Matrix transposition

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Task
Matrix transposition
You are encouraged to solve this task according to the task description, using any language you may know.
Transpose an arbitrarily sized rectangular Matrix.

Contents

[edit] ACL2

(defun cons-each (xs xss)
(if (or (endp xs) (endp xss))
nil
(cons (cons (first xs) (first xss))
(cons-each (rest xs) (rest xss)))))
 
(defun list-each (xs)
(if (endp xs)
nil
(cons (list (first xs))
(list-each (rest xs)))))
 
(defun transpose-list (xss)
(if (endp (rest xss))
(list-each (first xss))
(cons-each (first xss)
(transpose-list (rest xss)))))

[edit] ActionScript

In ActionScript, multi-dimensional arrays are created by making an "Array of arrays" where each element is an array.

function transpose( m:Array):Array
{
//Assume each element in m is an array. (If this were production code, use typeof to be sure)
 
//Each element in m is a row, so this gets the length of a row in m,
//which is the same as the number of rows in m transpose.
var mTranspose = new Array(m[0].length);
for(var i:uint = 0; i < mTranspose.length; i++)
{
//create a row
mTranspose[i] = new Array(m.length);
//set the row to the appropriate values
for(var j:uint = 0; j < mTranspose[i].length; j++)
mTranspose[i][j] = m[j][i];
}
return mTranspose;
}
var m:Array = [[1, 2, 3, 10],
[4, 5, 6, 11],
[7, 8, 9, 12]];
var M:Array = transpose(m);
for(var i:uint = 0; i < M.length; i++)
trace(M[i]);

[edit] Ada

Transpose is a function of the standard Ada library provided for matrices built upon any floating-point or complex type. The relevant packages are Ada.Numerics.Generic_Real_Arrays and Ada.Numerics.Generic_Complex_Arrays, correspondingly.

This example illustrates use of Transpose for the matrices built upon the standard type Float:

with Ada.Numerics.Real_Arrays;  use Ada.Numerics.Real_Arrays;
with Ada.Text_IO; use Ada.Text_IO;
 
procedure Matrix_Transpose is
procedure Put (X : Real_Matrix) is
type Fixed is delta 0.01 range -500.0..500.0;
begin
for I in X'Range (1) loop
for J in X'Range (2) loop
Put (Fixed'Image (Fixed (X (I, J))));
end loop;
New_Line;
end loop;
end Put;
 
Matrix : constant Real_Matrix :=
( (0.0, 0.1, 0.2, 0.3),
(0.4, 0.5, 0.6, 0.7),
(0.8, 0.9, 1.0, 1.1)
);
begin
Put_Line ("Before Transposition:");
Put (Matrix);
New_Line;
Put_Line ("After Transposition:");
Put (Transpose (Matrix));
end Matrix_Transpose;

Sample output:

Before Transposition:
 0.00 0.10 0.20 0.30
 0.40 0.50 0.60 0.70
 0.80 0.90 1.00 1.10

After Transposition:
 0.00 0.40 0.80
 0.10 0.50 0.90
 0.20 0.60 1.00
 0.30 0.70 1.10

[edit] Agda

module Matrix where
 
open import Data.Nat
open import Data.Vec
 
Matrix : (A : Set) → ℕ → ℕ → Set
Matrix A m n = Vec (Vec A m) n
 
transpose : ∀ {A m n} → Matrix A m n → Matrix A n m
transpose [] = replicate []
transpose (xs ∷ xss) = zipWith _∷_ xs (transpose xss)
 
a = (1 ∷ 2 ∷ 3 ∷ []) ∷ (4 ∷ 5 ∷ 6 ∷ []) ∷ []
b = transpose a

b evaluates to the following normal form:

(1 ∷ 4 ∷ []) ∷ (2 ∷ 5 ∷ []) ∷ (3 ∷ 6 ∷ []) ∷ []

[edit] ALGOL 68

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
main:(
 
[,]REAL m=((1, 1, 1, 1),
(2, 4, 8, 16),
(3, 9, 27, 81),
(4, 16, 64, 256),
(5, 25,125, 625));
 
OP ZIP = ([,]REAL in)[,]REAL:(
[2 LWB in:2 UPB in,1 LWB in:1UPB in]REAL out;
FOR i FROM LWB in TO UPB in DO
out[,i]:=in[i,]
OD;
out
);
 
PROC pprint = ([,]REAL m)VOID:(
FORMAT real fmt = $g(-6,2)$; # width of 6, with no '+' sign, 2 decimals #
FORMAT vec fmt = $"("n(2 UPB m-1)(f(real fmt)",")f(real fmt)")"$;
FORMAT matrix fmt = $x"("n(UPB m-1)(f(vec fmt)","lxx)f(vec fmt)");"$;
# finally print the result #
printf((matrix fmt,m))
);
 
printf(($x"Transpose:"l$));
pprint((ZIP m))
)

Output:

Transpose:
((  1.00,  2.00,  3.00,  4.00,  5.00),
 (  1.00,  4.00,  9.00, 16.00, 25.00),
 (  1.00,  8.00, 27.00, 64.00,125.00),
 (  1.00, 16.00, 81.00,256.00,625.00));

[edit] APL

 
3 3⍴⍳10
1 2 3
4 5 6
7 8 9
⍉ 3 3⍴⍳10
1 4 7
2 5 8
3 6 9
 


[edit] AutoHotkey

a = a
m = 10
n = 10
Loop, 10
{
i := A_Index - 1
Loop, 10
{
j := A_Index - 1
%a%%i%%j% := i - j
}
}
before := matrix_print("a", m, n)
transpose("a", m, n)
after := matrix_print("a", m, n)
MsgBox % before . "`ntransposed:`n" . after
Return
 
transpose(a, m, n)
{
Local i, j, row, matrix
Loop, % m
{
i := A_Index - 1
Loop, % n
{
j := A_Index - 1
temp%i%%j% := %a%%j%%i%
}
}
Loop, % m
{
i := A_Index - 1
Loop, % n
{
j := A_Index - 1
%a%%i%%j% := temp%i%%j%
}
}
}
 
matrix_print(a, m, n)
{
Local i, j, row, matrix
Loop, % m
{
i := A_Index - 1
row := ""
Loop, % n
{
j := A_Index - 1
row .= %a%%i%%j% . ","
}
StringTrimRight, row, row, 1
matrix .= row . "`n"
}
Return matrix
}
 

[edit] Using Objects

Transpose(M){
R := []
for i, row in M
for j, col in row
R[j,i] := col
return R
}
Examples:
Matrix := [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]
MsgBox % ""
. "Original Matrix :`n" Print(Matrix)
. "`nTransposed Matrix :`n" Print(Transpose(Matrix))
 
Print(M){
for i, row in M
for j, col in row
Res .= (A_Index=1?"":"`t") col (Mod(A_Index,M[1].MaxIndex())?"":"`n")
return Trim(Res,"`n")
}
Outputs:
Original Matrix :
1	2	3
4	5	6
7	8	9
10	11	12

Transposed Matrix :
1	4	7	10
2	5	8	11
3	6	9	12

[edit] AWK

 
# syntax: GAWK -f MATRIX_TRANSPOSITION.AWK filename
{ if (NF > nf) {
nf = NF
}
for (i=1; i<=nf; i++) {
row[i] = row[i] $i " "
}
}
END {
for (i=1; i<=nf; i++) {
printf("%s\n",row[i])
}
exit(0)
}
 

input:

1 2 3 4
5 6 7 8
9 10 11 12

output:

1 5 9
2 6 10
3 7 11
4 8 12

[edit] BASIC

Works with: QuickBasic version 4.5
CLS
DIM m(1 TO 5, 1 TO 4) 'any dimensions you want

'set up the values in the array
FOR rows = LBOUND(m, 1) TO UBOUND(m, 1) 'LBOUND and UBOUND can take a dimension as their second argument
       FOR cols = LBOUND(m, 2) TO UBOUND(m, 2)
       m(rows, cols) = rows ^ cols 'any formula you want
       NEXT cols
NEXT rows

'declare the new matrix
DIM trans(LBOUND(m, 2) TO UBOUND(m, 2), LBOUND(m, 1) TO UBOUND(m, 1))

