// version 1.1.51 import java.util.Arrays typealias IAE = IllegalArgumentException fun seqLen(start: Int, end: Int) = when { start == end -> IntArray(end + 1) { it + 1 } start < end -> IntArray(end - start + 1) { start + it } else -> IntArray(start - end + 1) { start - it } } var baseArr: DoubleArray? = null fun compareIncrease(a: Int, b: Int): Int = baseArr!![b].compareTo(baseArr!![a]) fun compareDecrease(a: Int, b: Int): Int = baseArr!![a].compareTo(baseArr!![b]) fun order(array: DoubleArray, decreasing: Boolean): IntArray { val size = array.size var idx = IntArray(size) { it } baseArr = array.copyOf() if (!decreasing) { idx = Arrays.stream(idx) .boxed() .sorted { a, b -> compareDecrease(a, b) } .mapToInt { it } .toArray() } else { idx = Arrays.stream(idx) .boxed() .sorted { a, b -> compareIncrease(a, b) } .mapToInt { it } .toArray() } baseArr = null return idx } fun cummin(array: DoubleArray): DoubleArray { val size = array.size if (size < 1) throw IAE("cummin requires at least one element") val output = DoubleArray(size) var cumulativeMin = array[0] for (i in 0 until size) { if (array[i] < cumulativeMin) cumulativeMin = array[i] output[i] = cumulativeMin } return output } fun cummax(array: DoubleArray): DoubleArray { val size = array.size if (size < 1) throw IAE("cummax requires at least one element") val output = DoubleArray(size) var cumulativeMax = array[0] for (i in 0 until size) { if (array[i] > cumulativeMax) cumulativeMax = array[i] output[i] = cumulativeMax } return output } fun pminx(array: DoubleArray, x: Double): DoubleArray { val size = array.size if (size < 1) throw IAE("pmin requires at least one element") return DoubleArray(size) { if (array[it] < x) array[it] else x } } fun doubleSay(array: DoubleArray) { print("[ 1] %e".format(array[0])) for (i in 1 until array.size) { print(" %.10f".format(array[i])) if ((i + 1) % 5 == 0) print("\n[%2d]".format(i + 1)) } println() } fun intToDouble(array: IntArray) = DoubleArray(array.size) { array[it].toDouble() } fun doubleArrayMin(array: DoubleArray) = if (array.size < 1) throw IAE("pAdjust requires at least one element") else array.min()!! fun pAdjust(pvalues: DoubleArray, str: String): DoubleArray { val size = pvalues.size if (size < 1) throw IAE("pAdjust requires at least one element") val type = when(str.toLowerCase()) { "bh", "fdr" -> 0 "by" -> 1 "bonferroni" -> 2 "hochberg" -> 3 "holm" -> 4 "hommel" -> 5 else -> throw IAE("'$str' doesn't match any accepted FDR types") } if (type == 2) { // Bonferroni method return DoubleArray(size) { val b = pvalues[it] * size when { b >= 1 -> 1.0 0 <= b && b < 1 -> b else -> throw RuntimeException("$b is outside [0, 1)") } } } else if (type == 4) { // Holm method val o = order(pvalues, false) val o2Double = intToDouble(o) val cummaxInput = DoubleArray(size) { (size - it) * pvalues[o[it]] } val ro = order(o2Double, false) val cummaxOutput = cummax(cummaxInput) val pmin = pminx(cummaxOutput, 1.0) return DoubleArray(size) { pmin[ro[it]] } } else if (type == 5) { // Hommel method val indices = seqLen(size, size) val o = order(pvalues, false) val p = DoubleArray(size) { pvalues[o[it]] } val o2Double = intToDouble(o) val ro = order(o2Double, false) val q = DoubleArray(size) val pa = DoubleArray(size) val npi = DoubleArray(size) { p[it] * size / indices[it] } val min = doubleArrayMin(npi) q.fill(min) pa.fill(min) for (j in size - 1 downTo 2) { val ij = seqLen(1, size - j + 1) for (i in 0 until size - j + 1) ij[i]-- val i2Length = j - 1 val i2 = IntArray(i2Length) { size - j + 2 + it - 1 } val pi2Length = i2Length var q1 = j * p[i2[0]] / 2.0 for (i in 1 until pi2Length) { val temp_q1 = p[i2[i]] * j / (2.0 + i) if(temp_q1 < q1) q1 = temp_q1 } for (i in 0 until size - j + 1) { q[ij[i]] = minOf(p[ij[i]] * j, q1) } for (i in 0 until i2Length) q[i2[i]] = q[size - j] for (i in 0 until size) if (pa[i] < q[i]) pa[i] = q[i] } for (index in 0 until size) q[index] = pa[ro[index]] return q } val ni = DoubleArray(size) val o = order(pvalues, true) val oDouble = intToDouble(o) for (index in 0 until size) { if (pvalues[index] !in 0.0 .. 