[r] Create dataframe from a matrix

You can use stack from the base package. But, you need first to coerce your matrix to a data.frame and to reorder the columns once the data is stacked.

mat <- as.data.frame(mat)
res <- data.frame(time= mat$time,stack(mat,select=-time))
res[,c(3,1,2)]

  ind time values
1 C_0  0.0    0.1
2 C_0  0.5    0.2
3 C_0  1.0    0.3
4 C_1  0.0    0.3
5 C_1  0.5    0.4
6 C_1  1.0    0.5

Note that stack is generally more efficient than the reshape2 package.

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