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This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
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{{task|Matrices}}
;Task: Multiply two matrices together.
They can be of any dimensions, so long as the number of columns of the first matrix is equal to the number of rows of the second matrix.
360 Assembly
* Matrix multiplication 06/08/2015
MATRIXRC CSECT Matrix multiplication
USING MATRIXRC,R13
SAVEARA B STM-SAVEARA(R15)
DC 17F'0'
STM STM R14,R12,12(R13)
ST R13,4(R15)
ST R15,8(R13)
LR R13,R15
LA R7,1 i=1
LOOPI1 CH R7,M do i=1 to m (R7)
BH ELOOPI1
LA R8,1 j=1
LOOPJ1 CH R8,P do j=1 to p (R8)
BH ELOOPJ1
LR R1,R7 i
BCTR R1,0
MH R1,P
LR R6,R8 j
BCTR R6,0
AR R1,R6
SLA R1,2
LA R6,0
ST R6,C(R1) c(i,j)=0
LA R9,1 k=1
LOOPK1 CH R9,N do k=1 to n (R9)
BH ELOOPK1
LR R1,R7 i
BCTR R1,0
MH R1,P
LR R6,R8 j
BCTR R6,0
AR R1,R6
SLA R1,2
L R2,C(R1) R2=c(i,j)
LR R10,R1 R10=offset(i,j)
LR R1,R7 i
BCTR R1,0
MH R1,N
LR R6,R9 k
BCTR R6,0
AR R1,R6
SLA R1,2
L R3,A(R1) R3=a(i,k)
LR R1,R9 k
BCTR R1,0
MH R1,P
LR R6,R8 j
BCTR R6,0
AR R1,R6
SLA R1,2
L R4,B(R1) R4=b(k,j)
LR R15,R3 a(i,k)
MR R14,R4 a(i,k)*b(k,j)
LR R3,R15
AR R2,R3 R2=R2+a(i,k)*b(k,j)
ST R2,C(R10) c(i,j)=c(i,j)+a(i,k)*b(k,j)
LA R9,1(R9) k=k+1
B LOOPK1
ELOOPK1 LA R8,1(R8) j=j+1
B LOOPJ1
ELOOPJ1 LA R7,1(R7) i=i+1
B LOOPI1
ELOOPI1 MVC Z,=CL80' ' clear buffer
LA R7,1
LOOPI2 CH R7,M do i=1 to m
BH ELOOPI2
LA R8,1
LOOPJ2 CH R8,P do j=1 to p
BH ELOOPJ2
LR R1,R7 i
BCTR R1,0
MH R1,P
LR R6,R8 j
BCTR R6,0
AR R1,R6
SLA R1,2
L R6,C(R1) c(i,j)
LA R3,Z
AH R3,IZ
XDECO R6,W
MVC 0(5,R3),W+7 output c(i,j)
LH R3,IZ
LA R3,5(R3)
STH R3,IZ
LA R8,1(R8) j=j+1
B LOOPJ2
ELOOPJ2 XPRNT Z,80 print buffer
MVC IZ,=H'0'
LA R7,1(R7) i=i+1
B LOOPI2
ELOOPI2 L R13,4(0,R13)
LM R14,R12,12(R13)
XR R15,R15
BR R14
A DC F'1',F'2',F'3',F'4',F'5',F'6',F'7',F'8' a(4,2)
B DC F'1',F'2',F'3',F'4',F'5',F'6' b(2,3)
C DS 12F c(4,3)
N DC H'2' dim(a,2)=dim(b,1)
M DC H'4' dim(a,1)
P DC H'3' dim(b,2)
Z DS CL80
IZ DC H'0'
W DS CL16
YREGS
END MATRIXRC
{{out}}
9 12 15
19 26 33
29 40 51
39 54 69
Ada
Ada has matrix multiplication predefined for any floating-point or complex type. The implementation is provided by the standard library packages Ada.Numerics.Generic_Real_Arrays and Ada.Numerics.Generic_Complex_Arrays correspondingly. The following example illustrates use of real matrix multiplication for the type Float:
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Numerics.Real_Arrays; use Ada.Numerics.Real_Arrays;
procedure Matrix_Product is
procedure Put (X : Real_Matrix) is
type Fixed is delta 0.01 range -100.0..100.0;
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;
A : constant Real_Matrix :=
( ( 1.0, 1.0, 1.0, 1.0),
( 2.0, 4.0, 8.0, 16.0),
( 3.0, 9.0, 27.0, 81.0),
( 4.0, 16.0, 64.0, 256.0)
);
B : constant Real_Matrix :=
( ( 4.0, -3.0, 4.0/3.0, -1.0/4.0 ),
(-13.0/3.0, 19.0/4.0, -7.0/3.0, 11.0/24.0),
( 3.0/2.0, -2.0, 7.0/6.0, -1.0/4.0 ),
( -1.0/6.0, 1.0/4.0, -1.0/6.0, 1.0/24.0)
);
begin
Put (A * B);
end Matrix_Product;
{{out}}
1.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00
