Matrix transposition
Transpose an arbitrarily sized rectangular Matrix.
You are encouraged to solve this task according to the task description, using any language you may know.
11l
<lang 11l>F transpose(&matrix)
V toRet = [[0] * matrix.len] * matrix[0].len
L(row) (0 .< matrix.len)
L(col) (0 .< matrix[row].len)
toRet[col][row] = matrix[row][col]
R toRet
V m = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] print("Original") print(m) print("After Transposition") print(transpose(&m))</lang>
- Output:
Original [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] After Transposition [[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]]
360 Assembly
<lang 360asm>... KN EQU 3 KM EQU 5 N DC AL2(KN) M DC AL2(KM) A DS (KN*KM)F matrix a(n,m) B DS (KM*KN)F matrix b(m,n) ...
- b(j,i)=a(i,j)
- transposition using Horner's formula
LA R4,0 i,from 1
LA R7,KN to n
LA R6,1 step 1
LOOPI BXH R4,R6,ELOOPI do i=1 to n
LA R5,0 j,from 1
LA R9,KM to m
LA R8,1 step 1
LOOPJ BXH R5,R8,ELOOPJ do j=1 to m
LR R1,R4 i
BCTR R1,0 i-1
MH R1,M (i-1)*m
LR R2,R5 j
BCTR R2,0 j-1
AR R1,R2 r1=(i-1)*m+(j-1)
SLA R1,2 r1=((i-1)*m+(j-1))*itemlen
L R0,A(R1) r0=a(i,j)
LR R1,R5 j
BCTR R1,0 j-1
MH R1,N (j-1)*n
LR R2,R4 i
BCTR R2,0 i-1
AR R1,R2 r1=(j-1)*n+(i-1)
SLA R1,2 r1=((j-1)*n+(i-1))*itemlen
ST R0,B(R1) b(j,i)=r0
B LOOPJ next j
ELOOPJ EQU * out of loop j
B LOOPI next i
ELOOPI EQU * out of loop i ...</lang>
ACL2
<lang Lisp>(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)))))</lang>
ActionScript
In ActionScript, multi-dimensional arrays are created by making an "Array of arrays" where each element is an array. <lang ActionScript>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]);</lang>
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: <lang ada>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;</lang>
- 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
Agda
<lang 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</lang>
b evaluates to the following normal form:
<lang agda>(1 ∷ 4 ∷ []) ∷ (2 ∷ 5 ∷ []) ∷ (3 ∷ 6 ∷ []) ∷ []</lang>
ALGOL 68
<lang algol68>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))
)</lang>
- 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));
APL
If M is a matrix, ⍉M is its transpose. For example, <lang 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 </lang>
AppleScript
We can do this iteratively, by manually setting up two nested loops, and initialising iterators and empty lists,
<lang applescript>on run
transpose([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
--> {{1, 4, 7, 10}, {2, 5, 8, 11}, {3, 6, 9, 12}}
end run
on transpose(xss)
set lstTrans to {}
repeat with iCol from 1 to length of item 1 of xss
set lstCol to {}
repeat with iRow from 1 to length of xss
set end of lstCol to item iCol of item iRow of xss
end repeat
set end of lstTrans to lstCol
end repeat
return lstTrans
end transpose</lang>
or, if our library contains some generic basics like map(), and we use the AS script mechanism for closures, we can delegate the iterative details and write transpose() a little more declaratively, without having to reach for set, repeat, or return inside its definition.
<lang applescript>-- TRANSPOSE -----------------------------------------------------------------
-- transpose :: a -> a on transpose(xss)
script column
on |λ|(_, iCol)
script row
on |λ|(xs)
item iCol of xs
end |λ|
end script
map(row, xss)
end |λ|
end script
map(column, item 1 of xss)
end transpose
-- TEST ----------------------------------------------------------------------
on run
transpose([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
--> {{1, 4, 7, 10}, {2, 5, 8, 11}, {3, 6, 9, 12}}
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn</lang>
- Output:
<lang AppleScript>{{1, 4, 7, 10}, {2, 5, 8, 11}, {3, 6, 9, 12}}</lang>
AutoHotkey
<lang 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
} </lang>
Using Objects
<lang AutoHotkey>Transpose(M){ R := [] for i, row in M for j, col in row R[j,i] := col return R }</lang> Examples:<lang AutoHotkey>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") }</lang>
- Output:
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
AWK
<lang 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)
} </lang>
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
Using 2D-Arrays
<lang AWK># Usage: GAWK -f MATRIX_TRANSPOSITION.AWK filename {
i = NR
for (j = 1; j <= NF; j++) {
a[i,j] = $j
}
ranka1 = i
ranka2 = max(ranka2, NF)
} END {
rankb1 = ranka2
rankb2 = ranka1
b[rankb1, rankb2] = 0
transpose_matrix(b, a)
for (i = 1; i <= rankb1; i++) {
for (j = 1; j <= rankb2; j++) {
printf("%g%c", b[i,j], j < rankb2 ? " " : "\n");
}
}
} function transpose_matrix(target, source, key, idx) {
for (key in source) {
split(key, idx, SUBSEP)
target[idx[2], idx[1]] = source[idx[1], idx[2]]
}
} function max(m, n) {
return m > n ? m : n
}</lang>
Input:
1 2 3 4 5 6
- Output:
1. 4. 2. 5. 3. 6.
BASIC
CLS
DIM m(1 TO 5, 1 TO 4) 'any dimensions you want
'set up the values in the array
FOR rows = LBOUND(m, 1) TO UBOUND(m, 1) 'LBOUND and UBOUND can take a dimension as their second argument
FOR cols = LBOUND(m, 2) TO UBOUND(m, 2)
m(rows, cols) = rows ^ cols 'any formula you want
NEXT cols
NEXT rows
'declare the new matrix
DIM trans(LBOUND(m, 2) TO UBOUND(m, 2), LBOUND(m, 1) TO UBOUND(m, 1))
'copy the values
FOR rows = LBOUND(m, 1) TO UBOUND(m, 1)
FOR cols = LBOUND(m, 2) TO UBOUND(m, 2)
trans(cols, rows) = m(rows, cols)
NEXT cols
NEXT rows
'print the new matrix
FOR rows = LBOUND(trans, 1) TO UBOUND(trans, 1)
FOR cols = LBOUND(trans, 2) TO UBOUND(trans, 2)
PRINT trans(rows, cols);
NEXT cols
PRINT
NEXT rows
BBC BASIC
<lang bbcbasic> INSTALL @lib$+"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%</lang>
- 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
Burlesque
<lang 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 </lang>
C
Transpose a 2D double array. <lang c>#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; }</lang>
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. <lang c>#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; }</lang>
- 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
C#
<lang csharp>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; } } }</lang>
C++
C++ does not have a built-in or standard-library Matrix class, so many users have rolled their own. Boost supplies one (boost::numeric::ublas::matrix<element_t> in the example below). Many users have rolled their own matrix class; a (long) code sample below shows such a class.
<lang cpp>#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;
}</lang>
- Output:
[3,3]((0,3,6),(1,4,7),(2,5,8))
Generic solution
- main.cpp
<lang 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() */</lang>
- matrix.h
<lang cpp>#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 */</lang>
- 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
Easy Mode
<lang cpp>#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;
}</lang>
- 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
Clojure
<lang lisp>(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] (apply mapv vector mtx))
</lang>
- Output:
=> (matrix-transpose [[1 2 3] [4 5 6]]) [[1 4] [2 5] [3 6]]
CoffeeScript
<lang coffeescript>transpose = (matrix) ->
(t[i] for t in matrix) for i in [0...matrix[0].length]</lang>
- Output:
> transpose [[1,2,3],[4,5,6]] [[1,4],[2,5],[3,6]]
Common Lisp
If the matrix is given as a list: <lang lisp>(defun transpose (m)
(apply #'mapcar #'list m))</lang>
If the matrix A is given as a 2D array: <lang lisp>;; 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))</lang>
D
Standard Version
<lang d>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);
}</lang>
- Output:
10 14 18 11 15 19 12 16 20 13 17 21
Locally Procedural Style
<lang d>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);
}</lang> Same output.
Functional Style
<lang d>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);
}</lang> Same output.
Delphi
See #Pascal;
EchoLisp
<lang scheme> (lib 'matrix)
(define M (list->array (iota 6) 3 2)) (array-print M)
0 1 2 3 4 5
(array-print (matrix-transpose M))
0 2 4 1 3 5
</lang>
EDSAC order code
In these two programs the matrix elements are stored in consecutive memory locations, in row-major order (that is, the 1st row from left to right, then the 2nd row, etc). For simplicity, matrix elements are short values, each occupying one memory location. The programs could be modified so that each element occupies two memory locations, as in the EDSAC library subroutines for vectors and matrices.
Create a new matrix
<lang edsac>
[Demo of matrix transposition. Not in place, creates a new matrix.
