使用FFTW进行FFT一维变换

问题描述

我有一个3维数组U(z，y，x)，我想对y和x的所有值在z中执行复杂的傅立叶变换.我打算使用FFTW库.我从FFTW手册中发现，有一种方法可以一次执行多个1d转换(如下所述).

I have a 3-dimensional array U(z,y,x) and I want to perform a complex Fourier transform in z for all values of y and x. I am planning to use the FFTW library. I figured out from the FFTW manual that there is a way to perform multiple 1d transforms at once(mentioned below).

CALL dfftw_plan_many_dft(计划，等级，n，Howmany，进，嵌入式，同位，同位，出，onembed，ostride，odist，FFTW_MEASURE)

CALL dfftw_plan_many_dft(PLAN, rank, n, howmany, in, inembed, istride, idist, out, onembed, ostride, odist, FFTW_MEASURE)

我不太清楚嵌入和嵌入的含义.当我刚接触Fortran时，您能否提供更多的见解?我不确定如何使用它吗?

I don't clearly understand what inembed and outembed means. Could you provide more insight into this as I am new to Fortran and I am not entirely sure how to use this?

更新了Fortran代码

updated the Fortran code

推荐答案

在这里实际上已经很好地描述了它: http://www.fftw.org/fftw3_doc/Advanced-Complex-DFTs.html

It's described here actually quite well:http://www.fftw.org/fftw3_doc/Advanced-Complex-DFTs.html

inmbed 和 outembed 允许将传入和传出的数据嵌入到更大的数据集中:

inembed and outembed allow one to embed the incoming and outgoing data into a larger dataset:

想象一下，您想对 O 元素表示的 in 的子矩阵进行FFT.可能会将结果嵌入到 out 变量的 O 字段中.

Imagine that you would like to FFT the sub-matrix of in denoted by the O elements. And possibly outembed the result into the out variable's O fields.

     X X X X X           X X X X X X
     X X X X X           X O O X X X
in = X O O X X     out = X O O X X X
     X O O X X
     X X X X X

inmbed 将为[2，1](主要列)，而 outmbed [1，1].然后跨步将使您从切片到切片/从卷到卷等.使用 stride 和 embed ，您告诉FFTW如何找到 O 元素对于每个要转换的子数据，同样地，将其放置在较大的数据集中.

inembed then would be [2, 1] (column-major) and outmbed [1, 1]. Then stride would take you from slice to slice / volume to volume etc. Using stride and embed you tell FFTW, how to find the O elements for each sub-data to transform and equally, where to put them in a larger dataset.

希望这可以解释它.如果您现在已经是BLAS界面，您会发现 inmbed 和 outembed 对应于 LDA ， LDB 许多例程.当然，BLAS例程仅限于矩阵，即假设二维运算.您当然可以在任意数量的维度上进行FFT.

Hope this explains it. If you already now the the BLAS interface, you will find that inembed and outembed correspond to LDA, LDB of many routines. Of course BLAS routines are limited to matrices, i.e. assume 2 dimensional operations. FFTs you may of course do in as many dimensions as you like.

如果将 inmbed 和 outembed 设置为 NULL ，则FFTW假定其中没有 X 字段要么分别输入我们的输出.

If you set inembed and outembed as NULL, then FFTW assumes that there are no X fields in either input our output respectively.

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