### 计算机代写|并行计算作业代写Parallel Computing代考|Sliced Variables

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• Foundations of Data Science 数据科学基础

## 计算机代写|并行计算作业代写Parallel Computing代考|Characteristics of a Sliced Variable

If a variable in a parfor-loop has all the following characteristics, then the variable is sliced:

• Type of First-Level Indexing – The first level of indexing is either parentheses, ( ), or braces, {} .
• Fixed Index Listing – Within the first-level parentheses or braces, the list of indices is the same for all occurrences of a given variable.
• Form of Indexing – Within the list of indices for the variable, exactly one index involves the loop variable.
• Shape of Array – The array maintains a constant shape. In assigning to a sliced variable, the right side of the assignment cannot be [] or $”$, because these operators attempt to delete elements.
Type of First-Level Indexing. For a sliced variable, the first level of indexing is enclosed in either parentheses, ( ), or braces, {} .
Here are the forms for the first level of indexing for arrays that are sliced and not sliced.
\begin{tabular}{|l|l|}
\hline Not Sliced & Sliced \
\hline A. $x$ & A $(\ldots)$ \
\hline A. $(\ldots)$ & A{…. \
\hline
\end{tabular}
After the first level, you can use any type of valid MATLAB indexing in the second and subsequent levels.
The variable A shown here on the left is not sliced; that shown on the right is sliced.
A. $q{i, 12}$
$$A{i, 12} \text {. } q$$
Fixed Index Listing. Within the first-level indexing of a sliced variable, the list of indices is the same for all occurrences of a given variable.

The variable A on the left is not sliced because $\mathrm{A}$ is indexed by $i$ and $i+1$ in different places. In the code on the right, variable $A$ is sliced correctly.

## 计算机代写|并行计算作业代写Parallel Computing代考|Sliced Input and Output Variables

A sliced variable can be an input variable, an output variable, or both. MATLAB transmits sliced input variables from the client to the workers, and sliced output variables from workers back to the client. If a variable is both input and output, it is transmitted in both directions.
In this parfor-loop, A is a sliced input variable and B is a sliced output variable.
$A=\operatorname{rand}(1,10)$ :
$A=$ rand $(1,10):$
parfor ii $=1: 10$
$\quad B(i i)=A(i i)$
end
$\mathrm{B}(i i)=1: 10$
end

However, if MATLAB determines that, in each iteration, the sliced variable elements are set before any use, then MATLAB does not transmit the variable to the workers. In this example, all elements of A are set before any use.
parfor ii $=1: \mathrm{n}$
if someCondition
$\mathrm{A}($ ii $)=32$;
else
$A(i i)=17$;
end
parfor ii $=1: \mathrm{n}$
if someCondition
$\mathrm{A}(\mathrm{ii})=32 ;$
else
$\quad \mathrm{A}(\mathrm{ii})=17 ;$
end
io loop code that uses $\mathrm{A}(\mathrm{ii})$
\& loop code that uses A(ii)
end
Sliced-output variables can grow dynamically through indexed assignments with default values inserted at intermediate indices. In this example, you can see that the default value of 0 has been inserted at several places in A.
$A=[1]$
parfor idx $=1: 10$
if rand $<0.5$
$A(i d x)=i d x$;
end
end
$\operatorname{disp}(A)$;
$\begin{array}{llllllllll}0 & 2 & 0 & 4 & 5 & 0 & 0 & 8 & 9 & 10\end{array}$
Even if a sliced variable is not explicitly referenced as an input, implicit usage can make it so. In the following example, not all elements of $A$ are necessarily set inside the parfor-loop. Therefore the original values of the array are received, held, and then returned from the loop.
$\mathrm{A}=1: 10$;
parfor ii $=1: 10$
if rand $<0.5$
$A(i i)=0$;
end
end
Under some circumstances, parfor-loops must assume that a worker may need all segments of a sliced variable. In this example, it is not possible to determine which elements of the sliced variable will be read before execution, so parfor sends all possible segments.
$\mathrm{A}=1: 10$;
parfor $i i=1: 11$
if ii $<=\operatorname{randi}\left(\left[\begin{array}{ll}1 \theta & 11\end{array}\right]\right)$
$A=1: 10 ;$
parfor ii=1:11
$\quad$ if $i i<=$ randi $\left(\left[\begin{array}{ll}10 & 11]\end{array}\right]\right.$
end $\quad \mathrm{A}(\mathrm{ii})=\mathrm{A}(\mathrm{i} i)+1 ;$
end
$A(i i)=A(i i)+1$
end
end
Note that in these circumstances, the code can attempt to index a sliced variable outside of the array bounds and generate an error.

