# How do you extract each column of a matrix as a column vector

**URL:** <https://discourse.mc-stan.org/t/how-do-you-extract-each-column-of-a-matrix-as-a-column-vector/12494>\
**Category:** General\
**Created:** [January 4, 2020, 2:10am UTC](https://discourse.mc-stan.org/t/how-do-you-extract-each-column-of-a-matrix-as-a-column-vector/12494 "2020-01-04T02:10:27Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![xiaodi321](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/xiaodi321/32/9386_2.png) [@xiaodi321](https://discourse.mc-stan.org/u/xiaodi321)\
**Post date:** [January 4, 2020, 2:10am UTC](https://discourse.mc-stan.org/t/how-do-you-extract-each-column-of-a-matrix-as-a-column-vector/12494/1 "2020-01-04T02:10:27Z")

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Hi! Thank you for your help.Now I have some troubles in the matrix. For a matrix(p\*n),I want to extract each column of the matrix as a column vector named as mi(i=1…n）, then calculate mi times transpose(mi), then we will get n matrices.After that ,I want to calculate the sum of n matrices.  
Thank you for you help .

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**Author:** ![FJCC](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/fjcc/32/6653_2.png) [@FJCC](https://discourse.mc-stan.org/u/FJCC)\
**Post date:** [January 4, 2020, 3:45am UTC](https://discourse.mc-stan.org/t/how-do-you-extract-each-column-of-a-matrix-as-a-column-vector/12494/2 "2020-01-04T03:45:54Z")

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I am a novice with Stan so there may be far better ways to do this. If I understood you correctly, the R code below makes the calculation directly in R and then in Stan. I did the calculation in R so I could compare the results with what the Stan code produced. I included as comments in the Stan code the declaration and population of an array to hold each of the p x p matrices, if those are of interest.

```stan
library(rstan)
MAT <- matrix(1:20, nrow = 4)
print(MAT)
# [,1] [,2] [,3] [,4] [,5]
# [1,] 1 5 9 13 17
# [2,] 2 6 10 14 18
# [3,] 3 7 11 15 19
# [4,] 4 8 12 16 20

#R code to do the same calcualtion
Tot <- matrix(rep(0, 16), nrow = 4)

for (i in 1:5){
  Tot <- Tot + (MAT[, i] %*% t(MAT[, i]))
}
print(Tot)
# [,1] [,2] [,3] [,4]
# [1,] 565 610 655 700
# [2,] 610 660 710 760
# [3,] 655 710 765 820
# [4,] 700 760 820 880

MODEL <- "
data {
  int p; //number of rows
  int n; //number of columns
  matrix[p,n] M;
}
transformed data {
 // matrix[p,p] Mats[n];
  matrix[p,p] Total;
  vector[p] tmp;

  Total = rep_matrix(0, p, p);

  for ( i in 1:n) {
    for (j in 1:p) {
      tmp[j] = M[j,i];
    }
    //Mats[i] = tmp * tmp';
    Total += tmp * tmp';
  }

  print(Total);
}
model {

}
"
dataList <- list(p = nrow(MAT), n = ncol(MAT), M = MAT)
FIT <- stan(model_code = MODEL, data = dataList, iter = 1, chains = 1, 
            warmup = 0, algorithm = "Fixed_param")
# [[565,610,655,700],[610,660,710,760],[655,710,765,820],[700,760,820,880]]

```

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**Author:** ![FJCC](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/fjcc/32/6653_2.png) [@FJCC](https://discourse.mc-stan.org/u/FJCC)\
**Post date:** [January 4, 2020, 6:06am UTC](https://discourse.mc-stan.org/t/how-do-you-extract-each-column-of-a-matrix-as-a-column-vector/12494/3 "2020-01-04T06:06:31Z")

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Here is slightly improved Stan code using the col() function

```stan
MODEL <- "
data {
  int p; //number of rows
  int n; //number of columns
  matrix[p,n] M;
}
transformed data {
 // matrix[p,p] Mats[n];
  matrix[p,p] Total;
  vector[p] tmp;

  Total = rep_matrix(0, p, p);

  for ( i in 1:n) {
      tmp = col(M,i);
      //Mats[i] = tmp * tmp';
      Total += tmp * tmp';
  }

  print(Total);
}
"

```

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<div class="post-metadata">

**Author:** ![xiaodi321](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/xiaodi321/32/9386_2.png) [@xiaodi321](https://discourse.mc-stan.org/u/xiaodi321)\
**Post date:** [January 4, 2020, 7:13am UTC](https://discourse.mc-stan.org/t/how-do-you-extract-each-column-of-a-matrix-as-a-column-vector/12494/4 "2020-01-04T07:13:09Z")

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Thank you very much ! It’s very useful for my working.