'copy the values
FOR rows = LBOUND(m, 1) TO UBOUND(m, 1)
       FOR cols = LBOUND(m, 2) TO UBOUND(m, 2)
       trans(cols, rows) = m(rows, cols)
       NEXT cols
NEXT rows

'print the new matrix
FOR rows = LBOUND(trans, 1) TO UBOUND(trans, 1)
       FOR cols = LBOUND(trans, 2) TO UBOUND(trans, 2)
       PRINT trans(rows, cols);
       NEXT cols
PRINT
NEXT rows

[edit] BBC BASIC

      INSTALL @lib$+"ARRAYLIB"
 
DIM matrix(3,4), transpose(4,3)
matrix() = 78,19,30,12,36,49,10,65,42,50,30,93,24,78,10,39,68,27,64,29
 
PROC_transpose(matrix(), transpose())
 
FOR row% = 0 TO DIM(matrix(),1)
FOR col% = 0 TO DIM(matrix(),2)
PRINT ;matrix(row%,col%) " ";
NEXT
PRINT
NEXT row%
 
PRINT
 
FOR row% = 0 TO DIM(transpose(),1)
FOR col% = 0 TO DIM(transpose(),2)
PRINT ;transpose(row%,col%) " ";
NEXT
PRINT
NEXT row%

Output:

78 19 30 12 36
49 10 65 42 50
30 93 24 78 10
39 68 27 64 29

78 49 30 39
19 10 93 68
30 65 24 27
12 42 78 64
36 50 10 29

[edit] Burlesque

 
blsq ) {{78 19 30 12 36}{49 10 65 42 50}{30 93 24 78 10}{39 68 27 64 29}}tpsp
78 49 30 39
19 10 93 68
30 65 24 27
12 42 78 64
36 50 10 29
 

[edit] C

Transpose a 2D double array.

#include <stdio.h>
 
void transpose(void *dest, void *src, int src_h, int src_w)
{
int i, j;
double (*d)[src_h] = dest, (*s)[src_w] = src;
for (i = 0; i < src_h; i++)
for (j = 0; j < src_w; j++)
d[j][i] = s[i][j];
}
 
int main()
{
int i, j;
double a[3][5] = {{ 0, 1, 2, 3, 4 },
{ 5, 6, 7, 8, 9 },
{ 1, 0, 0, 0, 42}};
double b[5][3];
transpose(b, a, 3, 5);
 
for (i = 0; i < 5; i++)
for (j = 0; j < 3; j++)
printf("%g%c", b[i][j], j == 2 ? '\n' : ' ');
return 0;
}

Transpose a matrix of size w x h in place with only O(1) space and without moving any element more than once. See the Wikipedia article for more information.

#include <stdio.h>
 
void transpose(double *m, int w, int h)
{
int start, next, i;
double tmp;
 
for (start = 0; start <= w * h - 1; start++) {
next = start;
i = 0;
do { i++;
next = (next % h) * w + next / h;
} while (next > start);
if (next < start || i == 1) continue;
 
tmp = m[next = start];
do {
i = (next % h) * w + next / h;
m[next] = (i == start) ? tmp : m[i];
next = i;
} while (next > start);
}
}
 
void show_matrix(double *m, int w, int h)
{
int i, j;
for (i = 0; i < h; i++) {
for (j = 0; j < w; j++)
printf("%2g ", m[i * w + j]);
putchar('\n');
}
}
 
int main(void)
{
int i;
double m[15];
for (i = 0; i < 15; i++) m[i] = i + 1;
 
puts("before transpose:");
show_matrix(m, 3, 5);
 
transpose(m, 3, 5);
 
puts("\nafter transpose:");
show_matrix(m, 5, 3);
 
return 0;
}

output

before transpose:
 1  2  3 
 4  5  6 
 7  8  9 
10 11 12 
13 14 15 

after transpose:
 1  4  7 10 13 
 2  5  8 11 14 
 3  6  9 12 15 

[edit] C++

Library: Boost.uBLAS
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>
 
int main()
{
using namespace boost::numeric::ublas;
 
matrix<double> m(3,3);
 
for(int i=0; i!=m.size1(); ++i)
for(int j=0; j!=m.size2(); ++j)
m(i,j)=3*i+j;
 
std::cout << trans(m) << std::endl;
}

Output:

[3,3]((0,3,6),(1,4,7),(2,5,8))

[edit] Generic solution

main.cpp
#include <iostream>
#include "matrix.h"
 
#if !defined(ARRAY_SIZE)
#define ARRAY_SIZE(x) (sizeof((x)) / sizeof((x)[0]))
#endif
 
template<class T>
void printMatrix(const Matrix<T>& m) {
std::cout << "rows = " << m.rowNum() << " columns = " << m.colNum() << std::endl;
for (unsigned int i = 0; i < m.rowNum(); i++) {
for (unsigned int j = 0; j < m.colNum(); j++) {
std::cout << m[i][j] << " ";
}
std::cout << std::endl;
}
} /* printMatrix() */
 
int main() {
int am[2][3] = {
{1,2,3},
{4,5,6},
};
 
Matrix<int> a(ARRAY_SIZE(am), ARRAY_SIZE(am[0]), am[0], ARRAY_SIZE(am)*ARRAY_SIZE(am[0]));
 
try {
std::cout << "Before transposition:" << std::endl;
printMatrix(a);
std::cout << std::endl;
a.transpose();
std::cout << "After transposition:" << std::endl;
printMatrix(a);
} catch (MatrixException& e) {
std::cerr << e.message() << std::endl;
return e.errorCode();
}
 
} /* main() */
matrix.h
#ifndef _MATRIX_H
#define _MATRIX_H
 
#include <sstream>
#include <string>
#include <vector>
#include <algorithm>
 
#define MATRIX_ERROR_CODE_COUNT 5
#define MATRIX_ERR_UNDEFINED "1 Undefined exception!"
#define MATRIX_ERR_WRONG_ROW_INDEX "2 The row index is out of range."
#define MATRIX_ERR_MUL_ROW_AND_COL_NOT_EQUAL "3 The row number of second matrix must be equal with the column number of first matrix!"
#define MATRIX_ERR_MUL_ROW_AND_COL_BE_GREATER_THAN_ZERO "4 The number of rows and columns must be greater than zero!"
#define MATRIX_ERR_TOO_FEW_DATA "5 Too few data in matrix."
 
class MatrixException {
private:
std::string message_;
int errorCode_;
public:
MatrixException(std::string message = MATRIX_ERR_UNDEFINED);
 
inline std::string message() {
return message_;
};
 
inline int errorCode() {
return errorCode_;
};
};
 
MatrixException::MatrixException(std::string message) {
errorCode_ = MATRIX_ERROR_CODE_COUNT + 1;
std::stringstream ss(message);
ss >> errorCode_;
if (errorCode_ < 1) {
errorCode_ = MATRIX_ERROR_CODE_COUNT + 1;
}
std::string::size_type pos = message.find(' ');
if (errorCode_ <= MATRIX_ERROR_CODE_COUNT && pos != std::string::npos) {
message_ = message.substr(pos + 1);
} else {
message_ = message + " (This an unknown and unsupported exception!)";
}
}
 
/**
* Generic class for matrices.
*/

template <class T>
class Matrix {
private:
std::vector<T> v; // the data of matrix
unsigned int m; // the number of rows
unsigned int n; // the number of columns
protected:
 
virtual void clear() {
v.clear();
m = n = 0;
}
public:
 