EDSAC, Initial Orders 2.]
..PZ [blank tape and terminator]
T 50 K [to call matrix transpose subroutine with 'G X']
P 200 F [address of matrix transpose subroutine]
T 47 K [to call matrix print subroutine with 'G M']
P 100 F [address of matrix print subroutine]
T 46 K [to call print subroutine with 'G N']
P 56 F [address of print subroutine (EDSAC library P1)]
[Subroutine to transpose a matrix of 17-bit real numbers, not in place.
Caller must ensure original and transpose don't overlap.
Parameters, all in the address field (i.e. denote n by P n F)
10F = width (number of columns)
11F = height (number of rows)
12F = start address of input matrix
13F = start address of output matrix]
E25K TX GK
[The subroutine loads elements by working down each column in turn.
Elements are stored at consecutive locations in the transposed matrix.]
A3F T31@ [set up return to caller]
A13F A33@ T14@ [initialize T order for storing transpose]
A12F A32@ U13@ [initialize A order for loading original]
T36@ [also save as A order for top of current column]
S10 F [negative of width]
[10] T35@ [initialize negative counter]
S11 F [negative of height]
[12] T34@ [initialize negative counter]
[13] AF [maunfactured order; load matrix element]
[14] TF [maunfactured order; store matrix element]
A14@ A2F T14@ [update address in T order]
A13@ A10F T13@ [update address in A order]
A34@ A2F G12@ [inner loop till finished this column]
A36@ A2F U36@ T13@ [update address for start of column]
A35@ A2F G10@ [outer loop till finished all columns]
[31] ZF [exit]
[32] AF [added to an address to make A order for that address]
[33] TF [added to an address to make T order for that address]
[34] PF [negative counter for rows]
[35] PF [negative counter for columns]
[36] AF [load order for first element in current column]
[Subroutine to print a matrix of 17-bit real numbers.
Straightforward, so given in condensed form.
Parameters (in the address field, i.e. pass n as PnF):
10F = width (number of columns)
11F = height (number of rows)
12F = start address of matrix
13F = number of decimals]
E25K TM
GKA3FT30@A13FT18@A12FA31@T14@S11FT36@S10FT37@O34@O35@TDAFT1FA16@
GN [call library subroutine P1]
PFA14@A2FT14@A37@A2FG10@O32@O33@A36@A2FG8@ZFAF@F&F!FMFPFPF
[Library subroutine P1.
Prints number in 0D to n places of decimals, where
n is specified by 'P n F' pseudo-order after subroutine call.]
E25K TN
GKA18@U17@S20@T5@H19@PFT5@VDUFOFFFSFL4FTDA5@A2FG6@EFU3FJFM1F
[Main routine]
PK T300K GK
[Constants]
[0] #F [figures shift on teleprinter]
[1] @F [carriage return]
[2] &F [line feed]
[3] P3F [number of columns (in address field)]
[4] P5F [number of rows (in address field)]
[5] P400F [address of matrix]
[6] P500F [address of transposed matrix]
[7] P2F [number of decimals when printing matrix]
[8] TF [add to address to make T order]
[9] P328F [0.0100097...., matrix elements are multiples of this]
[Variables]
[10] PF [matrix element, initialized to 0.00]
[11] PF [negative counter]
[Enter with acc = 0]
[12] O@ [set figures mode on teleprinter]
A5@ [address of matrix]
A8@ [make T order to store first elememt]
T24@ [plant in code]
H4@ N3@ L64F L32F [acc := negative number of entries]
[20] T11@ [initialize negative counter]
A10@ A9@ U10@ [increment matrix element]
[24] TF [store in matrix]
A24@ A2F T24@ [inc store address]
A11@ A2F G20@ [inc negative counter, loop till zero]
[Matrix is set up, now print it]
A3@ T10F [10F := width]
A4@ T11F [11F := height]
A5@ T12F [12F := address of matrix]
A7@ T13F [13F := number of decimals]
[39] A39@ GM [call print subroutine]
O1@ O2@ [add CR LF]
[Transpose matrix: 10F, 11F, 12F stay the same]
A6@ T13F [13F := address of transpose]
[45] A45@ GX [call transpose routine]
[Print transpose]
A10F TF A11F T10F AF T11F [swap width and height]
A13F T12F [12F := address of transpose]
A7@ T13F [13F := number of decimals]
[57] A57@ GM [call print subroutine]
O@ [figures mode, dummy to flush teleprinter buffer]
ZF [stop]
E12Z [enter at 12 (relative)]
PF [accumulator = 0 on entry]
</lang>
- Output:
.01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 .13 .14 .15 .01 .04 .07 .10 .13 .02 .05 .08 .11 .14 .03 .06 .09 .12 .15
Transpose in place
That's a neat C program after the complications on Wikipedia. The way EDSAC handles arrays makes it convenient to modify the second half of the program. In C, the updated value of "next" has to be parked in another variable until m[next] (old "next") has been assigned to. In EDSAC, the instruction that assigns to m[next] can be planted before "next" is updated, and won't be affected by that update. Once the EDSAC program has been modified in this way, the code to update "next" is the same in both halves of the program and can be taken out as a subroutine. <lang edsac> [Transpose a matrix in place. EDSAC, Initial Orders 2.]
..PZ [blank tape and terminator]
T50K [to call matrix transpose with 'G X']
P160F [address of matrix transpose subroutine]
T47K [to call matrix print subroutine with 'G M']
P120F [address of matrix print subroutine]
T46K [to call print subroutine with 'G N']
P56F [address of print subroutine (P1 in EDSAC library)]
T48K [to call division subroutine with 'G &']
P77F [address of division subroutine]
[Subroutine to transpose a matrix of 17-bit values in place.
Translated and slightly modified from C version on Rosetta Code website.
Parameters, all in the address field (i.e. n is stored as P n F):
10F = width (number of columns, "w" in C program)
11F = height (number of rows, "h" in C program)
12F = start address of matrix]
E25K TX GK
A3F T64@ [set up return to caller]
H10F V11F L32F L64F [acc := size of matrix as width*height]
T84@ T85@ [store size; C variable start := 0]
[8] TF A85@ T86@ T87@ [set C variables, next := start, i := 0]
[12] TF A87@ A2F T87@ [i++]
A16@ G65@ [call subroutine to update "next"]
A85@ S86@ G12@ [acc := start - next, loop back if < 0]
[Skip to location 58 if acc > 0 or i = 1.
We already know that acc >= 0 and i > 0.]
S2F E58@ [subtract 1 from acc, skip if still >= 0]
S2F A87@ G58@ [acc := -2 + i, skip if < 0]
[The assignment next := start in the C program is unnecessary]
TF A86@ A12F A81@ T31@ [make and plant order to load m{next}]
[31] AF T83@ [tmp := m{next}]
[33] TF [clear acc; also added to an address to make T order for that address]
[34] A86@ A12F A33@ T54@ [make and plant order to store m{next}]
A38@ G65@ [call subroutine to update "next"]
A86@ S85@ G48@ [go to 48 if i < start]
S2F E48@ [go to 48 if i > start]
TF A82@ G52@ [make order to load tmp, and go to 52]
[48] TF A86@ A12F A81@ [make order to load m{next}]
[52] T53@ [plant order to load tmp or m{next}]
[53] AF [manufactured order; if i = start loads tmp, else loads m{next}]
[54] TF [manufactured order; stores m{next}, using old value of "next"]
A85@ S86@ G33@ [acc := start - next, loop back if < 0]
[58] TF A85@ A2F U85@ [start++]
S84@ G8@ [loop until start = size]
[64] ZF [overwritten by return to caller]
[Subroutine to execute next = (next % h) * w + next / h in C program]
[65] A3F T80@ [set up return to caller]
A86@ T4F A11F T5F [set up parameters to divide "next" by "h"]
A71@ G& [call division subroutine]
[In case anybody is following this in detail, note that "next" and "h" are
stored in the address field, so we need to shift the quotient 1 left]
H4F V10F L64F L16F A5F LD T86@ [compute RHS and store in "next"]
[80] ZF [overwritten by return to caller]
[Constants]
[81] AF [added to an address to make A order for that address]
[82] A83@ [order to load C variable "tmp"]
[Variables; integers are stored in the address field for convenience.]
[83] PF [C variable "tmp" (holds value of a matrix element)]
[84] PF [size of matrix, width*height]
[85] PF [C variable "start"]
[86] PF [C variable "next"]
[87] PF [C variable "i"]
[Subroutine to print a matrix of 17-bit real numbers.]
