{
"cells": [
{
"cell_type": "markdown",
"id": "6f8f5cfe-b12b-4e8f-9a05-a852c5cd7bc1",
"metadata": {},
"source": [
"# 2025-10-01 QR Retrospective\n",
"\n",
"* Householder $QR$\n",
"\n",
"* Comparison of interfaces\n",
"\n",
"* Profiling\n",
"\n",
"* Cholesky $QR$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "43e8204d-d27a-4804-ab4d-46dc3e76566a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"vander (generic function with 2 methods)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using LinearAlgebra\n",
"using Plots\n",
"using Polynomials\n",
"default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n",
"\n",
"# Here's our Vandermonde matrix again\n",
"function vander(x, k=nothing)\n",
" if isnothing(k)\n",
" k = length(x)\n",
" end\n",
" m = length(x)\n",
" V = ones(m, k)\n",
" for j in 2:k\n",
" V[:, j] = V[:, j-1] .* x\n",
" end\n",
" V\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "7ce52c94-4114-46a9-a991-bea55f693843",
"metadata": {},
"source": [
"## Gram-Schmidt orthogonalization\n",
"\n",
"Suppose we're given some vectors and want to find an orthogonal basis for their span.\n",
"\n",
"$$ A = \\begin{split} \\Bigg[ a_1 \\Bigg| a_2 \\Bigg] = \\Bigg[ q_1 \\Bigg| q_2 \\Bigg] \\begin{bmatrix} r_{11} & r_{12} \\\\ 0 & r_{22} \\end{bmatrix} \\end{split} = Q R$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "17e2eec9-644a-4e2c-aa0c-63cb77813cae",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"gram_schmidt_naive (generic function with 1 method)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's form Q and R by making each column orthonormal to all previous columns\n",
"function gram_schmidt_naive(A)\n",
" m, n = size(A)\n",
" Q = zeros(m, n) # Orthonormal basis\n",
" R = zeros(n, n) # Upper triangular\n",
" for j in 1:n\n",
" v = A[:, j] # current column to normalize\n",
" for k in 1:j-1\n",
" # We do a projection against the previous columns of Q. Why?\n",
" r = Q[:, k]' * v \n",
" v -= Q[:, k] * r\n",
" R[k, j] = r # What is this factor?\n",
" end\n",
" # Normalize and store our final v\n",
" R[j, j] = norm(v)\n",
" Q[:, j] = v / R[j, j]\n",
" end\n",
" Q, R\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "c3de7a73-1e82-4fcc-a446-84dd9db314f2",
"metadata": {},
"source": [
"## A variant with more parallelism\n",
"\n",
"$$ q_2 q_2^T \\left( q_1 q_1^T v \\right) = q_2 \\left( q_2^T q_1 \\right) q_1^T v = 0 $$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "59dadf03-95bb-45f2-b459-93d705cceadb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"gram_schmidt_classical (generic function with 1 method)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Let's form Q and R by making each column orthonormal to all previous columns\n",
"function gram_schmidt_classical(A)\n",
" m, n = size(A)\n",
" # Same setup as our naive version\n",
" Q = zeros(m, n)\n",
" R = zeros(n, n)\n",
" for j in 1:n\n",
" v = A[: ,j]\n",
" # Here we make the current column othogonal to all previous\n",
" R[1:j-1, j] = Q[:, 1:j-1]' * v\n",
" v -= Q[:, 1:j-1] * R[1:j-1, j]\n",
" # And normalize our result\n",
" R[j, j] = norm(v)\n",
" Q[:, j] = v / norm(v)\n",
" end\n",
" Q, R\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "b50ce5c0-27a9-4a83-9ee7-b66b6c6ad499",
"metadata": {},
"source": [
"## Right-looking modified Gram-Schmidt\n",
"\n",
"There are inherent data dependencies in this process.\n",
"\n",
"$$\n",
"\\begin{split} \\Bigg[ q_1 \\Bigg| q_2 \\Bigg| q_3 \\Bigg| q_4 \\Bigg| q_5 \\Bigg]\n",
"\\begin{bmatrix} r_{11} & r_{12} & r_{13} & r_{14} & r_{15} \\\\\n",
" & r_{22} & r_{23} & r_{24} & r_{25} \\\\\n",
" & & r_{33} & r_{34} & r_{35} \\\\\n",
" & & & r_{44} & r_{45} \\\\\n",
" & & & & r_{55}\n",
"\\end{bmatrix}\n",
"\\end{split}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "f7bfe5b0-6bdb-4498-8037-4bf6d7256455",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"gram_schmidt_modified (generic function with 1 method)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function gram_schmidt_modified(A)\n",
" m, n = size(A)\n",
" Q = copy(A)\n",
" R = zeros(n, n)\n",
" for j in 1:n\n",
" # First we normalize our column\n",
" R[j, j] = norm(Q[:, j])\n",
" Q[:, j] /= R[j, j]\n",
" # Then we make all following columns orthogonal to the current\n",
" R[j, j+1:end] = Q[:, j]' * Q[:, j+1:end]\n",
" Q[:, j+1:end] -= Q[:, j] * R[j, j+1:end]'\n",
" end\n",
" Q, R\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "cce3c259-48f8-4085-beb9-2e09ab3f44bc",
"metadata": {},
"source": [
"## Householder QR\n",
"\n",
"Gram-Schmidt constructed a triangular matrix $R$ to orthogonalize $A$ into $Q$.\n",
"Each step was a projector, which is a rank-deficient operation.\n",
"Householder uses orthogonal transformations (reflectors) to triangularize.\n",
"\n",
"$$ \\underbrace{Q_{n} \\dotsb Q_1}_{Q^T} A = R $$\n",
"\n",
"The structure of the algorithm is\n",
"\n",
"$$ \\begin{split} \\underbrace{\\begin{bmatrix} * & * & * \\\\ * & * & * \\\\ * & * & * \\\\ * & * & * \\\\ * & * & * \\\\ \\end{bmatrix}}_{A} \\to\n",
"\\underbrace{\\begin{bmatrix} * & * & * \\\\ 0 & * & * \\\\ 0 & * & * \\\\ 0 & * & * \\\\ 0 & * & * \\\\ \\end{bmatrix}}_{Q_1 A} \\to\n",
"\\underbrace{\\begin{bmatrix} * & * & * \\\\ 0 & * & * \\\\ 0 & 0 & * \\\\ 0 & 0 & * \\\\ 0 & 0 & * \\\\ \\end{bmatrix}}_{Q_2 Q_1 A} \\to\n",
"\\underbrace{\\begin{bmatrix} * & * & * \\\\ 0 & * & * \\\\ 0 & 0 & * \\\\ 0 & 0 & 0 \\\\ 0 & 0 & 0 \\\\ \\end{bmatrix}}_{Q_3 Q_2 Q_1 A}\n",
"\\end{split} $$"
]
},
{
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/Z/feey9XXXXV/01f8iVfwgN9wzd8A1f9+9x77738d/iSL/kSHugbvuEbuOqqq6666n8lgv8Bvu/7vo+rrnpRvfRLvzQvild/9Vfnfr/+67/Of7Q3fMM35F/y5m/+5vxv9YQnPIHXfu3X5sVe7MX4l3zkR34kD/Q+7/M+XHXV/0bf+q3fyn+kpz3tadzvbd7mbbjq3+8jP/Ij+f/ol37pl7jfi73Yi3HVVRsbG7wwX/IlX8JP//RPc9VVV/3v9LSnPY37vc3bvA3/W/zSL/0S93uxF3sx/rt967d+K//dnva0p3G/t3mbt+E/wy/90i9xvxd7sRfjqhfdL/3SL3G/F3uxF+Oqq/6v+qVf+iXu92Iv9mL8f/BLv/RL3O/FXuzF+A9A8F/gQQ96EF/3dV/H8/MLv/ALXHXVv8YrvMIr8KJ4/dd/fe73sz/7s/x3+LzP+zz+t3r0ox/Nu73bu/Fv8ZEf+ZH8S44fP86jH/1orrrqf4qnPOUp/Ef71m/9Vu73bu/2blz1H+uzPuuz+Je82Zu9Gfd79KMfzf9Wt99+O/d7mZd5Ga76/2dvb48HOn36NC/MJ3/yJ/Pbv/3bPLcHPehBPPrRj+aqq676n+1bv/Vbud+7vdu78b/F7bffzv1e5mVehv9OT3nKU/if4Fu/9Vu537u927vxn+H222/nfi/zMi/DVS+622+/nfu9zMu8DFdd9X/V7bffzv1e5mVehv8Pbr/9du73Mi/zMvwHQLbNv5IkHsg2L8yDHvQgPv7jP56P+IiP4H+qr//6r2dvb48HP/jBvOu7vivPz0d8xEewt7fH/b7ne76HF+a93uu9uN/3fM/38C+58847ud8NN9yAJO535513cr8bb7yRF8WjHvUonvSkJ/FAj3zkI3niE5/IfwdJ3M82/xqSuJ9tXhSf8zmfw2d/9mdzP9v8e0nift/6rd/KB3zAB/DCvMzLvAx//dd/zf2+8Au/kE/5lE/h/xpJ3O+zP/uz+azP+iz+Pd7rvd6L+33P93wP/17v9V7vxc7ODl/3dV/Hv8V7vdd7cb/v+Z7v4b/K+73f+zFNE6/6qq/KB33QB/H8vNd7vRcA7/7u784bvMEb8O/xXu/1Xtzve77ne/j3eq/3ei/u9z3f8z38W73Xe70X9/ue7/keXhSPetSjuN8Tn/hEXhTXXnst9913HwDDMNB1HQCPetSjAHjP93xPPu3TPo1/DUnczzb/FpK4n23+s33ER3wEe3t7vNRLvRQf+7Efy/PzXu/1Xtzve77ne/jXkMT9bPOvJYn72eZf8mZv9mb84i/+IgC2+beSxP1s82/xXu/1Xtzve77ne/jXkMT9bPOieNSjHsX9nvjEJ/Lv9V7v9V7c73u+53v41/iIj/gI9vb2eKmXeik+9mM/lufnwoULfMzHfAz3+57v+R7+vd7rvd6L+33P93wP/5v9wA/8AO/+7u/O/WzzwkjCNv8e7/Ve78X9vud7vocX1Ud8xEewt7fHS73US/GxH/uxPD/v9V7vxf2+53u+h/8MH/ERH8He3h4v9VIvxcd+7Mfy/Fy4cIGP+ZiP4X7f8z3fw7/Ge73Xe3G/7/me7+E/ykd8xEewt7fHS73US/GxH/uxPD8XLlzgYz7mY7jf93zP9/DCvNd7vRf3+57v+R7+I0nifrb5l3zER3wEe3t7vNRLvRQf+7Efy/PzXu/1Xtzve77ne3hBHvWoR3G/Jz7xifx7vdd7vRf3+57v+R7+Ld7rvd4LgDd4gzfg3d/93fm3kMT9bPNf6b3e67243/d8z/fwryGJ+9nm3+O93uu9AHiDN3gD3v3d351/rWuvvZb77rsPgGEY6LoOgEc96lEAvOd7vief9mmfxovqUY96FPd74hOfyItKEvezzQvzqEc9ivs98YlP5EUlifvZ5kX1Xu/1Xtzve77ne/jf6lGPehT3e+ITn8i/hiTuZ5v/Co961KO43xOf+ET+rd7rvd6L+33P93wP/xUe9ahHcb8nPvGJvCg+4iM+gr29PV7qpV6Kj/3Yj+X5uXDhAh/zMR/D/b7ne76HF+a93uu9uN/3fM/38KJ6v/d7P6Zp4lVf9VX5oA/6IJ6f93qv9wLg3d/93XmDN3gD/j3e673ei/t9z/d8D/8aH/ERH8He3h4v9VIvxcd+7Mfy/LzXe70X9/ue7/keXhhJ3M82/x7v9V7vBcAbvMEb8O7v/u78a3zER3wEe3t7vNRLvRQf+7Efy/Nz4cIFPuZjPob7fc/3fA//FpK4n23+AxD8DyUJSUhCEpKQhCReFOfOneO7vuu7kIQkJCEJSbzP+7wPAHfeeSeSkMSXfdmX8QVf8AW827u9G5I4f/48AJKQhCS+/uu/nu/93u/le7/3e/ne7/1enh9JSEIS3/u938v3fu/38r3f+728IJKQhCRuuukmbrrpJm666SamaQLgq77qq5DETTfdxE033cRNN92EJF4YSUjiSU96Ek984hOxjW2+9Eu/lCc96UlIQhL/WzzmMY/hP8Kf/Mmf8O9lG9vY5gM+4AP413qFV3gF/q95vdd7Pf4jSeJ7v/d7efEXf3G+93u/F0m8MJKQhCSeH0l87/d+L1//9V/Pq7/6q/OvIQlJfP/3fz8v/uIvzqVLl5CEJP6zSeI7v/M7efEXf3E++IM/GEk8kCQk8eIv/uK8+Iu/OG/4hm+IJPb39/nXkoQkvv/7v58Xf/EX59KlS0hCEv8WkpDEi7/4i/PiL/7ivPiLvziSkMS/hiQk8eIv/uK8+Iu/OC/+4i+OJCTxwkjiSU96Eu///u/Pk570JCTxorjvvvt4IElI4v3f//15//d/fz790z8dSfzN3/wN/xUkIYmI4Eu/9Et5q7d6KyQhif8skvj6r/96XvzFX5yP+7iPQxIPJAlJvPiLvzgv/uIvzt13340kJPEvkYQkIoIv/dIv5a3e6q2QhCReGElIQhKSeCBJSEISkpCEJCQhCUn84i/+IgB93/NvIQlJRARf+qVfylu91VshCUm8qCQhie///u/nxV/8xXnxF39xJCGJ50cSkpCEJCTxQJKQhCQk8Wu/9ms8N0k86UlP4v3f//150pOehCT+rSQhie///u/nxV/8xbl06RKSkMSLQhJf//Vfz4u/+IvzcR/3cUjigV7v9V4PSZw6dYoXf/EX58Vf/MX53u/9XiQhiX8LSUjixV/8xXnxF39xXvzFXxxJSOJ/q3d/93fnRbWxscG/hyQk8f3f//28+Iu/OJcuXUISkviXSOLrv/7refEXf3E+7uM+Dkk8kCQk8eIv/uK8+Iu/OHfffTeSkMR/JEl8/dd/PS/+4i/Ox33cxyGJB3q913s9JHHq1Cle/MVfnBd/8Rfne7/3e5GEJF4Ukvje7/1eXvzFX5zv/d7vRRIvzN/8zd8gCUm83uu9Hi+IJL7+67+eF3/xF+fjPu7jkMQDvd7rvR6SOHXqFC/+4i/Oi7/4i/O93/u9SEISD/QTP/ETSEISL/7iL86Lv/iL8zu/8ztIQhL/XpKQRETwpV/6pbzVW70VkpDECyKJr//6r+fFX/zF+biP+zgk8UCSkMSLv/iL8+Iv/uLcfffdSEISz00ST3rSk3j/939/nvSkJyGJfytJSOL7v//7efEXf3Fe/MVfHElI4kUlCUm8+Iu/OC/+4i/Oj//4jyOJ+0lCEv9TSUISL/7iL86Lv/iL8+Iv/uJIQhLPjyQkIQlJSOKBJCEJSUji137t13hRSEISL/7iL86Lv/iL8+M//uNI4n6SkMS/5L777uOBJCGJ93//9+f93//9+fRP/3Qk8Td/8zf8SyTxpCc9ifd///fnSU96EpL4jyaJJz3pSbz/+78/T3rSk5DE8yMJSUhCEpJ4IElIQhKS+LVf+zWeH0l87/d+Ly/+4i/O937v9yKJF+Zv/uZvkIQkPuRDPoT/KSTxpCc9ifd///fnSU96EpJ4QSQhCUlIQhIPJAlJSEISv/Zrv8Z/NEk86UlP4v3f//150pOehCT+tSQhiRd/8RfnxV/8xXnxF39xJCGJ/0ySeNKTnsT7v//786QnPQlJ/Esk8fVf//W8+Iu/OB/3cR+HJB7o9V7v9ZDEqVOnePEXf3Fe/MVfnO/93u9FEpJ4oJ/4iZ9AEpJ48Rd/cV78xV+c3/md30ESkviXSOI7v/M7efEXf3E++IM/GEk8kCQk8eIv/uK8+Iu/OG/4hm+IJPb39/nXkoQkvv/7v58Xf/EX59KlS0hCEi8KSXz91389L/7iL87HfdzHIYkHkoQkXvzFX5wXf/EX5+6770YSkgCQhCQkIQlJPJAkJCEJSfzar/0aLwpJSOLFX/zFefEXf3F+/Md/HEncTxKSeEEk8fVf//W8+Iu/OB/3cR+HJB7o9V7v9ZDEqVOnePEXf3Fe/MVfnO/93u9FEpJ4YSQhCUlIQhIPJAlJSEISv/Zrv8a/AbJt/pUk8UC2eWEk8bVf+7V8xEd8BC8qSbwgtvmXnDx5kosXLwKwu7vLsWPHyExe5VVehT/90z/lJV/yJfmHf/gHPvADP5Bv/MZvBOD06dOcP38egHPnznHq1CnuJ4nnZpsXRBIPZJvnRxLPzzAMdF2HJP72b/+Wl3iJl+ClXuql+Nu//VsAvvEbv5EP+ZAP4bnt7Oywv78PwDAMdF3Hc5MEwGd/9mfzWZ/1WfxXkcT9bPOiesxjHsMTnvAE7mebF8XnfM7n8Nmf/dnc74//+I95pVd6Jf6r3H777dxyyy08kG3+r3m913s9fvM3f5P72ebfShL33XcfZ86cASAisA2AbZ4fSdzPNs9NEvd7tVd7NX7/93+ff4kk7meb5yYJANv8Z/igD/ogvvVbv5VhGOi6jh/4gR/g3d/93QG4++67uf766wGwzQNJAuD7v//7ebd3ezf+JZK4n22emyQAbPOi+KM/+iNe9VVfFQDbPDdJANjmhfmjP/ojXvVVXxUA2zw3SQDY5rlJAsA2ABGBbQBs88JI4rnZ5oEkAfDZn/3ZfNZnfRYvzJ//+Z/zCq/wCtzPNv+Spz3taTzsYQ/jfrZ5bpIAsM1/pE/5lE/hi7/4i7nvvvs4c+YMv/RLv8SbvumbAvD93//9vPu7vzsAtrmfJO73hV/4hXzKp3wKD/S0pz2Nhz3sYdzPNs9NEgC2+Zc87nGP48Ve7MW4n21emN///d/nNV7jNQC45ppruPfee3lRPO1pT+NhD3sY97PNc5MEgG1eEEnczzbPTRIAtnlhPuiDPohv/dZvBeDHf/zHebu3ezteGEkA2AYgIrANgG1eVJK4n22emyQAbPOCfMqnfApf/MVfzH333ceZM2f4pV/6Jd70Td8UANv8xm/8Bq//+q+PbR7ob/7mb3jpl35pAF73dV+X3/iN3+BF8Ud/9Ee86qu+KgC2eW6SALDN/zaSeCDbPD9f//Vfz0d8xEcAYJt/DUnczzbPTRIAtnl+PuVTPoUv/uIv5r777uPMmTP80i/9Em/6pm8KwPd///fz7u/+7gDY5n6SuN8XfuEX8imf8in8e33Kp3wKX/zFX8x9993HmTNn+KVf+iXe9E3fFADb/MZv/Aav//qvj20e6G/+5m946Zd+aQBe93Vfl9/4jd/gBZEEgG0AIgLbANjm+fne7/1e3uu93guA133d1+U3fuM3eG6f8imfwhd/8Rdz3333cebMGX7pl36JN33TNwXANr/xG7/B67/+62ObB/qbv/kbXvqlXxqA133d1+U3fuM3+KM/+iNe9VVfFds8N0nczzb/Gk972tN42MMexv1s89wkAWCbB/qUT/kUvviLv5j77ruPM2fO8Eu/9Eu86Zu+KQDf//3fz7u/+7sDYJv7SeJ+X/iFX8infMqnACAJANsARAS2AbDNi0oS97PNc5MEgG1ekK/8yq/k4z7u4wCwzQNJ4rnZ5oX58z//c17hFV6B+9nmP9Mf/dEf8aqv+qoA2Oa5SQLANi/MB33QB/Gt3/qtAPz4j/84b/d2b8e/xld+5VfycR/3cQDY5oEk8dxs88JI4rnZ5oEkAfDZn/3ZfNZnfRbPjyQAbAMQEdgGwDYvzJ//+Z/zCq/wCtzPNs+PJABsAxAR2AbANi/MB33QB/Gt3/qtAPz4j/84b/d2b8e/RBIAtgGICGwDYJvn53u/93t5r/d6LwA++IM/mG/6pm/iv5skAGwDEBHYBsA2/5IP+qAP4lu/9VsB+PEf/3He7u3ejv9MkgCwDUBEYBsA2/xL/uiP/ohXfdVXBcA2z00SALb5jyYJANsARAS2AbDN8/Mpn/IpfPEXfzH33XcfZ86c4Zd+6Zd40zd9UwBs8xu/8Ru8/uu/PrZ5oL/5m7/hpV/6pQF43dd9XX7jN36DP/qjP+JVX/VVsc1zk8T9bPP8fNAHfRDf+q3fyjAMdF3HD/zAD/Du7/7uANx9991cf/31ANjmgSQB8P3f//2827u9G/8SSdzPNs9NEgC2eUE+5VM+hS/+4i/mvvvu48yZM/zSL/0Sb/qmbwrA93//9/Pu7/7uANjmfpK43xd+4RfyKZ/yKTzQB33QB/Gt3/qtAPz4j/84b/d2b8e/xld+5VfycR/3cQDY5oEk8dxs89w+5VM+hS/+4i/mvvvu48yZM/zSL/0Sb/qmbwqAbX7jN36D13/918c2D/Q3f/M3vPRLvzQAr/u6r8tv/MZv8KL4oA/6IL71W78VgB//8R/n7d7u7fgPQPCfTBL/Fraxzed+7ufyr/FZn/VZSOLixYs88pGPpLXGsWPHAIgI/uRP/gSAv/3bv6W1xju+4ztyv3d7t3fjfhsbGzyQbc6cOcOL6ujoiBeFbWzzuZ/7uTw3SbzUS70UL/ESLwHA3/7t33K/e++9l+cmif39fQAuXbpE13W8MJ/92Z/N67zO63DVf45bbrmF/w9+8zd/k/8In/IpnwLA6dOnuZ9t/r1e//Vfn38NSdxvvV7z/LzES7wEAJI4d+4c/9G+9Vu/FYCu63hu119/PTfddBO2eUHe/d3fnX+JJO63Xq95fl7iJV4CAEmcO3eOf8mrvuqrArBer3l+JAHwu7/7u7wwr/qqrwrAer3m+ZEEwO/+7u/yQJ/yKZ8CQGZyP9u8KP7kT/6E52abF+SzP/uz+Ze82Zu9Gf9aD3vYw7jfer3mv9KXf/mXA3DmzBme27u/+7vT9z22ud/LvMzL8C952MMexv3W6zX/Xh/xER/B/X77t3+bf8lrvMZrcL/HP/7xvKge9rCHcb/1es2/hSTut16veW6nT59GEgC/+7u/ywvzrd/6rbyoPuVTPgWAzOR+tvnXksT91us1z89LvMRLACCJc+fO8fx88Rd/MQBnzpzhuS0WC17/9V+fc+fO8dxe6qVeiltuuQWA3/qt3+JF9aqv+qoArNdrnh9JAPzu7/4u/5u8wzu8Ay+K06dP8xEf8REAfNM3fRP/GpK433q95vl5iZd4CQAkce7cOZ7bl3/5lwNw5swZntu7v/u70/c9trnfy7zMy/Cf4Yu/+IsBOHPmDM9tsVjw+q//+pw7d47n9lIv9VLccsstAPzWb/0WL8infMqnAJCZ3M82/5L3eq/34l/yxV/8xQCcOXOG57ZYLHj91399zp07x3N7qZd6KW655RYAfuu3fouHPvShvOqrvirnzp3j+fniL/5i/q0e9rCHcb/1es2/xpd/+ZcDcObMGZ7bu7/7u9P3Pba538u8zMvw/HzKp3wKAJnJ/WzzryWJ+63Xa57b6dOnkQTA7/7u7/L8fNzHfRwf93EfB8C5c+d4bn/913/Nv9abvdmb8V/pVV/1VQFYr9c8P5IA+N3f/V1emG/91m/l3+rjPu7j+LiP+zgAzp07x3P767/+a/41/uRP/oTnZpsX5LM/+7N5fj7lUz4FgMzkfrZ5Ub3Zm70Z/5JP+ZRPASAzuZ9tXlTf+q3fyr/Gp3zKpwCQmdzPNv+S93qv9+J+X/7lX85/t0/5lE8BIDO5n23+Nb71W7+V/yqf8imfAkBmcj/b/Gu86qu+KgDr9ZrnRxIAv/u7v8t/pE/5lE8BIDO5n23+JV/8xV8MwJkzZ3hui8WC13/91+fcuXM8t5d6qZfilltuAeC3fuu3eOhDH8qrvuqrcu7cOZ6fL/7iL+Zf8q3f+q0AdF3Hc7v++uu56aabsM0L8u7v/u78SyRxv/V6zfPzEi/xEgBI4ty5czw/X/7lXw7AmTNneG7v/u7vTt/32OZ+L/MyL8O/5Fu/9Vv5t/q4j/s4Pu7jPg6Ac+fO8dz++q//mhfFF3/xFwNw5swZnttiseD1X//1OXfuHM/tpV7qpbjlllsA+K3f+i1eVN/6rd/KfwKC/wCf9VmfxWd91mfxWZ/1WXzWZ30Wn/VZn8VnfdZnIYl/r8/4jM/gmmuu4UX1uZ/7udzviU98IhHBc7PN/X7oh36I+33N13wNtrHNYrHguUniRbVYLPjX+IzP+AyuueYa7tf3PQ972MP467/+a56fG264gQf6yZ/8SR5oZ2eHF+S2227jfru7u1z1n+/666/HNle9YF/8xV/MK7/yKyOJF9XP/dzP8S/5tV/7NV5UH/ABH8D9Wmv0fc/z87mf+7nczzb/Gd70Td+U+337t387D3T77bfzL7ntttt4QT7gAz6A+7XW6Pue5+dzP/dzuZ9tXpgP+qAPAmAYBvq+57lJwjb/kg/6oA8CYBgG+r7nuUnCNs/PF3/xF/PKr/zKSOLfq7XGv+RJT3oSL8z58+e53zAMvDBPf/rTkQTAS7zES2Cbvu95fk6cOMF/hmmaeOVXfmXu9zVf8zU80Hq95oV50zd9U+739Kc/HUkAvMRLvAS26fue5+fEiRP8Wxw/fpx/jZMnT/IvefrTn44kAF7iJV4C2/R9z/Nz4sQJXhBJ3K+1Rt/3PNDXfd3Xcf78eWzzr/V2b/d2vDBf/MVfzCu/8isjiX+rD/iAD+B+rTX6vuf5+dzP/VzuZ5sX5JVf+ZW539d8zddwv9Vqxfd8z/dw6tQpXhjbvCg+6IM+CIBhGOj7nucmCdv8XyEJSUhCEpI4f/4899ve3uZF9QEf8AHcr7VG3/c8P5/7uZ/L/Wzz3KZp4pVf+ZW539d8zdfwQOv1mhfmTd/0TfmP8sqv/Mrc72u+5mu432q14nu+53s4deoUL4xtXpAv/uIv5pVf+ZWRxL/Vb/zGb/CCvPIrvzL3+5qv+Rrut1qt+J7v+R5OnTrFC2Obpz/96bz/+78/p06d4j/K05/+dCQB8BIv8RLYpu97np8TJ07w/EzTxCu/8itzv6/5mq/hgdbrNS/Mm77pmwLwxV/8xbzyK78ykvi3ksT9Wmv0fc8Dfd3XfR3nz5/HNi/Ix37sx/KVX/mVAHzzN38zp06d4rk9/OEP55ZbbuFf4/z589xvGAb+M33QB30QAMMw0Pc9z00StvnXeru3ezteVB/7sR/LV37lVwLwzd/8zZw6dYrn9vCHP5xbbrmFf6vWGv+SJz3pSTy3L/7iL+aVX/mVkcS/xfnz57nfMAw8P1/8xV/MK7/yKyOJf6+3e7u341/yxV/8xbzyK78ykvi32tzc5L/bF3/xF/PKr/zKSOI/wtu93dvxn+mLv/iLeeVXfmUk8W/xQR/0QQAMw0Df9zw3SdjmP8MXf/EX88qv/MpI4l/rlV/5lbnf13zN13C/1WrF93zP93Dq1CleGNs8/elP5/3f//05deoU/x5v+qZvyv2+/du/nQe6/fbb+ZfcdtttvCAf8AEfwP1aa/R9z/PzuZ/7udzPNs/PNE288iu/Mvf7mq/5Gh5ovV7zwrzpm74pL8zbvd3b8aL62I/9WL7yK78SgG/+5m/m1KlTPLeHP/zh3HLLLbwoXvmVX5n7fc3XfA33W61WfM/3fA+nTp3ihbHNv8Xbvd3b8R+Eyn+Az/3cz+V/gi/+4i/mX+tbv/VbecYznsEv//Iv8z/Nl3zJl/BAtpEEwAd+4AfyQG/3dm/H/b71W7+VF2Y+n3O/v/7rv+aq/3if8AmfwAPddddd/F8kiQd6zdd8Tf49Xu3VXo37/dIv/RL/kr/8y7/kfl/7tV/Lv4ck7vemb/qmRAQvyFu/9Vtzv3d913fl137t1/iP9gu/8Avc77d/+7e530d+5Efyojh//jy33HILz00S93vTN31TIoIX5K3f+q2537u+67vya7/2a7wg3/qt38oL8nVf93U80Gu+5mvygnzrt34rL8jXfd3X8UCv+ZqvyXN7tVd7Ne73S7/0S7yoXvmVX5n7vembvikRwb/knnvu4ZGPfCQvSGsNgGuuuQZJvDAPfehDud/bvd3b8YKsVisuXrzIf5ZXe7VX436/8iu/wv1uuukmnttf/dVf8UM/9EP84A/+ID/3cz/HAz30oQ/lfm/3dm/HC7Jarbh48SIvqt/8zd8EoJTCzs4O/9Ee+tCHcr+3e7u34wVZrVZcvHiR50cS93vTN31TIoLn9pEf+ZE80Gu+5mvyH+nVXu3VuN8v/dIv8a8hifu96Zu+KRHBC/LWb/3W3O9d3/Vd+bVf+zWenz/6oz/ifr/yK7/CA73ne74n/1G+9Vu/lRfk677u63ig13zN1+R/kx//8R/ngd78zd+c5/ZLv/RLtNa437u927vxopDE/d70Td+UiOAFeeu3fmvu967v+q782q/9Gs/t1V7t1bjfr/zKr3C/m266ief2V3/1V/zQD/0QP/iDP8jP/dzP8R/pj/7oj7jfr/zKr/BA7/me78m/16u92qtxv1/6pV/iP9If/dEfcb9f+ZVf4YHe8z3fkxfVt33bt/Ef6aEPfSj3e7u3eztekNVqxcWLF3lBXu3VXo37/cqv/Ar3u+mmm3huf/VXf8UP/dAP8YM/+IP83M/9HA/0aq/2atzvl37pl/jXkMT93vRN35SI4Ll95Ed+JA/0mq/5mjzQ7u4uX/VVX8X93u/93o/nZ3Nzk5MnT3LbbbcBYJt/SWsNgGuuuQZJ/Gf61m/9Vl6Qr/u6r+OBXvM1X5P/aLu7u3zVV30V93u/93s/np/NzU1OnjzJbbfdBoBtXphXfuVX5n5v+qZvSkTwL7nnnnt45CMfyXN7tVd7Ne73S7/0S/xrtNYAuOaaa5DEC/Jqr/Zq3O+XfumX+M/2aq/2atzvl37pl/jf6tVe7dW43y/90i/xP92rvdqrcb9f+qVf4l/jW7/1W3lBvu7rvo4Hes3XfE3+o73aq70a9/ulX/olXlR/9Ed/xP1+5Vd+hQd6z/d8T15U3/Zt38a/1y/8wi9wv9/+7d/mfh/5kR/Ji+L8+fPccsstPDdJ3O9N3/RNiQhekLd+67fmfu/6ru/Kr/3ar/H8vNqrvRr3+5Vf+RXud9NNN/Hc/uqv/oof+qEf4gd/8Af5uZ/7Of6j7O7u8lVf9VXc7/3e7/14fjY3Nzl58iS33XYbALZ5Qf7oj/6I+/3Kr/wKD/Se7/me/C9A8B/ANraxjW1sY5s77riD/0qXLl3i3+Lee+/lf6K3e7u347nZxjb/HmfOnOGBfuAHfoCr/mN9+Zd/Off72I/9WP6/+Nqv/Vr+Pb78y7+c+73pm74p93v3d393np/P/uzP5kXxrd/6rfxr/MIv/AL/XSTxQO/0Tu/EA33N13wN/1F+4Rd+gf8KH/ERH8Gtt94KQGbyb/URH/ER3HrrrQBkJs/Pl3/5l3O/N33TN+V+7/7u786L6hd+4Rf495LE/V7+5V+eWisvyKd+6qfyQJ/1WZ/FC3L27FkAPuuzPov/SJIA+PIv/3Ken9tuu43n513e5V34uZ/7OR7oUz/1U3mgz/qsz+IFOXv2LACf9Vmfxb/GjTfeyEMe8hBemJ/4iZ/gX+NTP/VTeaDP+qzP4gU5e/YsAJ/1WZ/FC/MLv/ALPD9f8zVfw/0yk/9oX/7lX8793vRN35T7vfu7vzv/Gr/wC7/Av4ckXpjM5AX5m7/5G2677Tb+o3zER3wEt956KwCZyf92P/dzP8fP/dzP8XM/93P83M/9HD/3cz/HNE185Ed+JP8ev/ALv8C/lSQAvvzLv5zn57bbbuP5eZd3eRd+7ud+jv8oknhhMpMX5G/+5m+47bbbeFF8+Zd/Ofd70zd9U+737u/+7jw/n/u5n8u/RBIvTGbygvzN3/wNt912G/fLTF6YT/7kT+Zf41M/9VN5oM/6rM/iBTl79iwAn/VZn8UDSQLgy7/8y3l+brvtNp6fd3mXd+Hnfu7neG5f/uVfzv3e9E3flPu9+7u/O/8av/ALv8Dz8zVf8zXcLzN5bk984hO535u+6ZtSa+X5uf322/nrv/5rXlSSuN/Lv/zLU2vlv8tHfMRHcOuttwKQmfxneOITn8j93vRN35RaK8/P7bffzl//9V/zb/ELv/AL/Ht8+Zd/Ofd70zd9U+737u/+7rwwkrjfy7/8y1Nr5QX58i//cu73pm/6ptzv3d/93fnP8OVf/uXc703f9E2537u/+7vz/Hzu534u/xN9+Zd/Ofd70zd9U+737u/+7vxP9OVf/uXc703f9E2537u/+7vz7/ERH/ER3HrrrQBkJv8ZvvzLv5z7vembvin3e/d3f3eeH0m8MJnJC/I3f/M33HbbbdwvM3lhPvmTP5kXRhIP9E7v9E480Nd8zdfwH+UXfuEX+PeQBMCXf/mX8/zcdtttPD/v8i7vws/93M/xH+mJT3wi93vTN31Taq08P7fffjt//dd/zQsjiRcmM3lB/uZv/obbbruN/yEI/hPdeOON2Oaq/1xv93ZvxwN9wAd8AP8atrnqP8YwDEjifp/8yZ/MV3zFV/D/wZkzZ3jwgx/Mv4UkHuibv/mbeaDv+77v41/yER/xEfxLvvVbv5Xn59GPfjT/U2Um9/ucz/kc/j0e/ehH85+t73v++I//mOf2oAc9CNtI4kXR9z1//Md/zHN70IMehG0k8UCSeKBv/uZv5oG+7/u+jxfkUz7lU7jfh3zIh/Af7dM+7dN4Yb7oi76I+/3kT/4kL8hLv/RLc8sttwDwzu/8zvxn+qAP+iDu9wmf8AlI4kX1RV/0RdzvJ3/yJ3lBXvqlX5pbbrkFgHd+53fmXyKJf6sP/MAP5F/yRV/0RdzvJ3/yJ3lBXvqlX5pbbrkFgHd+53fmgR796EfzovjIj/xIbGMbSbww1157Lff70R/9UV4YSTzQN3/zN/NA3/d938cL8+hHP5r/TB/0QR/E/T7hEz4BSbwoXvd1X5d/jb7v+eM//mOe24Me9CBsI4n/zT7ncz6HF+RrvuZrANjb2+NF8ehHP5r/LB/0QR/E/T7hEz4BSfx3+KAP+iDu9wmf8AlI4kXxuq/7ujw/knigb/7mb+aBvu/7vo/nxzb3e7/3ez9eFB/0QR/E/T7hEz4BSbwoXuIlXgJJ/Ef6oi/6Iu73kz/5k7wgL/3SL80tt9wCwDu/8zvzwnzQB30Q9/uET/gEJPGikMQDffM3fzMP9H3f9328MI9+9KN5UXzkR34ktrGNJB7o+7//+3nlV35l/rVe+qVfmn+NT/u0T+O/St/3/PEf/zHP7UEPehC2kcQLc+2113K/H/3RH+VF8f3f//288iu/Mv9aL/3SL80L8ymf8inc70M+5EP4t5LEA33zN38zD/R93/d9vKg+7dM+jedHEg/0zd/8zTzQ933f9/HCXHvttdzvR3/0R/mXSOKBvvmbv5kH+r7v+z6eH9vc72u/9mv57yaJB/rmb/5mHuj7vu/7+Jdce+213O9Hf/RH+c8kiQf65m/+Zh7o+77v+3hR9X3PH//xH/PcHvSgB2EbSfxHksQDffM3fzMP9H3f9328KD7ogz6I+33CJ3wCknhRvMRLvASS+I+Umdzvcz7nc/j3ePSjH81/pg/6oA/ifp/wCZ+AJP61rr32Wu73oz/6o7wovv/7v59XfuVX5l/rpV/6pXlRfNAHfRD3+4RP+AQk8aJ43dd9XV4U1157Lff70R/9Uf4DEfwXuOWWW7jqP89P/uRPctX/DL/8y7/M/d793d+dL/qiL+L/qqc//ek80GKx4NixY/xb2MY29/urv/or7vfjP/7jPD8v8zIvw/3e7u3ejhfmAz/wAymlcOzYMZ7bz/zMz/DEJz6R+9nmX/IyL/My/GexjW3u9+M//uPc7zVe4zX4t/qZn/kZnvjEJ3I/2/xLXuZlXoZ/i1d5lVdBEt/3fd/H933f9/Fv9Sqv8ipI4vu+7/v4vu/7Pl4Y29jmfn/1V3/F/X78x3+cF+bv//7vud/LvMzL8B/tVV/1VXlBfuZnfoYHepu3eRvu933f93183/d9H5KQxN/8zd/wMR/zMdjm0Y9+NP+RbGOb+z35yU/mfq/0Sq/Ei+pnfuZneKC3eZu34X7f933fx/d93/chCUn8zd/8DR/zMR+DbR796Efzr/GMZzyDf8nbv/3bc79XfuVX5oX5mZ/5GR7obd7mbbjf933f9/F93/d9SEISf/M3f8PHfMzHYJtHP/rR3O9nfuZneOITn8j9bPMfYX9/n/u99Vu/NS+MbWxzv7/6q7/ifj/+4z/OC/MzP/MzPPGJT+R+tvmXvMzLvAwvjG1sc78nP/nJ3O+VXumVeGFe+qVfmvu94Ru+If9ar/Iqr4Ikvu/7vo/v+77v43+zH/iBH+CBXuM1XoMX5KM+6qMA6LqOf8nP/MzP8MQnPpH72eZf8jIv8zK8ILaxzf2e/OQnc79XeqVX4r+KbWxzvyc/+cnc75Ve6ZV4YV76pV+a+73hG74hz49tbHO/v/qrv+J+P/7jP84L8tmf/dnc76Ve6qV4fmxjm/s9+clP5n6v9EqvxAvz0i/90tzvzJkzvDCv8iqvwv3e+q3fmn/Jz/zMz/BAb/M2b8P9vu/7vo/v+77vQxKS+Ju/+Rs+5mM+Bts8+tGP5oFsY5v7PfnJT+Z+r/RKr8SLyja2ud9f/dVfcb8f//Ef54X5mZ/5GZ74xCdyP9v8W/zIj/wID/QLv/ALvCC33HIL93vzN39z/jVe9VVflf9Kr/Iqr4Ikvu/7vo/v+77v419jf3+f+731W781L4of+ZEf4YF+4Rd+gRfklltu4X5v/uZvzgvz93//99zvZV7mZfi3so1t7vdXf/VX3O/Hf/zH+dd41Vd9VZ4f29jmfn/1V3/F/X78x3+cf8n+/j73e+u3fmv+Jbaxzf3+6q/+ivv9+I//OC/IZ3/2Z3O/Rz/60fx3s41t7vdXf/VX3O/Hf/zHeVHs7+9zv7d+67fmP5NtbHO/v/qrv+J+P/7jP86/1qu8yqsgie/7vu/j+77v+/jPZBvb3O+v/uqvuN+P//iP84LYxjb3e/KTn8z9XumVXokX5qVf+qW535kzZ3hhXuVVXoX7vfVbvzXPj21sc78f//Ef536v8Rqvwb/Vz/zMz/DEJz6R+9nmX/IyL/MyvDC2sc39nvzkJ3O/V3qlV+LfYn9/n/u99Vu/NS+KH/mRH+GBfuEXfoEX5JZbbuF+b/7mb87zYxvb3O/JT34y93ulV3olXpiXfumX5n5v+IZvyItif3+f+731W781/4GQbfOvJIkHss0L86AHPYiP//iP5yM+4iP4t7j22mu57777uJ9tnp+/+Zu/4aVf+qW5n21eEEnc75d+6Zd44zd+Y/4l1157Lffddx/3s80LI4n72eZfcu2113LfffdxP9u8KCTx7/F93/d9vPu7vzv/2SRxP9u8qB7zmMfwhCc8gfvZ5kXxOZ/zOXz2Z3829/vjP/5jXumVXon/LF3XMU0TAB/5kR/J13zN1/B/2Q/8wA/w7u/+7tzPNv9RJHG/n/mZn+Et3/IteW4v