## 计算机代写|并行计算作业代写Parallel Computing代考|Requirements for Reduction Assignments

Reduction Assignments. In addition to the specific forms of reduction assignment listed in the table in “Reduction Variables” on page $2-42$, the only other (and more general) form of a reduction assignment is
Required (static): $f$ can be a function or a variable. If $f$ is a variable, then you cannot change $f$ in the parfor body (in other words, it is a broadcast variable).

If $f$ is a variable, then for all practical purposes its value at run time is a function handle. However, as long as the right side can be evaluated, the resulting value is stored in $X$.

The parfor-loop on the left does not execute correctly because the statement $f=$ etimes causes $f$ to be classified as a temporary variable. Therefore $f$ is cleared at the beginning of each iteration. The parfor-loop on the right is correct, because it does not assign $f$ inside the loop.

The operators $\& \&$ and || are not listed in the table in “Reduction Variables” on page 2-42. Except for $\& \&$ and | $\mid$, all the matrix operations of MATLAB have a corresponding function $f$, such that $u$ op $v$ is equivalent to $f(u, v)$. For $\& \&$ and || , such a function cannot be written because u\&\&v and $u|| v$ might or might not evaluate $v$. However, $f(u, v)$ always evaluates v before calling $f$. Therefore \&\& and || are excluded from the table of allowed reduction assignments for a par for-loop.
Every reduction assignment has an associated function $f$. The properties of $f$ that ensure deterministic behavior of a parfor statement are discussed in the following sections.
Associativity in Reduction Assignments. The following practice is recommended for the function $f$, as used in the definition of a reduction variable. However, this rule does not generate an error if not adhered to. Therefore, it is up to you to ensure that your code meets this recommendation.

## 计算机代写|并行计算作业代写Parallel Computing代考|Characteristics of a Sliced Variable

• 第一级索引的类型 – 第一级索引是圆括号 ( ) 或大括号 {} 。
• 固定索引列表 – 在第一级括号或大括号内，索引列表对于给定变量的所有出现都是相同的。
• 索引形式——在变量的索引列表中，只有一个索引涉及循环变量。
• 阵列形状 – 阵列保持不变的形状。在赋值给切片变量时，赋值的右边不能是 [] 或”，因为这些运算符试图删除元素。
一级索引的类型。对于切片变量，第一级索引用括号 ( ) 或大括号 {} 括起来。
以下是切片和未切片数组的第一级索引形式。
\begin{tabular}{|l|l|}
\hline Not Sliced & Sliced \
\hline A.X＆ 一种(…)\
\ hline A.(…)＆ 一种{…。\
\hline
\end{tabular}
在第一层之后，您可以在第二层和后续层中使用任何类型的有效 MATLAB 索引。
左边这里显示的变量 A 没有被切片；右边显示的是切片。
一种。q一世,12
一种一世,12. q
固定索引列表。在切片变量的第一级索引中，索引列表对于给定变量的所有出现都是相同的。

parfor ii=1:10

parfor ii=1:n

parfor ii=1:n

\& 使用 A(ii)
end

parfor idx=1:10

02045008910

parfor ii=1:10

end
end

parfor ii=1:11

end
end

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## MATLAB代写

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