E25K TM
GKA3FT30@A13FT18@A12FA31@T14@S11FT36@S10FT37@O34@O35@TDAFT1FA16@
GN
PFA14@A2FT14@A37@A2FG10@O32@O33@A36@A2FG8@ZFAF@F&F!FMFPFPF
[Library subroutine P1. Prints positive number in 0D to n places of decimals, where n is specified by 'P n F' pseudo-order after subroutine call.] E25K TN GKA18@U17@S20@T5@H19@PFT5@VDUFOFFFSFL4FTDA5@A2FG6@EFU3FJFM1F
[Integer division: number at 4F, divisor at 5F Returns remainder at 4F, quotient at 5F Working location 0D. 37 locations.] E25K T& GKA3FT34@A5FUFT35@A4FRDS35@G13@T1FA35@LDE4@T1FT5FA4FS35@G22@ T4FA5FA36@T5FT1FAFS35@E34@T1FA35@RDT35@A5FLDT5FE15@EFPFPD
[Main routine] [Given in condensed form, since it's the same as in part 1, except that the address of the transposed matrix is not required.] PKT250KGK#F@F&FP7FP4FP320FP2FTFP328FPFPFO@A5@A7@T23@H4@N3@L64FL32F T10@A9@A8@U9@TFA23@A2FT23@A10@A2FG19@A3@T10FA4@T11FA5@T12FA6@T13F A38@GMO1@O2@A42@GXA10FTFA11FT10FAFT11FA50@GMO@ZFE11ZPF
</lang>
- Output:
.01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 .13 .14 .15 .16 .17 .18 .19 .20 .21 .22 .23 .24 .25 .26 .27 .28 .01 .08 .15 .22 .02 .09 .16 .23 .03 .10 .17 .24 .04 .11 .18 .25 .05 .12 .19 .26 .06 .13 .20 .27 .07 .14 .21 .28
Elixir
<lang elixir>m = [[1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25,125, 625]]
transpose = fn(m)-> List.zip(m) |> Enum.map(&Tuple.to_list(&1)) end
IO.inspect transpose.(m)</lang>
- Output:
[[1, 2, 3, 4, 5], [1, 4, 9, 16, 25], [1, 8, 27, 64, 125], [1, 16, 81, 256, 625]]
ELLA
Sample originally from ftp://ftp.dra.hmg.gb/pub/ella (a now dead link) - Public release.
Code for matrix transpose hardware design verification:<lang ella>MAC TRANSPOSE = ([INT n][INT m]TYPE t: matrix) -> [m][n]t:
[INT i = 1..m] [INT j = 1..n] matrix[j][i].</lang>
Emacs Lisp
<lang lisp> (defun transpose (m)
(apply #'mapcar* #'list m))
- test for transposition function
(transpose '((2 3 4 5) (3 5 6 9) (9 9 9 9))) </lang>
- Output:
((2 3 9) (3 5 9) (4 6 9) (5 9 9))
Erlang
A nice introduction http://langintro.com/erlang/article2/ which is much more explicit.
<lang erlang> -module(transmatrix). -export([trans/1,transL/1]).
% using built-ins hd = head, tl = tail
trans([[]|_]) -> []; trans(M) ->
[ lists:map(fun hd/1, M) | transpose( lists:map(fun tl/1, M) ) ].
% Purist version
transL( [ [Elem | Rest] | List] ) ->
[ [Elem | [H || [H | _] <- List] ] |
transL( [Rest |
[ T || [_ | T] <- List ] ]
) ];
transL([ [] | List] ) -> transL(List); transL([]) -> []. </lang>
- Output:
2> transmatrix:transL( [ [1,2,3],[4,5,6],[7,8,9] ] ). [[1,4,7],[2,5,8],[3,6,9]] 3> transmatrix:trans( [ [1,2,3],[4,5,6],[7,8,9] ] ). [[1,4,7],[2,5,8],[3,6,9]]
Euphoria
<lang 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)</lang>
- Output:
{
{1,5,9},
{2,6,10},
{3,7,11},
{4,8,12}
}
F#
Very straightforward solution... <lang fsharp>let transpose (mtx : _ [,]) = Array2D.init (mtx.GetLength 1) (mtx.GetLength 0) (fun x y -> mtx.[y,x])</lang>
Factor
flip can be used.
<lang factor>( scratchpad ) { { 1 2 3 } { 4 5 6 } } flip .
{ { 1 4 } { 2 5 } { 3 6 } }</lang>
Forth
<lang forth>S" fsl-util.fs" REQUIRED S" fsl/dynmem.seq" REQUIRED
- F+! ( addr -- ) ( F: r -- ) DUP F@ F+ F! ;
- FSQR ( F: r1 -- r2 ) FDUP F* ;
S" fsl/gaussj.seq" REQUIRED
5 3 float matrix a{{ 1e 2e 3e 4e 5e 6e 7e 8e 9e 10e 11e 12e 13e 14e 15e 5 3 a{{ }}fput float dmatrix b{{
a{{ 5 3 & b{{ transpose 3 5 b{{ }}fprint</lang>
Fortran
In ISO Fortran 90 or later, use the TRANSPOSE intrinsic function: <lang fortran>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</lang>
In ANSI FORTRAN 77 with MIL-STD-1753 extensions or later, use nested structured DO loops: <lang fortran>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</lang>
In ANSI FORTRAN 66 or later, use nested labeled DO loops: <lang fortran> 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</lang>
Explicit transposition via DO-loops was available from the start. Less obvious is that Fortran uses what is called "column major" order rather than "row major", which is to say that consecutive elements of the array are stored in memory with indices counting down the columns first, not along the rows. The above examples acknowledge this in the DATA statement with the ((A(row,col),row=1,3),col=1,5) which could therefore be replaced with just A, however one could use ((A(row,col),col=1,5),row=1,3) instead and the DATA values could be arranged so as to appear in the same layout as one expects for a matrix. Consider <lang Fortran> DIMENSION A(3,5),B(5,3),C(5,3)
EQUIVALENCE (A,C) !Occupy the same storage.
DATA A/
1 1, 2, 3, 4, 5,
2 6, 7, 8, 9,10,
3 11,12,13,14,15/ !Supplies values in storage order.
WRITE (6,*) "Three rows of five values:"
WRITE (6,1) A !This shows values in storage order.
WRITE (6,*) "...written as C(row,column):"
WRITE (6,2) ((C(I,J),J = 1,3),I = 1,5)
WRITE (6,*) "... written as A(row,column):"
WRITE (6,1) ((A(I,J),J = 1,5),I = 1,3)
WRITE (6,*)
WRITE (6,*) "B = Transpose(A)"
DO 10 I = 1,3
DO 10 J = 1,5
10 B(J,I) = A(I,J)
WRITE (6,*) "Five rows of three values:"
WRITE (6,2) B
WRITE (6,*) "... written as B(row,column):"
WRITE (6,2) ((B(I,J),J = 1,3),I = 1,5)
1 FORMAT (5F6.1) !Five values per line.
2 FORMAT (3F6.1) !Three values per line.
END</lang>
Output:
Three rows of five values: 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 ...written as C(row,column): 1.0 6.0 11.0 2.0 7.0 12.0 3.0 8.0 13.0 4.0 9.0 14.0 5.0 10.0 15.0 ... written as A(row,column): 1.0 4.0 7.0 10.0 13.0 2.0 5.0 8.0 11.0 14.0 3.0 6.0 9.0 12.0 15.0 B = Transpose(A) Five rows of three values: 1.0 4.0 7.0 10.0 13.0 2.0 5.0 8.0 11.0 14.0 3.0 6.0 9.0 12.0 15.0 ... written as B(row,column): 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0
Thus, the first output of A replicates the layout of the DATA statement, and the output of matrix C gives its transpose. But, the values in matrix A do not appear where they would be expected to appear in terms of (row,column) as applied to the layout of the DATA statement. Only after the transposition is this so. Put another way, the ordering of array values for statements just naming the matrix (the DATA statement, and the simple write statements of A and B) is the transpose of the (row,column) expectation for a matrix. All input and output statements for matrices should thus explicitly specify the index order, even for temporary debugging, lest confusion ensue.
FreeBASIC
<lang freebasic>Dim matriz(0 To 3, 0 To 4) As Integer = {{78,19,30,12,36},_ {49,10,65,42,50},_ {30,93,24,78,10},_ {39,68,27,64,29}} Dim As Integer mtranspuesta(Lbound(matriz, 2) To Ubound(matriz, 2), Lbound(matriz, 1) To Ubound(matriz, 1)) Dim As Integer fila, columna
For fila = Lbound(matriz,1) To Ubound(matriz,1)
For columna = Lbound(matriz,2) To Ubound(matriz,2)
mtranspuesta(columna, fila) = matriz(fila, columna)
Print ; matriz(fila,columna); " ";
Next columna
Print
Next fila Print
For fila = Lbound(mtranspuesta,1) To Ubound(mtranspuesta,1)
For columna = Lbound(mtranspuesta,2) To Ubound(mtranspuesta,2)
Print ; mtranspuesta(fila,columna); " ";
Next columna
Print
Next fila Sleep</lang>
- 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
Frink
The built-in array method transpose transposes a 2-dimensional array.
