Minor refactoring before starting on velocity tracker changes.
Bug: 6413587
Change-Id: I5eba2bb57193bff78cb3740de5f87aca0b31d154
diff --git a/libs/androidfw/VelocityTracker.cpp b/libs/androidfw/VelocityTracker.cpp
new file mode 100644
index 0000000..2fb094e
--- /dev/null
+++ b/libs/androidfw/VelocityTracker.cpp
@@ -0,0 +1,444 @@
+/*
+ * Copyright (C) 2012 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#define LOG_TAG "VelocityTracker"
+//#define LOG_NDEBUG 0
+
+// Log debug messages about velocity tracking.
+#define DEBUG_VELOCITY 0
+
+// Log debug messages about least squares fitting.
+#define DEBUG_LEAST_SQUARES 0
+
+#include <math.h>
+#include <limits.h>
+
+#include <androidfw/VelocityTracker.h>
+#include <utils/BitSet.h>
+#include <utils/String8.h>
+#include <utils/Timers.h>
+
+namespace android {
+
+// --- VelocityTracker ---
+
+const uint32_t VelocityTracker::DEFAULT_DEGREE;
+const nsecs_t VelocityTracker::DEFAULT_HORIZON;
+const uint32_t VelocityTracker::HISTORY_SIZE;
+
+static inline float vectorDot(const float* a, const float* b, uint32_t m) {
+ float r = 0;
+ while (m--) {
+ r += *(a++) * *(b++);
+ }
+ return r;
+}
+
+static inline float vectorNorm(const float* a, uint32_t m) {
+ float r = 0;
+ while (m--) {
+ float t = *(a++);
+ r += t * t;
+ }
+ return sqrtf(r);
+}
+
+#if DEBUG_LEAST_SQUARES || DEBUG_VELOCITY
+static String8 vectorToString(const float* a, uint32_t m) {
+ String8 str;
+ str.append("[");
+ while (m--) {
+ str.appendFormat(" %f", *(a++));
+ if (m) {
+ str.append(",");
+ }
+ }
+ str.append(" ]");
+ return str;
+}
+
+static String8 matrixToString(const float* a, uint32_t m, uint32_t n, bool rowMajor) {
+ String8 str;
+ str.append("[");
+ for (size_t i = 0; i < m; i++) {
+ if (i) {
+ str.append(",");
+ }
+ str.append(" [");
+ for (size_t j = 0; j < n; j++) {
+ if (j) {
+ str.append(",");
+ }
+ str.appendFormat(" %f", a[rowMajor ? i * n + j : j * m + i]);
+ }
+ str.append(" ]");
+ }
+ str.append(" ]");
+ return str;
+}
+#endif
+
+VelocityTracker::VelocityTracker() {
+ clear();
+}
+
+void VelocityTracker::clear() {
+ mIndex = 0;
+ mMovements[0].idBits.clear();
+ mActivePointerId = -1;
+}
+
+void VelocityTracker::clearPointers(BitSet32 idBits) {
+ BitSet32 remainingIdBits(mMovements[mIndex].idBits.value & ~idBits.value);
+ mMovements[mIndex].idBits = remainingIdBits;
+
+ if (mActivePointerId >= 0 && idBits.hasBit(mActivePointerId)) {
+ mActivePointerId = !remainingIdBits.isEmpty() ? remainingIdBits.firstMarkedBit() : -1;
+ }
+}
+
+void VelocityTracker::addMovement(nsecs_t eventTime, BitSet32 idBits, const Position* positions) {
+ if (++mIndex == HISTORY_SIZE) {
+ mIndex = 0;
+ }
+
+ while (idBits.count() > MAX_POINTERS) {
+ idBits.clearLastMarkedBit();
+ }
+
+ Movement& movement = mMovements[mIndex];
+ movement.eventTime = eventTime;
+ movement.idBits = idBits;
+ uint32_t count = idBits.count();
+ for (uint32_t i = 0; i < count; i++) {
+ movement.positions[i] = positions[i];
+ }
+
+ if (mActivePointerId < 0 || !idBits.hasBit(mActivePointerId)) {
+ mActivePointerId = count != 0 ? idBits.firstMarkedBit() : -1;
+ }
+
+#if DEBUG_VELOCITY
+ ALOGD("VelocityTracker: addMovement eventTime=%lld, idBits=0x%08x, activePointerId=%d",
+ eventTime, idBits.value, mActivePointerId);
+ for (BitSet32 iterBits(idBits); !iterBits.isEmpty(); ) {
+ uint32_t id = iterBits.firstMarkedBit();
+ uint32_t index = idBits.getIndexOfBit(id);
+ iterBits.clearBit(id);
+ Estimator estimator;
+ getEstimator(id, DEFAULT_DEGREE, DEFAULT_HORIZON, &estimator);
+ ALOGD(" %d: position (%0.3f, %0.3f), "
+ "estimator (degree=%d, xCoeff=%s, yCoeff=%s, confidence=%f)",
+ id, positions[index].x, positions[index].y,
+ int(estimator.degree),
+ vectorToString(estimator.xCoeff, estimator.degree).string(),
+ vectorToString(estimator.yCoeff, estimator.degree).string(),
+ estimator.confidence);
+ }
+#endif
+}
+
+void VelocityTracker::addMovement(const MotionEvent* event) {
+ int32_t actionMasked = event->getActionMasked();
+
+ switch (actionMasked) {
+ case AMOTION_EVENT_ACTION_DOWN:
+ case AMOTION_EVENT_ACTION_HOVER_ENTER:
+ // Clear all pointers on down before adding the new movement.