Matrix() {
clear();
}
Matrix(unsigned int, unsigned int, T* = 0, unsigned int = 0);
Matrix(unsigned int, unsigned int, const std::vector<T>&);
 
virtual ~Matrix() {
clear();
}
Matrix& operator=(const Matrix&);
std::vector<T> operator[](unsigned int) const;
Matrix operator*(const Matrix&);
void transpose();
 
inline unsigned int rowNum() const {
return m;
}
 
inline unsigned int colNum() const {
return n;
}
 
inline unsigned int size() const {
return v.size();
}
 
inline void add(const T& t) {
v.push_back(t);
}
};
 
template <class T>
Matrix<T>::Matrix(unsigned int row, unsigned int col, T* data, unsigned int dataLength) {
clear();
if (row > 0 && col > 0) {
m = row;
n = col;
unsigned int mxn = m * n;
if (dataLength && data) {
for (unsigned int i = 0; i < dataLength && i < mxn; i++) {
v.push_back(data[i]);
}
}
}
}
 
template <class T>
Matrix<T>::Matrix(unsigned int row, unsigned int col, const std::vector<T>& data) {
clear();
if (row > 0 && col > 0) {
m = row;
n = col;
unsigned int mxn = m * n;
if (data.size() > 0) {
for (unsigned int i = 0; i < mxn && i < data.size(); i++) {
v.push_back(data[i]);
}
}
}
}
 
template<class T>
Matrix<T>& Matrix<T>::operator=(const Matrix<T>& other) {
clear();
if (other.m > 0 && other.n > 0) {
m = other.m;
n = other.n;
unsigned int mxn = m * n;
for (unsigned int i = 0; i < mxn && i < other.size(); i++) {
v.push_back(other.v[i]);
}
}
return *this;
}
 
template<class T>
std::vector<T> Matrix<T>::operator[](unsigned int index) const {
std::vector<T> result;
if (index >= m) {
throw MatrixException(MATRIX_ERR_WRONG_ROW_INDEX);
} else if ((index + 1) * n > size()) {
throw MatrixException(MATRIX_ERR_TOO_FEW_DATA);
} else {
unsigned int begin = index * n;
unsigned int end = begin + n;
for (unsigned int i = begin; i < end; i++) {
result.push_back(v[i]);
}
}
return result;
}
 
template<class T>
Matrix<T> Matrix<T>::operator*(const Matrix<T>& other) {
Matrix result(m, other.n);
if (n != other.m) {
throw MatrixException(MATRIX_ERR_MUL_ROW_AND_COL_NOT_EQUAL);
} else if (m <= 0 || n <= 0 || other.n <= 0) {
throw MatrixException(MATRIX_ERR_MUL_ROW_AND_COL_BE_GREATER_THAN_ZERO);
} else if (m * n > size() || other.m * other.n > other.size()) {
throw MatrixException(MATRIX_ERR_TOO_FEW_DATA);
} else {
for (unsigned int i = 0; i < m; i++) {
for (unsigned int j = 0; j < other.n; j++) {
T temp = v[i * n] * other.v[j];
for (unsigned int k = 1; k < n; k++) {
temp += v[i * n + k] * other.v[k * other.n + j];
}
result.v.push_back(temp);
}
}
}
return result;
}
 
template<class T>
void Matrix<T>::transpose() {
if (m * n > size()) {
throw MatrixException(MATRIX_ERR_TOO_FEW_DATA);
} else {
std::vector<T> v2;
std::swap(v, v2);
for (unsigned int i = 0; i < n; i++) {
for (unsigned int j = 0; j < m; j++) {
v.push_back(v2[j * n + i]);
}
}
std::swap(m, n);
}
}
 
#endif /* _MATRIX_H */

Output:

Before transposition:
rows = 2   columns = 3
1  2  3  
4  5  6  

After transposition:
rows = 3   columns = 2
1  4  
2  5  
3  6

[edit] Easy Mode

#include <iostream>
 
int main(){
const int l = 5;
const int w = 3;
int m1[l][w] = {{1,2,3}, {4,5,6}, {7,8,9}, {10,11,12}, {13,14,15}};
int m2[w][l];
 
for(int i=0; i<w; i++){
for(int x=0; x<l; x++){
m2[i][x]=m1[x][i];
}
}
 
// This is just output...
 
std::cout << "Before:";
for(int i=0; i<l; i++){
std::cout << std::endl;
for(int x=0; x<w; x++){
std::cout << m1[i][x] << " ";
}
}
 
std::cout << "\n\nAfter:";
for(int i=0; i<w; i++){
std::cout << std::endl;
for(int x=0; x<l; x++){
std::cout << m2[i][x] << " ";
}
}
 
std::cout << std::endl;
 
return 0;
}
Output:
Before:
1 2 3 
4 5 6 
7 8 9 
10 11 12 
13 14 15 

After:
1 4 7 10 13 
2 5 8 11 14 
3 6 9 12 15

[edit] C#

using System;
using System.Text;
 
namespace prog
{
class MainClass
{
public static void Main (string[] args)
{
double[,] m = { {1,2,3},{4,5,6},{7,8,9} };
 
double[,] t = Transpose( m );
 
for( int i=0; i<t.GetLength(0); i++ )
{
for( int j=0; j<t.GetLength(1); j++ )
Console.Write( t[i,j] + " " );
Console.WriteLine("");
}
}
 
public static double[,] Transpose( double[,] m )
{
double[,] t = new double[m.GetLength(1),m.GetLength(0)];
for( int i=0; i<m.GetLength(0); i++ )
for( int j=0; j<m.GetLength(1); j++ )
t[j,i] = m[i,j];
 
return t;
}
}
}

[edit] Clojure

(defmulti matrix-transpose
"Switch rows with columns."
class)
 
(defmethod matrix-transpose clojure.lang.PersistentList
[mtx]
(apply map list mtx))
 
(defmethod matrix-transpose clojure.lang.PersistentVector
[mtx]
(vec (apply map vector mtx)))

Sample output:

=> (matrix-transpose [[1 2 3] [4 5 6]])
[[1 4] [2 5] [3 6]]

[edit] CoffeeScript

transpose = (matrix) ->
(t[i] for t in matrix) for i in [0...matrix[0].length]
> transpose [[1,2,3],[4,5,6]]

[[1,4],[2,5],[3,6]]

[edit] Common Lisp

If the matrix is given as a list:

(defun transpose (m)
(apply #'mapcar #'list m))

If the matrix A is given as a 2D array:

;; Transpose a mxn matrix A to a nxm matrix B=A'.
(defun mtp (A)
(let* ((m (array-dimension A 0))
(n (array-dimension A 1))
(B (make-array `(,n ,m) :initial-element 0)))
(loop for i from 0 below m do
(loop for j from 0 below n do
(setf (aref B j i)
(aref A i j))))
B))

[edit] D

[edit] Standard Version

void main() {
import std.stdio, std.range;
 
/*immutable*/ auto M = [[10, 11, 12, 13],
[14, 15, 16, 17],
[18, 19, 20, 21]];
writefln("%(%(%2d %)\n%)", M.transposed);
}
Output:
10 14 18
11 15 19
12 16 20
13 17 21

[edit] Locally Procedural Style

T[][] transpose(T)(in T[][] m) pure nothrow {
auto r = new typeof(return)(m[0].length, m.length);
foreach (immutable nr, const row; m)
foreach (immutable nc, immutable c; row)
r[nc][nr] = c;
return r;
}
 
void main() {
import std.stdio;
 
immutable M = [[10, 11, 12, 13],
[14, 15, 16, 17],
[18, 19, 20, 21]];
writefln("%(%(%2d %)\n%)", M.transpose);
}

Same output.

[edit] Functional Style

import std.stdio, std.algorithm, std.range, std.functional;
 
auto transpose(T)(in T[][] m) pure nothrow {
return m[0].length.iota.map!(curry!(transversal, m));
}
 
void main() {
immutable M = [[10, 11, 12, 13],
[14, 15, 16, 17],
[18, 19, 20, 21]];
writefln("%(%(%2d %)\n%)", M.transpose);
}

Same output.

[edit] ELLA

Sample originally from ftp://ftp.dra.hmg.gb/pub/ella (a now dead link) - Public release.

Code for matrix transpose hardware design verification:
MAC TRANSPOSE = ([INT n][INT m]TYPE t: matrix) -> [m][n]t:
[INT i = 1..m] [INT j = 1..n] matrix[j][i].

[edit] Euphoria

function transpose(sequence in)
sequence out
out = repeat(repeat(0,length(in)),length(in[1]))
for n = 1 to length(in) do
for m = 1 to length(in[1]) do
out[m][n] = in[n][m]
end for
end for
return out
end function
 
sequence m
m = {
{1,2,3,4},
{5,6,7,8},
{9,10,11,12}
}
 
? transpose(m)

Output:

 {
   {1,5,9},
   {2,6,10},
   {3,7,11},
   {4,8,12}
 }

[edit] Factor

flip can be used.