<lang frink>
a = [[1,2,3],
[4,5,6],
[7,8,9]]
join["\n",a.transpose[]] </lang>
Fōrmulæ
In this page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
GAP
<lang 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);</lang>
Go
Library gonum/mat
<lang go>package main
import (
"fmt"
"gonum.org/v1/gonum/mat"
)
func main() {
m := mat.NewDense(2, 3, []float64{
1, 2, 3,
4, 5, 6,
})
fmt.Println(mat.Formatted(m))
fmt.Println()
fmt.Println(mat.Formatted(m.T()))
}</lang>
- Output:
⎡1 2 3⎤ ⎣4 5 6⎦ ⎡1 4⎤ ⎢2 5⎥ ⎣3 6⎦
Library go.matrix
<lang go>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)
}</lang>
- Output:
original:
{1, 2, 3,
4, 5, 6}
transpose:
{1, 4,
2, 5,
3, 6}
2D representation
Go arrays and slices are only one-dimensional. The obvious way to represent two-dimensional arrays is with a slice of slices: <lang go>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
}</lang>
- Output:
[1 2 3] [4 5 6] [1 4] [2 5] [3 6]
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. <lang go>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
}</lang>
- Output:
original: [1 2 3] [4 5 6] transpose: [1 4] [2 5] [3 6]
Transpose in place
Note representation is "flat," as above, but without the fluff of constructing from rows. <lang go>package main
import "fmt"
type matrix struct {
stride int ele []float64
}
func main() {
m := matrix{3, []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
}</lang> Output same as above.
Groovy
The Groovy extensions to the List class provides a transpose method: <lang groovy>def matrix = [ [ 1, 2, 3, 4 ],
[ 5, 6, 7, 8 ] ]
matrix.each { println it } println() def transpose = matrix.transpose()
transpose.each { println it }</lang>
- Output:
[1, 2, 3, 4] [5, 6, 7, 8] [1, 5] [2, 6] [3, 7] [4, 8]
Haskell
For matrices represented as lists, there's transpose: <lang haskell>*Main> transpose [[1,2],[3,4],[5,6]] [[1,3,5],[2,4,6]]</lang>
For matrices in arrays, one can use ixmap: <lang haskell>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</lang>
With Numeric.LinearAlgebra
<lang haskell>import Numeric.LinearAlgebra
a :: Matrix I a = (3><2)
[1,2 ,3,4 ,5,6]
main = do
print $ a print $ tr a</lang>
- Output:
(3><2) [ 1, 2 , 3, 4 , 5, 6 ] (2><3) [ 1, 3, 5 , 2, 4, 6 ]
Haxe
<lang haxe>class Matrix {
static function main() {
var m = [ [1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256],
[5, 25, 125, 625] ];
var t = [ for (i in 0...m[0].length)
[ for (j in 0...m.length) 0 ] ];
for(i in 0...m.length)
for(j in 0...m[0].length)
t[j][i] = m[i][j];
for(aa in [m, t])
for(a in aa) Sys.println(a);
}
}</lang>
- Output:
[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]
HicEst
<lang hicest>REAL :: mtx(2, 4)
mtx = 1.1 * $ WRITE() mtx
SOLVE(Matrix=mtx, Transpose=mtx) WRITE() mtx</lang>
- 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
Hope
<lang hope>uses lists; dec transpose : list (list alpha) -> list (list alpha); --- transpose ([]::_) <= []; --- transpose n <= map head n :: transpose (map tail n);</lang>
Icon and Unicon
<lang Icon>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</lang>
- Output:
Start: 1 2 3 4 5 6 Transposed: 1 4 2 5 3 6
IDL
Standard IDL function transpose() <lang idl>m=[[1,1,1,1],[2, 4, 8, 16],[3, 9,27, 81],[5, 25,125, 625]] print,transpose(m)</lang>
Idris
<lang idris>Idris> transpose [[1,2],[3,4],[5,6]] [[1, 3, 5], [2, 4, 6]] : List (List Integer)</lang>
J
Solution:
Transpose is the monadic primary verb |:
Example: <lang j> ]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</lang>
As an aside, note that . and : are token forming suffixes (if they immediately follow a token forming character, they are a part of the token). This usage is in analogy to the use of diacritics in many languages. (If you want to use : or . as tokens by themselves you must precede them with a space - beware though that wiki rendering software may sometimes elide the preceding space in <code> .</code> contexts.)
Java
<lang 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));
}
}
}</lang>
JavaScript
ES5
for the print() function
<lang javascript>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());</lang>
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
Or, as a functional expression (rather than an imperative procedure):
<lang javascript>
(function () {
'use strict';
function transpose(lst) {
return lst[0].map(function (_, iCol) {
return lst.map(function (row) {
return row[iCol];
})
});
}
return transpose(
[[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
);
})(); </lang>
- Output:
[[1, 4, 7, 10], [2, 5, 8, 11], [3, 6, 9, 12]]
ES6
<lang JavaScript>(() => {
'use strict';
// transpose :: a -> a const transpose = xs => xs[0].map((_, iCol) => xs.map(row => row[iCol]));
// TEST -----------------------------------------------
return(
transpose([
[1, 2],
[3, 4],
[5, 6]
])
);
})();</lang>
- Output:
<lang JavaScript>[[1, 3, 5], [2, 4, 6]]</lang>
Joy
For matrices represented as lists, there's transpose, defined in seqlib like this: <lang joy>DEFINE transpose == [ [null] [true] [[null] some] ifte ]
[ pop [] ]
[ [[first] map] [[rest] map] cleave ]
[ cons ]
linrec .</lang>
jq
Recent versions of jq include a more general "transpose" that can be used to transpose jagged matrices.
The following definition of transpose/0 expects its input to be a non-empty array, each element of which should be an array of the same size. The result is an array that represents the transposition of the input. <lang jq>def transpose:
if (.[0] | length) == 0 then [] else [map(.[0])] + (map(.[1:]) | transpose) end ;</lang>
Examples
[[], []] | transpose # => []
[[1], [3]] | transpose # => 1,3
[[1,2], [3,4]] | transpose # => [[1,3],[2,4]]
Jsish
From the Javascript Matrix entries.
First a module, shared by the Transposition, Multiplication and Exponentiation tasks.
<lang javascript>/* Matrix transposition, multiplication, identity, and exponentiation, in Jsish */ 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 transposed 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);
};
// returns a matrix as the product of two others Matrix.prototype.mult = function(other) {
if (this.width != other.height) throw "error: incompatible sizes";
var result = [];
for (var i = 0; i < this.height; i++) {
result[i] = [];
for (var j = 0; j < other.width; j++) {
var sum = 0;
for (var k = 0; k < this.width; k++) sum += this.mtx[i][k] * other.mtx[k][j];
result[i][j] = sum;
}
}
return new Matrix(result);
};
// IdentityMatrix is a "subclass" of Matrix function IdentityMatrix(n) {
this.height = n;
this.width = n;
this.mtx = [];
for (var i = 0; i < n; i++) {
this.mtx[i] = [];
for (var j = 0; j < n; j++) this.mtx[i][j] = (i == j ? 1 : 0);
}
} IdentityMatrix.prototype = Matrix.prototype;
// the Matrix exponentiation function Matrix.prototype.exp = function(n) {
var result = new IdentityMatrix(this.height); for (var i = 1; i <= n; i++) result = result.mult(this); return result;
};
provide('Matrix', '0.60');</lang>
Then a unitTest of the transposition.
<lang javascript>/* Matrix transposition, in Jsish */ require('Matrix');
if (Interp.conf('unitTest')) {
var m = new Matrix([[1,1,1,1],[2,4,8,16],[3,9,27,81],[4,16,64,256],[5,25,125,625]]);
- m;
- m.transpose();
}
/*
!EXPECTSTART!
m ==> { height:5, mtx:[ [ 1, 1, 1, 1 ], [ 2, 4, 8, 16 ], [ 3, 9, 27, 81 ], [ 4, 16, 64, 256 ], [ 5, 25, 125, 625 ] ], width:4 } m.transpose() ==> { height:4, mtx:[ [ 1, 2, 3, 4, 5 ], [ 1, 4, 9, 16, 25 ], [ 1, 8, 27, 64, 125 ], [ 1, 16, 81, 256, 625 ] ], width:5 }
!EXPECTEND!
- /</lang>
- Output:
prompt$ jsish -u matrixTranspose.jsi [PASS] matrixTranspose.jsi
Julia
The transposition is obtained by quoting the matrix. <lang Julia>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 LinearAlgebra.Adjoint{Int64,Array{Int64,2}}:
1 4 2 5 3 6</lang>
If you do not want change the type, convert the result back to Array{Int64,2}.
