blocks|key|1453888|text|它指的是在单个步骤中对数字列表或“向量”执行单个数学运算的能力。你经常会在Fortran中看到它，因为它与科学计算有关，而科学计算与超级计算有关，向量化算术最早出现在超级计算中。如今，几乎所有的桌面CPU都通过像Intel的SSE这样的技术提供某种形式的矢量化算法。GPU还提供了一种矢量化算法。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1453889|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

It refers to a the ability to do single mathematical operation on a list -- or "vector" -- of numbers in a single step. You see it often with Fortran because that's associated with scientific computing, which is associated with supercomputing, where vectorized arithmetic first appeared. Nowadays almost all desktop CPUs offer some form of vectorized arithmetic, through technologies like Intel's SSE. GPUs also offer a form of vectorized arithmetic.

blocks|key|1453915|text|请参阅上面的两个答案。我只想补充说，想要进行向量化的原因是，这些操作可以很容易地在超级计算机和多处理器上并行执行，从而产生巨大的性能增益。在单处理器计算机上，不会有任何性能提升。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1453916|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

See the two answers above. I just wanted to add that the reason for wanting to do vectorization is that these operations can easily be performed in paraell by supercomputers and multi-processors, yielding a big performance gain. On single processor computers there will be no performance gain.

blocks|key|1239054|text|矢量化是将标量程序转换为矢量程序的术语。矢量化程序可以从一条指令运行多个操作，而标量一次只能对操作数对进行操作。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1239055|来自wikipedia|offset|length|1239056|标量方法：|1239057|for+(i+=+0;+i+<+1024;+i%2B%2B)
{
+++C[i]+=+A[i]*B[i];
}|code-block|syntax|javascript|1239058|矢量化方法：|1239059|for+(i+=+0;+i+<+1024;+i%2B=4)
{
+++C[i:i%2B3]+=+A[i:i%2B3]*B[i:i%2B3];
}|1239060|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Vectorization_(computer_science))^0|0|2|9|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|Y|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|Z|8|@]|9|@$D|10|E|11|1|12]]|A|$]]|$1|F|3|G|5|6|7|13|8|@]|9|@]|A|$]]|$1|H|3|I|5|J|7|14|8|@]|9|@]|A|$K|L]]|$1|M|3|N|5|6|7|15|8|@]|9|@]|A|$]]|$1|O|3|P|5|J|7|16|8|@]|9|@]|A|$K|L]]|$1|Q|3|-4|5|6|7|17|8|@]|9|@]|A|$]]]|R|$S|$5|T|U|V|A|$W|X]]]]

Vectorization is the term for converting a scalar program to a vector program. Vectorized programs can run multiple operations from a single instruction, whereas scalar can only operate on pairs of operands at once.

From <a href="http://en.wikipedia.org/wiki/Vectorization_(computer_science)" rel="noreferrer">wikipedia</a>:

Scalar approach:

<pre><code>for (i = 0; i &lt; 1024; i++)
{
 C[i] = A[i]*B[i];
}
</code></pre>

Vectorized approach:

<pre><code>for (i = 0; i &lt; 1024; i+=4)
{
 C[i:i+3] = A[i:i+3]*B[i:i+3];
}
</code></pre>

blocks|key|1454002|text|简单地说，矢量化意味着优化算法，以便它可以在处理器中利用SIMD指令。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1454003|AVX、AVX2和AVX512是在一条指令中对多个数据执行相同操作的指令集(英特尔)。例如。AVX512表示一次可以操作16个整数值(4个字节)。这意味着，如果你有16个整数的向量，你想把每个整数的值加倍，然后再加上10。您可以将值加载到通用寄存器a、b、c+16次并执行相同的操作，也可以通过将所有16个值加载到SIMD寄存器xmm、ymm并执行一次操作来执行相同的操作。这可以加快矢量数据的计算速度。|1454004|在矢量化中，我们利用这一点作为我们的优势，通过重塑我们的数据，以便我们可以对其执行SIMD操作，并加快程序速度。|1454005|矢量化唯一的问题是处理条件。因为条件是执行流程的分支。这可以通过屏蔽来处理。通过将条件建模为算术运算。例如：如果我们想在value上加10，如果它大于100。我们两个都可以。|1454006|if(x[i]+>+100)+x[i]+%2B=+10;+//+this+will+branch+execution+flow.|code-block|syntax|javascript|1454007|或者我们可以将条件建模为创建条件向量c的算术运算，|1454008|c[i]+=+x[i]+>+100;+//+storing+the+condition+on+masking+vector
x[i]+=+x[i]+%2B+(c[i]+&+10)+//+using+mask|1454009|这是一个非常琐碎的例子。因此，c是我们的掩蔽向量，我们使用它来根据它的值执行二进制操作。这避免了执行流的分支，并实现了矢量化。|1454010|向量化和并行化一样重要。因此，我们应该尽可能地利用它。所有现代处理器都有针对繁重计算工作负载的SIMD指令。我们可以使用矢量化来优化我们的代码以使用这些SIMD指令，这类似于将我们的代码并行化以在现代处理器上可用的多个内核上运行。|1454011|最后我想提一下OpenMP，它可以让你使用编译指示向量化代码。我认为这是一个很好的起点。OpenACC也是如此。|1454012|entityMap^0|0|0|0|0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|Y|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|Z|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|10|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|11|8|@]|9|@]|A|$]]|$1|H|3|I|5|J|7|12|8|@]|9|@]|A|$K|L]]|$1|M|3|N|5|6|7|13|8|@]|9|@]|A|$]]|$1|O|3|P|5|J|7|14|8|@]|9|@]|A|$K|L]]|$1|Q|3|R|5|6|7|15|8|@]|9|@]|A|$]]|$1|S|3|T|5|6|7|16|8|@]|9|@]|A|$]]|$1|U|3|V|5|6|7|17|8|@]|9|@]|A|$]]|$1|W|3|-4|5|6|7|18|8|@]|9|@]|A|$]]]|X|$]]