+ZIvyd/93d8BcNttt3HzzTfzgkjimmuu4d577+W5PeYxj+EJT3gC97PNv+QlX/Il+bu/+zsAXv/1X59f+7Vf4z+LJO5nmxdkuVyysbHB/f7yL/+Sl3mZl+F+j3nMY3jCE57A/WzzL3nJl3xJ/u7v/g6A13/91+fXfu3XeEE+5mM+hq/+6q/mBbn55pu57bbb+Jd8zMd8DF/91V/NC3LzzTdz22238S+RxP1+5md+hrd8y7fkBZHE/WzzggzDwGw2436/8zu/w2u+5mvy3FarFYvFgvvZ5gV5zGMewxOe8ARekK2tLQB+8Rd/kdd4jdfgv4ok7mebF9VjHvMYnvCEJ/CCbG1tAfCLv/iLvMZrvAb/GpK4n21emKOjIzY3N7mfbV6YxzzmMTzhCU/gBdna2gLgF3/xF3mN13gNnp/HPOYxPOEJT+B+tvmPIAmAN33TN+UXfuEX+NeQxP1+5md+hrd8y7fkBXnMYx7DE57wBO5nm3/JS77kS/J3f/d3ALz+678+v/Zrv8YLI4n72eaFkcT9bPOi+JiP+Ri++qu/mhfk5ptv5rbbbuN/m4jANvezzQvywR/8wXzLt3wLtvmXPOYxj+EJT3gC97PNv+QlX/Il+bu/+zsAXv/1X59f+7Vf4wWRxP1s899FEvezzQsjifvZ5kUhifv9zM/8DG/5lm/Jczs4OGB7e5v72eZFIYn72eaFkcT9bPPCvOIrviJ/9md/BsATnvAEHvWoR/HCPOYxj+EJT3gCL8jW1hYAv/iLv8hrvMZr8KKSxP1s828lifv9zM/8DG/5lm/JC/KYxzyGJzzhCdzPNv8Wkrjft37rt/IBH/ABvCCSuJ9tXpjVasViseB+tvnP9jEf8zF89Vd/NS/IzTffzG233ca/RBIAb/qmb8ov/MIv8KKQxP2+9Vu/lQ/4gA/gBZHE/WzzwkjifrZ5QYZhYDabcb/f+Z3f4TVf8zV5QSRxv5/5mZ/hLd/yLXlBVqsVi8WC+9nmRSGJ+/3Mz/wMb/mWb8kLIwmAN33TN+UXfuEX+NeSxP1+5md+hrd8y7fkuR0cHLC9vc39bPM/jSTu9zM/8zO85Vu+Jf8SSQC86Zu+Kb/wC7/AfyVJ3O9nfuZneMu3fEv+JR/zMR/DV3/1V/OC3Hzzzdx22238Z5PE/X7mZ36Gt3zLt+RFIYn72eaFkcT9bPPCvOIrviJ/9md/BsATnvAEHvWoR/EvkcT9bPOCLJdLNjY2uN9f/uVf8jIv8zLc7zGPeQxPeMITuJ9t/iUv+ZIvyd/93d8B8Pqv//r82q/9Gi+MJO5nm38LSQC86Zu+Kb/wC7/Ai0IS9/vWb/1WPuADPoAXRBL3s82LQhL3s80LI4n72eZFIQmAN33TN+UXfuEX+A9E5f+Ql3qpl+KBfvd3f5fXfM3X5Ln9yI/8CPd78Rd/cd74jd+Y/0tsc9V/rXd4h3dgmiYA7rnnHq699lr+r3v3d393/iu85Vu+Jc/P3/3d3/Gv8VM/9VM8P094whP41/q7v/s77vfpn/7p/E/wyZ/8yTzQIx7xCB7oCU94Av9af/d3f8f9Pv3TP50X5qu+6qt467d+a177tV+b5+f2229HErZ5Yb7qq76Kt37rt+a1X/u1eX5uv/12JGGbF9VbvuVb8h/hW77lW3igl3qpl+L5+ZzP+RxeVE94whN4INv8b/aEJzyBB7LNf4cP+qAP4n5f/MVfzL/kCU94Ag9km3+tJzzhCfxHk8R/lLd8y7fkhXnCE57Av9bf/d3fcb9P//RP57/bV33VV/HWb/3WvPZrvzbPz+23344kbPO/iW1eVN/yLd/Cy77sy/KieMITnsC/1t/93d9xv0//9E/nquf0lm/5ljw/r/Ear8H/JH/2Z3/G/W655Rb+JU94whN4INv8T/WWb/mWvDBPeMIT+J/scz7nc/iv9lVf9VW89Vu/Na/92q/N83P77bcjCdu8IJL43+hbvuVbeKCXeqmX4kX1lm/5lrwwn/M5n8O/11u+5VvywkjiP9JbvuVb8vy8xmu8Bvf7kR/5Ef6ne8u3fEv+JZL4n+It3/IteVF81Vd9FW/91m/Na7/2a/P83H777UjCNv9V3vIt35L/bn/2Z3/G/W655Rb+I33yJ38yD/SIRzyCB3rCE57Av9bf/d3fcb9P//RP5z+bJP6/kcR/Iir/BZ7xjGfwX8U2kgD4oi/6Il7zNV+T5/bO7/zO3O/v/u7vuOp/tsc//vFI4t/rlV7plfjP8uM//uMA2Oaq/3z7+/s80M0338wL8jM/8zMAvOqrvir/kvvuu49/yf7+Pg/02Mc+lv8sX//1X8/9+r7nhfnrv/5rHmhra4sX5L777uNfsr+/zwM99rGP5V/yWq/1WtjmfpL4t3it13otbHM/SfxrXHvttfxn+O3f/m0e6NixYzw/f/7nf879vvVbv5UX1X333cf/Jffddx//UZ7whCfwr/GEJzyB+73kS74k/xr33Xcf/1733Xcf/9F+4Rd+gX+Na6+9ln+r++67j3/J/v4+D/TYxz6W/yif8zmfw7/Va73Wa2Gb+0ni/5K+73lhbPNvcd999/Ev2d/f54Ee+9jH8n/J53zO5/Cf5ezZs9zvtttu4z/an/zJn/CiOnv2LA+0WCz417jvvvv4n+Taa6/l3+q+++7jP8IHfMAH8IL8zd/8Df8af/7nf879vvVbv5X/Kq/1Wq+Fbe4niX+rX/iFX+Df4gM+4AN4Qf7mb/6G/wy//du/zQMdO3aMF+Taa6/lX+PP//zPud+3fuu38qK49tpr+bf6hV/4Bf6znD17lvu9yqu8Cv/TXHvttfx7/MIv/AL/la699lr+rV7rtV4L29xPEv+Vrr32Wv6z/cmf/AkvqrNnz/JAi8WCf8nXf/3Xc7++73lh/vqv/5oH2tra4gW57777+Jfs7+/zQI997GP5r/QLv/AL/Ft8wAd8AC/I3/zN3/Cf6XM+53P49/iFX/gF/oMR/B8UEQD88i//MpL4/d//fQBWqxUnT57kft/wDd/A/wUPfehDueq/xy/90i8hCQDbvDAPetCD+KIv+iL+L9rY2OA/yrXXXsv9HvrQh/L87O7ucr+I4IX51m/9Vl5UEcG/ZHd3lwc6c+YM/1k+8iM/kvs96lGP4oX53d/9Xe73/d///bwwEcG/ZHd3lwc6c+YM/1q2sc0Dfc7nfA7/WraxzQN9zud8Di/Ifffdx/2GYeCFecxjHsP9HvSgB/HC/ORP/iT3++zP/mxekF//9V/nftvb2/xvc+2113K/hz70ofxP8Bd/8Rfc7yM/8iP5l/z5n/8593uTN3kT/qtFBP/d7rvvPu43DAP/GhHBv2R3d5cHOnPmDC/Mtddey/0e+tCH8sJ89md/Nvf72q/9Wv49bGObB/qcz/kc/reQxAM96lGP4j9DRPAv2d3d5YHOnDnDC3Lttddyv4c+9KH8d7n22mu530Mf+lBemM/+7M/mfl/7tV/Li+Laa6/lfg996EN5Qe68807uV2vlRXHttddyv4c+9KG8ML/8y7/M/U6dOsULc80113C/Rz/60fx3ufbaa7nfQx/6UP6t7rvvPu43DAP/GhHBv8VjHvMYXlS/+7u/y/0++7M/m3/Jr//6r3O/7e1t/rvYxjYP9Dmf8zn8R3rMYx7Di+p3f/d3ud9nf/Zn88I85jGP4X4PetCDeGF+8id/kvt99md/Ni/Mfffdx/2GYeBf8uu//uvcb3t7mxfFfffdx/2GYeA/27XXXsv9HvrQh/KC3Hnnndzv5ptv5n+a++67j/sNw8D/dPfddx/3G4aBfw/b2OaBPudzPof/LPfddx/3G4aBF9W1117L/R760IfywvzyL/8y9zt16hQvzDXXXMP9Hv3oR/Oi+MiP/Eju96hHPYoX5nd/93e53/d///fzwkQE/5Ld3V0e6MyZM7ww1157Lfd76EMfyn+VxzzmMbyofvd3f5f7ffZnfzYvimuvvZb7PfShD+WF+ezP/mzu97Vf+7X8D0Dwf8w3fdM3kZnY5u///u/50A/9UF7jNV4DSSwWC97lXd6FH/3RH8U2H/qhH8r/BU996lN5oJ/4iZ/g/7Jv+7Zv40Xx2Z/92dzvkz/5k/nP8KZv+qYA2Ob/s/d///fnP8MTnvAE/iUv+ZIvyQvzW7/1W7z92789L4pTp07xL7nlllu4n23+M9nmfn/7t3/LC/LGb/zGPNCbvdmb8cKcOnWKf8ktt9zC/WzzgrzUS70UFy9e5IX52q/9Wv4lL/VSL8XFixd5Yb72a7+Wf403fdM3pes6AH7hF36Bl3qpl+Ld3/3deUH+7M/+jBfkAz7gA3igD/mQD+FF8c7v/M7c76Ve6qX41E/9VF6QM2fO8D/NE57wBP6tzpw5w/80L/VSL8XXfM3X8MKcOXOGf69Tp07xn225XPJSL/VSfMmXfAkvzJu+6ZvSdR0Av/ALv8BLvdRL8e7v/u68MKdOneJfcsstt3A/2/xrPOEJT+BF9REf8RHc76Ve6qV49Vd/dZ7bS73US3Hx4kVemK/92q/l/4K//du/5T/DqVOn+Jfccsst3M82L6onPOEJ/E/whCc8gRfVR3zER3C/l3qpl+LVX/3V+Zc84QlP4Pm55557eKDrr7+e+73US70U3/d938e/5AlPeAIvzDd90zdxv8/6rM/iRfX4xz+e+73US70UL/VSL8WFCxd4Yc6cOcN/tCc84Qn8e73pm74pXdcB8Au/8Au81Eu9FO/+7u/OC3Pq1Cn+s33Jl3wJz89LvdRL8Yqv+Iq8MO/8zu/M/V7qpV6KT/3UT+U/0ku91Etx8eJFXpiv/dqv5d9ruVzyUi/1UnzJl3wJ/1Zf8iVfwvPzUi/1UrziK74iL8if/dmf8YJ8wAd8AA/0IR/yIbwo3vRN35Su6wD4hV/4BV7qpV6Kd3/3d+eFeed3fmfu91Iv9VJ86qd+Ki/Mm77pm9J1HQC/8Au/wEu91Evx7u/+7vxrLJdLXuqlXoov+ZIv4UXxhCc8gefnnnvu4X+LN33TN6XrOgB+4Rd+gZd6qZfi3d/93fnXWi6XvNRLvRRf8iVfwn+mN33TN6XrOgB+4Rd+gZd6qZfi3d/93XluL/VSL8XFixd5Yb72a7+W/0pv+qZvStd1APzCL/wCL/VSL8W7v/u786J4whOewAvzTd/0Tdzvsz7rs3hRPf7xj+d+L/VSL8VLvdRLceHCBZ6bbe73t3/7t7wgb/zGb8wDvdmbvRkvzKlTp/iX3HLLLdzPNv8aT3jCE/iPtlwueamXeim+5Eu+hH+rL/mSL+H5eamXeile8RVfkX/JE57wBF5UH/ERH8H9XuqlXopXf/VX519ruVzyUi/1UnzJl3wJ/0YE/8d86Id+KPd7sRd7Mb7hG74B29jGNt/wDd/AO7zDO/Cf7bd/+7f573LhwgVeVJ/1WZ/F3/zN3/B/3Q033MB/tNd4jdcAYJomXhS33XYbn/Ipn8L/BZJ4oDd90zflP8p9990HwCMf+UhKKTw/t9xyC/f70A/9UF6Qz/qsz2K5XHLy5En+I3zd130d/x1e6qVeihfmV37lV7jfp33ap3H8+HH+Pb7u676Of8ljHvMYJPG3f/u3nDx5khfmIz7iI7jfZ33WZ/FAj3nMY5DE3/7t33Ly5ElemI/4iI/gfp/1WZ/F8yOJ+737u78799vd3eVv//Zv+f7v/37+Lb7927+d+33oh34o11xzDf+ST/qkT+J+EcHf/u3f8oqv+Ir8R/isz/os/rPcd999ADzykY+klMJ/hc/6rM/ihXn3d3937vemb/qmvKgkcb+zZ8/yt3/7t7zES7wE/1E+67M+i3+vz/qsz+L5+ZRP+RTu95Zv+ZY8t8/93M/lb//2b/mkT/oknpsk7vfu7/7u3G93d5e//du/5fu///v59/i6r/s6/rXuu+8+AB75yEdSSuEFeZmXeRnu93Ef93E80N/+7d/y+7//+9zvMY95DJL427/9W06ePMkL8xEf8RHc77M+67P43+ilXuql+O/ydV/3dfxr3HfffQA88pGPpJTCf5f77rsPgEc+8pGUUnhBXuZlXob7fdzHfRwP9Ld/+7f8/u//Ps/PfffdB8AjH/lISik8P+M4cr/rr7+e+/3Wb/0Wf/u3f8sjHvEInp/77rsPgEc+8pGUUnhh7r33Xu73yq/8yrwg3/Zt38b9XuM1XoMH+tu//Vt+/dd/nZMnT/If5bM+67N4Qe677z4AHvnIR1JK4d9CEvd793d/d+63u7vL3/7t3/L93//9/Ef5rM/6LP4t7rzzTu73WZ/1Wdzvb//2b3mbt3kbXpBP+qRP4n4Rwd/+7d/yiq/4ivxHeMxjHoMk/vZv/5aTJ0/ywnzER3wE9/usz/osnp9P+ZRP4X5v+ZZvyXP73M/9XP72b/+WT/qkT+Lf6s477+R+n/VZn8X9/vZv/5a3eZu34d/i27/927nfh37oh3LNNdfwgkjifu/+7u/O/XZ3d/nbv/1bvv/7v58X5JM+6ZO4X0Twt3/7t7ziK74iz00S93v3d3937re7u8vf/u3f8v3f//080Kd8yqdwv7d8y7fkuX3u534uf/u3f8snfdIn8YLcd999ADzykY+klMLzM44j93vpl35p/qeRxP3e/d3fnfvt7u7yt3/7t3z/938/z+1TPuVTuN9bvuVb8tw+93M/l7/927/lkz7pk/iPJon7vfu7vzv3293d5W//9m/5/u//fu73mMc8Bkn87d/+LSdPnuSF+YiP+Aju91mf9Vn8Z5DE/d793d+d++3u7vK3f/u3fP/3fz8vyH333QfAIx/5SEopvDD33nsv93vlV35lXpBv+7Zv436v8RqvwQP97d/+Lb/+67/OyZMneUFe6qVeihfmV37lV7jfp33ap3H8+HH+Pb7u676Of6377rsPgEc+8pGUUvjX+pRP+RTu95Zv+ZY8t8/93M/lb//2b/mkT/ok/q3uvPNO7vdZn/VZ3O9v//ZveZu3eRuen/vuuw+ARz7ykZRSeEFe5mVehvt93Md9HA/0t3/7t/z+7/8+z+1TPuVTuN9bvuVb8tw+93M/l7/927/lkz7pk/g3IrjqP8Xv/M7v8F/pkz/5k7nfB37gB/Ki+tzP/Vz+7u/+jv/pvv7rv577PeMZz+Bf4yVf8iX5iI/4CF6QP//zP+c7vuM7WK1WvKhOnz7NX//1X2ObUgr/kmma+Jf8+Z//Od/xHd/BarXif5s3eqM34j/awx/+cCKCf8kHfMAH8IJ87ud+Lo94xCP4lm/5Fv4jfORHfiT3+9Zv/Vb+M0nifi/xEi/BC7JcLrnfYrHg8z//8/n3+siP/Eju963f+q08P6vVihfV133d1/GCrFYrXlRf93Vfx7/Gu7zLu3C/d3/3d+f5efzjH8+/JDO5X0TwDd/wDbwgf/EXf8H9Pu7jPo772eZhD3sYb/3Wb80DlVL413r0ox/N537u5/Kf4S/+4i+438Mf/nAign+NUgr/Wo9+9KP53M/9XF5Ub/RGb8QL89d//dc8P3/9138NwOu+7uvy3Eop/Gs9+tGP5nM/93P593j0ox/N537u5/JXf/VXPLd77rmH+735m785D3ThwgW++Iu/mBfFu7zLu3C/d3/3d+c/wkd+5Edyv2/91m/lX/IXf/EX3O/hD384EcEL8td//dfc7xM+4RO438bGBs9ttVrxovq6r/s6XhTf8R3fwXd8x3fwP8EznvEMHuglXuIl+O/ykR/5kdzvW7/1W3lh/uIv/oL7PfzhDyci+O/wF3/xF9zv4Q9/OBHBC/LXf/3X3O8TPuETuN/GxgYvioc//OFEBM/P3/7t33K/a6+9lvs98YlPBOCVX/mVeW5/8Rd/wf0e/vCHExG8IC/zMi/DA73CK7wCL8gHfuAHcr93eqd34n6f9EmfBECtleenlMK/1qMf/Wg+93M/l+fnL/7iL7jfwx/+cCKCf693eZd34X7v/u7vzn+kRz/60Xzu534uf/VXfwXA4x//eF4Ur/d6r8fz83d/93cAfMqnfAoP9Bd/8Rfc7+M+7uO4n20e9rCH8dZv/db8R1itVryovu7rvo5/yT333MP93vzN35wHunDhAl/8xV/M8/P4xz+eF8Xrvd7r8fz83d/9HQCf8imfwgM9/vGP51+SmdwvIviGb/gGXlTv8i7vwv3e/d3fnefnL/7iL7jfx33cx3E/2zzsYQ/jrd/6rXlh3uVd3oX7vfu7vzvPzz333MP93vzN35wHunDhAl/8xV/Mi+rhD384EcHzc8stt3C/xz72sfxLvuM7voNf/dVf5b/Du7zLu3C/d3/3d+cFueeee7jfm7/5m/NAFy5c4Iu/+Iv5r/Au7/Iu3O/d3/3deW6r1YoX1dd93dfxX+ld3uVduN+7v/u788L8xV/8Bfd7+MMfTkTwgrzMy7wMD/QKr/AKvCAf+IEfyP3e6Z3eift90id9EgC1Vp6bJO73Ei/xErwgy+WS+y0WCz7/8z+ff6+P/MiP5H7f+q3fyr/kL/7iL7jfwx/+cCKCf6177rmH+735m785D3ThwgW++Iu/mOfn8Y9/PC+K13u91+P5+bu/+zsAPuVTPoXn9hd/8Rfc7+EPfzgRwQvy13/919zvEz7hE7jfxsYGL8g999zD/d78zd+cB7pw4QJf/MVfzL8Tsm3+lSTxQLb5z3Tttddy3333cT/bvCCSAHjrt35rfuqnfor/SNdeey333Xcf97PNCyKJB7LNv+Taa6/lvvvu4362eVHt7e1x7Ngx7mebf8lXfdVX8bEf+7EcHh6ysbHBfzZJ3M82/1qSuJ9t/iWSALjtttu4+eabeUEkcb8f+7Ef4+3f/u15YV78xV+cf/iHf+C+++7jzJkzvChe4iVegr//+7/HNi+IJO73Yz/2Y7z92789/1NJ4n4/8iM/wju+4zvyH+X06dOcP3+eN33TN+UXfuEXeH4kcT/bPD+/+Iu/yJu92Zvxi7/4i7zJm7wJL4gk7mebF+Sd3/md+ZEf+RHuZ5v/TJK437u/+7vzfd/3fTw/krjf677u6/Ibv/EbPD+SuJ9tXpB3fud35kd+5Ee4n22eH0k8kG1ekO3tbQ4ODgCwzQNJ4oFs84Jsb29zcHAAgG2eH0nczzb3k0Tf96zXa56bJADuu+8+zpw5w3OTxP1uueUWnvGMZ/CCSOJ+rTUiAgBJ/PiP/zhv93ZvxwM95jGP4QlPeAIA586d49SpU7wwd911FzfeeCMAtvmPJon7nTt3jlOnTvGv8ZjHPIYnPOEJAJw7d45Tp07xwtx1113ceOONANjmBZHE/WzzwmxsbLBcLgG44447uPHGGwGQBIBtnttjHvMYnvCEJwBw7tw5Tp06xQtz1113ceONNwJgGwBJ3M82/5K77rqLG2+8EQDbPDdJ3O/g4IDNzU3ud/z4cS5dusQdd9zBjTfeyHOTxP1scz9J9H3Per3muUnifrZ5Qd75nd+ZH/mRH+F+tvmXSOJ+586d49SpU7wgkrifbe4nCQDb3E8SD2SbF2R7e5uDgwMAbPP8SOJ+j33sY/mHf/gH/jt90Ad9EN/6rd/K/S5cuMCJEyf4jyKJ+9nmBXnnd35nfuRHfoT72eaFkcT9zp07x6lTp/jvIIn7nTt3jlOnTvGCSOJ+trmfJABs8/xIAuBN3/RN+YVf+AWeH0nc79577+Waa64BQBIAtnlukrjfuXPnOHXqFC/Iy7zMy/DXf/3XAPzJn/wJr/iKr8gLIon72eZ+i8WC1WqFbZ6fxzzmMTzhCU8A4Ny5c5w6dYoX5q677uLGG28EwDbPTRL3O3fuHKdOneLfQhL3s839JNH3Pev1mucmifvZ5l9y1113ceONNwJgm/tJ4n62eW5HR0dsbm5yv1/5lV/hDd/wDQF40IMexG233YZtHkgS92utEREASOLHf/zHebu3ezv+I0jigWzzgmxvb3NwcACAbZ4fSdzv4OCAzc1N7nf8+HEuXbrEHXfcwY033shzk8T9bPPcjo6O2Nzc5H6/8iu/whu+4RsC8KAHPYjbbrsN2zw3SQDcd999nDlzhucmifvdcsstPOMZz+CFkcT9bHM/SfR9z3q95oEkcb/WGhEBgCR+/Md/nLd7u7fjuUnifra5nyT6vme9XvNAkrjfwcEBm5ub3O/48eNcunSJO+64gxtvvJEXRBIAb/qmb8ov/MIv8PxI4n62eUGuvfZa7rvvPu43DANd1/GfTRL3s839JNH3Pev1mucmifsdHBywubnJ/Y4fP86lS5e44447uPHGG/mPJon72eZ+kuj7nvV6zf0k8UC2eUG2t7c5ODgAwDb/GSRxP9vcTxJ937Ner3l+JHG/c+fOcerUKV6Ql3mZl+Gv//qvAfiTP/kTXvEVX5EXRBL3s839FosFq9UK2zw3Sdzv3d/93fm+7/s+nh9J3O91X/d1+Y3f+A2eH0nczzYvyDu/8zvzIz/yI9zPNv8SSdzv3LlznDp1in8tSdzv4OCAzc1N7nf8+HEuXbrEHXfcwY033shzk8T9bPPcjo6O2Nzc5H6/8iu/whu+4RsC8KAHPYjbbrsN2zw3Sdzv3LlznDp1ihdEEvezzf0kAWCb5yaJ+x0cHLC5ucn9jh8/zqVLl7jjjju48cYb+Tci+D/qp3/6p5GEJCQhCUlIQhKS+Ju/+Rv+Ne69915eFF/yJV/Cf7WdnR2+/uu/nvu92Zu9Gf+SH/7hH+alX/ql2djY4H+De+65hxeVJABuuukmbr75Zl4QSTzQZ33WZ/HCfMqnfAr/8A//AMA111yDJCQhCUlIQhKSkIQkJPH3f//3vDCSeKDP+qzP4n+qiOCBzpw5w3+kUgoAv/iLv8g4jjy3j/iIj+CBvuRLvoTn5+u//usBeJM3eRNemB/4gR/gfmfPnuX5OTw85Ed+5EcA+J7v+R5s81/p+7//+3l+PuIjPoL7/c3f/A2/8Ru/wQvyAz/wA9zv7NmzPD+Hh4f8yI/8CADf8z3fg21ekEc/+tEA2MY2L8zBwQHHjh3DNs/t0Y9+NAC2sc0Lc3BwwLFjx7DNv+Rbv/Vbud93fMd3ALBer/nX+oiP+Aju97u/+7s84xnP4EUVEQD80i/9EgAv/dIvzXN7/OMfz/0ykxfmIz7iI7jxxhsBsM1/tlOnTvGv9fjHP577ZSYvzEd8xEdw4403AmCbF8Vv/uZv8q9x4403AvBt3/ZtAHz91389z8/jH/947peZvDAf8REfwY033giAbe73Az/wA9zv7NmzvDAf8REfwY033giAbf4lm5ubPNClS5f4lm/5Fm688UZemG/91m/lft/xHd8BwHq95vn5gR/4Ae539uxZnp/Dw0N+5Ed+BIDv+Z7vwTb/WqdOneJF8dIv/dLc70lPehIA3//9388DPfrRjwbANrZ5YQ4ODjh27Bi2eX4+//M/n/9pvvVbv5UHOnHiBP+RfuAHfoD7nT17lufn8PCQH/mRHwHge77ne7DNv8apU6f4n+DUqVO8KF76pV+a+z3pSU8C4Pu///t5Qa655hpemI/4iI/gga655hoAPuqjPgqAr//6r+dfcurUKV6Yv/7rv+Z+119/Pf8Wq9WKV33VV+UFefzjH8/9MpMX5iM+4iO48cYbAbDNv+TUqVP8e33rt34r9/uO7/gOANbrNc/PD/zAD3C/s2fP8sJ8xEd8BDfeeCMAtvnX2Nzc5IGuvfZa7nfbbbfxDu/wDrwwEQHAL/3SLwHw0i/90vxHefSjHw2AbWzzwhwcHHDs2DFs86LY3NzkgS5dusS3fMu3cOONN/Jvsbm5yQNde+213O+2227jHd7hHfjX+oiP+Aju97u/+7s84xnP4EX1rd/6rdzvO77jOwBYr9e8MBEBwC/90i8B8NIv/dK8MN/6rd/K/b7jO74DgPV6zQuzubnJA126dIlv+ZZv4cYbb+SFueaaa3hhPuIjPoL7vembvikvzH333ccDffRHfzTL5ZL/Kt/6rd/K/b7jO74DgPV6zb9kc3OTB7p06RLf8i3fwo033sh/pm/91m/lft/xHd8BwHq95oEe/ehHA2Ab27wwBwcHHDt2DNv8Z/vWb/1W7vcd3/EdAKzXa14Up06d4oX567/+a+53/fXX82+xWq141Vd9Vf4l3//938/z8xEf8RHc72/+5m/4jd/4DV6QH/iBH+B+Z8+e5fk5PDzkR37kRwD4nu/5Hmzzr3Xq1Cn+vTY3N3mgS5cu8S3f8i3ceOON/Ftsbm7yQNdeey33u+2223iHd3gH/iWnTp3iRfHSL/3S3O9JT3oSAN///d/Pv2Rzc5MHunTpEt/yLd/CjTfeyL8Dwb/SE57wBJ7bW7zFW/A/hW1eVC/90i/N8ePHecQjHsG/xU/8xE/w3H7gB36AT/7kT+b7vu/7eCBJ/Nqv/Rq/9mu/xv7+Pv8ZPuzDPox3fMd3BOAXf/EXkcTz82u/9mtI4vz58/zVX/0V/xV+53d+hwd66Zd+af61rr32WiQBIIlf/MVf5PmRxP3e4i3egv8oT3nKU/jiL/5i/r/4wz/8Q37t136NX/u1X+PXfu3X+LVf+zW+4Au+ANs80Ou+7uvya7/2a/zar/0av/Zrv8av/dqv8cd//Mf8W917773cr+97Hugv/uIv+Pqv/3re8A3fkPt98id/Ms9NEr/0S7/Em7zJm/Avedd3fVce8pCHAHDNNdfw3D75kz+Zra0tAG655Rbe8z3fk/9sj3/843lutVYe6OEPfzhf//VfD8BrvuZr8pIv+ZK8MO/6ru/KQx7yEACuueYantsnf/Ins7W1BcAtt9zCe77ne/LCvNqrvRoAkhjHkefnZ3/2Z5EEwO7uLs/Pq73aqwEgiXEceX5+9md/FkkA7O7u8q/x67/+67z/+78/N9xwAy/IQx7yEACuueYaHug1X/M1+fqv/3oAXv7lX57XeI3X4F9imwd6/OMfz5u+6ZsC8LCHPYzn5zu+4zsAuOaaa3h+fvZnfxZJfP3Xfz3v/u7vjm3+J/uO7/gOAK655hqen5/92Z9FEl//9V/Pu7/7u2ObF0YS/xpHR0c8tw/8wA9EEh/2YR/GC/Id3/EdAFxzzTU8Pz/7sz+LJL7+67+ed3/3d8c2D/Su7/quPOQhDwHgmmuu4fn52Z/9WSTx9V//9bz7u787tnlBPvmTP5nn9uu//utIAuADP/ADeVH9+q//Ou///u/PDTfcwAvyru/6rjzkIQ8B4JprruG5ffInfzJbW1sA3HLLLbzne74n/xWe+MQn8qhHPQqAd3u3d+OBXu3VXg0ASYzjyPPzsz/7s0gCYHd3lxfkB37gB/jv9mu/9mv82q/9Gr/2a7/Gr/3ar/Hcfu3Xfo1f+7Vf49d+7df4tV/7Nf693vVd35WHPOQhAFxzzTU8t0/+5E9ma2sLgFtuuYX3fM/35P+LJz7xiTzqUY8C4N3e7d14QV77tV8bgF/8xV/kF3/xF3mgl3mZl+Hrv/7rue2223huX/u1X8uxY8f4sA/7MP49VqsVD3TzzTfzr3F0dIQkAP7gD/6AF+Y7vuM7ALjmmmt4fn72Z38WSXz913897/7u745t/qv9+q//Ou///u/PDTfcwAvyru/6rjzkIQ8B4JprruH5+dmf/Vkk8fVf//W8+7u/O7Z5bp/8yZ/M/e68807u97d/+7dIAuCv//qveW7f/M3fDMC7vdu78dxs80CPf/zjedM3fVMAHvawh/Ef5dVe7dUAkMQ4jjw/P/uzP4skAHZ3d3lhPvmTP5nn9uu//utIAuADP/ADeUE++ZM/mfvdeeed3O9v//ZvkQTAX//1X/PcvvmbvxmAd3u3d+P5echDHgLANddcwwO95mu+Jl//9V8PwMu//MvzGq/xGvxb/Pqv/zrv//7vzw033MDzY5sHevzjH8+bvumbAvCwhz2MF8Wv//qv8/7v//7ccMMNPD+f/MmfzHP79V//dSQB8IEf+IH8S177tV8bgF/8xV/kF3/xF3mgl3mZl+Hrv/7rud8rvuIr8q/xjd/4jazXa/6r/fqv/zrv//7vzw033MAL8smf/Mk8t1//9V9HEgAf+IEfyH+VX//1X+f93//9ueGGG3hur/ZqrwaAJMZx5Pn52Z/9WSQBsLu7y3+lX//1X+f93//9ueGGG/iPsFqteKCbb76Zf42joyMkAfAHf/AHPLfHP/7xPLdaKw/08Ic/nK//+q8H4DVf8zV5yZd8SV6