K
Transpose is the monadic verb +
<lang k> {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)</lang>
Klong
Transpose is the monadic verb +
<lang k> [5 5]:^!25
[[0 1 2 3 4]
[5 6 7 8 9] [10 11 12 13 14] [15 16 17 18 19] [20 21 22 23 24]]
+[5 5]:^!25
[[0 5 10 15 20]
[1 6 11 16 21] [2 7 12 17 22] [3 8 13 18 23] [4 9 14 19 24]]</lang>
Kotlin
<lang scala>// version 1.1.3
typealias Vector = DoubleArray typealias Matrix = Array<Vector>
fun Matrix.transpose(): Matrix {
val rows = this.size
val cols = this[0].size
val trans = Matrix(cols) { Vector(rows) }
for (i in 0 until cols) {
for (j in 0 until rows) trans[i][j] = this[j][i]
}
return trans
}
fun printMatrix(m: Matrix) {
for (i in 0 until m.size) println(m[i].contentToString())
}
fun main(args: Array<String>) {
val m = arrayOf(
doubleArrayOf( 1.0, 2.0, 3.0),
doubleArrayOf( 4.0, 5.0, 6.0),
doubleArrayOf( 7.0, 8.0, 9.0),
doubleArrayOf(10.0, 11.0, 12.0)
)
printMatrix(m.transpose())
}</lang>
- Output:
[1.0, 4.0, 7.0, 10.0] [2.0, 5.0, 8.0, 11.0] [3.0, 6.0, 9.0, 12.0]
Lang5
<lang Lang5>12 iota [3 4] reshape 1 + dup . 1 transpose .</lang>
- 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 ] ]
LFE
<lang lisp> (defun transpose (matrix)
(transpose matrix '()))
(defun transpose (matrix acc)
(cond
((lists:any
(lambda (x) (== x '()))
matrix)
acc)
('true
(let ((heads (lists:map #'car/1 matrix))
(tails (lists:map #'cdr/1 matrix)))
(transpose tails (++ acc `(,heads)))))))
</lang>
Usage in the LFE REPL:
<lang lisp> > (transpose '((1 2 3)
(4 5 6)
(7 8 9)
(10 11 12)
(13 14 15)
(16 17 18)))
((1 4 7 10 13 16) (2 5 8 11 14 17) (3 6 9 12 15 18)) > </lang>
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. <lang lb>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$</lang>
- Output:
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 |
Lua
<lang 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</lang>
Using apply map list <lang lua>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 = #aarg
while true do
local a = map(function(b) return b[k] end, aarg)
if #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"))</lang>
--Edit: table.getn() deprecated, using # instead
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.
<lang Maple> M := <<2,3>|<3,4>|<5,6>>;
M^%T;
with(LinearAlgebra): Transpose(M); </lang>
- Output:
[2 3 5]
M := [ ]
[3 4 6]
[2 3]
[ ]
[3 4]
[ ]
[5 6]
[2 3]
[ ]
[3 4]
[ ]
[5 6]
Mathematica
<lang 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]</lang>
MATLAB
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.
<lang Matlab>>> transpose([1 2;3 4])
ans =
1 3
2 4
>> [1 2;3 4].'
ans =
1 3
2 4</lang>
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: <lang Matlab>
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
</lang>
Transposing nested cells using apply map list <lang Matlab>xy = {{1,2,3,4},{1,2,3,4},{1,2,3,4}} yx = feval(@(x) cellfun(@(varargin)[varargin],x{:},'un',0), xy)</lang>
Maxima
<lang 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);</lang>
MAXScript
Uses the built in transpose() function <lang maxscript>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</lang>
Nial
make an array <lang nial>|a := 2 3 reshape count 6 =1 2 3 =4 5 6</lang> transpose it <lang nial>|transpose a =1 4 =2 5 =3 6</lang>
Nim
For statically sized arrays: <lang nim>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 ""</lang>
- Output:
0 5 1 1 6 0 2 7 0 3 8 0 4 9 42
For dynamically sized seqs: <lang nim>proc transpose[T](s: seq[seq[T]]): seq[seq[T]] =
result = newSeq[seq[T]](s[0].len)
for i in 0 .. s[0].high:
result[i] = newSeq[T](s.len)
for j in 0 .. s.high:
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)</lang>
- Output:
@[@[0, 5, 1], @[1, 6, 0], @[2, 7, 0], @[3, 8, 0], @[4, 9, 42]]
Objeck
<lang 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();
};
}
}
} </lang>
- Output:
1 2 3 4 5 1 4 9 16 25 1 8 27 64 125 1 16 81 256 625
OCaml
Matrices can be represented in OCaml as a type 'a array array, or using the module Bigarray. The implementation below uses a bigarray:
<lang ocaml>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) ;;</lang>
- Output:
1 5 2 6 3 7 4 8
A version for lists: <lang ocaml>let rec transpose m =
assert (m <> []); if List.mem [] m then [] else List.map List.hd m :: transpose (List.map List.tl m)</lang>
Example:
# transpose [[1;2;3;4];
[5;6;7;8]];;
- : int list list = [[1; 5]; [2; 6]; [3; 7]; [4; 8]]
Octave
<lang 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</lang>
OxygenBasic
<lang 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 </lang>
PARI/GP
The GP function for matrix (or vector) transpose is mattranspose, but it is usually invoked with a tilde:
<lang parigp>M~</lang>
In PARI the function is
<lang C>gtrans(M)</lang>
though shallowtrans is also available when deep copying is not desired.
Pascal
<lang 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.</lang>
- 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
Perl
<lang 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;</lang>
- 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: <lang perl>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]);
}</lang>
Phix
Copy of Euphoria <lang Phix>function transpose(sequence in) sequence 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</lang>
PHP
Up to PHP version 5.6
<lang 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', $m);
}</lang>
Starting with PHP 5.6
<lang php>
function transpose($m) {
return count($m) == 0 ? $m : (count($m) == 1 ? array_chunk($m[0], 1) : array_map(null, ...$m));
} </lang>
PicoLisp
<lang PicoLisp>(de matTrans (Mat)
(apply mapcar Mat list) )
(matTrans '((1 2 3) (4 5 6)))</lang>
- Output:
-> ((1 4) (2 5) (3 6))
PL/I
<lang 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. */</lang> Traditional method: <lang PL/I>/* 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;</lang>
Pop11
<lang 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;</lang>
PostScript
<lang postscript>/transpose {
[ exch {
{ {empty? exch pop} map all?} {pop exit} ift
[ exch {} {uncons {exch cons} dip exch} fold counttomark 1 roll] uncons
} loop ] {reverse} map
}.</lang>
PowerBASIC
PowerBASIC has the MAT statement to simplify Matrix Algebra calculations; in conjunction with the TRN operation the actual transposition is just a one-liner. <lang powerbasic>#COMPILE EXE
- DIM ALL
- COMPILER PBCC 6
'---------------------------------------------------------------------- SUB TransposeMatrix(InitMatrix() AS DWORD, TransposedMatrix() AS DWORD) LOCAL l1, l2, u1, u2 AS LONG
l1 = LBOUND(InitMatrix, 1) l2 = LBOUND(InitMatrix, 2) u1 = UBOUND(InitMatrix, 1) u2 = UBOUND(InitMatrix, 2) REDIM TransposedMatrix(l2 TO u2, l1 TO u1) MAT TransposedMatrix() = TRN(InitMatrix())
END SUB '---------------------------------------------------------------------- SUB PrintMatrix(a() AS DWORD) LOCAL l1, l2, u1, u2, r, c AS LONG LOCAL s AS STRING * 8
l1 = LBOUND(a(), 1)
l2 = LBOUND(a(), 2)
u1 = UBOUND(a(), 1)
u2 = UBOUND(a(), 2)
FOR r = l1 TO u1
FOR c = l2 TO u2
RSET s = STR$(a(r, c))
CON.PRINT s;
NEXT c
CON.PRINT
NEXT r
END SUB '---------------------------------------------------------------------- SUB TranspositionDemo(BYVAL DimSize1 AS DWORD, BYVAL DimSize2 AS DWORD) LOCAL r, c, cc AS DWORD LOCAL a() AS DWORD LOCAL b() AS DWORD
cc = DimSize2
DECR DimSize1
DECR DimSize2
REDIM a(0 TO DimSize1, 0 TO DimSize2)
FOR r = 0 TO DimSize1
FOR c = 0 TO DimSize2
a(r, c)= (cc * r) + c + 1
NEXT c
NEXT r
CON.PRINT "initial matrix:"
PrintMatrix a()
TransposeMatrix a(), b()
CON.PRINT "transposed matrix:"
PrintMatrix b()
END SUB '---------------------------------------------------------------------- FUNCTION PBMAIN () AS LONG
TranspositionDemo 3, 3 TranspositionDemo 3, 7
END FUNCTION</lang>
- Output:
initial matrix:
1 2 3
4 5 6
7 8 9
transposed matrix:
1 4 7
2 5 8
3 6 9
initial matrix:
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
transposed matrix:
1 8 15
2 9 16
3 10 17
4 11 18
5 12 19
6 13 20
7 14 21
PowerShell
Any Matrix
<lang PowerShell> function transpose($a) {
$arr = @()
if($a) {
$n = $a.count - 1
if(0 -lt $n) {
$m = ($a | foreach {$_.count} | measure-object -Minimum).Minimum - 1
if( 0 -le $m) {
if (0 -lt $m) {
$arr =@(0)*($m+1)
foreach($i in 0..$m) {
$arr[$i] = foreach($j in 0..$n) {@($a[$j][$i])}
}
} else {$arr = foreach($row in $a) {$row[0]}}
}
} else {$arr = $a}
}
$arr
} function show($a) {
if($a) {
0..($a.Count - 1) | foreach{ if($a[$_]){"$($a[$_])"}else{""} }
}
}
$a = @(@(2, 0, 7, 8),@(3, 5, 9, 1),@(4, 1, 6, 3)) "`$a =" show $a "" "transpose `$a =" show (transpose $a) "" $a = @(1) "`$a =" show $a "" "transpose `$a =" show (transpose $a) "" "`$a =" $a = @(1,2,3) show $a "" "transpose `$a =" "$(transpose $a)" "" "`$a =" $a = @(@(4,7,8),@(1),@(2,3)) show $a "" "transpose `$a =" "$(transpose $a)" "" "`$a =" $a = @(@(4,7,8),@(1,5,9,0),@(2,3)) show $a "" "transpose `$a =" show (transpose $a) </lang> Output:
$a = 2 0 7 8 3 5 9 1 4 1 6 3 transpose $a = 2 3 4 0 5 1 7 9 6 8 1 3 $a = 1 transpose $a = 1 $a = 1 2 3 transpose $a = 1 2 3 $a = 4 7 8 1 2 3 transpose $a = 4 1 2 $a = 4 7 8 1 5 9 0 2 3 transpose $a = 4 1 2 7 5 3
Square Matrix
<lang PowerShell> function transpose($a) {
if($a) {
$n = $a.Count - 1
foreach($i in 0..$n) {
$j = 0
while($j -lt $i) {
$a[$i][$j], $a[$j][$i] = $a[$j][$i], $a[$i][$j]
$j++
}
}
}
$a
} function show($a) {
if($a) {
0..($a.Count - 1) | foreach{ if($a[$_]){"$($a[$_])"}else{""} }
}
} $a = @(@(2, 4, 7),@(3, 5, 9),@(4, 1, 6)) show $a "" show (transpose $a) </lang> Output:
2 4 7 3 5 9 4 1 6 2 3 4 4 5 1 7 9 6
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.
