函數
>
數據分析
>
平滑
>
範例：平滑時間序列
範例：平滑時間序列
若時間序列數據除了數據點索引本身之外，並沒有特定的自變數，則可建構 x 軸向量，再使用平滑函數。
1.
定義向量，以描述熱流。
<region id="ID0EB3GX" top="192.00000000000003" left="19.200000000000003" xml:lang="zh_TW" height="129.84" width="131.66666666666669" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="25" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW">data</id> <matrix rows="195" cols="1" xml:lang="zh_TW"> <display size="5,1" xml:lang="zh_TW" /> <real xml:lang="zh_TW">9.206</real> <real xml:lang="zh_TW">9.3</real> <real xml:lang="zh_TW">9.278</real> <real xml:lang="zh_TW">9.175</real> <real xml:lang="zh_TW">9.275</real> <real xml:lang="zh_TW">9.289</real> <real xml:lang="zh_TW">9.287</real> <real xml:lang="zh_TW">9.261</real> <real xml:lang="zh_TW">9.303</real> <real xml:lang="zh_TW">9.276</real> <real xml:lang="zh_TW">9.273</real> <real xml:lang="zh_TW">9.288</real> <real xml:lang="zh_TW">9.256</real> <real xml:lang="zh_TW">9.252</real> <real xml:lang="zh_TW">9.298</real> <real xml:lang="zh_TW">9.267</real> <real xml:lang="zh_TW">9.257</real> <real xml:lang="zh_TW">9.278</real> <real xml:lang="zh_TW">9.248</real> <real xml:lang="zh_TW">9.35</real> <real xml:lang="zh_TW">9.276</real> <real xml:lang="zh_TW">9.279</real> <real xml:lang="zh_TW">9.267</real> <real xml:lang="zh_TW">9.246</real> <real xml:lang="zh_TW">9.238</real> <real xml:lang="zh_TW">9.269</real> <real xml:lang="zh_TW">9.248</real> <real xml:lang="zh_TW">9.257</real> <real xml:lang="zh_TW">9.268</real> <real xml:lang="zh_TW">9.288</real> <real xml:lang="zh_TW">9.258</real> <real xml:lang="zh_TW">9.286</real> <real xml:lang="zh_TW">9.251</real> <real xml:lang="zh_TW">9.257</real> <real xml:lang="zh_TW">9.268</real> <real xml:lang="zh_TW">9.291</real> <real xml:lang="zh_TW">9.219</real> <real xml:lang="zh_TW">9.27</real> <real xml:lang="zh_TW">9.219</real> <real xml:lang="zh_TW">9.241</real> <real xml:lang="zh_TW">9.27</real> <real xml:lang="zh_TW">9.227</real> <real xml:lang="zh_TW">9.259</real> <real xml:lang="zh_TW">9.286</real> <real xml:lang="zh_TW">9.32</real> <real xml:lang="zh_TW">9.328</real> <real xml:lang="zh_TW">9.263</real> <real xml:lang="zh_TW">9.248</real> <real xml:lang="zh_TW">9.239</real> <real xml:lang="zh_TW">9.225</real> <real xml:lang="zh_TW">9.221</real> <real xml:lang="zh_TW">9.271</real> <real xml:lang="zh_TW">9.252</real> <real xml:lang="zh_TW">9.281</real> <real xml:lang="zh_TW">9.271</real> <real xml:lang="zh_TW">9.295</real> <real xml:lang="zh_TW">9.302</real> <real xml:lang="zh_TW">9.279</real> <real xml:lang="zh_TW">9.237</real> <real xml:lang="zh_TW">9.234</real> <real xml:lang="zh_TW">9.245</real> <real xml:lang="zh_TW">9.222</real> <real xml:lang="zh_TW">9.207</real> <real xml:lang="zh_TW">9.259</real> <real xml:lang="zh_TW">9.276</real> <real xml:lang="zh_TW">9.269</real> <real xml:lang="zh_TW">9.257</real> <real xml:lang="zh_TW">9.265</real> <real xml:lang="zh_TW">9.296</real> <real xml:lang="zh_TW">9.293</real> <real xml:lang="zh_TW">9.264</real> <real xml:lang="zh_TW">9.281</real> <real xml:lang="zh_TW">9.267</real> <real xml:lang="zh_TW">9.301</real> <real xml:lang="zh_TW">9.253</real> <real xml:lang="zh_TW">9.261</real> <real xml:lang="zh_TW">9.238</real> <real xml:lang="zh_TW">9.225</real> <real xml:lang="zh_TW">9.236</real> <real xml:lang="zh_TW">9.24</real> <real xml:lang="zh_TW">9.264</real> <real xml:lang="zh_TW">9.244</real> <real xml:lang="zh_TW">9.278</real> <real xml:lang="zh_TW">9.311</real> <real xml:lang="zh_TW">9.262</real> <real xml:lang="zh_TW">9.26</real> <real xml:lang="zh_TW">9.253</real> <real xml:lang="zh_TW">9.246</real> <real xml:lang="zh_TW">9.284</real> <real xml:lang="zh_TW">9.251</real> <real xml:lang="zh_TW">9.275</real> <real xml:lang="zh_TW">9.255</real> <real