+ clear();
+ break;
+ case AMOTION_EVENT_ACTION_POINTER_DOWN: {
+ // Start a new movement trace for a pointer that just went down.
+ // We do this on down instead of on up because the client may want to query the
+ // final velocity for a pointer that just went up.
+ BitSet32 downIdBits;
+ downIdBits.markBit(event->getPointerId(event->getActionIndex()));
+ clearPointers(downIdBits);
+ break;
+ }
+ case AMOTION_EVENT_ACTION_MOVE:
+ case AMOTION_EVENT_ACTION_HOVER_MOVE:
+ break;
+ default:
+ // Ignore all other actions because they do not convey any new information about
+ // pointer movement. We also want to preserve the last known velocity of the pointers.
+ // Note that ACTION_UP and ACTION_POINTER_UP always report the last known position
+ // of the pointers that went up. ACTION_POINTER_UP does include the new position of
+ // pointers that remained down but we will also receive an ACTION_MOVE with this
+ // information if any of them actually moved. Since we don't know how many pointers
+ // will be going up at once it makes sense to just wait for the following ACTION_MOVE
+ // before adding the movement.
+ return;
+ }
+
+ size_t pointerCount = event->getPointerCount();
+ if (pointerCount > MAX_POINTERS) {
+ pointerCount = MAX_POINTERS;
+ }
+
+ BitSet32 idBits;
+ for (size_t i = 0; i < pointerCount; i++) {
+ idBits.markBit(event->getPointerId(i));
+ }
+
+ nsecs_t eventTime;
+ Position positions[pointerCount];
+
+ size_t historySize = event->getHistorySize();
+ for (size_t h = 0; h < historySize; h++) {
+ eventTime = event->getHistoricalEventTime(h);
+ for (size_t i = 0; i < pointerCount; i++) {
+ positions[i].x = event->getHistoricalX(i, h);
+ positions[i].y = event->getHistoricalY(i, h);
+ }
+ addMovement(eventTime, idBits, positions);
+ }
+
+ eventTime = event->getEventTime();
+ for (size_t i = 0; i < pointerCount; i++) {
+ positions[i].x = event->getX(i);
+ positions[i].y = event->getY(i);
+ }
+ addMovement(eventTime, idBits, positions);
+}
+
+/**
+ * Solves a linear least squares problem to obtain a N degree polynomial that fits
+ * the specified input data as nearly as possible.
+ *
+ * Returns true if a solution is found, false otherwise.
+ *
+ * The input consists of two vectors of data points X and Y with indices 0..m-1.
+ * The output is a vector B with indices 0..n-1 that describes a polynomial
+ * that fits the data, such the sum of abs(Y[i] - (B[0] + B[1] X[i] + B[2] X[i]^2 ... B[n] X[i]^n))
+ * for all i between 0 and m-1 is minimized.
+ *
+ * That is to say, the function that generated the input data can be approximated
+ * by y(x) ~= B[0] + B[1] x + B[2] x^2 + ... + B[n] x^n.
+ *
+ * The coefficient of determination (R^2) is also returned to describe the goodness
+ * of fit of the model for the given data. It is a value between 0 and 1, where 1
+ * indicates perfect correspondence.