<lang 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).</lang>
PureBasic
Matrices represented by integer arrays using rows as the first dimension and columns as the second dimension. <lang PureBasic>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</lang>
- 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
Python
<lang 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)))</lang>
- Output:
[(1, 2, 3, 4, 5), (1, 4, 9, 16, 25), (1, 8, 27, 64, 125), (1, 16, 81, 256, 625)]
Note, however, that zip, while very useful, doesn't give us a simple type-safe transposition – it is actually a 'transpose + coerce' function rather than a pure transpose function; polymorphic in its inputs, but not in its outputs.
zip accepts matrices in any of the 4 permutations of (outer lists or tuples) * (inner lists or tuples), but it always and only returns a zip of tuples, losing any information about what the input type was.
For type-specific transpositions without coercion (and for a richer set of matrix types, and higher level of efficiency – transpositions are an inherently expensive operation) we can turn to numpy.
Meanwhile, for the four basic types of Python matrices (the cartesian product of (inner type, container type) * (tuple, list), the simplest (though not necessarily most efficient) approach (in the absence of numpy) may be to write a type-sensitive wrapper, which retains and restores the type information that zip discards.
Perhaps, for example, something like: <lang python># transpose :: Matrix a -> Matrix a def transpose(m):
if m:
inner = type(m[0])
z = zip(*m)
return (type(m))(
map(inner, z) if tuple != inner else z
)
else:
return m
if __name__ == '__main__':
# TRANSPOSING FOUR BASIC TYPES OF PYTHON MATRIX # Cartesian product of (Outer, Inner) with (List, Tuple)
# Matrix any = Tuple of Tuples of any type tts = ((1, 2, 3), (4, 5, 6), (7, 8, 9))
# Matrix any = Tuple of Lists of any type tls = ([1, 2, 3], [4, 5, 6], [7, 8, 9])
emptyTuple = ()
# Matrix any = List of Lists of any type lls = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
# Matrix any = List of Tuples of any type lts = [(1, 2, 3), (4, 5, 6), (7, 8, 9)]
emptyList = []
print('transpose function :: (Transposition without type change):\n')
for m in [emptyTuple, tts, tls, emptyList, lls, lts]:
tm = transpose(m)
print (
type(tm).__name__ + (
(' of ' + type(tm[0]).__name__) if m else
) + ' :: ' + str(m) + ' -> ' + str(tm)
)</lang>
- Output:
transpose function :: (Transposition without type change): tuple :: () -> () tuple of tuple :: ((1, 2, 3), (4, 5, 6), (7, 8, 9)) -> ((1, 4, 7), (2, 5, 8), (3, 6, 9)) tuple of list :: ([1, 2, 3], [4, 5, 6], [7, 8, 9]) -> ([1, 4, 7], [2, 5, 8], [3, 6, 9]) list :: [] -> [] list of list :: [[1, 2, 3], [4, 5, 6], [7, 8, 9]] -> [[1, 4, 7], [2, 5, 8], [3, 6, 9]] list of tuple :: [(1, 2, 3), (4, 5, 6), (7, 8, 9)] -> [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
Even with its type amnesia fixed, zip may still not be the instrument to reach for when it's possible that our matrices may contain gaps.
If any of the rows in a list of lists matrix are not wide enough for a full set of data for one or more of the columns, then zip(*xs) will drop all the data entirely, without warning or error message, returning no more than an empty list:
<lang python># Uneven list of lists uls = [[10, 11], [20], [], [30, 31, 32]]
print (
list(zip(*uls))
)
- --> []</lang>
At this point, short of turning to numpy, we might need to write a custom function. An obvious approach is to return the full number of potential columns, each containing such data as the rows do have. For example:
<lang python>Transposition of row sets with possible gaps
from collections import defaultdict
def listTranspose(xss):
Transposition of a matrix which may
contain gaps.
def go(xss):
if xss:
h, *t = xss
return (
[[h[0]] + [xs[0] for xs in t if xs]] + (
go([h[1:]] + [xs[1:] for xs in t])
)
) if h and isinstance(h, list) else go(t)
else:
return []
return go(xss)
- TEST ----------------------------------------------------
- main :: IO ()
def main():
Tests with various lists of rows or non-row data.
def labelledList(kxs):
k, xs = kxs
return k + ': ' + showList(xs)
print(
fTable(
__doc__ + ':\n'
)(labelledList)(fmapFn(showList)(snd))(
fmapTuple(listTranspose)
)([
('Square', [[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
('Rectangle', [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]),
('Rows with gaps', [[10, 11], [20], [], [31, 32, 33]]),
('Single row', 1, 2, 3),
('Single row, one cell', 1),
('Not rows', [1, 2, 3]),
('Nothing', [])
])
)
- TEST RESULT FORMATTING ----------------------------------
- fTable :: String -> (a -> String) ->
- (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
Heading -> x display function -> fx display function ->
f -> xs -> tabular string.
def go(xShow, fxShow, f, xs):
ys = [xShow(x) for x in xs]
w = max(map(len, ys))
return s + '\n' + '\n'.join(map(
lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
xs, ys
))
return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
xShow, fxShow, f, xs
)
- fmapFn :: (a -> b) -> (r -> a) -> r -> b
def fmapFn(f):
The application of f to the result of g.
fmap over a function is composition.
return lambda g: lambda x: f(g(x))
- fmapTuple :: (a -> b) -> (c, a) -> (c, b)
def fmapTuple(f):
A pair in which f has been
applied to the second item.
return lambda ab: (ab[0], f(ab[1])) if (
2 == len(ab)
) else None
- show :: a -> String
def show(x):
Stringification of a value.
def go(v):
return defaultdict(lambda: repr, [
('list', showList)
# ('Either', showLR),
# ('Maybe', showMaybe),
# ('Tree', drawTree)
])[
typeName(v)
](v)
return go(x)
- showList :: [a] -> String
def showList(xs):
Stringification of a list. return '[' + ','.join(show(x) for x in xs) + ']'
- snd :: (a, b) -> b
def snd(tpl):
Second member of a pair. return tpl[1]
- typeName :: a -> String
def typeName(x):
Name string for a built-in or user-defined type.