xml:lang="zh_TW">9.28</real> <real xml:lang="zh_TW">9.275</real> <real xml:lang="zh_TW">9.262</real> <real xml:lang="zh_TW">9.275</real> <real xml:lang="zh_TW">9.252</real> <real xml:lang="zh_TW">9.23</real> <real xml:lang="zh_TW">9.255</real> <real xml:lang="zh_TW">9.269</real> <real xml:lang="zh_TW">9.29</real> <real xml:lang="zh_TW">9.274</real> <real xml:lang="zh_TW">9.256</real> <real xml:lang="zh_TW">9.262</real> <real xml:lang="zh_TW">9.25</real> <real xml:lang="zh_TW">9.262</real> <real xml:lang="zh_TW">9.264</real> <real xml:lang="zh_TW">9.265</real> <real xml:lang="zh_TW">9.242</real> <real xml:lang="zh_TW">9.24</real> <real xml:lang="zh_TW">9.222</real> <real xml:lang="zh_TW">9.242</real> <real xml:lang="zh_TW">9.215</real> <real xml:lang="zh_TW">9.286</real> <real xml:lang="zh_TW">9.272</real> <real xml:lang="zh_TW">9.266</real> <real xml:lang="zh_TW">9.285</real> <real xml:lang="zh_TW">9.269</real> <real xml:lang="zh_TW">9.268</real> <real xml:lang="zh_TW">9.246</real> <real xml:lang="zh_TW">9.231</real> <real xml:lang="zh_TW">9.241</real> <real xml:lang="zh_TW">9.261</real> <real xml:lang="zh_TW">9.274</real> <real xml:lang="zh_TW">9.292</real> <real xml:lang="zh_TW">9.271</real> <real xml:lang="zh_TW">9.267</real> <real xml:lang="zh_TW">9.309</real> <real xml:lang="zh_TW">9.264</real> <real xml:lang="zh_TW">9.279</real> <real xml:lang="zh_TW">9.255</real> <real xml:lang="zh_TW">9.229</real> <real xml:lang="zh_TW">9.253</real> <real xml:lang="zh_TW">9.256</real> <real xml:lang="zh_TW">9.263</real> <real xml:lang="zh_TW">9.22</real> <real xml:lang="zh_TW">9.258</real> <real xml:lang="zh_TW">9.268</real> <real xml:lang="zh_TW">9.268</real> <real xml:lang="zh_TW">9.249</real> <real xml:lang="zh_TW">9.235</real> <real xml:lang="zh_TW">9.243</real> <real xml:lang="zh_TW">9.253</real> <real xml:lang="zh_TW">9.263</real> <real xml:lang="zh_TW">9.243</real> <real xml:lang="zh_TW">9.261</real> <real xml:lang="zh_TW">9.26</real> <real xml:lang="zh_TW">9.253</real> <real xml:lang="zh_TW">9.241</real> <real xml:lang="zh_TW">9.239</real> <real xml:lang="zh_TW">9.264</real> <real xml:lang="zh_TW">9.243</real> <real xml:lang="zh_TW">9.247</real> <real xml:lang="zh_TW">9.252</real> <real xml:lang="zh_TW">9.262</real> <real xml:lang="zh_TW">9.247</real> <real xml:lang="zh_TW">9.306</real> <real xml:lang="zh_TW">9.238</real> <real xml:lang="zh_TW">9.249</real> <real xml:lang="zh_TW">9.257</real> <real xml:lang="zh_TW">9.266</real> <real xml:lang="zh_TW">9.299</real> <real xml:lang="zh_TW">9.245</real> <real xml:lang="zh_TW">9.287</real> <real xml:lang="zh_TW">9.301</real> <real xml:lang="zh_TW">9.257</real> <real xml:lang="zh_TW">9.271</real> <real xml:lang="zh_TW">9.275</real> <real xml:lang="zh_TW">9.282</real> <real xml:lang="zh_TW">9.253</real> <real xml:lang="zh_TW">9.269</real> <real xml:lang="zh_TW">9.282</real> <real xml:lang="zh_TW">9.278</real> <real xml:lang="zh_TW">9.285</real> <real xml:lang="zh_TW">9.24</real> <real xml:lang="zh_TW">9.268</real> <real xml:lang="zh_TW">9.248</real> <real xml:lang="zh_TW">9.225</real> <real xml:lang="zh_TW">9.231</real> <real xml:lang="zh_TW">9.27</real> <real xml:lang="zh_TW">9.265</real> <real xml:lang="zh_TW">9.284</real> <real xml:lang="zh_TW">9.281</real> <real xml:lang="zh_TW">9.263</real> <real xml:lang="zh_TW">9.292</real> <real xml:lang="zh_TW">9.252</real> <real xml:lang="zh_TW">9.244</real> <real xml:lang="zh_TW">9.283</real> <real xml:lang="zh_TW">9.18</real> <real xml:lang="zh_TW">9.231</real> <real xml:lang="zh_TW">9.233</real> <real xml:lang="zh_TW">9.235</real> <real xml:lang="zh_TW">9.217</real> <real xml:lang="zh_TW">9.274</real> <real xml:lang="zh_TW">9.274</real> </matrix> </define> </math> </region>
2.