Yd33Xd+UhD3kIANdccw3P7ZM/+ZPZ2toC4JZbbuE93/M9+a/0yZ/8yTy3X//1X0cSAB/4gR/IC/LJn/zJ3O/OO+/kfn/7t3+LJAD++q//muf2zd/8zQC827u9G//RnvjEJ/KoRz0KgHd7t3fj+fnkT/5kntuv//qvIwmAD/zAD+TfCdk2/4LHPOYxPOEJT+Bf46//+q95qZd6Kf6tJPEveYd3eAd+9Ed/lOd27bXXct999/Gv9Tqv8zr85m/+Ji/MOI78wi/8Am/zNm8DwLu/+7vzfd/3fQBIAuCP//iPeaVXeiUk8fz85V/+JS/zMi8DgCReVLZ5UYzjSN/33M8295MEwB//8R/zSq/0SvxnkcS/1md91mfx2Z/92fxLlsslGxsbANjmgb7u676Oj/zIjwTg6OiIxWLBv0QS9/uxH/sx3v7t357n5zGPeQxPeMIT+LeyzQsjifv92I/9GG//9m/Pf6fHPOYxPOEJT+Df4qVf+qX5q7/6K/6tlsslGxsbAPz4j/84b/d2b8fh4SFbW1t86Id+KN/wDd/AarVisVhwP9sAbGxssFwuOTo6YrFY8KKSxP1sAyCJ+7XWiAj+K3zQB30Q3/qt38r9vv/7v593f/d35zd/8zd5ndd5HW6//XZuueUWAI6OjlgsFryoJHE/2wBI4n6tNSKCF8U4jvR9D4BtHkgSAL/4i7/I67/+69N1HS/IOI70fQ+AbR5IEgC/+Iu/yOu//uvTdR0vjCTuZxtJAKzXa/q+5wX5nd/5HV77tV+bb/3Wb+UDPuADAJAEwNHREYvFgheVJADuu+8+rrnmGgB2d3c5duwYL8jv/M7v8Nqv/doA2AbgHd7hHfjxH/9xAH7xF3+R13/916frOv6zfMqnfApf/MVfzP1s82/1O7/zO7z2a782ALYBeId3eAd+/Md/HIBf/MVf5PVf//Xpuo5/iSTuZ5sXhSQAJJGZSOLo6IjFYsEL8zu/8zu89mu/NgC2AXiHd3gHfvzHfxyAX/zFX+T1X//16bqOF0QS97MNwDu8wzvw4z/+4wD84i/+Iq//+q9P13X8SyQB8K3f+q18wAd8AJIAWK/X9H3PCyKJ+9lGEgDr9Zq+73lhJHE/2wBI4n6tNSKCF9WnfMqn8MVf/MXczzYvzMu8zMvw13/91wDYRhIAR0dHLBYLnts4jvR9D4BtHkgSAL/4i7/I67/+69N1HS/IarVisVhwv2maKKXwX0kS/xq2+Y8gifvZBkAS92utERG8KD7lUz6FL/7iL+Z+tvnv8Cmf8il88Rd/MfezzQvzMi/zMvz1X/81ALaRBMDR0RGLxYIX5v3e7/34zu/8TgBsAyAJgKOjIxaLBZIAeOmXfmn+6q/+CkmsVitmsxnP7VM+5VP44i/+Yu5nmxfk9ttv55ZbbuF+tnlhvu3bvo0P/MAPBMA2kgA4OjpisVjwL/md3/kdXvu1XxsA2wC8wzu8Az/+4z8OwC/+4i/y+q//+nRdxwvyKZ/yKXzxF38x97PNv5Uk7mcbSQCs12v6vueFkcT9bAPwDu/wDvz4j/84AL/4i7/I67/+69N1HS/I7/zO7/Dar/3aANgGQBIAtgH4uq/7Oj7yIz8SANtIAsA2z48kAO677z6uueYaAHZ3dzl27Bj/kcZxpO97AGzzQJIA+MVf/EVe//Vfn67r+JdIAuBbv/Vb+YAP+AAkAbBer+n7nhfmd37nd3jt135tAGwDIAkA2wB83dd9HR/5kR8JgG0kAWCbF+R3fud3eO3Xfm2+9Vu/lQ/4gA8AQBIAR0dHLBYLXlSSuJ9tJAGwXq/p+57nRxIA9913H9dccw0Au7u7HDt2jOdHEvezjSQA1us1fd/z/EgC4Fu/9Vv5gA/4ACQBsF6v6fueF8X7vd/78Z3f+Z0A2AZAEs9tHEdqrbwgknig3d1ddnZ2kMR/JknczzaSAFiv1/R9zwsiCYBv/dZv5QM+4AOQBMB6vabve/6zSOJ+tpEEwHq9pu97nts4jvR9D4BtHkgSAL/4i7/I67/+69N1Hf+ZJHE/20gCYL1e0/c9z8+nfMqn8MVf/MXczzYvyO23384tt9zC/Wzzwnzbt30bH/iBHwiAbSQBcHR0xGKx4Ll90Ad9EN/6rd/K/b7/+7+fd3/3d+c3f/M3eZ3XeR1uv/12brnlFgCOjo5YLBa8qCRxP9sASOJ+rTUighfVp3zKp/DFX/zF3M82/1aSAPjWb/1WPuADPgBJAKzXa/q+54X5nd/5HV77tV8bANsASALANgBf93Vfx0d+5EcCYBtJANjmuX3Kp3wKX/zFX8z9bPPCvMzLvAx//dd/DYBtJAFwdHTEYrHgBZEEwLd+67fyAR/wAUgCYL1e0/c9/07ItvkXfPM3fzPnz5/nX+P93//9ufbaa/m3+qAP+iD+JS//8i/PB3zAB/BAkgB45CMfyROf+ERekPvuu493eId34BnPeAbPeMYzuJ9t/jVe6qVeivu967u+K5/0SZ/E/V7qpV6K+/3N3/wNz88HfdAH8aL6lm/5Fv61Pv7jP55f+7Vf435/8zd/w3+FD/qgD+Jf6y3e4i148zd/c15Uknh+brnlFp7xjGfwojo6OmK5XHLixAkighfknnvuYZom/q1uuukmXpijoyOWyyUnTpwgIvjvdunSJVpr/FucPHmS/ygv9VIvxf3+5m/+hufnjd/4jbn77ru539/8zd/wb/V5n/d5/PiP/zj3+5u/+Rv+qz3iEY/gKU95CgA//uM/ztu93dsB8Hqv93r85m/+JgC2+ff4vM/7PH78x3+c+/3N3/wN/x4v9VIvxQP9zd/8Df8WL/VSL8UD/c3f/A3/Fi/1Ui8FwF/8xV9Qa+VF9VIv9VLc72/+5m/4t3qpl3op7vc3f/M3vKg+6IM+iG/91m/lfrb5r/RSL/VSAPzN3/wN/xE+6IM+iG/91m/lfrb515LE/WzzryEJANv8a3zQB30Q3/qt38r9bPOv9VIv9VI80N/8zd/wb/Har/3aXLhwAYC//Mu/pNbKi+qlXuqlAPiLv/gLaq38a3ze530eP/7jP879/uZv/oZ/q5d6qZcC4G/+5m94Ub3US70UAJ/8yZ/Mu7zLu/CieKmXeike6G/+5m/41zh//jwAJ06cICL4r3bhwgX+NU6ePMl/pM/7vM/jx3/8x7nf3/zN3/Bv8VIv9VIA/M3f/A3/nV7qpV4KgL/5m7/hRfVSL/VSAHzyJ38y7/Iu78K/xsu//MszjiMAf/M3f8Pz81Iv9VIA/M3f/A0vzEu91EsB8Dd/8zf8S97xHd+RJz7xifzN3/wNL6qXeqmXAuAhD3kIP/3TP82/1gd90Afxrd/6rdzPNv8aL/VSLwXA3/zN3/Af4aVe6qUA+Iu/+AtqrfxrvNRLvRQP9Dd/8zf8a33e530eP/7jPw7A3/zN3/D8vOM7viNPfOIT+Zu/+Rv+JS/1Ui/F/f7mb/6G/2wv9VIvxQP9zd/8Df8Wr/3ar82FCxcA+Mu//EtqrfxrfN7nfR4//uM/DsDf/M3f8Py84zu+I0984hP5m7/5G15UL/VSL8X9/uZv/oZ/j5d6qZcC4C/+4i+otfIveamXeinu9zd/8ze8KF7qpV4KgL/4i7+g1sq/5LVf+7W5cOECAH/5l39JrZV/i4jANgC2AZDE/WzzopLEMAx0Xcd/lZd6qZcC4C/+4i+otfKieO3Xfm0uXLgAwF/+5V9Sa+W/yku91EsB8Bd/8RfUWnlRvNRLvRQP9Dd/8zf8d3ipl3opAP7iL/6CWiv/kpd6qZcC4G/+5m/4l7zjO74jT3ziE/mbv/kbXlQv9VIvBcBDHvIQfvqnf5oX5BGPeARPecpTAPjxH/9x3u7t3g6A13u91+M3f/M3AbDNv8fnfd7n8eM//uPc72/+5m/4t3qpl3opAP7mb/6Gf6/Xfu3X5sKFCwD85V/+JbVW/jU+7/M+jx//8R8H4G/+5m94ft7xHd+RJz7xifzN3/wNL8xLvdRLAfA3f/M3vKhe6qVeCoBP/uRP5l3e5V14Ubz2a782Fy5cAOAv//IvqbXyHwTZNv9HSOJ+q9WK2WzGv2S1WrFYLLjf677u6/Ibv/EbXPW/w6233sru7i73e+mXfmmuuup/O0nc70/+5E94xVd8Ra666v8rSQD0fc96veaqq6666qqrrrrqqv98krifbV5UkrDNVVf9TyKJ+/3Jn/wJr/iKr8hVV/0bINvm/whJANjmX+tBD3oQt912GwC2ueqqq6767yKJ+9nmqqv+v4oIbANgm6uuuuqqq6666qqr/n2maaK1BsBsNuP5eb3Xez1+8zd/E4C//uu/5qVe6qV4Ubz/+78/d999N7/wC7/AVVf9TyKJ+9nmqqv+jQj+j5AEwCu/8ivzb/GMZzyDq6666qr/SX7u536Oq676/+K7vuu7eJM3eROuuuqqq6666qqrrvrP03Ud8/mc+XzOt33bt/H8/OZv/ib3e+hDH8qL6ju+4zv4vM/7PK666n+qn/u5n+Oqq/4dqFx11VVXXfU/hiTu90Zv9EZcddX/B9dffz333HMPAJKwDYBtAD70Qz+Uq6666qqrrrrqqqv+fb7pm76JB3rsYx/Lc/vqr/5q7mebF5UkPvRDP5SXfdmX5aqr/ieRxP3e6I3eiKuu+ndAts3/AZK4n23+tR70oAdx2223AWCbq6666qr/auM40vc997PNVVf9fyCJB7LNer1mPp8DYJurrrrqqquuuuqqq/59JHG/6667jrvvvpsH+vqv/3o+4iM+AoCP/MiP5Gu+5mt4UUgCwDZXXfU/yTiO9H3P/Wxz1VX/DgT/R9jmfmfPnuVf42/+5m+47bbbAPiyL/syrrrqqqv+O/zlX/4lV131/90v//IvA/Cbv/mbAHzxF38xV1111VVXXXXVVVf9+/3pn/4pALa5++67eW4f8REfwf2+5mu+hhfFN37jNwIwjiNXXfU/zV/+5V9y1VX/gQj+D7ENwDXXXMNXf/VX86K4ePEiL/3SLw3A137t1/LxH//xXHXVVVf9V5KEJF75lV+ZB5KEJCRx1VX/H7zyK78yb/RGb8Qv/uIv8qZv+qYAfNInfRJXXXXVVVddddVVV/37vcIrvAIAt9xyC0dHR9zvC77gC5AEwOd+7ud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"
}
},
"cell_type": "markdown",
"id": "5e7ddad5-23f9-4c35-8836-1c38d8cc6654",
"metadata": {},
"source": [
"### Constructing the $Q_j$\n",
"\n",
"$$ \\underbrace{Q_{n-1} \\dotsb Q_0}_{Q^T} A = R $$\n",
"\n",
"Each of our $Q_j$ will have the form\n",
"\n",
"$$ \\begin{split}Q_j = \\begin{bmatrix} I_j & 0 \\\\ 0 & F \\end{bmatrix}\\end{split} $$\n",
"\n",
"where $F$ is a \"reflection\" that achieves\n",
"\n",
"$$ \\begin{split} F x = \\begin{bmatrix} \\lVert x \\rVert \\\\ 0 \\\\ 0 \\\\ \\vdots \\end{bmatrix} \\end{split} $$\n",
"\n",
"where $x$ is the column of $R$ from the diagonal down.\n",
"This transformation is a reflection across a plane with normal $v = F x - x = \\left\\lvert \\left\\lvert x \\right\\rvert \\right\\rvert e_1 - x$.\n",
"\n",
"\n",
"\n",
"The reflection, as depicted above by Trefethen and Bau (1999) can be written as $F = I - 2 \\frac{v v^T}{v^T v}$.\n",
"We want the reflector that moves $x$ the largest distance."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "28237073-426e-4550-b56f-814e6011a140",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"qr_householder (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function qr_householder(A)\n",
" m, n = size(A)\n",
" R = copy(A)\n",
" V = [] # list of reflectors\n",
" for j in 1:n\n",
" # Build v for the current column\n",
" v = copy(R[j:end, j])\n",
" v[1] += sign(v[1]) * norm(v) # Here's the fix!\n",
" v = normalize(v)\n",
" # Build and apply F\n",
" R[j:end, j:end] -= 2 * v * (v' * R[j:end,j:end])\n",
" # Keep track of the reflectors\n",
" push!(V, v)\n",
" end\n",
" V, R\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "f3369b6b-37fb-4c7d-944d-9e3d63d2c553",
"metadata": {},
"source": [
"Remember these helpers to convert $V$ to $Q$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "ef35d3fb-624b-4c69-b565-9a3976d799c9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"reflectors_to_dense (generic function with 1 method)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Here's a function to apply the reflectors V to a vector x\n",