Selector for type-specific instances
of polymorphic functions.
if isinstance(x, dict):
return x.get('type') if 'type' in x else 'dict'
else:
return 'iter' if hasattr(x, '__next__') else (
type(x).__name__
)
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
Transposition of row sets with possible gaps:
Square: [[1,2,3],[4,5,6],[7,8,9]] -> [[1,4,7],[2,5,8],[3,6,9]]
Rectangle: [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] -> [[1,4,7,10],[2,5,8,11],[3,6,9,12]]
Rows with gaps: [[10,11],[20],[],[31,32,33]] -> [[10,20,31],[11,32],[33]]
Single row: [[1,2,3]] -> [[1],[2],[3]]
Single row, one cell: [[1]] -> [[1]]
Not rows: [1,2,3] -> []
Nothing: [] -> []
R
<lang R>b <- 1:5 m <- matrix(c(b, b^2, b^3, b^4), 5, 4) print(m) tm <- t(m) print(tm)</lang>
Racket
<lang racket>
- lang racket
(require math) (matrix-transpose (matrix [[1 2] [3 4]])) </lang>
- Output:
(array #[#[1 3] #[2 4]])
(Another method, without math, and using lists is demonstrated in the Scheme solution.)
Raku
(formerly Perl 6)
<lang perl6># Transposition can be done with the reduced zip meta-operator
- on list-of-lists data structures
say [Z] (<A B C D>, <E F G H>, );
- For native shaped arrays, a more traditional procedure of copying item-by-item
- Here the resulting matrix is also a native shaped array
my @a[3;4] =
[ [<A B C D>], [<E F G H>], [], ];
(my $n, my $m) = @a.shape; my @b[$m;$n]; for ^$m X ^$n -> (\i, \j) {
@b[i;j] = @a[j;i];
}
say @b;</lang>
- Output:
((A E I) (B F J) (C G K) (D H L)) [[A E I] [B F J] [C G K] [D H L]]
Rascal
<lang 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> };</lang>
REXX
<lang rexx>/*REXX program transposes any sized rectangular matrix, displays before & after matrices*/ @.=; @.1 = 1.02 2.03 3.04 4.05 5.06 6.07 7.08
@.2 = 111 2222 33333 444444 5555555 66666666 777777777
w=0
do row=1 while @.row\==
do col=1 until @.row==; parse var @.row A.row.col @.row
w=max(w, length(A.row.col) ) /*max width for elements*/
end /*col*/ /*(used to align ouput).*/
end /*row*/ /* [↑] build matrix A from the @ lists*/
row= row-1 /*adjust for DO loop index increment.*/
do j=1 for row /*process each row of the matrix.*/
do k=1 for col /* " " column " " " */
B.k.j= A.j.k /*transpose the A matrix (into B). */
end /*k*/
end /*j*/
call showMat 'A', row, col /*display the A matrix to terminal.*/ call showMat 'B', col, row /* " " B " " " */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ showMat: arg mat,rows,cols; say; say center( mat 'matrix', (w+1)*cols +4, "─")
do r=1 for rows; _= /*newLine*/
do c=1 for cols; _=_ right( value( mat'.'r"."c), w) /*append.*/
end /*c*/
say _ /*1 line.*/
end /*r*/; return</lang>
- output when using the default input:
─────────────────────────────────A matrix─────────────────────────────────
1.02 2.03 3.04 4.05 5.06 6.07 7.08
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
7.08 777777777
Ring
<lang ring> load "stdlib.ring" transpose = newlist(5,4) matrix = [[78,19,30,12,36], [49,10,65,42,50], [30,93,24,78,10], [39,68,27,64,29]] for i = 1 to 5
for j = 1 to 4
transpose[i][j] = matrix[j][i]
see "" + transpose[i][j] + " "
next
see nl
next </lang> Output:
78 49 30 39 19 10 93 68 30 65 24 27 12 42 78 64 36 50 10 29
RLaB
<lang 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</lang>
Ruby
<lang 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</lang>
- 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 <lang ruby>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</lang>
- 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: <lang ruby>def transpose(m)
m[0].zip(*m[1..-1])
end p transpose([[1,2,3],[4,5,6]])</lang>
- Output:
[[1, 4], [2, 5], [3, 6]]
Run BASIC
<lang runbasic>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 "
" w = val(word$(in$, 1, ",")) h = val(word$(in$, 2, ",")) for i =0 to h -1 html "" for j =1 to w term$ = word$(in$, j +2 +i *w, ",") html ""next jhtml "" next i html "
| ";val(term$);" |
"
end sub</lang>
- Output:
Transpose of matrix
| 0 | 0.1 | 0.2 | 0.3 |
| 0.4 | 0.5 | 0.6 | 0.7 |
| 0.8 | 0.9 | 1.0 | 1.1 |
=
| 0 | 0.4 | 0.8 |
| 0.1 | 0.5 | 0.9 |
| 0.2 | 0.6 | 1.0 |
| 0.3 | 0.7 | 1.1 |
Rust
version 1
<lang rust> struct Matrix {
dat: [[i32; 3]; 3]
}
impl Matrix {
pub fn transpose_m(a: Matrix) -> Matrix
{
let mut out = Matrix {
dat: [[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
]
};
for i in 0..3{
for j in 0..3{
out.dat[i][j] = a.dat[j][i];
}
}
out
}
pub fn print(self)
{
for i in 0..3 {
for j in 0..3 {
print!("{} ", self.dat[i][j]);
}
print!("\n");
}
}
}
fn main() {
let a = Matrix {
dat: [[1, 2, 3],
[4, 5, 6],
[7, 8, 9] ]
};
let c = Matrix::transpose_m(a);
c.print();
} </lang>
version 2
<lang rust> fn main() {
let m = vec![vec![1, 2, 3], vec![4, 5, 6]];
println!("Matrix:\n{}", matrix_to_string(&m));
let t = matrix_transpose(m);
println!("Transpose:\n{}", matrix_to_string(&t));
}
fn matrix_to_string(m: &Vec<Vec<i32>>) -> String {
m.iter().fold("".to_string(), |a, r| {
a + &r
.iter()
.fold("".to_string(), |b, e| b + "\t" + &e.to_string())
+ "\n"
})
}
fn matrix_transpose(m: Vec<Vec<i32>>) -> Vec<Vec<i32>> {
let mut t = vec![Vec::with_capacity(m.len()); m[0].len()];
for r in m {
for i in 0..r.len() {
t[i].push(r[i]);
}
}
t
} </lang>
Output:
Matrix: 1 2 3 4 5 6 Transpose: 1 4 2 5 3 6
Scala
<lang scala>scala> Array.tabulate(4)(i => Array.tabulate(4)(j => i*4 + j)) res12: Array[Array[Int]] = Array(Array(0, 1, 2, 3), Array(4, 5, 6, 7), Array(8, 9, 10, 11), Array(12, 13, 14, 15))
scala> res12.transpose res13: Array[Array[Int]] = Array(Array(0, 4, 8, 12), Array(1, 5, 9, 13), Array(2, 6, 10, 14), Array(3, 7, 11, 15))
scala> res12 map (_ map ("%2d" format _) mkString " ") mkString "\n" res16: String =
0 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15
scala> res13 map (_ map ("%2d" format _) mkString " ") mkString "\n" res17: String =
0 4 8 12 1 5 9 13 2 6 10 14 3 7 11 15</lang>
Scheme
<lang scheme>(define (transpose m)
(apply map list m))</lang>
Seed7
<lang seed7>$ 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;</lang>
- 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
Sidef
<lang ruby>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...);
}</lang>
- Output:
1 2 3 4 5
1 4 9 16 25
1 8 27 64 125
1 16 81 256 625SPAD
<lang SPAD>(1) -> originalMatrix := matrix [[1, 1, 1, 1],[2, 4, 8, 16], _
[3, 9, 27, 81],[4, 16, 64, 256], _
[5, 25, 125, 625]]
+1 1 1 1 +
| |
|2 4 8 16 |
| |
(1) |3 9 27 81 |
| |
|4 16 64 256|
| |
+5 25 125 625+
Type: Matrix(Integer)
(2) -> transposedMatrix := transpose(originalMatrix)
+1 2 3 4 5 +
| |
|1 4 9 16 25 |
(2) | |
|1 8 27 64 125|
| |
+1 16 81 256 625+
Type: Matrix(Integer)</lang>
Domain:Matrix(R)
Sparkling
<lang sparkling>function transpose(A) {
return map(range(sizeof A), function(k, idx) {
return map(A, function(k, row) {
return row[idx];
});
});
}</lang>
Stata
Stata matrices are always real, so there is no ambiguity about the transpose operator. Mata matrices, however, may be real or complex. The transpose operator is actually a conjugate transpose, but there is also a transposeonly() function.