0.00 0.00 1.00 0.00
0.00 0.00 0.00 1.00
The following code illustrates how matrix multiplication could be implemented from scratch:
package Matrix_Ops is
type Matrix is array (Natural range <>, Natural range <>) of Float;
function "*" (Left, Right : Matrix) return Matrix;
end Matrix_Ops;
package body Matrix_Ops is
---------
-- "*" --
---------
function "*" (Left, Right : Matrix) return Matrix is
Temp : Matrix(Left'Range(1), Right'Range(2)) := (others =>(others => 0.0));
begin
if Left'Length(2) /= Right'Length(1) then
raise Constraint_Error;
end if;
for I in Left'range(1) loop
for J in Right'range(2) loop
for K in Left'range(2) loop
Temp(I,J) := Temp(I,J) + Left(I, K)*Right(K, J);
end loop;
end loop;
end loop;
return Temp;
end "*";
end Matrix_Ops;
ALGOL 68
{{works with|ALGOL 68|Revision 1 - no extensions to language used}}
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}} {{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of FORMATted transput}} An example of user defined Vector and Matrix Multiplication Operators:
MODE FIELD = LONG REAL; # field type is LONG REAL #
INT default upb:=3;
MODE VECTOR = [default upb]FIELD;
MODE MATRIX = [default upb,default upb]FIELD;
# crude exception handling #
PROC VOID raise index error := VOID: GOTO exception index error;
# define the vector/matrix operators #
OP * = (VECTOR a,b)FIELD: ( # basically the dot product #
FIELD result:=0;
IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;
FOR i FROM LWB a TO UPB a DO result+:= a[i]*b[i] OD;
result
);
OP * = (VECTOR a, MATRIX b)VECTOR: ( # overload vector times matrix #
[2 LWB b:2 UPB b]FIELD result;
IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI;
FOR j FROM 2 LWB b TO 2 UPB b DO result[j]:=a*b[,j] OD;
result
);
# this is the task portion #
OP * = (MATRIX a, b)MATRIX: ( # overload matrix times matrix #
[LWB a:UPB a, 2 LWB b:2 UPB b]FIELD result;
IF 2 LWB a/=LWB b OR 2 UPB a/=UPB b THEN raise index error FI;
FOR k FROM LWB result TO UPB result DO result[k,]:=a[k,]*b OD;
result
);
# Some sample matrices to test #
test:(
MATRIX a=((1, 1, 1, 1), # matrix A #
(2, 4, 8, 16),
(3, 9, 27, 81),
(4, 16, 64, 256));
MATRIX b=(( 4 , -3 , 4/3, -1/4 ), # matrix B #
(-13/3, 19/4, -7/3, 11/24),
( 3/2, -2 , 7/6, -1/4 ),
( -1/6, 1/4, -1/6, 1/24));
MATRIX prod = a * b; # actual multiplication example of A x B #
FORMAT real fmt = $g(-6,2)$; # width of 6, with no '+' sign, 2 decimals #
PROC real matrix printf= (FORMAT real fmt, MATRIX m)VOID:(
FORMAT vector fmt = $"("n(2 UPB m-1)(f(real fmt)",")f(real fmt)")"$;
FORMAT matrix fmt = $x"("n(UPB m-1)(f(vector fmt)","lxx)f(vector fmt)");"$;
# finally print the result #
printf((matrix fmt,m))
);
# finally print the result #
print(("Product of a and b: ",new line));
real matrix printf(real fmt, prod)
EXIT
exception index error:
putf(stand error, $x"Exception: index error."l$)
)
{{out}}
Product of a and b:
(( 1.00, -0.00, -0.00, -0.00),
( -0.00, 1.00, -0.00, -0.00),
( -0.00, -0.00, 1.00, -0.00),
( -0.00, -0.00, -0.00, 1.00));
Parallel processing
