展开/填充 Matlab 矩阵

Question

我对 Matlab 还很陌生，所以需要一个简单的解释。

我有一些 MIDI 数据，看起来有点像这样：

时间开/关音符
10 1 61
90 0 61
90 1 72
92 1 87
100 0 72

我想要做的是扩展或“填充”空白，以便我在每个时刻都有一行，并且我有显示哪些音符处于打开状态的列（通常有多个音符同时）。

最终目标是对给定时间的音符（和声不和谐音）之间的整体关系进行一些计算。

所以我想也许我需要为每个可能的音符（有 127 个）创建一个新列，然后每次都添加 1 或 0。或者也许我可以有一个矩阵，它只告诉我哪些音符处于打开状态（因此列数有所不同）。

我自己写了伪代码，但不知道如何实现。我怀疑有一个简单的函数可以做到这一点。这是我的伪代码：

从 0 开始，在新的“注释矩阵”中的时间 0
对于数字：0 到 n
如果该数字与时间列中的数字匹配，请转到该行的开/关列。
如果开/关列中为 1，则将注释列中的数字复制到相应行的“注释矩阵”
如果为 0，则不复制/不执行任何操作。

如果数字与时间列中的数字不匹配
复制上一行（如果没有注释，则可以为空）。

对于新“注释矩阵”中的每一行，将数字从低到高排列在不同的列中。

那么谁能告诉我该怎么办？我在这里用头撞砖墙！

Answer 1

即使列表的顺序完全随机，这里的解决方案也可以工作。它基于以下思想：向量[0 1 0 0 -1 0 0]的累积和为[0 1 1 1 0 0 0]。这对应于时间 2 中的“on”，以及时间 5 中的“off”。现在我们需要做的就是用 1 和 -1 填充一个数组，然后运行CUMSUM 将其转换为每列都有 1 的数组每当声音开启时。

我假设有 128 个音符 (0-127)，并且您希望在最后有一个静音时间步长（如果所有音符最终结束）。请注意，Matlab 从 1 开始计数，因此时间 0 对应于行 #1。

%# midiData is a n-by-3 array with [time,on/off,note]
midiData = [...
10 1 61
90 0 61
90 1 72
92 1 87
100 0 72];

%# do not call unique here, because repeated input rows are relevant

%# note values can be from 0 to 127
nNotes = 128;

%# nTimepoints: find the highest entry in midiData's time-column
%# add 2, because midiData starts counting time at 0
%# and since we want to have one additional timepoint in the end
nTimepoints = max(midiData(:,1))+2; 




%# -- new solution ---
%# because the input is a bit messed up, we have to use a more complicated
%# solution. We'll use `accumarray`, with which we sum up all the
%# entries for on (+1) and off (-1) for each row(time)/column(note) pair.
%# after that, we'll apply cumsum

%# transform the input, so that 'off' is -1
%# wherever the second col of midiData is 0
%# replace it with -1
midiData(midiData(:,2)==0,2) = -1;

%# create output in one step
%# for every same coordinate (time,note), sum all the 
%# on/offs (@sum). Force the output to be 
%# a nTimepoints-by-nNotes array, and fill in zeros
%# where there's no information
output = accumarray(midiData(:,[1 3])+1,midiData(:,2),...
    [nTimepoints,nNotes],@sum,0);

%# cumsum, and we're done
output = cumsum(output,1);

为了完整性，之前的解决方案：

%# --- old solution ---

 %# create output array, which we'll first populate with 1 and -1
%# after which we transform it into an on-off array
%# rows are timepoints, columns are notes
output = zeros(nTimepoints,nNotes);

%# find all on's 
%# onIdx is 1 if the second column of midiData is 1
onIdx = midiData(:,2) == 1;

%# convert time,note pairs into linear indices for
%# writing into output in one step
%# Add 1 to time and note, respectively, so that we start counting at 1
plusOneIdx = sub2ind([nTimepoints,nNotes],midiData(onIdx,1)+1,midiData(onIdx,3)+1);

%# write "1" wherever a note turns on
output(plusOneIdx) = 1;

%# now do the same for -1
offIdx = midiData(:,2) == 0;
minusOneIdx = sub2ind([nTimepoints,nNotes],midiData(offIdx,1)+1,midiData(offIdx,3)+1);

%# instead of overwrite the value in output, subtract 1
%# so that time/note that are both on and off become zeros
output(minusOneIdx) = output(minusOneIdx) - 1;

%# run cumsum on the array to transform the +1/-1 into stretches of 1 and 0
%# the 'dim' argument is 1, because we want to sum in the direction in 
%# which rows are counted
output = cumsum(output,1);

%# for fun, visualize the result
%# there's white whenever a note is on
imshow(output)