+ *
+ * This function first expands the X vector to a m by n matrix A such that
+ * A[i][0] = 1, A[i][1] = X[i], A[i][2] = X[i]^2, ..., A[i][n] = X[i]^n.
+ *
+ * Then it calculates the QR decomposition of A yielding an m by m orthonormal matrix Q
+ * and an m by n upper triangular matrix R. Because R is upper triangular (lower
+ * part is all zeroes), we can simplify the decomposition into an m by n matrix
+ * Q1 and a n by n matrix R1 such that A = Q1 R1.
+ *
+ * Finally we solve the system of linear equations given by R1 B = (Qtranspose Y)
+ * to find B.
+ *
+ * For efficiency, we lay out A and Q column-wise in memory because we frequently
+ * operate on the column vectors. Conversely, we lay out R row-wise.
+ *
+ * http://en.wikipedia.org/wiki/Numerical_methods_for_linear_least_squares
+ * http://en.wikipedia.org/wiki/Gram-Schmidt
+ */
+static bool solveLeastSquares(const float* x, const float* y, uint32_t m, uint32_t n,
+ float* outB, float* outDet) {
+#if DEBUG_LEAST_SQUARES
+ ALOGD("solveLeastSquares: m=%d, n=%d, x=%s, y=%s", int(m), int(n),
+ vectorToString(x, m).string(), vectorToString(y, m).string());
+#endif
+
+ // Expand the X vector to a matrix A.
+ float a[n][m]; // column-major order
+ for (uint32_t h = 0; h < m; h++) {
+ a[0][h] = 1;
+ for (uint32_t i = 1; i < n; i++) {
+ a[i][h] = a[i - 1][h] * x[h];
+ }
+ }
+#if DEBUG_LEAST_SQUARES
+ ALOGD(" - a=%s", matrixToString(&a[0][0], m, n, false /*rowMajor*/).string());
+#endif
+
+ // Apply the Gram-Schmidt process to A to obtain its QR decomposition.
+ float q[n][m]; // orthonormal basis, column-major order
+ float r[n][n]; // upper triangular matrix, row-major order
+ for (uint32_t j = 0; j < n; j++) {
+ for (uint32_t h = 0; h < m; h++) {
+ q[j][h] = a[j][h];
+ }
+ for (uint32_t i = 0; i < j; i++) {
+ float dot = vectorDot(&q[j][0], &q[i][0], m);
+ for (uint32_t h = 0; h < m; h++) {
+ q[j][h] -= dot * q[i][h];
+ }
+ }
+
+ float norm = vectorNorm(&q[j][0], m);
+ if (norm < 0.000001f) {
+ // vectors are linearly dependent or zero so no solution
+#if DEBUG_LEAST_SQUARES
+ ALOGD(" - no solution, norm=%f", norm);
+#endif
+ return false;
+ }
+
+ float invNorm = 1.0f / norm;
+ for (uint32_t h = 0; h < m; h++) {
+ q[j][h] *= invNorm;
+ }
+ for (uint32_t i = 0; i < n; i++) {
+ r[j][i] = i < j ? 0 : vectorDot(&q[j][0], &a[i][0], m);
+ }
+ }
+#if DEBUG_LEAST_SQUARES
+ ALOGD(" - q=%s", matrixToString(&q[0][0], m, n, false /*rowMajor*/).string());
+ ALOGD(" - r=%s", matrixToString(&r[0][0], n, n, true /*rowMajor*/).string());
+
+ // calculate QR, if we factored A correctly then QR should equal A
+ float qr[n][m];
+ for (uint32_t h = 0; h < m; h++) {
+ for (uint32_t i = 0; i < n; i++) {
+ qr[i][h] = 0;
+ for (uint32_t j = 0; j < n; j++) {
+ qr[i][h] += q[j][h] * r[j][i];
+ }
+ }
+ }
+ ALOGD(" - qr=%s", matrixToString(&qr[0][0], m, n, false /*rowMajor*/).string());
+#endif
+
+ // Solve R B = Qt Y to find B. This is easy because R is upper triangular.
+ // We just work from bottom-right to top-left calculating B's coefficients.