Alternatively - for multicore CPUs - use the following parallel code... The next step might be to augment with [http://www.csse.monash.edu.au/~lloyd/tildeProgLang/Algol68/strassen.a68 Strassen's O(n^log2(7)) recursive matrix multiplication algorithm]: '''int''' default upb := 3; '''mode''' '''field''' = '''long''' '''real'''; '''mode''' '''vector''' = [default upb]'''field'''; '''mode''' '''matrix''' = [default upb, default upb]'''field''';
¢ crude exception handling ¢ '''proc''' '''void''' raise index error := '''void''': '''goto''' exception index error;
'''sema''' idle cpus = '''level''' ( 8 - 1 ); ¢ 8 = number of CPU cores minus parent CPU ¢
¢ define an operator to slice array into quarters ¢ '''op''' '''top''' = ('''matrix''' m)'''int''': ( ⌊m + ⌈m ) %2, '''bot''' = ('''matrix''' m)'''int''': '''top''' m + 1, '''left''' = ('''matrix''' m)'''int''': ( 2 ⌊m + 2 ⌈m ) %2, '''right''' = ('''matrix''' m)'''int''': '''left''' m + 1, '''left''' = ('''vector''' v)'''int''': ( ⌊v + ⌈v ) %2, '''right''' = ('''vector''' v)'''int''': '''left''' v + 1; '''prio''' '''top''' = 8, '''bot''' = 8, '''left''' = 8, '''right''' = 8; ¢ Operator priority - same as LWB & UPB ¢
'''op''' × = ('''vector''' a, b)'''field''': ( ¢ dot product ¢ '''if''' (⌊a, ⌈a) ≠ (⌊b, ⌈b) '''then''' raise index error '''fi'''; '''if''' ⌊a = ⌈a '''then''' a[⌈a] × b[⌈b] '''else''' '''field''' begin, end; []'''proc''' '''void''' schedule=( '''void''': begin:=a[:'''left''' a] × b[:'''left''' b], '''void''': end :=a['''right''' a:] × b['''right''' b:] ); '''if''' '''level''' idle cpus = 0 '''then''' ¢ use current CPU ¢ '''for''' thread '''to''' ⌈schedule '''do''' schedule[thread] '''od''' '''else''' '''par''' ( ¢ run vector in parallel ¢ schedule[1], ¢ assume parent CPU ¢ ( ↓idle cpus; schedule[2]; ↑idle cpus) ) '''fi'''; begin+end '''fi''' );
'''op''' × = ('''matrix''' a, b)'''matrix''': ¢ matrix multiply ¢ '''if''' (⌊a, 2 ⌊b) = (⌈a, 2 ⌈b) '''then''' a[⌊a, ] × b[, 2 ⌈b] ¢ dot product ¢ '''else''' [⌈a, 2 ⌈b] '''field''' out; '''if''' (2 ⌊a, 2 ⌈a) ≠ (⌊b, ⌈b) '''then''' raise index error '''fi'''; []'''struct'''('''bool''' required, '''proc''' '''void''' thread) schedule = ( ( '''true''', ¢ calculate top left corner ¢ '''void''': out[:'''top''' a, :'''left''' b] := a[:'''top''' a, ] × b[, :'''left''' b]), ( ⌊a ≠ ⌈a, ¢ calculate bottom left corner ¢ '''void''': out['''bot''' a:, :'''left''' b] := a['''bot''' a:, ] × b[, :'''left''' b]), ( 2 ⌊b ≠ 2 ⌈b, ¢ calculate top right corner ¢ '''void''': out[:'''top''' a, '''right''' b:] := a[:'''top''' a, ] × b[, '''right''' b:]), ( (⌊a, 2 ⌊b) ≠ (⌈a, 2 ⌈b) , ¢ calculate bottom right corner ¢ '''void''': out['''bot''' a:, '''right''' b:] := a['''bot''' a:, ] × b[, '''right''' b:]) ); '''if''' '''level''' idle cpus = 0 '''then''' ¢ use current CPU ¢ '''for''' thread '''to''' ⌈schedule '''do''' (required →schedule[thread] | thread →schedule[thread] ) '''od''' '''else''' '''par''' ( ¢ run vector in parallel ¢ thread →schedule[1], ¢ thread is always required, and assume parent CPU ¢ ( required →schedule[4] | ↓idle cpus; thread →schedule[4]; ↑idle cpus), ¢ try to do opposite corners of matrix in parallel if CPUs are limited ¢ ( required →schedule[3] | ↓idle cpus; thread →schedule[3]; ↑idle cpus), ( required →schedule[2] | ↓idle cpus; thread →schedule[2]; ↑idle cpus) ) '''fi'''; out '''fi''';