( scratchpad ) { { 1 2 3 } { 4 5 6 } } flip .
{ { 1 4 } { 2 5 } { 3 6 } }

[edit] Fortran

In ISO Fortran 90 or later, use the TRANSPOSE intrinsic function:

integer, parameter   :: n = 3, m = 5
real, dimension(n,m) :: a = reshape( (/ (i,i=1,n*m) /), (/ n, m /) )
real, dimension(m,n) :: b
 
b = transpose(a)
 
do i = 1, n
print *, a(i,:)
end do
 
do j = 1, m
print *, b(j,:)
end do

In ANSI FORTRAN 77 with MIL-STD-1753 extensions or later, use nested structured DO loops:

REAL A(3,5), B(5,3)
DATA ((A(I,J),I=1,3),J=1,5) /1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15/
 
DO I = 1, 3
DO J = 1, 5
B(J,I) = A(I,J)
END DO
END DO

In ANSI FORTRAN 66 or later, use nested labeled DO loops:

   REAL A(3,5), B(5,3)
DATA ((A(I,J),I=1,3),J=1,5) /1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15/
 
DO 10 I = 1, 3
DO 20 J = 1, 5
B(J,I) = A(I,J)
20 CONTINUE
10 CONTINUE

[edit] F#

Very straightforward solution...

let transpose (mtx : _ [,]) = Array2D.init (mtx.GetLength 1) (mtx.GetLength 0) (fun x y -> mtx.[y,x])

[edit] GAP

originalMatrix := [[1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25, 125, 625]];
transposedMatrix := TransposedMat(originalMatrix);

[edit] Go

[edit] 2D representation

Go arrays and slices are only one-dimensional. The obvious way to represent two-dimensional arrays is with a slice of slices:

package main
 
import "fmt"
 
type row []float64
type matrix []row
 
func main() {
m := matrix{
{1, 2, 3},
{4, 5, 6},
}
printMatrix(m)
t := transpose(m)
printMatrix(t)
}
 
func printMatrix(m matrix) {
for _, s := range m {
fmt.Println(s)
}
}
 
func transpose(m matrix) matrix {
r := make(matrix, len(m[0]))
for x, _ := range r {
r[x] = make(row, len(m))
}
for y, s := range m {
for x, e := range s {
r[x][y] = e
}
}
return r
}
Output:
[1 2 3]
[4 5 6]
[1 4]
[2 5]
[3 6]

[edit] Flat representation

Slices of slices turn out to have disadvantages. It is possible to construct ill-formed matricies with a different number of elements on different rows, for example. They require multiple allocations, and the compiler must generate complex address calculations to index elements.

A flat element representation with a stride is almost always better.

package main
 
import "fmt"
 
type matrix struct {
ele []float64
stride int
}
 
// construct new matrix from slice of slices
func matrixFromRows(rows [][]float64) *matrix {
if len(rows) == 0 {
return &matrix{nil, 0}
}
m := &matrix{make([]float64, len(rows)*len(rows[0])), len(rows[0])}
for rx, row := range rows {
copy(m.ele[rx*m.stride:(rx+1)*m.stride], row)
}
return m
}
 
func main() {
m := matrixFromRows([][]float64{
{1, 2, 3},
{4, 5, 6},
})
m.print("original:")
m.transpose().print("transpose:")
}
 
func (m *matrix) print(heading string) {
if heading > "" {
fmt.Print("\n", heading, "\n")
}
for e := 0; e < len(m.ele); e += m.stride {
fmt.Println(m.ele[e : e+m.stride])
}
}
 
func (m *matrix) transpose() *matrix {
r := &matrix{make([]float64, len(m.ele)), len(m.ele) / m.stride}
rx := 0
for _, e := range m.ele {
r.ele[rx] = e
rx += r.stride
if rx >= len(r.ele) {
rx -= len(r.ele) - 1
}
}
return r
}
Output:
original:
[1 2 3]
[4 5 6]

transpose:
[1 4]
[2 5]
[3 6]

[edit] Transpose in place

Translation of: C

Note representation is "flat," as above.

package main
 
import "fmt"
 
type matrix struct {
ele []float64
stride int
}
 
// construct new matrix from slice of slices
func matrixFromRows(rows [][]float64) *matrix {
if len(rows) == 0 {
return &matrix{nil, 0}
}
m := &matrix{make([]float64, len(rows)*len(rows[0])), len(rows[0])}
for rx, row := range rows {
copy(m.ele[rx*m.stride:(rx+1)*m.stride], row)
}
return m
}
 
func main() {
m := matrixFromRows([][]float64{
{1, 2, 3},
{4, 5, 6},
})
m.print("original:")
m.transposeInPlace()
m.print("transpose:")
}
 
func (m *matrix) print(heading string) {
if heading > "" {
fmt.Print("\n", heading, "\n")
}
for e := 0; e < len(m.ele); e += m.stride {
fmt.Println(m.ele[e : e+m.stride])
}
}
 
func (m *matrix) transposeInPlace() {
h := len(m.ele) / m.stride
for start := range m.ele {
next := start
i := 0
for {
i++
next = (next%h)*m.stride + next/h
if next <= start {
break
}
}
if next < start || i == 1 {
continue
}
 
next = start
tmp := m.ele[next]
for {
i = (next%h)*m.stride + next/h
if i == start {
m.ele[next] = tmp
} else {
m.ele[next] = m.ele[i]
}
next = i
if next <= start {
break
}
}
}
m.stride = h
}

Output same as above.

[edit] Library

package main
 
import (
"fmt"
 
mat "github.com/skelterjohn/go.matrix"
)
 
func main() {
m := mat.MakeDenseMatrixStacked([][]float64{
{1, 2, 3},
{4, 5, 6},
})
fmt.Println("original:")
fmt.Println(m)
m = m.Transpose()
fmt.Println("transpose:")
fmt.Println(m)
}
Output:
original:
{1, 2, 3,
 4, 5, 6}
transpose:
{1, 4,
 2, 5,
 3, 6}

[edit] Groovy

The Groovy extensions to the List class provides a transpose method:

def matrix = [ [ 1, 2, 3, 4 ],
[ 5, 6, 7, 8 ] ]
 
matrix.each { println it }
println()
def transpose = matrix.transpose()
 
transpose.each { println it }

Output:

[1, 2, 3, 4]
[5, 6, 7, 8]

[1, 5]
[2, 6]
[3, 7]
[4, 8]

[edit] Haskell

For matrices represented as lists, there's transpose:

*Main> transpose [[1,2],[3,4],[5,6]]
[[1,3,5],[2,4,6]]

For matrices in arrays, one can use ixmap:

import Data.Array
 
swap (x,y) = (y,x)
 
transpArray :: (Ix a, Ix b) => Array (a,b) e -> Array (b,a) e
transpArray a = ixmap (swap l, swap u) swap a where
(l,u) = bounds a

[edit] Hope

uses lists;
dec transpose : list (list alpha) -> list (list alpha);
--- transpose ([]::_) <= [];
--- transpose n <= map head n :: transpose (map tail n);

[edit] HicEst

REAL :: mtx(2, 4)
 
mtx = 1.1 * $
WRITE() mtx
 
SOLVE(Matrix=mtx, Transpose=mtx)
WRITE() mtx

Output:

1.1 2.2 3.3 4.4 
5.5 6.6 7.7 8.8
 
1.1 5.5
2.2 6.6
3.3 7.7
4.4 8.8

[edit] Icon and Unicon

procedure transpose_matrix (matrix)
result := []
# for each column
every (i := 1 to *matrix[1]) do {
col := []
# extract the number in each row for that column
every (row := !matrix) do put (col, row[i])
# and push that column as a row in the result matrix
put (result, col)
}
return result
end
 
procedure print_matrix (matrix)
every (row := !matrix) do {
every writes (!row || " ")
write ()
}
end
 
procedure main ()
matrix := [[1,2,3],[4,5,6]]
write ("Start:")
print_matrix (matrix)
transposed := transpose_matrix (matrix)
write ("Transposed:")
print_matrix (transposed)
end