"function reflectors_mult(V, x)\n",
" y = copy(x)\n",
" for v in reverse(V)\n",
" n = length(v) - 1\n",
" # This is applying F as we did to form R\n",
" y[end-n:end] -= 2 * v * (v' * y[end-n:end])\n",
" end\n",
" y\n",
"end\n",
"\n",
"# Create a dense matrix Q from reflectors V\n",
"function reflectors_to_dense(V)\n",
" m = length(V[1])\n",
" Q = diagm(ones(m))\n",
" # Apply the reflectors to the identity matrix to build Q\n",
" for j in 1:m\n",
" Q[:, j] = reflectors_mult(V, Q[:,j])\n",
" end\n",
" Q\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "b49955b6-96c0-4544-9987-b1c8be8d3210",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tau = [1.894427190999916, 2.0]\n",
"V1 = [[1.0, -0.2360679774997897], [1.0]]\n",
"R =\n"
]
},
{
"data": {
"text/plain": [
"2×2 Matrix{Float64}:\n",
" -2.23607e-10 1.78885e-10\n",
" 0.0 -1.34164e-10"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's try it out\n",
"A = [2 -1; -1 2] * 1e-10\n",
"\n",
"V, R = qr_householder(A)\n",
"tau = [2*v[1]^2 for v in V]\n",
"@show tau\n",
"V1 = [v ./ v[1] for v in V]\n",
"@show V1\n",
"println(\"R =\")\n",
"display(R)"
]
},
{
"cell_type": "markdown",
"id": "f4ec20a0-09df-4d1a-b26b-3e4f731009f7",
"metadata": {},
"source": [
"## Householder is backward stable\n",
"\n",
"We have finally fixed our loss of orthogonality problem!"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a3175ccc-507d-493e-8170-31b27b1cdbf5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(Q' * Q - I) = 5.932687575393109e-15\n",
"norm(Q * R - A) = 6.6179593854314975e-15\n"
]
}
],
"source": [
"# Let's try an example with Vandermonde\n",
"m = 40\n",
"x = LinRange(-1, 1, m)\n",
"A = vander(x, m)\n",
"\n",
"V, R = qr_householder(A)\n",
"Q = reflectors_to_dense(V)\n",
"@show norm(Q' * Q - I)\n",
"@show norm(Q * R - A);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "ab82859f-d8a5-414b-afcf-b91a4f74b716",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(v) = 1.4245900685395503\n"
]
},
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = 20\n",
"x = LinRange(-1, 1, a)\n",
"A = vander(x)\n",
"Q, _ = gram_schmidt_classical(A)\n",
"\n",
"v = A[:, end]\n",
"@show norm(v)\n",
"# Note, if v is actually orthogonal, these should be 0\n",
"scatter(abs.(Q[:, 1:end-1]' * v), yscale=:log10, xticks=range(1, a-1; step=2), label=\"\\$v \\\\cdot Q_{:, j}\\$\")"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "bbd0efe4-3310-4832-b374-66e4d67a9bdc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(v) = 1.4245900685395503\n"
]
},
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"V, R = qr_householder(A)\n",
"Q = reflectors_to_dense(V)\n",
"\n",
"v = A[:, end]\n",
"@show norm(v)\n",
"# Note, if v is actually orthogonal, these should be 0\n",
"scatter(abs.(Q[:, 1:end-1]' * v), yscale=:log10, xticks=range(1, a-1; step=2), label=\"\\$v \\\\cdot Q_{:, j}\\$\")"
]
},
{
"cell_type": "markdown",
"id": "894b95bc-b969-4efd-a795-7b0650410ff5",
"metadata": {},
"source": [
"## Composition of reflectors\n",
"\n",
"$$ \\begin{align}\n",
"(I - 2 v v^T) (I - 2 w w^T) &= I - 2 v v^T - 2 w w^T + 4 v (v^T w) w^T \\\\\n",
"&= I - \\Bigg[v \\Bigg| w \\Bigg] \\begin{bmatrix} 2 & -4 v^T w \\\\ 0 & 2 \\end{bmatrix} \\begin{bmatrix} v^T \\\\ w^T \\end{bmatrix}\n",
"\\end{align} $$\n",
"\n",
"This turns applying reflectors from a sequence of vector operations to a sequence of (smallish) matrix operations.\n",
"It's the key to high performance and the native format (`QRCompactWY`) returned by Julia's `qr()`."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7f3078d7-13a1-4312-9e2f-3307d2095e3b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearAlgebra.QRCompactWY{Float64, Matrix{Float64}, Matrix{Float64}}\n",
"Q factor: 20×20 LinearAlgebra.QRCompactWYQ{Float64, Matrix{Float64}, Matrix{Float64}}\n",
"R factor:\n",
"20×20 Matrix{Float64}:\n",
" -4.47214 0.0 -1.64763 0.0 … -0.514468 2.22045e-16\n",
" 0.0 2.71448 1.11022e-16 1.79412 -2.22045e-16 0.823354\n",
" 0.0 0.0 -1.46813 -4.16334e-17 -0.944961 -1.68268e-16\n",
" 0.0 0.0 0.0 -0.774796 -7.26415e-17 -0.913056\n",
" 0.0 0.0 0.0 0.0 0.797217 -2.39731e-16\n",
" 0.0 0.0 0.0 0.0 … -1.30513e-16 0.637796\n",
" 0.0 0.0 0.0 0.0 -0.455484 -5.47058e-16\n",
" 0.0 0.0 0.0 0.0 3.85024e-17 -0.313652\n",
" 0.0 0.0 0.0 0.0 -0.183132 1.28256e-15\n",
" 0.0 0.0 0.0 0.0 -2.51101e-16 0.109523\n",
" 0.0 0.0 0.0 0.0 … 0.0510878 1.68268e-15\n",
" 0.0 0.0 0.0 0.0 -8.39606e-16 0.0264553\n",
" 0.0 0.0 0.0 0.0 -0.0094344 1.00961e-15\n",
" 0.0 0.0 0.0 0.0 -4.68375e-16 0.00417208\n",
" 0.0 0.0 0.0 0.0 0.0010525 -6.32307e-16\n",
" 0.0 0.0 0.0 0.0 … -1.40892e-15 -0.000385264\n",
" 0.0 0.0 0.0 0.0 -5.9057e-5 2.88344e-16\n",
" 0.0 0.0 0.0 0.0 -4.61672e-16 -1.66202e-5\n",
" 0.0 0.0 0.0 0.0 -1.04299e-6 -9.8606e-17\n",
" 0.0 0.0 0.0 0.0 0.0 1.71467e-7"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Q, R = qr(A)"
]
},
{
"cell_type": "markdown",
"id": "07113b56-0c77-4c9c-9225-518b24bace58",
"metadata": {},
"source": [
"## Nonsquare matrices\n",
"\n",
"$QR$ factorization also works for very nonsquare matrices."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "d45be9c4-7f95-4b55-8b48-989d5f1d01e9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"size(Q) = (1000000, 1000000)\n",
"norm(Q * R - A) = 3.538426971490534e-12\n"
]
},
{
"data": {
"text/plain": [
"5×5 Matrix{Float64}:\n",
" -577.089 -432.471 -432.415 -433.388 -432.676\n",
" 0.0 -381.619 -162.868 -163.531 -163.242\n",
" 0.0 0.0 345.058 103.666 103.216\n",
" 0.0 0.0 0.0 329.259 76.1959\n",
" 0.0 0.0 0.0 0.0 -320.434"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Much, much 'longer' than 'wide'\n",
"A = rand(1000000, 5)\n",
"Q, R = qr(A)\n",
"@show size(Q)\n",
"@show norm(Q*R - A)\n",
"R"
]
},
{
"cell_type": "markdown",
"id": "80d34bc9-1a94-4f2d-b93f-62960e1c3988",
"metadata": {},
"source": [
"This is a \"full\" (or \"complete\") $QR$ factorization, in contrast to the reduced $QR$ factorization in which $Q$ has the same shape as $A$.\n",
"\n",
"How much memory does $Q$ use?\n",
"\n",
"You can compare with [`numpy.linalg.qr`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.qr.html)\n",
"\n",
"* Need to decide up-front weather you want full or reduced $QR$\n",
"\n",
"* Full $QR$ is expensive to represent"
]
},
{
"cell_type": "markdown",
"id": "1b929dc1-fffc-4b8c-9506-712e516b06d1",
"metadata": {},
"source": [
"## Cholesky $QR$\n",
"\n",
"The [**Cholesky decomposition**](https://en.wikipedia.org/wiki/Cholesky_decomposition) takes a [**Hermitian**](https://en.wikipedia.org/wiki/Hermitian_matrix), [**positive-definite**](https://en.wikipedia.org/wiki/Positive-definite_matrix) matrix and creates the lower triangular matrix $L$ such that $A = L L^T$ (more formally $A = L L^*$ where $L^*$ is the conjugate transpose, but we will stick to the real case here).\n",
"\n",
"Consider the product $A^T A$.\n",
"Using the $QR$ factorization, we have\n",
"\n",