+ for (uint32_t i = n; i-- != 0; ) {
+ outB[i] = vectorDot(&q[i][0], y, m);
+ for (uint32_t j = n - 1; j > i; j--) {
+ outB[i] -= r[i][j] * outB[j];
+ }
+ outB[i] /= r[i][i];
+ }
+#if DEBUG_LEAST_SQUARES
+ ALOGD(" - b=%s", vectorToString(outB, n).string());
+#endif
+
+ // Calculate the coefficient of determination as 1 - (SSerr / SStot) where
+ // SSerr is the residual sum of squares (squared variance of the error),
+ // and SStot is the total sum of squares (squared variance of the data).
+ float ymean = 0;
+ for (uint32_t h = 0; h < m; h++) {
+ ymean += y[h];
+ }
+ ymean /= m;
+
+ float sserr = 0;
+ float sstot = 0;
+ for (uint32_t h = 0; h < m; h++) {
+ float err = y[h] - outB[0];
+ float term = 1;
+ for (uint32_t i = 1; i < n; i++) {
+ term *= x[h];
+ err -= term * outB[i];
+ }
+ sserr += err * err;
+ float var = y[h] - ymean;
+ sstot += var * var;
+ }
+ *outDet = sstot > 0.000001f ? 1.0f - (sserr / sstot) : 1;
+#if DEBUG_LEAST_SQUARES
+ ALOGD(" - sserr=%f", sserr);
+ ALOGD(" - sstot=%f", sstot);
+ ALOGD(" - det=%f", *outDet);
+#endif
+ return true;
+}
+
+bool VelocityTracker::getVelocity(uint32_t id, float* outVx, float* outVy) const {
+ Estimator estimator;
+ if (getEstimator(id, DEFAULT_DEGREE, DEFAULT_HORIZON, &estimator)) {
+ if (estimator.degree >= 1) {
+ *outVx = estimator.xCoeff[1];
+ *outVy = estimator.yCoeff[1];
+ return true;
+ }
+ }
+ *outVx = 0;
+ *outVy = 0;
+ return false;
+}
+
+bool VelocityTracker::getEstimator(uint32_t id, uint32_t degree, nsecs_t horizon,
+ Estimator* outEstimator) const {
+ outEstimator->clear();
+
+ // Iterate over movement samples in reverse time order and collect samples.
+ float x[HISTORY_SIZE];
+ float y[HISTORY_SIZE];
+ float time[HISTORY_SIZE];
+ uint32_t m = 0;
+ uint32_t index = mIndex;
+ const Movement& newestMovement = mMovements[mIndex];
+ do {
+ const Movement& movement = mMovements[index];
+ if (!movement.idBits.hasBit(id)) {
+ break;
+ }
+
+ nsecs_t age = newestMovement.eventTime - movement.eventTime;
+ if (age > horizon) {
+ break;
+ }
+
+ const Position& position = movement.getPosition(id);
+ x[m] = position.x;
+ y[m] = position.y;
+ time[m] = -age * 0.000000001f;
+ index = (index == 0 ? HISTORY_SIZE : index) - 1;
+ } while (++m < HISTORY_SIZE);
+
+ if (m == 0) {
+ return false; // no data
+ }
+
+ // Calculate a least squares polynomial fit.
+ if (degree > Estimator::MAX_DEGREE) {
+ degree = Estimator::MAX_DEGREE;
+ }
+ if (degree > m - 1) {
+ degree = m - 1;
+ }
+ if (degree >= 1) {
+ float xdet, ydet;
+ uint32_t n = degree + 1;
+ if (solveLeastSquares(time, x, m, n, outEstimator->xCoeff, &xdet)
+ && solveLeastSquares(time, y, m, n, outEstimator->yCoeff, &ydet)) {
+ outEstimator->degree = degree;
+ outEstimator->confidence = xdet * ydet;
+#if DEBUG_LEAST_SQUARES
+ ALOGD("estimate: degree=%d, xCoeff=%s, yCoeff=%s, confidence=%f",
+ int(outEstimator->degree),
+ vectorToString(outEstimator->xCoeff, n).string(),
+ vectorToString(outEstimator->yCoeff, n).string(),
+ outEstimator->confidence);
+#endif
+ return true;
+ }
+ }
+
+ // No velocity data available for this pointer, but we do have its current position.
+ outEstimator->xCoeff[0] = x[0];
+ outEstimator->yCoeff[0] = y[0];
+ outEstimator->degree = 0;
+ outEstimator->confidence = 1;
+ return true;
+}
+
+} // namespace android