Output:

Start:
1 2 3 
4 5 6 
Transposed:
1 4 
2 5 
3 6

[edit] IDL

Standard IDL function transpose()

m=[[1,1,1,1],[2, 4, 8, 16],[3, 9,27, 81],[5, 25,125, 625]]
print,transpose(m)

[edit] J

Solution:
Transpose is the monadic primary verb |:

Example:

   ]matrix=: (^/ }:) >:i.5    NB. make and show example matrix
1 1 1 1
2 4 8 16
3 9 27 81
4 16 64 256
5 25 125 625
|: matrix
1 2 3 4 5
1 4 9 16 25
1 8 27 64 125
1 16 81 256 625

[edit] Java

import java.util.Arrays;
public class Transpose{
public static void main(String[] args){
double[][] m = {{1, 1, 1, 1},
{2, 4, 8, 16},
{3, 9, 27, 81},
{4, 16, 64, 256},
{5, 25, 125, 625}};
double[][] ans = new double[m[0].length][m.length];
for(int rows = 0; rows < m.length; rows++){
for(int cols = 0; cols < m[0].length; cols++){
ans[cols][rows] = m[rows][cols];
}
}
for(double[] i:ans){//2D arrays are arrays of arrays
System.out.println(Arrays.toString(i));
}
}
}

[edit] JavaScript

Works with: SpiderMonkey
for the print() function
function Matrix(ary) {
this.mtx = ary
this.height = ary.length;
this.width = ary[0].length;
}
 
Matrix.prototype.toString = function() {
var s = []
for (var i = 0; i < this.mtx.length; i++)
s.push( this.mtx[i].join(",") );
return s.join("\n");
}
 
// returns a new matrix
Matrix.prototype.transpose = function() {
var transposed = [];
for (var i = 0; i < this.width; i++) {
transposed[i] = [];
for (var j = 0; j < this.height; j++) {
transposed[i][j] = this.mtx[j][i];
}
}
return new Matrix(transposed);
}
 
var m = new Matrix([[1,1,1,1],[2,4,8,16],[3,9,27,81],[4,16,64,256],[5,25,125,625]]);
print(m);
print();
print(m.transpose());

produces

1,1,1,1
2,4,8,16
3,9,27,81
4,16,64,256
5,25,125,625

1,2,3,4,5
1,4,9,16,25
1,8,27,64,125
1,16,81,256,625

Transposition using functional style influence

 
transpose = function(a) {
return a[0].map(function(x,i) {
return a.map(function(y,k) {
return y[i];
});
});
}
 
A = [[1,2,3],[4,5,6],[7,8,9],[10,11,12]];
 
JSON.stringify(transpose(A));
"[[1,4,7,10],[2,5,8,11],[3,6,9,12]]"
 

[edit] Joy

For matrices represented as lists, there's transpose, defined in seqlib like this:

DEFINE transpose == [ [null] [true] [[null] some] ifte ]
[ pop [] ]
[ [[first] map] [[rest] map] cleave ]
[ cons ]
linrec .

[edit] Julia

The transposition is obtained by quoting the matrix.

julia> [1 2 3 ; 4 5 6]  # a 2x3 matrix
2x3 Array{Int64,2}:
1 2 3
4 5 6
 
julia> [1 2 3 ; 4 5 6]' # note the quote
3x2 Array{Int64,2}:
1 4
2 5
3 6

[edit] K

Transpose is the monadic verb +

  {x^\:-1_ x}1+!:5
(1 1 1 1.0
2 4 8 16.0
3 9 27 81.0
4 16 64 256.0
5 25 125 625.0)
 
+{x^\:-1_ x}1+!:5
(1 2 3 4 5.0
1 4 9 16 25.0
1 8 27 64 125.0
1 16 81 256 625.0)

[edit] Lang5

12 iota [3 4] reshape 1 + dup .
1 transpose .
Output:
[
  [    1     2     3     4  ]
  [    5     6     7     8  ]
  [    9    10    11    12  ]
][
  [    1     5     9  ]
  [    2     6    10  ]
  [    3     7    11  ]
  [    4     8    12  ]
]

[edit] Liberty BASIC

There is no native matrix capability. A set of functions is available at http://www.diga.me.uk/RCMatrixFuncs.bas implementing matrices of arbitrary dimension in a string format.

MatrixC$ ="4, 3,          0, 0.10, 0.20, 0.30,       0.40, 0.50, 0.60, 0.70,      0.80, 0.90, 1.00, 1.10"
 
print "Transpose of matrix"
call DisplayMatrix MatrixC$
print " ="
MatrixT$ =MatrixTranspose$( MatrixC$)
call DisplayMatrix MatrixT$

Transpose of matrix
| 0.00000 0.10000 0.20000 0.30000 |
| 0.40000 0.50000 0.60000 0.70000 |
| 0.80000 0.90000 1.00000 1.10000 |

=
| 0.00000 0.40000 0.80000 |
| 0.10000 0.50000 0.90000 |
| 0.20000 0.60000 1.00000 |
| 0.30000 0.70000 1.10000 |

[edit] Lua

function Transpose( m )
local res = {}
 
for i = 1, #m[1] do
res[i] = {}
for j = 1, #m do
res[i][j] = m[j][i]
end
end
 
return res
end
 
-- a test for Transpose(m)
mat = { { 1, 2, 3 }, { 4, 5, 6 } }
erg = Transpose( mat )
for i = 1, #erg do
for j = 1, #erg[1] do
io.write( erg[i][j] )
io.write( " " )
end
io.write( "\n" )
end

Using apply map list

function map(f, a)
local b = {}
for k,v in ipairs(a) do b[k] = f(v) end
return b
end
 
function mapn(f, ...)
local c = {}
local k = 1
local aarg = {...}
local n = table.getn(aarg)
while true do
local a = map(function(b) return b[k] end, aarg)
if table.getn(a) < n then return c end
c[k] = f(unpack(a))
k = k + 1
end
end
 
function apply(f1, f2, a)
return f1(f2, unpack(a))
end
 
xy = {{1,2,3,4},{1,2,3,4},{1,2,3,4}}
yx = apply(mapn, function(...) return {...} end, xy)
print(table.concat(map(function(a) return table.concat(a,",") end, xy), "\n"),"\n")
print(table.concat(map(function(a) return table.concat(a,",") end, yx), "\n"))


[edit] Maple

The Transpose function in Maple's LinearAlgebra package computes this. The computation can also be accomplished by raising the Matrix to the %T power. Similarly for HermitianTranspose and the %H power.

 
M := <<2,3>|<3,4>|<5,6>>;
 
M^%T;
 
with(LinearAlgebra):
Transpose(M);
 

Output:

                                    [2  3  5]
                               M := [       ]
                                    [3  4  6]

                                   [2  3]
                                   [    ]
                                   [3  4]
                                   [    ]
                                   [5  6]

                                   [2  3]
                                   [    ]
                                   [3  4]
                                   [    ]
                                   [5  6]

[edit] Mathematica

originalMatrix = {{1, 1, 1, 1},
{2, 4, 8, 16},
{3, 9, 27, 81},
{4, 16, 64, 256},
{5, 25, 125, 625}}
transposedMatrix = Transpose[originalMatrix]

[edit] MATLAB / Octave

Matlab contains two built-in methods of transposing a matrix: by using the transpose() function, or by using the .' operator. The ' operator yields the complex conjugate transpose.