'''format''' real fmt = $g(-6,2)$; ¢ width of 6, with no '+' sign, 2 decimals ¢ '''proc''' real matrix printf= ('''format''' real fmt, '''matrix''' m)'''void''':( '''format''' vector fmt = $"("n(2 ⌈m-1)(f(real fmt)",")f(real fmt)")"$; '''format''' matrix fmt = $x"("n(⌈m-1)(f(vector fmt)","lxx)f(vector fmt)");"$; ¢ finally print the result ¢ printf((matrix fmt,m)) );
¢ Some sample matrices to test ¢ '''matrix''' a=((1, 1, 1, 1), ¢ matrix A ¢ (2, 4, 8, 16), (3, 9, 27, 81), (4, 16, 64, 256));
'''matrix''' b=(( 4 , -3 , 4/3, -1/4 ), ¢ matrix B ¢ (-13/3, 19/4, -7/3, 11/24), ( 3/2, -2 , 7/6, -1/4 ), ( -1/6, 1/4, -1/6, 1/24));
'''matrix''' c = a × b; ¢ actual multiplication example of A x B ¢
print((" A x B =",new line)); real matrix printf(real fmt, c).
exception index error: putf(stand error, $x"Exception: index error."l$)
AppleScript
{{trans|JavaScript}}
-- matrixMultiply :: Num a => [[a]] -> [[a]] -> [[a]]
to matrixMultiply(a, b)
script rows
property xs : transpose(b)
on |λ|(row)
script columns
on |λ|(col)
my dotProduct(row, col)
end |λ|
end script
map(columns, xs)
end |λ|
end script
map(rows, a)
end matrixMultiply
-- TEST -----------------------------------------------------------
on run
matrixMultiply({¬
{-1, 1, 4}, ¬
{6, -4, 2}, ¬
{-3, 5, 0}, ¬
{3, 7, -2} ¬
}, {¬
{-1, 1, 4, 8}, ¬
{6, 9, 10, 2}, ¬
{11, -4, 5, -3}})
--> {{51, -8, 26, -18}, {-8, -38, -6, 34},
-- {33, 42, 38, -14}, {17, 74, 72, 44}}
end run
-- GENERIC FUNCTIONS ----------------------------------------------
-- dotProduct :: [n] -> [n] -> Maybe n
on dotProduct(xs, ys)
script mult
on |λ|(a, b)
a * b
end |λ|
end script
if length of xs is not length of ys then
missing value
else
sum(zipWith(mult, xs, ys))
end if
end dotProduct
-- foldr :: (a -> b -> a) -> a -> [b] -> a
on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldr
-- 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
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- 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
-- product :: Num a => [a] -> a
on product(xs)
script mult
on |λ|(a, b)
a * b
end |λ|
end script
foldr(mult, 1, xs)
end product
-- sum :: Num a => [a] -> a
on sum(xs)
script add
on |λ|(a, b)
a + b
end |λ|
end script
foldr(add, 0, xs)
end sum
-- 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
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end zipWith
{{Out}}
{{51, -8, 26, -18}, {-8, -38, -6, 34}, {33, 42, 38, -14}, {17, 74, 72, 44}}
APL
Matrix multiply in APL is just +.×. For example:
x ← +.×
A ← ↑A*¨⊂A←⍳4 ⍝ Same A as in other examples (1 1 1 1⍪ 2 4 8 16⍪ 3 9 27 81,[0.5] 4 16 64 256)
B ← ⌹A ⍝ Matrix inverse of A
'F6.2' ⎕FMT A x B
1.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00
0.00 0.00 1.00 0.00
0.00 0.00 0.00 1.00
By contrast, A×B is for element-by-element multiplication of arrays of the same shape, and if they are simple elements, this is ordinary multiplication.