建立大小與矩陣
data
相同的整數向量。
<region id="ID0E24GX" top="364.80000000000007" left="19.200000000000003" xml:lang="zh_TW" height="25.6" width="121.73666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="27" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">i</id> <range xml:lang="zh_TW"> <real xml:lang="zh_TW">0</real> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">last</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data</id> </apply> </range> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EN5GX" top="384.00000000000006" left="19.200000000000003" xml:lang="zh_TW" height="36.800000000000004" width="41.646666666666668" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="29" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <indexer xml:lang="zh_TW" /> <id labels="*" xml:space="preserve" xml:lang="zh_TW">x</id> <id labels="*" xml:space="preserve" xml:lang="zh_TW">i</id> </apply> <id xml:space="preserve" xml:lang="zh_TW">i</id> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
3.
視需要呼叫平滑函數，使用向量
x
作為引數。
<region id="ID0EHAHX" top="480.00000000000006" left="19.200000000000003" xml:lang="zh_TW" height="25.6" width="183.52" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="31" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">Yss</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">supsmooth</id> <sequence xml:lang="zh_TW"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">x</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data</id> </sequence> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EZAHX" top="499.20000000000005" left="19.200000000000003" xml:lang="zh_TW" height="25.6" width="186.57000000000002" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="33" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">Yks</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">ksmooth</id> <sequence xml:lang="zh_TW"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">x</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data</id> <real xml:lang="zh_TW">9</real> </sequence> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0ELBHX" top="518.40000000000009" left="19.200000000000003" xml:lang="zh_TW" height="25.6" width="183.11666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="35" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve" xml:lang="zh_TW">Yvs</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">VSmooth</id> <sequence xml:lang="zh_TW"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">data</id> <real xml:lang="zh_TW">11</real> </sequence> </apply> </define> <resultFormat xml:lang="zh_TW"> <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
4.
繪製原始數據集與平滑數據集。
<region id="ID0EADHX" top="595.2" left="0" xml:lang="zh_TW" height="312" width="621" xmlns="http://schemas.mathsoft.com/worksheet50"> <plot xml:lang="zh_TW"> <xyPlot xml:lang="zh_TW"> <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" /> <legend xml:lang="zh_TW" /> <traces xml:lang="zh_TW"> <trace resultRef="37" xml:lang="zh_TW"> <traceStyle color="#FF00008B" symbol="rhombus" line-weight="1" line-style="None" xml:lang="zh_TW">線條</traceStyle> </trace> <trace resultRef="38" xml:lang="zh_TW"> <traceStyle color="#FF0000FF" symbol="none" line-weight="2" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> <trace resultRef="39" xml:lang="zh_TW"> <traceStyle color="#FF008000" symbol="none" line-weight="2" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> <trace resultRef="40" xml:lang="zh_TW"> <traceStyle color="#FFFF0000" symbol="none" line-weight="2" line-style="Solid" xml:lang="zh_TW">線條</traceStyle> </trace> </traces> <graph-size width="501.8" height="235.2" xml:lang="zh_TW" /> <axes xml:lang="zh_TW"> <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="200" xml:lang="zh_TW"> <axisLine position="ticknumberlock" positionticmark="5" legendWidth="60.93" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">11</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <numberFormat xml:lang="zh_TW"> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> </numberFormat> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="41" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">x</id> </math> <math resultRef="42" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </startValue> <endValue xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </endValue> </xyDomain> </xAxis> <yAxis rank="1" legend-position="PlotBoundaryLeft" start="9.175" end="9.355" xml:lang="zh_TW"> <axisLine position="ticknumberlock" positionticmark="0" legendWidth="83.1233333333333" xml:lang="zh_TW" /> <axisGrid xml:lang="zh_TW"> <gridFrequency xml:lang="zh_TW">13</gridFrequency> <gridLabels display="true" xml:lang="zh_TW" /> <gridLines xml:lang="zh_TW" /> <tickMarks display="true" xml:lang="zh_TW" /> </axisGrid> <axisLabel xml:lang="zh_TW" /> <markers xml:lang="zh_TW" /> <numberFormat xml:lang="zh_TW"> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" /> </numberFormat> <plotEquations xml:lang="zh_TW"> <plotEquation xml:lang="zh_TW"> <math resultRef="43" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">data</id> </math> <math resultRef="44" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math resultRef="45" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">Yss</id> </math> <math resultRef="46" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math resultRef="47" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">Yks</id> </math> <math resultRef="48" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> <plotEquation xml:lang="zh_TW"> <math resultRef="49" xml:lang="zh_TW"> <id xml:space="preserve" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">Yvs</id> </math> <math resultRef="50" xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </math> </plotEquation> </plotEquations> <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW"> <startValue xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </startValue> <endValue xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" /> </endValue> </xyDomain> </yAxis> </axes> </xyPlot> </plot> </region>
複製運算式