>> transpose([1 2;3 4])
 
ans =
 
1 3
2 4
 
>> [1 2;3 4].'
 
ans =
 
1 3
2 4

But, you can, obviously, do the transposition of a matrix without a built-in method, in this case, the code can be this hereafter code:

 
 
B=size(A); %In this code, we assume that a previous matrix "A" has already been inputted.
for j=1:B(1)
for i=1:B(2)
C(i,j)=A(j,i);
end %The transposed A-matrix should be C
end
 
 

Transposing nested cells using apply map list

xy = {{1,2,3,4},{1,2,3,4},{1,2,3,4}}
yx = feval(@(x) cellfun(@(varargin)[varargin],x{:},'un',0), xy)

[edit] Maxima

originalMatrix : matrix([1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25, 125, 625]);
transposedMatrix : transpose(originalMatrix);

[edit] MAXScript

Uses the built in transpose() function

m = bigMatrix 5 4
for i in 1 to 5 do for j in 1 to 4 do m[i][j] = pow i j
m = transpose m

[edit] Nial

make an array

|a := 2 3 reshape count 6
=1 2 3
=4 5 6

transpose it

|transpose a
=1 4
=2 5
=3 6

[edit] Nimrod

For statically sized arrays:

proc transpose[X, Y; T](s: array[Y, array[X, T]]): array[X, array[Y, T]] =
for i in low(X)..high(X):
for j in low(Y)..high(Y):
result[i][j] = s[j][i]
 
let b = [[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[ 1, 0, 0, 0,42]]
let c = transpose(b)
for r in c:
for i in r:
stdout.write i, " "
echo ""

Output:

0 5 1 
1 6 0 
2 7 0 
3 8 0 
4 9 42

For dynamically sized seqs:

proc transpose[T](s: seq[seq[T]]): seq[seq[T]] =
result = newSeq[seq[T]](s[0].len)
for i in 0 .. < s[0].len:
result[i] = newSeq[T](s.len)
for j in 0 .. < s.len:
result[i][j] = s[j][i]
 
let a = @[@[ 0, 1, 2, 3, 4],
@[ 5, 6, 7, 8, 9],
@[ 1, 0, 0, 0,42]]
echo transpose(a)

Output:

@[@[0, 5, 1], @[1, 6, 0], @[2, 7, 0], @[3, 8, 0], @[4, 9, 42]]

[edit] Objeck

 
bundle Default {
class Transpose {
function : Main(args : String[]) ~ Nil {
input := [[1, 1, 1, 1]
[2, 4, 8, 16]
[3, 9, 27, 81]
[4, 16, 64, 256]
[5, 25, 125, 625]];
dim := input->Size();
 
output := Int->New[dim[0],dim[1]];
for(i := 0; i < dim[0]; i+=1;) {
for(j := 0; j < dim[1]; j+=1;) {
output[i,j] := input[i,j];
};
};
 
Print(output);
}
 
function : Print(matrix : Int[,]) ~ Nil {
dim := matrix->Size();
for(i := 0; i < dim[0]; i+=1;) {
for(j := 0; j < dim[1]; j+=1;) {
IO.Console->Print(matrix[i,j])->Print('\t');
};
'\n'->Print();
};
}
}
}
 

Output:

1	2	3	4	5	
1	4	9	16	25	
1	8	27	64	125	
1	16	81	256	625

[edit] OCaml

Matrices can be represented in OCaml as a type 'a array array, or using the module Bigarray. The implementation below uses a bigarray:

open Bigarray
 
let transpose b =
let dim1 = Array2.dim1 b
and dim2 = Array2.dim2 b in
let kind = Array2.kind b
and layout = Array2.layout b in
let b' = Array2.create kind layout dim2 dim1 in
for i=0 to pred dim1 do
for j=0 to pred dim2 do
b'.{j,i} <- b.{i,j}
done;
done;
(b')
;;
 
let array2_display print newline b =
for i=0 to Array2.dim1 b - 1 do
for j=0 to Array2.dim2 b - 1 do
print b.{i,j}
done;
newline();
done;
;;
 
let a = Array2.of_array int c_layout [|
[| 1; 2; 3; 4 |];
[| 5; 6; 7; 8 |];
|]
 
array2_display (Printf.printf " %d") print_newline (transpose a) ;;

This will output:

1 5
2 6
3 7
4 8

A version for lists:

let rec transpose m =
assert (m <> []);
if List.mem [] m then
[]
else
List.map List.hd m :: transpose (List.map List.tl m)

Example:

# transpose [[1;2;3;4];
             [5;6;7;8]];;
- : int list list = [[1; 5]; [2; 6]; [3; 7]; [4; 8]]

[edit] Octave

a = [ 1, 1, 1, 1 ;
2, 4, 8, 16 ;
3, 9, 27, 81 ;
4, 16, 64, 256 ;
5, 25, 125, 625 ];
tranposed = a.'; % tranpose
ctransp = a'; % conjugate transpose

[edit] OxygenBasic

 
function Transpose(double *A,*B, sys nx,ny)
'==========================================
sys x,y
indexbase 0
for x=0 to <nx
for y=0 to <ny
B[y*nx+x]=A[x*ny+y]
next
next
end function
 
function MatrixShow(double*A, sys nx,ny) as string
'=================================================
sys x,y
indexbase 0
string pr="",tab=chr(9),cr=chr(13)+chr(10)
for y=0 to <ny
for x=0 to <nx
pr+=tab A[x*ny+y]
next
pr+=cr
next
return pr
end function
 
'====
'DEMO
'====
 
double A[5*4],B[4*5]
'columns x
'rows y
 
A <= 'y minor, x major
11,12,13,14,15,
21,22,23,24,25,
31,32,33,34,35,
41,42,43,44,45
 
print MatrixShow A,5,4
Transpose A,B,5,4
print MatrixShow B,4,5
 

[edit] PARI/GP

The GP function for matrix (or vector) transpose is mattranspose, but it is usually invoked with a tilde:

M~

In PARI the function is

gtrans(M)

though shallowtrans is also available when deep copying is not desired.

[edit] Pascal

Program Transpose;
 
const
A: array[1..3,1..5] of integer = (( 1, 2, 3, 4, 5),
( 6, 7, 8, 9, 10),
(11, 12, 13, 14, 15)
);
var
B: array[1..5,1..3] of integer;
i, j: integer;
 
begin
for i := low(A) to high(A) do
for j := low(A[1]) to high(A[1]) do
B[j,i] := A[i,j];
 
writeln ('A:');
for i := low(A) to high(A) do
begin
for j := low(A[1]) to high(A[1]) do
write (A[i,j]:3);
writeln;
end;
 
writeln ('B:');
for i := low(B) to high(B) do
begin
for j := low(B[1]) to high(B[1]) do
write (B[i,j]:3);
writeln;
end;
end.

Output:

% ./Transpose
A:
  1  2  3  4  5
  6  7  8  9 10
 11 12 13 14 15
B:
  1  6 11
  2  7 12
  3  8 13
  4  9 14
  5 10 15

[edit] Perl

use Math::Matrix;
 
$m = Math::Matrix->new(
[1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25, 125, 625],
);
 
$m->transpose->print;

Output:

1.00000    2.00000    3.00000    4.00000    5.00000 
1.00000    4.00000    9.00000   16.00000   25.00000 
1.00000    8.00000   27.00000   64.00000  125.00000 
1.00000   16.00000   81.00000  256.00000  625.00000

Manually:

my @m = (
[1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25, 125, 625],
);
 
my @transposed;
foreach my $j (0..$#{$m[0]}) {
push(@transposed, [map $_->[$j], @m]);
}

[edit] Perl 6

sub transpose(@m)
{
my @t;
for ^@m X ^@m[0] -> $x, $y { @t[$y][$x] = @m[$x][$y] }
return @t;
}
 
# creates a random matrix
my @a;
for (^10).pick X (^10).pick -> $x, $y { @a[$x][$y] = (^100).pick; }
 
say "original: ";
.perl.say for @a;
 
my @b = transpose(@a);
 
say "transposed: ";
.perl.say for @b;

A more concise solution:

sub transpose (@m) { 
@m[0].keys.map: {[ @m».[$_] ]};
}
 
my @a = [< a b c d e >],
[< f g h i j >],
[< k l m n o >],
[< p q r s t >];
 
.say for @a.&transpose;

Output:

a f k p
b g l q
c h m r
d i n s
e j o t

[edit] PHP

function transpose($m) {
if (count($m) == 0) // special case: empty matrix
return array();
else if (count($m) == 1) // special case: row matrix
return array_chunk($m[0], 1);
 
// array_map(NULL, m[0], m[1], ..)
array_unshift($m, NULL); // the original matrix is not modified because it was passed by value
return call_user_func_array('array_map', $m);
}

[edit] PicoLisp

(de matTrans (Mat)
(apply mapcar Mat list) )
 