Vectorization, in simple words, means optimizing the algorithm so that it can utilize SIMD instructions in the processors. 

AVX, AVX2 and AVX512 are the instruction sets (intel) that perform same operation on multiple data in one instruction. for eg. AVX512 means you can operate on 16 integer values(4 bytes) at a time. What that means is that if you have vector of 16 integers and you want to double that value in each integers and then add 10 to it. You can either load values on to general register [a,b,c] 16 times and perform same operation or you can perform same operation by loading all 16 values on to SIMD registers [xmm,ymm] and perform the operation once. This lets speed up the computation of vector data. 

In vectorization we use this to our advantage, by remodelling our data so that we can perform SIMD operations on it and speed up the program. 

Only problem with vectorization is handling conditions. Because conditions branch the flow of execution. This can be handled by masking. By modelling the condition into an arithmetic operation. eg. if we want to add 10 to value if it is greater then 100. we can either.

<pre><code>if(x[i] &gt; 100) x[i] += 10; // this will branch execution flow.
</code></pre>

or we can model the condition into arithmetic operation creating a condition vector c,

<pre><code>c[i] = x[i] &gt; 100; // storing the condition on masking vector
x[i] = x[i] + (c[i] &amp; 10) // using mask
</code></pre>

this is very trivial example though... thus, c is our masking vector which we use to perform binary operation based on its value. This avoid branching of execution flow and enables vectorization.

Vectorization is as important as Parallelization. Thus, we should make use of it as much possible. All modern days processors have SIMD instructions for heavy compute workloads. We can optimize our code to use these SIMD instructions using vectorization, this is similar to parrallelizing our code to run on multiple cores available on modern processors. 

I would like to leave with the mention of OpenMP, which lets yo vectorize the code using pragmas. I consider it as a good starting point. Same can be said for OpenACC.

blocks|key|1239153|text|希望你一切都好！|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1239154|矢量化是指将缩放器实现转换为向量化实现的所有技术。在向量化实现中，单个操作一次处理单个实体，而单个操作同时处理多个实体。|1239155|矢量化指的是一种技术，通过这种技术，我们可以优化代码，以便有效地处理大量数据。矢量化在科学应用中的应用，如NumPy、pandas，你也可以在使用Matlab语言、图像处理、自然语言处理等方面使用这种技术。总的来说，它优化了程序的运行时和内存分配。|1239156|希望你能得到你的答案！|1239157|谢谢。|1239158|entityMap^0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|M|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|N|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|O|8|@]|9|@]|A|$]]|$1|H|3|I|5|6|7|P|8|@]|9|@]|A|$]]|$1|J|3|-4|5|6|7|Q|8|@]|9|@]|A|$]]]|K|$]]

hope you are well!
vectorization refers to all the techniques that convert scaler implementation, in which a single operation processes a single entity at a time to vector implementation in which a single operation processes multiple entities at the same time.
Vectorization refers to a technique with the help of which we optimize the code to work with huge chunks of data efficiently. application of vectorization seen in scientific applications like NumPy, pandas also you can use this technique while working with Matlab, image processing, NLP, and much more. Overall it optimizes the runtime and memory allocation of the program.
Hope you may get your answer!
Thank you.

Several times now, I've encountered this term in matlab, fortran ... some other ... but I've never found an explanation what does it mean, and what it does? So I'm asking here, what is vectorization, and what does it mean for example, that "a loop is vectorized" ?

What is "vectorization"?

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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现在，我已经在matlab，fortran中遇到过这个术语好几次了。其他的..。但是我从来没有找到一个解释它是什么意思，它是做什么的？所以我在这里问，什么是矢量化，它是什么意思，例如，“循环是矢量化的”？

问什么是“向量化”？
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问什么是“向量化”？EN