water.util.MathUtils Maven / Gradle / Ivy
package water.util;
import water.fvec.Frame;
import edu.emory.mathcs.jtransforms.dct.DoubleDCT_1D;
import edu.emory.mathcs.jtransforms.dct.DoubleDCT_2D;
import edu.emory.mathcs.jtransforms.dct.DoubleDCT_3D;
import edu.emory.mathcs.utils.ConcurrencyUtils;
import water.exceptions.H2OIllegalArgumentException;
import water.fvec.Chunk;
import water.fvec.NewChunk;
import water.fvec.Vec;
import water.MRTask;
import java.util.Arrays;
public class MathUtils {
public static double weightedSigma(long nobs, double wsum, double xSum, double xxSum) {
double reg = 1.0/wsum;
return nobs <= 1? 0 : Math.sqrt(xxSum*reg - (xSum*xSum) * reg * reg);
}
/** Fast approximate sqrt
* @return sqrt(x) with up to 5% relative error */
public static double approxSqrt(double x) {
return Double.longBitsToDouble(((Double.doubleToLongBits(x) >> 32) + 1072632448) << 31);
}
/** Fast approximate sqrt
* @return sqrt(x) with up to 5% relative error */
public static float approxSqrt(float x) {
return Float.intBitsToFloat(532483686 + (Float.floatToRawIntBits(x) >> 1));
}
/** Fast approximate 1./sqrt
* @return 1./sqrt(x) with up to 2% relative error */
public static double approxInvSqrt(double x) {
double xhalf = 0.5d*x; x = Double.longBitsToDouble(0x5fe6ec85e7de30daL - (Double.doubleToLongBits(x)>>1)); return x*(1.5d - xhalf*x*x);
}
/** Fast approximate 1./sqrt
* @return 1./sqrt(x) with up to 2% relative error */
public static float approxInvSqrt(float x) {
float xhalf = 0.5f*x; x = Float.intBitsToFloat(0x5f3759df - (Float.floatToIntBits(x)>>1)); return x*(1.5f - xhalf*x*x);
}
/** Fast approximate exp
* @return exp(x) with up to 5% relative error */
public static double approxExp(double x) {
return Double.longBitsToDouble(((long)(1512775 * x + 1072632447)) << 32);
}
/** Fast approximate log for values greater than 1, otherwise exact
* @return log(x) with up to 0.1% relative error */
public static double approxLog(double x){
if (x > 1) return ((Double.doubleToLongBits(x) >> 32) - 1072632447d) / 1512775d;
else return Math.log(x);
}
/** Fast calculation of log base 2 for integers.
* @return log base 2 of n */
public static int log2(int n) {
if (n <= 0) throw new IllegalArgumentException();
return 31 - Integer.numberOfLeadingZeros(n);
}
public static float[] div(float[] nums, float n) {
assert !Float.isInfinite(n) : "Trying to divide " + Arrays.toString(nums) + " by " + n; // Almost surely not what you want
for (int i=0; i= 0 && to <= a.length);
float result = 0;
final int cols = to-from;
final int extra=cols-cols%8;
final int multiple = (cols/8)*8-1;
float psum1 = 0, psum2 = 0, psum3 = 0, psum4 = 0;
float psum5 = 0, psum6 = 0, psum7 = 0, psum8 = 0;
for (int c = from; c < from + multiple; c += 8) {
psum1 += a[c ]*a[c ];
psum2 += a[c+1]*a[c+1];
psum3 += a[c+2]*a[c+2];
psum4 += a[c+3]*a[c+3];
psum5 += a[c+4]*a[c+4];
psum6 += a[c+5]*a[c+5];
psum7 += a[c+6]*a[c+6];
psum8 += a[c+7]*a[c+7];
}
result += psum1 + psum2 + psum3 + psum4;
result += psum5 + psum6 + psum7 + psum8;
for (int c = from + extra; c < to; ++c) {
result += a[c]*a[c];
}
return result;
}
/**
* Compare two numbers to see if they are within one ulp of the smaller decade.
* Order of the arguments does not matter.
*
* @param a First number
* @param b Second number
* @return true if a and b are essentially equal, false otherwise.
