Scalable Performance Analysis Using Statistical Clustering
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1 Scalable Performance Analysis Using Statistical Clustering Adam Bordelon, Rob Fowler, Bradley Broom, and Ken Kennedy Department of Computer Science Rice University
2 Supercomputers need Super Tools Parallel systems and applications are constantly increasing in scale and complexity We can profile these systems with very low overhead and generate detailed performance data What can we do with all this data to make it useful to the human analyst?
3 Current Tools Don t Scale
4 Scalable Data Management Problem 1: Find performance anomalies without bogging down a single node Assume numerous performance profiles each stored locally on its compute node Strategy: Take advantage of the inherent similarities in performance between individual nodes. Exploit the resources of the parallel system to scalably manage data aggregation and comparison.
5 Approach 1. Sample Profiles: Sample a random subset of nodes and retrieve full performance profiles from these nodes. 2. Generate Summary: Using these full profiles, estimate the average system profile. Based on user or performance-defined bounds, generate an application performance summary with detailed performance data in the code regions of interest, and only higher-level information for less important regions. 3. Distributed Diff: Broadcast the performance summary to the unsampled nodes. They locally compare their performance against the summary and return key differences to the user-side tool.
6 Scalable Data Analysis Problem 2: Finding complex performance patterns in large-scale data HPCToolkit performance data output Hierarchical format with aggregate measures at each level of source construct Measured performance counter values listed for each metric on each node at each level What do we want to find? Application performance characteristics System variation across nodes Anomalies (app bugs, system effects)
7 Statistical Clustering Similarity measure defines clustering 1-way: k-means, hierarchical, geneshaving, etc 2-way: biclustering constant values, coherent values or biclusters with coherent evolutions structures: single biclusters, overlapping or not overlapping biclusters, etc
8 Performance Data Analysis Transform the data to 2D matrix Rows: Source code regions Columns: Processors (or threads) Values: Performance metrics Run the performance matrix through one of the clustering algorithms Output should give us: Subspace clusters: Groups of code regions that behave similarly on sets of nodes Node partitions: high/low performance
9 Cluster 1: 62% of variance in Sweep3D Weight Clone ID sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep:535 c I-inflows for block (i=i0 boundary) c if (ew_rcv.ne. 0) then call rcv_real(ew_rcv, phiib, nib, ew_tag, info) else if (i2.lt.0.or. ibc.eq.0) then do mi = 1, mmi do lk = 1, nk do j = 1, jt phiib(j,lk,mi) = 0.0d+0 ` if (ew_snd.ne. 0) then call snd_real(ew_snd, phiib, nib, ew_tag, info) c nmess = nmess + 1 c mess = mess + nib else if (i2.lt.0.and. ibc.ne.0) then leak = 0.0 do mi = 1, mmi m = mi + mio do lk = 1, nk k = k0 + sign(lk-1,k2) do j = 1, jt phiibc(j,k,m,k3,j3) = phiib(j,lk,mi) leak = leak & + wmu(m)*phiib(j,lk,mi)*dj(j)*dk(k) leakage(1+i3) = leakage(1+i3) + leak else leak = 0.0 do mi = 1, mmi m = mi + mio do lk = 1, nk k = k0 + sign(lk-1,k2) do j = 1, jt leak =leak+ wmu(m)*phiib(j,lk,mi)*dj(j)*dk(k) leakage(1+i3) = leakage(1+i3) + leak endif endif
10 Cluster 2: 36% of variance Weight Clone ID sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep: sweep.f,sweep:574 c J-inflows for block (j=j0 boundary) c if (ns_rcv.ne. 0) then call rcv_real(ns_rcv, phijb, njb, ns_tag, info) else if (j2.lt.0.or. jbc.eq.0) then do mi = 1, mmi do lk = 1, nk do i = 1, it phijb(i,lk,mi) = 0.0d+0 if (ns_snd.ne. 0) then call snd_real(ns_snd, phijb, njb, ns_tag, info) c nmess = nmess + 1 c mess = mess + njb else if (j2.lt.0.and. jbc.ne.0) then leak = 0.0 do mi = 1, mmi m = mi + mio do lk = 1, nk k = k0 + sign(lk-1,k2) do i = 1, it phijbc(i,k,m,k3) = phijb(i,lk,mi) leak = leak + weta(m)*phijb(i,lk,mi)*di(i)*dk(k) leakage(3+j3) = leakage(3+j3) + leak else leak = 0.0 do mi = 1, mmi m = mi + mio do lk = 1, nk k = k0 + sign(lk-1,k2) do i = 1, it leak = leak + weta(m)*phijb(i,lk,mi)*di(i)*dk(k) leakage(3+j3) = leakage(3+j3) + leak endif endif
11 Cluster 3: 1% of variance Weight Clone ID sweep.f,sweep: sweep.f,sweep: sweep.f,sweep:445 c fixup i,j, & k if negative ifixed = continue if (ti.lt. 0.0d+0) then dl = dl - ci ti = 1.0 / dl ql = ql - 0.5d+0*ci*phiir phi(i) = ql * ti ti = 0.0d+0 if (tj.ne. 0.0d+0) tj=2.0d+0*phi(i) -phijb(i,lk,mi) if (tk.ne. 0.0d+0) tk=2.0d+0*phi(i) - phikb(i,j,mi) ifixed = 1 endif if (tj.lt. 0.0d+0) then dl = dl - cj tj = 1.0 / dl ql = ql - 0.5d+0*cj*phijb(i,lk,mi) phi(i) = ql * tj tj = 0.0d+0 if (tk.ne. 0.) tk = 2.0d+0*phi(i) - phikb(i,j,mi) if (ti.ne. 0.)ti = 2.0d+0*phi(i) - phiir ifixed = 1 go to 111 endif if (tk.lt. 0.0d+0) then c and it continues See cluster 4.
12 Cluster 4: 0.8% of variance Weight Clone ID initialize.f,initxs: sweep.f,sweep: sweep.f,sweep: initialize.f,initxs: sweep.f,sweep:452 Initialize.f do k = 1+k_l, kt-k_r do j_g = max(1+j_l,jstart), min(jt_g-j_r,jstop) do i_g = max(1+i_l,istart), min(it_g-i_r,istop) j = j_g - jstart + 1 i = i_g - istart + 1 Srcx(i,j,k) = 1.0d+0 Sweep.f if (tk.lt. 0.0d+0) then dl = dl - ck tk = 1.0 / dl ql = ql - 0.5d+0*ck*phikb(i,j,mi) phi(i) = ql * tk tk = 0.0d+0 if (ti.ne. 0.0d+0) ti = 2.0d+0*phi(i) - phiir if (tj.ne. 0.0d+0) tj = 2.0d+0*phi(i)-phijb(i,lk,mi) ifixed = 1 go to 111 endif
13 Future Work Integrate with Eclipse PTP Explore other clustering algorithms Adapt to other performance data types Communication data Multiple metrics Parallelize clustering
14 Conclusions As parallel systems and applications scale up, performance analysis tools must adapt their strategies to scale with the data. We can take advantage of statistical techniques like sampling and clustering to scalably manage and analyze large-scale performance data.
15 Thanks! Questions? This material is based on work supported by the National Science Foundation under Grant No. EIA and Grant No. CNS , and the Department of Energy under Contract Nos G, , , and/or from the Los Alamos National Laboratory.
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