Stata matrices
<lang stata>. mat a=1,2,3\4,5,6 . mat b=a' . mat list a
a[2,3]
c1 c2 c3
r1 1 2 3 r2 4 5 6
. mat list b
b[3,2]
r1 r2
c1 1 4 c2 2 5 c3 3 6</lang>
Mata
<lang stata>: a=1,1i
- a
1 2 +-----------+ 1 | 1 1i | +-----------+
- a'
1 +-------+ 1 | 1 | 2 | -1i | +-------+
- transposeonly(a)
1 +------+ 1 | 1 | 2 | 1i | +------+</lang>
Swift
<lang swift>@inlinable public func matrixTranspose<T>(_ matrix: T) -> T {
guard !matrix.isEmpty else {
return []
}
var ret = Array(repeating: [T](), count: matrix[0].count)
for row in matrix {
for j in 0..<row.count {
ret[j].append(row[j])
}
}
return ret
}
@inlinable public func printMatrix<T>(_ matrix: T) {
guard !matrix.isEmpty else {
print()
return }
let rows = matrix.count let cols = matrix[0].count
for i in 0..<rows {
for j in 0..<cols {
print(matrix[i][j], terminator: " ")
}
print() }
}
let m1 = [
[1, 2, 3], [4, 5, 6]
]
print("Input:") printMatrix(m1)
let m2 = matrixTranspose(m1)
print("Output:") printMatrix(m2)</lang>
- Output:
Input: 1 2 3 4 5 6 Output: 1 4 2 5 3 6
Tailspin
<lang tailspin> templates transpose
def a: $; [1..$a(1)::length -> $a(1..last;$)] !
end transpose
templates printMatrix&{w:}
templates formatN @: []; $ -> # '$@ -> $::length~..$w -> ' ';$@(last..1:-1)...;' ! when <1..> do ..|@: $ mod 10; $ ~/ 10 -> # end formatN $... -> '|$(1) -> formatN;$(2..last)... -> ', $ -> formatN;';|
' ! end printMatrix
def m: [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]; 'before: ' -> !OUT::write $m -> printMatrix&{w:2} -> !OUT::write
def mT: $m -> transpose; ' transposed: ' -> !OUT::write $mT -> printMatrix&{w:2} -> !OUT::write </lang>
- Output:
before: | 1, 2, 3, 4| | 5, 6, 7, 8| | 9, 10, 11, 12| transposed: | 1, 5, 9| | 2, 6, 10| | 3, 7, 11| | 4, 8, 12|
Tcl
With core Tcl, representing a matrix as a list of lists: <lang tcl>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"</lang>
- Output:
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
<lang tcl>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</lang>
- Output:
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
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
Ursala
Matrices are stored as lists of lists, and transposing them is a built in operation. <lang Ursala>#cast %eLL
example =
~&K7 <
<1.,2.,3.,4.>, <5.,6.,7.,8.>, <9.,10.,11.,12.>></lang>
For a more verbose version, replace the ~&K7 operator with the standard library function named transpose.
- 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>>
VBA
<lang vb>Function transpose(m As Variant) As Variant
transpose = WorksheetFunction.transpose(m)
End Function</lang>
VBScript
<lang vb> 'create and display the initial matrix WScript.StdOut.WriteLine "Initial Matrix:" x = 4 : y = 6 : n = 1 Dim matrix() ReDim matrix(x,y) For i = 0 To y For j = 0 To x matrix(j,i) = n If j < x Then WScript.StdOut.Write n & vbTab Else WScript.StdOut.Write n End If n = n + 1 Next WScript.StdOut.WriteLine Next
'display the trasposed matrix WScript.StdOut.WriteBlankLines(1) WScript.StdOut.WriteLine "Transposed Matrix:" For i = 0 To x For j = 0 To y If j < y Then WScript.StdOut.Write matrix(i,j) & vbTab Else WScript.StdOut.Write matrix(i,j) End If Next WScript.StdOut.WriteLine Next </lang>
- Output:
Initial Matrix: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Transposed Matrix: 1 6 11 16 21 26 31 2 7 12 17 22 27 32 3 8 13 18 23 28 33 4 9 14 19 24 29 34 5 10 15 20 25 30 35
Visual Basic
<lang vb>Option Explicit '---------------------------------------------------------------------- Function TransposeMatrix(InitMatrix() As Long, TransposedMatrix() As Long) Dim l1 As Long, l2 As Long, u1 As Long, u2 As Long, r As Long, c As Long
l1 = LBound(InitMatrix, 1)
l2 = LBound(InitMatrix, 2)
u1 = UBound(InitMatrix, 1)
u2 = UBound(InitMatrix, 2)
ReDim TransposedMatrix(l2 To u2, l1 To u1)
For r = l1 To u1
For c = l2 To u2
TransposedMatrix(c, r) = InitMatrix(r, c)
Next c
Next r
End Function '---------------------------------------------------------------------- Sub PrintMatrix(a() As Long) Dim l1 As Long, l2 As Long, u1 As Long, u2 As Long, r As Long, c As Long Dim s As String * 8
l1 = LBound(a(), 1)
l2 = LBound(a(), 2)
u1 = UBound(a(), 1)
u2 = UBound(a(), 2)
For r = l1 To u1
For c = l2 To u2
RSet s = Str$(a(r, c))
Debug.Print s;
Next c
Debug.Print
Next r
End Sub '---------------------------------------------------------------------- Sub TranspositionDemo(ByVal DimSize1 As Long, ByVal DimSize2 As Long) Dim r, c, cc As Long Dim a() As Long Dim b() As Long
cc = DimSize2
DimSize1 = DimSize1 - 1
DimSize2 = DimSize2 - 1
ReDim a(0 To DimSize1, 0 To DimSize2)
For r = 0 To DimSize1
For c = 0 To DimSize2
a(r, c) = (cc * r) + c + 1
Next c
Next r
Debug.Print "initial matrix:"
PrintMatrix a()
TransposeMatrix a(), b()
Debug.Print "transposed matrix:"
PrintMatrix b()
End Sub '---------------------------------------------------------------------- Sub Main()
TranspositionDemo 3, 3 TranspositionDemo 3, 7
End Sub</lang>
- Output:
initial matrix:
1 2 3
4 5 6
7 8 9
transposed matrix:
1 4 7
2 5 8
3 6 9
initial matrix:
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
transposed matrix:
1 8 15
2 9 16
3 10 17
4 11 18
5 12 19
6 13 20
7 14 21Wortel
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.
<lang wortel>@zipm [[1 2 3] [4 5 6] [7 8 9]]</lang>
Returns:
[[1 4 7] [2 5 8] [3 6 9]]
Wren
<lang ecmascript>import "/matrix" for Matrix import "/fmt" for Fmt
var m = Matrix.new([
[ 1, 2, 3], [ 4, 5, 6], [ 7, 8, 9], [10, 11, 12]
])
System.print("Original:\n") Fmt.mprint(m, 2, 0) System.print("\nTransposed:\n") Fmt.mprint(m.transpose, 2, 0)</lang>
- Output:
Original: | 1 2 3| | 4 5 6| | 7 8 9| |10 11 12| Transposed: | 1 4 7 10| | 2 5 8 11| | 3 6 9 12|
zkl
Using the GNU Scientific Library: <lang zkl>var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library) GSL.Matrix(2,3).set(1,2,3, 4,5,6).transpose().format(5).println(); // in place println("---"); GSL.Matrix(2,2).set(1,2, 3,4).transpose().format(5).println(); // in place println("---"); GSL.Matrix(3,1).set(1,2,3).transpose().format(5).println(); // in place</lang>
- Output:
1.00, 4.00 2.00, 5.00 3.00, 6.00 --- 1.00, 3.00 2.00, 4.00 --- 1.00, 2.00, 3.00
Or, using lists:
<lang zkl>fcn transpose(M){
if(M.len()==1) M[0].pump(List,List.create); // 1 row --> n columns else M[0].zip(M.xplode(1));
}</lang> The list xplode method pushes list contents on to the call stack. <lang zkl>m:=T(T(1,2,3),T(4,5,6)); transpose(m).println(); m:=L(L(1,"a"),L(2,"b"),L(3,"c")); transpose(m).println(); transpose(L(L(1,2,3))).println(); transpose(L(L(1),L(2),L(3))).println(); transpose(L(L(1))).println();</lang>
- Output:
L(L(1,4),L(2,5),L(3,6))
L(L(1,2,3),L("a","b","c"))
L(L(1),L(2),L(3))
(L(1,2,3))
L(L(1))
zonnon
<lang zonnon> module MatrixOps; type Matrix = array {math} *,* of integer;
procedure WriteMatrix(x: array {math} *,* of integer);
var
i,j: integer;
begin
for i := 0 to len(x,0) - 1 do
for j := 0 to len(x,1) - 1 do
write(x[i,j]);
end;
writeln;
end
end WriteMatrix;
procedure Transposition; var m,x: Matrix; begin m := [[1,2,3],[3,4,5]]; (* matrix initialization *) x := !m; (* matrix trasposition *) WriteMatrix(x); end Transposition;
begin Transposition; end MatrixOps. </lang>