : int

    Returns

    intRow dimension

    identity

    identity(int $m, int $n) : \Matrix

    Generate an identity matrix.

    Parameters

    $m

    int

    Row dimension

    $n

    int

    Column dimension

    Returns

    \MatrixIdentity matrix

    Matrix inverse or pseudoinverse.

    inverse() : \Matrix

    Returns

    \Matrix... Inverse(A) if A is square, pseudoinverse otherwise.

    minus

    minus() : \Matrix

    A - B

    Returns

    \MatrixSum

    minusEquals

    minusEquals() : \Matrix

    A = A - B

    Returns

    \MatrixSum

    plus

    plus() : \Matrix

    A + B

    Returns

    \MatrixSum

    plusEquals

    plusEquals() : \Matrix

    A = A + B

    Returns

    \MatrixSum

    power

    power() : \Matrix

    A = A ^ B

    Returns

    \MatrixSum

    set

    set(int $i, int $j, mixed $c) : mixed

    Set the i,j-th element of the matrix.

    Parameters

    $i

    int

    Row position

    $j

    int

    Column position

    $c

    mixed

    Int/float/double value

    Returns

    mixedElement (int/float/double)

    Solve A*X = B.

    solve(\Matrix $B) : \Matrix

    Parameters

    $B

    \Matrix

    Right hand side

    Returns

    \Matrix... Solution if A is square, least squares solution otherwise

    times

    times() : \Matrix

    Matrix multiplication

    Returns

    \MatrixProduct

    trace

    trace() : float

    Sum of diagonal elements

    Returns

    floatSum of diagonal elements

    transpose

    transpose() : \Matrix

    Tranpose matrix

    Returns

    \MatrixTransposed matrix

    uminus

    uminus() : \Matrix

    Unary minus matrix -A

    Returns

    \MatrixUnary minus matrix

     Properties

     

    $A : array
    access public
     

    $m : int
    access private
     

    $n : int
    access private

     Constants

     

    ArgumentBoundsException

    ArgumentBoundsException 
     

    ArgumentTypeException

    ArgumentTypeException 
     

    ArrayLengthException

    ArrayLengthException 
     

    MatrixDimensionException

    MatrixDimensionException 
     

    PolymorphicArgumentException

    PolymorphicArgumentException