(matTrans '((1 2 3) (4 5 6)))

Output:

-> ((1 4) (2 5) (3 6))

[edit] PL/I

/* The short method: */
declare A(m, n) float, B (n,m) float defined (A(2sub, 1sub));
/* Any reference to B gives the transpose of matrix A. */

Traditional method:

/* Transpose matrix A, result at B. */
transpose: procedure (a, b);
declare (a, b) (*,*) float controlled;
declare (m, n) fixed binary;
 
if allocation(b) > 0 then free b;
 
m = hbound(a,1); n = hbound(a,2);
 
allocate b(n,m);
 
do i = 1 to m;
b(*,i) = a(i,*);
end;
end transpose;

[edit] Pop11

define transpose(m) -> res;
lvars bl = boundslist(m);
if length(bl) /= 4 then
throw([need_2d_array ^a])
endif;
lvars i, i0 = bl(1), i1 = bl(2);
lvars j, j0 = bl(3), j1 = bl(4);
newarray([^j0 ^j1 ^i0 ^i1], 0) -> res;
for i from i0 to i1 do
for j from j0 to j1 do
m(i, j) -> res(j, i);
endfor;
endfor;
enddefine;

[edit] PostScript

Library: initlib
/transpose {
[ exch {
{ {empty? exch pop} map all?} {pop exit} ift
[ exch {} {uncons {exch cons} dip exch} fold counttomark 1 roll] uncons
} loop ] {reverse} map
}.

[edit] Prolog

Predicate transpose/2 exists in libray clpfd of SWI-Prolog.
In Prolog, a matrix is a list of lists. transpose/2 can be written like that.

Works with: SWI-Prolog
% transposition of a rectangular matrix
% e.g. [[1,2,3,4], [5,6,7,8]]
% give [[1,5],[2,6],[3,7],[4,8]]
 
transpose(In, Out) :-
In = [H | T],
maplist(initdl, H, L),
work(T, In, Out).
 
% we use the difference list to make "quick" appends (one inference)
initdl(V, [V | X] - X).
 
work(Lst, [H], Out) :-
maplist(my_append_last, Lst, H, Out).
 
work(Lst, [H | T], Out) :-
maplist(my_append, Lst, H, Lst1),
work(Lst1, T, Out).
 
my_append(X-Y, C, X1-Y1) :-
append_dl(X-Y, [C | U]- U, X1-Y1).
 
my_append_last(X-Y, C, X1) :-
append_dl(X-Y, [C | U]- U, X1-[]).
 
% "quick" append
append_dl(X-Y, Y-Z, X-Z).

[edit] PureBasic

Matrices represented by integer arrays using rows as the first dimension and columns as the second dimension.

Procedure transposeMatrix(Array a(2), Array trans(2))
Protected rows, cols
 
Protected ar = ArraySize(a(), 1) ;rows in original matrix
Protected ac = ArraySize(a(), 2) ;cols in original matrix
 
;size the matrix receiving the transposition
Dim trans(ac, ar)
 
;copy the values
For rows = 0 To ar
For cols = 0 To ac
trans(cols, rows) = a(rows, cols)
Next
Next
EndProcedure
 
Procedure displayMatrix(Array a(2), text.s = "")
Protected i, j
Protected cols = ArraySize(a(), 2), rows = ArraySize(a(), 1)
 
PrintN(text + ": (" + Str(rows + 1) + ", " + Str(cols + 1) + ")")
For i = 0 To rows
For j = 0 To cols
Print(LSet(Str(a(i, j)), 4, " "))
Next
PrintN("")
Next
PrintN("")
EndProcedure
 
;setup a matrix of arbitrary size
Dim m(random(5), random(5))
 
Define rows, cols
;fill matrix with 'random' data
For rows = 0 To ArraySize(m(),1) ;ArraySize() can take a dimension as its second argument
For cols = 0 To ArraySize(m(), 2)
m(rows, cols) = random(10) - 10
Next
Next
 
Dim t(0,0) ;this will be resized during transposition
If OpenConsole()
displayMatrix(m(), "matrix before transposition")
transposeMatrix(m(), t())
displayMatrix(t(), "matrix after transposition")
 
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
EndIf

Sample output:

matrix m, before: (3, 4)
-4  -9  -7  -9
-3  -6  -4  -6
-1  -2  0   -6

matrix m after transposition: (4, 3)
-4  -3  -1
-9  -6  -2
-7  -4  0
-9  -6  -6

[edit] Python

m=((1,  1,  1,   1),
(2, 4, 8, 16),
(3, 9, 27, 81),
(4, 16, 64, 256),
(5, 25,125, 625))
print(zip(*m))
# in Python 3.x, you would do:
# print(list(zip(*m)))

Output:

[(1, 2, 3, 4, 5),
 (1, 4, 9, 16, 25),
 (1, 8, 27, 64, 125),
 (1, 16, 81, 256, 625)]

[edit] R

b <- 1:5
m <- matrix(c(b, b^2, b^3, b^4), 5, 4)
print(m)
tm <- t(m)
print(tm)

[edit] Racket

 
#lang racket
(require math)
(matrix-transpose (matrix [[1 2] [3 4]]))
 

Output:

(array #[#[1 3] #[2 4]])

[edit] Rascal

public rel[real, real, real] matrixTranspose(rel[real x, real y, real v] matrix){
return {<y, x, v> | <x, y, v> <- matrix};
}
 
//a matrix
public rel[real x, real y, real v] matrixA = {
<0.0,0.0,12.0>, <0.0,1.0, 6.0>, <0.0,2.0,-4.0>,
<1.0,0.0,-51.0>, <1.0,1.0,167.0>, <1.0,2.0,24.0>,
<2.0,0.0,4.0>, <2.0,1.0,-68.0>, <2.0,2.0,-41.0>
};

[edit] REXX

/*REXX program transposes a matrix,  shows  before and after  matrixes. */
x. =
x.1 = 1.02 2.03 3.04 4.05 5.06 6.07 7.07
x.2 = 111 2222 33333 444444 5555555 66666666 777777777
 
do r=1 while x.r\=='' /*build the "A" matric from X. numbers */
do c=1 while x.r\==''
parse var x.r a.r.c x.r
end /*c*/
end /*r*/
 
rows = r-1; cols = c-1
L=0 /*L is the maximum width element value.*/
do i=1 for rows
do j=1 for cols
b.j.i = a.i.j; L=max(L,length(b.j.i))
end /*j*/
end /*i*/
 
call showMat 'A', rows, cols
call showMat 'B', cols, rows
exit /*stick a fork in it, we're done.*/
/*─────────────────────────────────────SHOWMAT subroutine───────────────*/
showMat: parse arg mat,rows,cols; say
say center(mat 'matrix', cols*(L+1) +4, "─")
 
do r=1 for rows; _=
do c=1 for cols; _ = _ right(value(mat'.'r'.'c), L)
end /*c*/
say _
end /*r*/
return

output

─────────────────────────────────A matrix─────────────────────────────────
      1.02      2.03      3.04      4.05      5.06      6.07      7.07
       111      2222     33333    444444   5555555  66666666 777777777

────────B matrix────────
      1.02       111
      2.03      2222
      3.04     33333
      4.05    444444
      5.06   5555555
      6.07  66666666
      7.07 777777777

[edit] RLaB

 >> m = rand(3,5)
0.41844289 0.476591435 0.75054022 0.226388925 0.963880314
0.91267171 0.941762397 0.464227895 0.693482786 0.203839405
0.261512966 0.157981873 0.26582235 0.11557427 0.0442493069
>> m'
0.41844289 0.91267171 0.261512966
0.476591435 0.941762397 0.157981873
0.75054022 0.464227895 0.26582235
0.226388925 0.693482786 0.11557427
0.963880314 0.203839405 0.0442493069

[edit] Ruby

m=[[1,  1,  1,   1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25,125, 625]]
puts m.transpose

Output:

[[1, 2, 3, 4, 5], [1, 4, 9, 16, 25], [1, 8, 27, 64, 125], [1, 16, 81, 256, 625]]

or using 'matrix' from the standard library

require 'matrix'
 
m=Matrix[[1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25,125, 625]]
puts m.transpose

Output:

Matrix[[1, 2, 3, 4, 5], [1, 4, 9, 16, 25], [1, 8, 27, 64, 125], [1, 16, 81, 256, 625]]

or using zip:

def transpose(m)
m[0].zip(*m[1..-1])
end
p transpose([[1,2,3],[4,5,6]])

Output:

 [[1, 4], [2, 5], [3, 6]]

[edit] Run BASIC

mtrx$ ="4, 3,   0, 0.10, 0.20, 0.30,   0.40, 0.50, 0.60, 0.70,  0.80, 0.90, 1.00, 1.10"
 
print "Transpose of matrix"
call DisplayMatrix mtrx$
print " ="
MatrixT$ =MatrixTranspose$(mtrx$)
call DisplayMatrix MatrixT$
 
end
 
function MatrixTranspose$(in$)
w = val(word$(in$, 1, ",")) ' swap w and h parameters
h = val(word$(in$, 2, ","))
t$ = str$(h); ","; str$(w); ","
for i =1 to w
for j =1 to h
t$ = t$ +word$(in$, 2 +i +(j -1) *w, ",") +","
next j
next i
MatrixTranspose$ =left$(t$, len(t$) -1)
end function
 
sub DisplayMatrix in$ ' Display looking like a matrix!
html "<table border=2>"
w = val(word$(in$, 1, ","))
h = val(word$(in$, 2, ","))
for i =0 to h -1
html "<tr align=right>"
for j =1 to w
term$ = word$(in$, j +2 +i *w, ",")
html "<td>";val(term$);"</td>"
next j
html "</tr>"
next i
html "</table>"
end sub
Output:
Transpose of matrix
00.10.20.3
0.40.50.60.7
0.80.91.01.1
=
00.40.8
0.10.50.9
0.20.61.0
0.30.71.1

[edit] Scala

scala> Array.tabulate(4)(i => Array.tabulate(4)(j => i*4 + j))
res12: Array[Array[Int]] = Array(Array(0, 1, 2, 3), Array(4, 5, 6, 7), Array(8, 9, 10, 11), Array(12, 13, 14, 15))
 
scala> res12.transpose
res13: Array[Array[Int]] = Array(Array(0, 4, 8, 12), Array(1, 5, 9, 13), Array(2, 6, 10, 14), Array(3, 7, 11, 15))
 
scala> res12 map (_ map ("%2d" format _) mkString " ") mkString "\n"
res16: String =
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
 
scala> res13 map (_ map ("%2d" format _) mkString " ") mkString "\n"
res17: String =
0 4 8 12
1 5 9 13
2 6 10 14
3 7 11 15

[edit] Scheme

(define (transpose m)
(apply map list m))

[edit] Seed7

$ include "seed7_05.s7i";
include "float.s7i";
 
const type: matrix is array array float;
 
const func matrix: transpose (in matrix: aMatrix) is func
result
var matrix: transposedMatrix is matrix.value;
local
var integer: i is 0;
var integer: j is 0;
begin
transposedMatrix := length(aMatrix[1]) times length(aMatrix) times 0.0;
for i range 1 to length(aMatrix) do
for j range 1 to length(aMatrix[1]) do
transposedMatrix[j][i] := aMatrix[i][j];
end for;
end for;
end func;
 
const proc: write (in matrix: aMatrix) is func
local
var integer: line is 0;
var integer: column is 0;
begin
for line range 1 to length(aMatrix) do
for column range 1 to length(aMatrix[line]) do
write(" " <& aMatrix[line][column] digits 2);
end for;
writeln;
end for;
end func;
 
const matrix: testMatrix is [] (
[] (0.0, 0.1, 0.2, 0.3),
[] (0.4, 0.5, 0.6, 0.7),
[] (0.8, 0.9, 1.0, 1.1));
 
const proc: main is func
begin
writeln("Before Transposition:");
write(testMatrix);
writeln;
writeln("After Transposition:");
write(transpose(testMatrix));
end func;

Output:

Before Transposition:
 0.00 0.10 0.20 0.30
 0.40 0.50 0.60 0.70
 0.80 0.90 1.00 1.10

After Transposition:
 0.00 0.40 0.80
 0.10 0.50 0.90
 0.20 0.60 1.00
 0.30 0.70 1.10

[edit] Sidef

func transpose(matrix) {
matrix[0].range.map{|i| matrix.map{_[i]}};
};
 
var m = [
[1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25, 125, 625],
];
 
transpose(m).each { |row|
"%5d" * row.len -> printlnf(row->...);
}
Output:
    1    2    3    4    5
    1    4    9   16   25
    1    8   27   64  125
    1   16   81  256  625

[edit] Sparkling

function transpose(A) {
return map(range(sizeof A), function(k, idx) {
return map(A, function(k, row) {
return row[idx];
});
});
}

[edit] Tcl

With core Tcl, representing a matrix as a list of lists:

package require Tcl 8.5
namespace path ::tcl::mathfunc
 
proc size {m} {
set rows [llength $m]
set cols [llength [lindex $m 0]]
return [list $rows $cols]
}
proc transpose {m} {
lassign [size $m] rows cols
set new [lrepeat $cols [lrepeat $rows ""]]
for {set i 0} {$i < $rows} {incr i} {
for {set j 0} {$j < $cols} {incr j} {
lset new $j $i [lindex $m $i $j]
}
}
return $new
}
proc print_matrix {m {fmt "%.17g"}} {
set max [widest $m $fmt]
lassign [size $m] rows cols
for {set i 0} {$i < $rows} {incr i} {
for {set j 0} {$j < $cols} {incr j} {
set s [format $fmt [lindex $m $i $j]]
puts -nonewline [format "%*s " [lindex $max $j] $s]
}
puts ""
}
}
proc widest {m {fmt "%.17g"}} {
lassign [size $m] rows cols
set max [lrepeat $cols 0]
for {set i 0} {$i < $rows} {incr i} {
for {set j 0} {$j < $cols} {incr j} {
set s [format $fmt [lindex $m $i $j]]
lset max $j [max [lindex $max $j] [string length $s]]
}
}
return $max
}
 
set m {{1 1 1 1} {2 4 8 16} {3 9 27 81} {4 16 64 256} {5 25 125 625}}
print_matrix $m "%d"
print_matrix [transpose $m] "%d"

outputs

1  1   1   1 
2  4   8  16 
3  9  27  81 
4 16  64 256 
5 25 125 625 
1  2  3   4   5 
1  4  9  16  25 
1  8 27  64 125 
1 16 81 256 625
Library: Tcllib (Package: struct::matrix)
package require struct::matrix
struct::matrix M
M deserialize {5 4 {{1 1 1 1} {2 4 8 16} {3 9 27 81} {4 16 64 256} {5 25 125 625}}}
M format 2string
M transpose
M format 2string

outputs

1 1  1   1  
2 4  8   16 
3 9  27  81 
4 16 64  256
5 25 125 625
1 2 3 4 5
1 4 9 16 25
         
1 8 27 64 125
         
         
1 16 81 256 625
         
         

[edit] TI-83 BASIC, TI-89 BASIC

TI-83: Assuming the original matrix is in [A], place its transpose in [B]:

[A]T->[B]

The T operator can be found in the matrix math menu.

TI-89: The same except that matrix variables do not have special names:

AT → B

[edit] Ursala

Matrices are stored as lists of lists, and transposing them is a built in operation.

#cast %eLL
 
example =
 
~&K7 <
<1.,2.,3.,4.>,
<5.,6.,7.,8.>,
<9.,10.,11.,12.>>

For a more verbose version, replace the ~&K7 operator with the standard library function named transpose. Here is the output:

<
   <1.000000e+00,5.000000e+00,9.000000e+00>,
   <2.000000e+00,6.000000e+00,1.000000e+01>,
   <3.000000e+00,7.000000e+00,1.100000e+01>,
   <4.000000e+00,8.000000e+00,1.200000e+01>>

[edit] Wortel

The @zipm operator zips together an array of arrays, this is the same as transposition if the matrix is represented as an array of arrays.

@zipm [[1 2 3] [4 5 6] [7 8 9]]

Returns:

[[1 4 7] [2 5 8] [3 6 9]]
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