1.0) { throw RuntimeException("array[$index] = ${pvalues[index]} is outside [0, 1]") } ni[index] = size.toDouble() / (size - index) } val ro = order(oDouble, false) val cumminInput = DoubleArray(size) if (type == 0) { // BH method for (index in 0 until size) { cumminInput[index] = ni[index] * pvalues[o[index]] } } else if (type == 1) { // BY method var q = 0.0 for (index in 1 until size + 1) q += 1.0 / index for (index in 0 until size) { cumminInput[index] = q * ni[index] * pvalues[o[index]] } } else if (type == 3) { // Hochberg method for (index in 0 until size) { cumminInput[index] = (index + 1) * pvalues[o[index]] } } val cumminArray = cummin(cumminInput) val pmin = pminx(cumminArray, 1.0) return DoubleArray(size) { pmin[ro[it]] } } fun main(args: Array) { val pvalues = doubleArrayOf( 4.533744e-01, 7.296024e-01, 9.936026e-02, 9.079658e-02, 1.801962e-01, 8.752257e-01, 2.922222e-01, 9.115421e-01, 4.355806e-01, 5.324867e-01, 4.926798e-01, 5.802978e-01, 3.485442e-01, 7.883130e-01, 2.729308e-01, 8.502518e-01, 4.268138e-01, 6.442008e-01, 3.030266e-01, 5.001555e-02, 3.194810e-01, 7.892933e-01, 9.991834e-01, 1.745691e-01, 9.037516e-01, 1.198578e-01, 3.966083e-01, 1.403837e-02, 7.328671e-01, 6.793476e-02, 4.040730e-03, 3.033349e-04, 1.125147e-02, 2.375072e-02, 5.818542e-04, 3.075482e-04, 8.251272e-03, 1.356534e-03, 1.360696e-02, 3.764588e-04, 1.801145e-05, 2.504456e-07, 3.310253e-02, 9.427839e-03, 8.791153e-04, 2.177831e-04, 9.693054e-04, 6.610250e-05, 2.900813e-02, 5.735490e-03 ) val correctAnswers = listOf( doubleArrayOf( // Benjamini-Hochberg 6.126681e-01, 8.521710e-01, 1.987205e-01, 1.891595e-01, 3.217789e-01, 9.301450e-01, 4.870370e-01, 9.301450e-01, 6.049731e-01, 6.826753e-01, 6.482629e-01, 7.253722e-01, 5.280973e-01, 8.769926e-01, 4.705703e-01, 9.241867e-01, 6.049731e-01, 7.856107e-01, 4.887526e-01, 1.136717e-01, 4.991891e-01, 8.769926e-01, 9.991834e-01, 3.217789e-01, 9.301450e-01, 2.304958e-01, 5.832475e-01, 3.899547e-02, 8.521710e-01, 1.476843e-01, 1.683638e-02, 2.562902e-03, 3.516084e-02, 6.250189e-02, 3.636589e-03, 2.562902e-03, 2.946883e-02, 6.166064e-03, 3.899547e-02, 2.688991e-03, 4.502862e-04, 1.252228e-05, 7.881555e-02, 3.142613e-02, 4.846527e-03, 2.562902e-03, 4.846527e-03, 1.101708e-03, 7.252032e-02, 2.205958e-02 ), doubleArrayOf( // Benjamini & Yekutieli 1.000000e+00, 1.000000e+00, 8.940844e-01, 8.510676e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 5.114323e-01, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.754486e-01, 1.000000e+00, 6.644618e-01, 7.575031e-02, 1.153102e-02, 1.581959e-01, 2.812089e-01, 1.636176e-02, 1.153102e-02, 1.325863e-01, 2.774239e-02, 1.754486e-01, 1.209832e-02, 2.025930e-03, 5.634031e-05, 3.546073e-01, 1.413926e-01, 2.180552e-02, 1.153102e-02, 2.180552e-02, 4.956812e-03, 3.262838e-01, 9.925057e-02 ), doubleArrayOf( // Bonferroni 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.019185e-01, 1.000000e+00, 1.000000e+00, 2.020365e-01, 1.516674e-02, 5.625735e-01, 1.000000e+00, 2.909271e-02, 1.537741e-02, 4.125636e-01, 6.782670e-02, 6.803480e-01, 1.882294e-02, 9.005725e-04, 1.252228e-05, 1.000000e+00, 4.713920e-01, 4.395577e-02, 1.088915e-02, 4.846527e-02, 3.305125e-03, 1.000000e+00, 2.867745e-01 ), doubleArrayOf( // Hochberg 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.632662e-01, 9.991834e-01, 9.991834e-01, 1.575885e-01, 1.383967e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.383967e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01 ), doubleArrayOf( // Holm 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 1.000000e+00, 4.632662e-01, 1.000000e+00, 1.000000e+00, 1.575885e-01, 1.395341e-02, 3.938014e-01, 7.600230e-01, 2.501973e-02, 1.395341e-02, 3.052971e-01, 5.426136e-02, 4.626366e-01, 1.656419e-02, 8.825610e-04, 1.252228e-05, 9.930759e-01, 3.394022e-01, 3.692284e-02, 1.023581e-02, 3.974152e-02, 3.172920e-03, 8.992520e-01, 2.179486e-01 ), doubleArrayOf( // Hommel 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.987624e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.595180e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 9.991834e-01, 4.351895e-01, 9.991834e-01, 9.766522e-01, 1.414256e-01, 1.304340e-02, 3.530937e-01, 6.887709e-01, 2.385602e-02, 1.322457e-02, 2.722920e-01, 5.426136e-02, 4.218158e-01, 1.581127e-02, 8.825610e-04, 1.252228e-05, 8.743649e-01, 3.016908e-01, 3.516461e-02, 9.582456e-03, 3.877222e-02, 3.172920e-03, 8.122276e-01, 1.950067e-01 ) ) val types = listOf("bh", "by", "bonferroni", "hochberg", "holm", "hommel") val f = "\ntype %d = '%s' has cumulative error of %g" for (type in 0 until types.size) { val q = pAdjust(pvalues, types[type]) var error = 0.0 for (i in 0 until pvalues.size) { error += Math.abs(q[i] - correctAnswers[type][i]) } doubleSay(q) println(f.format(type, types[type], error)) } }