# publicJuliaLang/julia

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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 `## BIDIAG ##bidiag(A) = bidiag(A, max(1,div(min(size(A)),2)), 2)function bidiag(A::Matrix{Float64}, nb, nargout)    (m,n) = size(A)    s=min(m,n)    w=max(m,n)    D=zeros(s)    E=zeros(s-1)    tauq=zeros(s); taup=zeros(s)    A0 = A = copy(A)    k = 1-nb    for k=1:nb:s-nb        Dblk = zeros(nb)        Eblk = zeros(nb)        tauqblk = zeros(nb)        taupblk = zeros(nb)        X = zeros(m-k+1, nb)        Y = zeros(n-k+1, nb)        ccall(dlsym(_jl_libLAPACK, :dlabrd_), Void,              (Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},               Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64},               Ptr{Float64},               Ptr{Int32}, Ptr{Float64}, Ptr{Int32}),              m-k+1, n-k+1, nb, A, m-k+1, Dblk, Eblk, tauqblk, taupblk,              X, m-k+1, Y, n-k+1)        b = k+nb-1 # end of block        # accumulate reduced leading portion        A0[k:b, k:end] = A[1:nb, :]        A0[k:end, k:b] = A[:, 1:nb]        D[k:b] = Dblk        E[k:b] = Eblk        tauq[k:b] = tauqblk        taup[k:b] = taupblk        # Update the trailing submatrix A[k+nb:m,k+nb:n],        # using an update of the form A := A - V*Y' - X*U'        l = nb+1        A = A[l:end,l:end]-A[l:end,1:nb]*Y[l:end,:]'-X[l:end,:]*A[1:nb,l:end]        A0[k+nb:m, k+nb:n] = A    end    k = k+nb    tauqblk = zeros(s-k+1)    taupblk = zeros(s-k+1)    ccall(dlsym(_jl_libLAPACK,:dgebd2_), Void,          (Ptr{Int32}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},           Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64},           Ptr{Float64}, Ptr{Int32}),          m-k+1, n-k+1, A, m-k+1, zeros(s-k+1), zeros(s-k),          tauqblk, taupblk, zeros(w-k+1), 0)    A0[k:m,k:n] = A    tauq[k:end] = tauqblk    taup[k:end] = taupblk    for j=k:s-1        l = j-k+1        D[j] = A[l,l]        if m >= n            E[j] = A[l,l+1]        else            E[j] = A[l+1,l]        end    end    D[s] = A[s-k+1,s-k+1]    if nargout == 2        return (D, E)    end    if m >= n        Q = copy(A0)        ccall(dlsym(_jl_libLAPACK,:dorgbr_), Void,              (Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},               Ptr{Int32}, Ptr{Int32}),              "Q", m, n, n, Q, m, tauq, zeros(s), s, 0)        PT = A0        ccall(dlsym(_jl_libLAPACK,:dorgbr_), Void,              (Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},               Ptr{Int32}, Ptr{Int32}),              "P", n, n, n, PT, m, taup, zeros(s), s, 0)        PT = PT[1:n,:]    else        Q = copy(A0)        ccall(dlsym(_jl_libLAPACK,:dorgbr_), Void,              (Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},               Ptr{Int32}, Ptr{Int32}),              "Q", m, m, n, Q, m, tauq, zeros(s), s, 0)        Q = Q[:,1:m]        PT = A0        ccall(dlsym(_jl_libLAPACK,:dorgbr_), Void,              (Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},               Ptr{Int32}, Ptr{Int32}),              "P", m, n, m, PT, m, taup, zeros(s), s, 0)    end    return (Q, D, E, PT)endblksvd(A) = blksvd(A, 1)function blksvd(A::Matrix{Float64}, nargout)    (m, n) = size(A)    nb = 3    (Q, D, E, PT) = bidiag(A, nb, 4)    if m >= n        ccall(dlsym(_jl_libLAPACK, :dbdsqr_), Void,              (Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},               Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}),              "U",              n, n, m, 0, D, E, PT, n, Q, m, zeros(1,1), 1, zeros(4*n,1), 0)    else        ccall(dlsym(_jl_libLAPACK, :dbdsqr_), Void,              (Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},               Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},               Ptr{Float64}, Ptr{Int32}),              "L",              m, n, m, 0, D, E, PT, m, Q, m, zeros(1,1), 1, zeros(4*m,1), 0)    end    S = D    if nargout == 1        return S    end    U = Q    VT = PT    V = VT'    S = diagm(S)    return (U, S, V)end`
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