AutoHotkey
ahk [http://www.autohotkey.com/forum/topic44657-150.html discussion]
Matrix("b"," ; rows separated by ","
, 1 2 ; entries separated by space or tab
, 2 3
, 3 0")
MsgBox % "B`n`n" MatrixPrint(b)
Matrix("c","
, 1 2 3
, 3 2 1")
MsgBox % "C`n`n" MatrixPrint(c)
MatrixMul("a",b,c)
MsgBox % "B * C`n`n" MatrixPrint(a)
MsgBox % MatrixMul("x",b,b)
Matrix(_a,_v) { ; Matrix structure: m_0_0 = #rows, m_0_1 = #columns, m_i_j = element[i,j], i,j > 0
Local _i, _j = 0
Loop Parse, _v, `,
If (A_LoopField != "") {
_i := 0, _j ++
Loop Parse, A_LoopField, %A_Space%%A_Tab%
If (A_LoopField != "")
_i++, %_a%_%_i%_%_j% := A_LoopField
}
%_a% := _a, %_a%_0_0 := _j, %_a%_0_1 := _i
}
MatrixPrint(_a) {
Local _i = 0, _t
Loop % %_a%_0_0 {
_i++
Loop % %_a%_0_1
_t .= %_a%_%A_Index%_%_i% "`t"
_t .= "`n"
}
Return _t
}
MatrixMul(_a,_b,_c) {
Local _i = 0, _j, _k, _s
If (%_b%_0_0 != %_c%_0_1)
Return "ERROR: inner dimensions " %_b%_0_0 " != " %_c%_0_1
%_a% := _a, %_a%_0_0 := %_b%_0_0, %_a%_0_1 := %_c%_0_1
Loop % %_c%_0_1 {
_i++, _j := 0
Loop % %_b%_0_0 {
_j++, _k := _s := 0
Loop % %_b%_0_1
_k++, _s += %_b%_%_k%_%_j% * %_c%_%_i%_%_k%
%_a%_%_i%_%_j% := _s
}
}
}
Using Objects
Multiply_Matrix(A,B){
if (A[1].MaxIndex() <> B.MaxIndex())
return
RCols := A[1].MaxIndex()>B[1].MaxIndex()?A[1].MaxIndex():B[1].MaxIndex()
RRows := A.MaxIndex()>B.MaxIndex()?A.MaxIndex():B.MaxIndex(), R := []
Loop, % RRows {
RRow:=A_Index
loop, % RCols {
RCol:=A_Index, v := 0
loop % A[1].MaxIndex()
col := A_Index, v += A[RRow, col] * B[col,RCol]
R[RRow,RCol] := v
}
}
return R
}
Examples:
A := [[1,2]
, [3,4]
, [5,6]
, [7,8]]
B := [[1,2,3]
, [4,5,6]]
if Res := Multiply_Matrix(A,B)
MsgBox % Print(Res)
else
MsgBox Error
return
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")
}
{{out}}
9 12 15
19 26 33
29 40 51
39 54 69
AWK
# Usage: GAWK -f MATRIX_MULTIPLICATION.AWK filename
# Separate matrices a and b by a blank line
BEGIN {
ranka1 = 0; ranka2 = 0
rankb1 = 0; rankb2 = 0
matrix = 1 # Indicate first (1) or second (2) matrix
i = 0
}
NF == 0 {
if (++matrix > 2) {
printf("Warning: Ignoring data below line %d.\n", NR)
}
i = 0
next
}
{
# Store first matrix in a, second matrix in b
if (matrix == 1) {
ranka1 = ++i
ranka2 = max(ranka2, NF)
for (j = 1; j <= NF; j++)
a[i,j] = $j
}
if (matrix == 2) {
rankb1 = ++i
rankb2 = max(rankb2, NF)
for (j = 1; j <= NF; j++)
b[i,j] = $j
}
}
END {
# Check ranks of a and b
if ((ranka1 < 1) || (ranka2 < 1) || (rankb1 < 1) || (rankb2 < 1) ||
(ranka2 != rankb1)) {
printf("Error: Incompatible ranks (%dx%d)*(%dx%d).\n", ranka1, ranka2, rankb1, rankb2)
exit
}
# Multiplication c = a * b
for (i = 1; i <= ranka1; i++) {
for (j = 1; j <= rankb2; j++) {
c[i,j] = 0
for (k = 1; k <= ranka2; k++)
c[i,j] += a[i,k] * b[k,j]
}
}
# Print matrix c
for (i = 1; i <= ranka1; i++) {
for (j = 1; j <= rankb2; j++)
printf("%g%s", c[i,j], j < rankb2 ? " " : "\n")
}
}
function max(m, n) {
return m > n ? m : n
}
Input:
6.5 2 3
4.5 1 5
10 16 23 50
12 -8 16 -4
70 60 -1 -2
{{out}}
299. 268. 178.5 311.