*/
public static boolean equalsWithinOneSmallUlp(float a, float b) {
float ulp_a = Math.ulp(a);
float ulp_b = Math.ulp(b);
float small_ulp = Math.min(ulp_a, ulp_b);
float absdiff_a_b = Math.abs(a - b); // subtraction order does not matter, due to IEEE 754 spec
return absdiff_a_b <= small_ulp;
}
public static boolean equalsWithinOneSmallUlp(double a, double b) {
double ulp_a = Math.ulp(a);
double ulp_b = Math.ulp(b);
double small_ulp = Math.min(ulp_a, ulp_b);
double absdiff_a_b = Math.abs(a - b); // subtraction order does not matter, due to IEEE 754 spec
return absdiff_a_b <= small_ulp;
}
/** Compare 2 doubles within a tolerance
* @param a double
* @param b double
* @param abseps - Absolute allowed tolerance
* @param releps - Relative allowed tolerance
* @return true if equal within tolerances */
public static boolean compare(double a, double b, double abseps, double releps) {
return
Double.compare(a, b) == 0 || // check for equality
Math.abs(a-b)/Math.max(a,b) < releps || // check for small relative error
Math.abs(a - b) <= abseps; // check for small absolute error
}
// some common Vec ops
public static double innerProduct(double [] x, double [] y){
double result = 0;
for (int i = 0; i < x.length; i++)
result += x[i] * y[i];
return result;
}
public static double l2norm2(double [] x){
double sum = 0;
for(double d:x)
sum += d*d;
return sum;
}
public static double l1norm(double [] x){
double sum = 0;
for(double d:x)
sum += d >= 0?d:-d;
return sum;
}
public static double l2norm(double [] x){
return Math.sqrt(l2norm2(x));
}
public static double [] wadd(double [] x, double [] y, double w){
for(int i = 0; i < x.length; ++i)
x[i] += w*y[i];
return x;
}
//First 1229 primes (up to 10000)
public static final long[] PRIMES = {
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973
};
public static double roundToNDigits(double d, int n) {
if(d == 0)return d;
int log = (int)Math.log10(d);
int exp = n;
exp -= log;
int ival = (int)(Math.round(d * Math.pow(10,exp)));
return ival/Math.pow(10,exp);
}
public enum Norm {L1,L2,L2_2,L_Infinite}
public static double[] min_max_mean_stddev(long[] counts) {
double min = Float.MAX_VALUE;
double max = Float.MIN_VALUE;
double mean = 0;
for (long tmp : counts) {
min = Math.min(tmp, min);
max = Math.max(tmp, max);
mean += tmp;
}
mean /= counts.length;
double stddev = 0;
for (long tmp : counts) {
stddev += Math.pow(tmp - mean, 2);
}
stddev /= counts.length;
stddev = Math.sqrt(stddev);
return new double[] {min,max,mean,stddev};
}
public static double sign(double d) {
if(d == 0)return 0;
return d < 0?-1:1;
}
public static class DCT {
public static void initCheck(Frame input, int width, int height, int depth) {
ConcurrencyUtils.setNumberOfThreads(1);
if (width < 1 || height < 1 || depth < 1)
throw new H2OIllegalArgumentException("dimensions must be >= 1");
if (width*height*depth != input.numCols())
throw new H2OIllegalArgumentException("dimensions HxWxD must match the # columns of the frame");
for (Vec v : input.vecs()) {
if (v.naCnt() > 0)
throw new H2OIllegalArgumentException("DCT can not be computed on rows with missing values");
if (!v.isNumeric())
throw new H2OIllegalArgumentException("DCT can only be computed on numeric columns");
}
}
/**
* Compute the 1D discrete cosine transform for each row in the given Frame, and return a new Frame
*
* @param input Frame containing numeric columns with data samples
* @param N Number of samples (must be less or equal than number of columns)
* @param inverse Whether to compute the inverse
* @return Frame containing 1D (inverse) DCT of each row (same dimensionality)
*/
public static Frame transform1D(Frame input, final int N, final boolean inverse) {
initCheck(input, N, 1, 1);
return new MRTask() {
@Override
public void map(Chunk[] cs, NewChunk[] ncs) {
double[] a = new double[N];
for (int row = 0; row < cs[0]._len; ++row) {
// fill 1D array
for (int i = 0; i < N; ++i)
a[i] = cs[i].atd(row);
// compute DCT for each row
if (!inverse)
new DoubleDCT_1D(N).forward(a, true);
else
new DoubleDCT_1D(N).inverse(a, true);
// write result to NewChunk
for (int i = 0; i < N; ++i)
ncs[i].addNum(a[i]);
}
}
}.doAll(input.numCols(), input).outputFrame();
}
/**
* Compute the 2D discrete cosine transform for each row in the given Frame, and return a new Frame
*
* @param input Frame containing numeric columns with data samples
* @param height height
* @param width width
* @param inverse Whether to compute the inverse
* @return Frame containing 2D DCT of each row (same dimensionality)
*/
public static Frame transform2D(Frame input, final int height, final int width, final boolean inverse) {
initCheck(input, height, width, 1);
return new MRTask() {
@Override
public void map(Chunk[] cs, NewChunk[] ncs) {
double[][] a = new double[height][width];
// each row is a 2D sample
for (int row = 0; row < cs[0]._len; ++row) {
for (int i = 0; i < height; ++i)
for (int j = 0; j < width; ++j)
a[i][j] = cs[i * width + j].atd(row);
// compute 2D DCT
if (!inverse)
new DoubleDCT_2D(height, width).forward(a, true);
else
new DoubleDCT_2D(height, width).inverse(a, true);
// write result to NewChunk
for (int i = 0; i < height; ++i)
for (int j = 0; j < width; ++j)
ncs[i * width + j].addNum(a[i][j]);
}
}
}.doAll(height * width, input).outputFrame();
}
/**
* Compute the 3D discrete cosine transform for each row in the given Frame, and return a new Frame
*
* @param input Frame containing numeric columns with data samples
* @param height height
* @param width width
* @param depth depth
* @param inverse Whether to compute the inverse
* @return Frame containing 3D DCT of each row (same dimensionality)
*/
public static Frame transform3D(Frame input, final int height, final int width, final int depth, final boolean inverse) {
initCheck(input, height, width, depth);
return new MRTask() {
@Override
public void map(Chunk[] cs, NewChunk[] ncs) {
double[][][] a = new double[height][width][depth];
// each row is a 3D sample
for (int row = 0; row < cs[0]._len; ++row) {
for (int i = 0; i < height; ++i)
for (int j = 0; j < width; ++j)
for (int k = 0; k < depth; ++k)
a[i][j][k] = cs[i*(width*depth) + j*depth + k].atd(row);
// compute 3D DCT
if (!inverse)
new DoubleDCT_3D(height, width, depth).forward(a, true);
else
new DoubleDCT_3D(height, width, depth).inverse(a, true);
// write result to NewChunk
for (int i = 0; i < height; ++i)
for (int j = 0; j < width; ++j)
for (int k = 0; k < depth; ++k)
ncs[i*(width*depth) + j*depth + k].addNum(a[i][j][k]);
}
}
}.doAll(height*width*depth, input).outputFrame();
}
}
public static class SquareError extends MRTask {
public double _sum;
@Override public void map( Chunk resp, Chunk pred ) {
double sum = 0;
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