"$$ A^T A = \\left( Q R \\right)^T Q R = R^T R $$\n",
"\n",
"so we should be able to use $A^T A = L L^T = R^T R$ to find $R$ and then use $R$ to compute $Q$ as $Q = A L^{-T}$."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "ac8addf4-f26f-4c6c-ae42-bf1f26eca379",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(Q' * Q - I) = 1.3680071283797385e-15\n",
"norm(Q * R - A) = 2.699098171834165e-16\n"
]
}
],
"source": [
"function qr_chol(A)\n",
" R = cholesky(A' * A).U\n",
" Q = A / R\n",
" Q, R\n",
"end\n",
"\n",
"A = rand(10, 4)\n",
"Q, R = qr_chol(A)\n",
"@show norm(Q' * Q - I)\n",
"@show norm(Q * R - A);"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "e3b6f5b8-b51b-4b9f-b0ec-47b502deb2d4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(Q' * Q - I) = 3.960393895764547e-5\n",
"norm(Q * R - A) = 5.044150263130546e-16\n"
]
}
],
"source": [
"# But let's pick on Vandermonde again\n",
"x = LinRange(-1, 1, 15)\n",
"A = vander(x)\n",
"Q, R = qr_chol(A)\n",
"@show norm(Q' * Q - I)\n",
"@show norm(Q * R - A);"
]
},
{
"cell_type": "markdown",
"id": "e0e5ec84-5fed-45c1-9150-82f8e48ef9a1",
"metadata": {},
"source": [
"We again see our loss of orthogonality."
]
},
{
"cell_type": "markdown",
"id": "82da497f-f645-4d3b-924e-6eaeb0f1ee85",
"metadata": {},
"source": [
"## Repairing Cholesky $QR$\n",
"\n",
"Note that the product of two triangular matrices is triangular."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "245ee292-ab0e-4270-afaf-914368eb5923",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5×5 Matrix{Float64}:\n",
" 0.622166 0.21456 0.613734 0.597838 0.964626\n",
" 0.0 0.0185025 0.343078 0.0464937 0.238227\n",
" 0.0 0.0 0.487927 0.109346 0.147878\n",
" 0.0 0.0 0.0 0.376023 0.0595793\n",
" 0.0 0.0 0.0 0.0 0.0054071"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"R = triu(rand(5,5))\n",
"R * R"
]
},
{
"cell_type": "markdown",
"id": "4ed4da37-100e-4bae-aeb5-fef272642245",
"metadata": {},
"source": [
"Let's apply this Cholesky process twice and multiply our two $R$ matrices together."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "2df953af-c79a-4883-8810-d0aae3afb1fc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"norm(Q' * Q - I) = 1.2262696169886244e-15\n",
"norm(Q * R - A) = 9.209900230881433e-16\n"
]
}
],
"source": [
"function qr_chol2(A)\n",
" Q, R = qr_chol(A) # QR factorization\n",
" Q, R1 = qr_chol(Q) # And again\n",
" Q, R1 * R\n",
"end\n",
"\n",
"x = LinRange(-1, 1, 15)\n",
"A = vander(x)\n",
"Q, R = qr_chol2(A)\n",
"@show norm(Q' * Q - I)\n",
"@show norm(Q * R - A);"
]
},
{
"cell_type": "markdown",
"id": "1b526404-725c-469c-a4ca-327ab590469b",
"metadata": {},
"source": [
"## Profiling investigation\n",
"\n",
"How fast are these methods?"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "15f609e9-cb99-4c5f-b95c-07bf1c289ca4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.243139 seconds (9 allocations: 77.396 MiB, 1.57% gc time)\n"
]
}
],
"source": [
"m, n = 5000, 2000\n",
"A = randn(m, n)\n",
"\n",
"@time qr(A);"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "649b8f16-310a-450b-93fc-9a6a51222e21",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.11/Project.toml`\n",
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.11/Manifest.toml`\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
"ProfileSVG.FGConfig(Node(FlameGraphs.NodeData(ip:0x0, 0x00, 1:200)), Dict{Symbol, Any}(), FlameGraphs.FlameColors(RGB{FixedPointNumbers.N0f8}[RGB{N0f8}(0.882,0.698,1.0), RGB{N0f8}(0.435,0.863,0.569), RGB{N0f8}(0.0,0.71,0.545), RGB{N0f8}(0.173,0.639,1.0)], RGB{N0f8}(1.0,1.0,1.0), RGB{N0f8}(0.0,0.0,0.0), RGB{FixedPointNumbers.N0f8}[RGB{N0f8}(0.953,0.0,0.302), RGB{N0f8}(0.894,0.0,0.255), RGB{N0f8}(0.831,0.129,0.216), RGB{N0f8}(0.773,0.192,0.184)], RGB{FixedPointNumbers.N0f8}[RGB{N0f8}(1.0,0.627,0.0), RGB{N0f8}(1.0,0.643,0.0), RGB{N0f8}(0.965,0.651,0.039), RGB{N0f8}(0.894,0.655,0.11)]), :fcolor, :fcolor, 1.0, false, 50, 2000, 960.0, 0.0, 2.0, \"inherit\", 12.0, false, :none, 0.001, \"Profile results\")"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Pkg\n",
"pkg\"add ProfileSVG\"\n",
"using ProfileSVG\n",
"\n",
"@profview qr(A) # Note that memory actions are expensive!"
]
},
{
"cell_type": "markdown",
"id": "3da0c7c4-5755-4fbc-b57d-9eccea2ab0b9",
"metadata": {},
"source": [
"## Profiling exploration\n",
"\n",
"Compare the profile for our different implementations of $QR$ we have seen in class.\n",
"What stands out as expensive?\n",
"\n",
"(Note, these commands are commented out as they take a while to run.)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "b9eec862-c63e-45db-ac22-60e5fb765ecc",
"metadata": {},
"outputs": [],
"source": [
"# We can adjust profiling settings\n",
"using Profile\n",
"\n",
"Profile.init() # returns the current settings\n",
"Profile.init(n = 10^5, delay = 0.001)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "edc372ae-bfaa-43c1-951d-3a87b99b3821",
"metadata": {},
"outputs": [],
"source": [
"# Let's use a smaller matrix\n",
"m, n = 5000, 200\n",
"A = randn(m, n);"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "21bfd51e-3e18-47f8-983c-0d25e3cc2cc6",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
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"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
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"text/plain": [
"ProfileSVG.FGConfig(Node(FlameGraphs.NodeData(ip:0x0, 0x00, 1:310)), Dict{Symbol, Any}(), FlameGraphs.FlameColors(RGB{FixedPointNumbers.N0f8}[RGB{N0f8}(0.882,0.698,1.0), RGB{N0f8}(0.435,0.863,0.569), RGB{N0f8}(0.0,0.71,0.545), RGB{N0f8}(0.173,0.639,1.0)], RGB{N0f8}(1.0,1.0,1.0), RGB{N0f8}(0.0,0.0,0.0), RGB{FixedPointNumbers.N0f8}[RGB{N0f8}(0.953,0.0,0.302), RGB{N0f8}(0.894,0.0,0.255), RGB{N0f8}(0.831,0.129,0.216), RGB{N0f8}(0.773,0.192,0.184)], RGB{FixedPointNumbers.N0f8}[RGB{N0f8}(1.0,0.627,0.0), RGB{N0f8}(1.0,0.643,0.0), RGB{N0f8}(0.965,0.651,0.039), RGB{N0f8}(0.894,0.655,0.11)]), :fcolor, :fcolor, 1.0, false, 50, 2000, 960.0, 0.0, 2.0, \"inherit\", 12.0, false, :none, 0.001, \"Profile results\")"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gram_schmidt_modified(A) # Run once to precompile\n",
"@profview gram_schmidt_modified(A)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "60550b8e-695f-499f-a12d-203c6ed9765a",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
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"text/html": [
"\n",
"\n",
"\n",
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]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qr_householder(A)\n",
"@profview qr_householder(A)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "ee254345-7af7-4194-af25-cca628b25c67",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
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"\n"
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]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qr_chol2(A)\n",
"@profview qr_chol2(A)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.11.6",
"language": "julia",
"name": "julia-1.11"
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