407. 364. 114.5 211.
BASIC
{{works with|QuickBasic|4.5}} {{trans|Java}}
Assume the matrices to be multiplied are a and b
IF (LEN(a,2) = LEN(b)) 'if valid dims
n = LEN(a,2)
m = LEN(a)
p = LEN(b,2)
DIM ans(0 TO m - 1, 0 TO p - 1)
FOR i = 0 TO m - 1
FOR j = 0 TO p - 1
FOR k = 0 TO n - 1
ans(i, j) = ans(i, j) + (a(i, k) * b(k, j))
NEXT k, j, i
'print answer
FOR i = 0 TO m - 1
FOR j = 0 TO p - 1
PRINT ans(i, j);
NEXT j
PRINT
NEXT i
ELSE
PRINT "invalid dimensions"
END IF
Full BASIC
{{works with|Full BASIC}} {{trans|BBC_BASIC}}
DIM matrix1(4,2),matrix2(2,3)
MAT READ matrix1
DATA 1,2
DATA 3,4
DATA 5,6
DATA 7,8
MAT READ matrix2
DATA 1,2,3
DATA 4,5,6
MAT product=matrix1*matrix2
MAT PRINT product
{{out}}
9 12 15
19 26 33
29 40 51
39 54 69
BBC BASIC
BBC BASIC has built-in matrix multiplication (assumes default lower bound of 0):
DIM matrix1(3,1), matrix2(1,2), product(3,2)
matrix1() = 1, 2, \
\ 3, 4, \
\ 5, 6, \
\ 7, 8
matrix2() = 1, 2, 3, \
\ 4, 5, 6
product() = matrix1() . matrix2()
FOR row% = 0 TO DIM(product(),1)
FOR col% = 0 TO DIM(product(),2)
PRINT product(row%,col%),;
NEXT
PRINT
NEXT
{{out}}
9 12 15
19 26 33
29 40 51
39 54 69
Burlesque
blsq ) {{1 2}{3 4}{5 6}{7 8}}{{1 2 3}{4 5 6}}mmsp
9 12 15
19 26 33
29 40 51
39 54 69
C
For performance critical work involving matrices, especially large or sparse ones, always consider using an established library such as BLAS first.
#include <stdio.h>
#include <stdlib.h>
/* Make the data structure self-contained. Element at row i and col j
is x[i * w + j]. More often than not, though, you might want
to represent a matrix some other way */
typedef struct { int h, w; double *x;} matrix_t, *matrix;
inline double dot(double *a, double *b, int len, int step)
{
double r = 0;
while (len--) {
r += *a++ * *b;
b += step;
}
return r;
}
matrix mat_new(int h, int w)
{
matrix r = malloc(sizeof(matrix_t) + sizeof(double) * w * h);
r->h = h, r->w = w;
r->x = (double*)(r + 1);
return r;
}
matrix mat_mul(matrix a, matrix b)
{
matrix r;
double *p, *pa;
int i, j;
if (a->w != b->h) return 0;
r = mat_new(a->h, b->w);
p = r->x;
for (pa = a->x, i = 0; i < a->h; i++, pa += a->w)
for (j = 0; j < b->w; j++)
*p++ = dot(pa, b->x + j, a->w, b->w);
return r;
}
void mat_show(matrix a)
{
int i, j;
double *p = a->x;
for (i = 0; i < a->h; i++, putchar('\n'))
for (j = 0; j < a->w; j++)
printf("\t%7.3f", *p++);
putchar('\n');
}
int main()
{
double da[] = { 1, 1, 1, 1,
2, 4, 8, 16,
3, 9, 27, 81,
4,16, 64, 256 };
double db[] = { 4.0, -3.0, 4.0/3,
-13.0/3, 19.0/4, -7.0/3,
3.0/2, -2.0, 7.0/6,
-1.0/6, 1.0/4, -1.0/6};
matrix_t a = { 4, 4, da }, b = { 4, 3, db };
matrix c = mat_mul(&a, &b);
/* mat_show(&a), mat_show(&b); */
mat_show(c);
/* free(c) */
return 0;
}
C#
This code should work with any version of the .NET Framework and C# language
public class Matrix
{
int n;
int m;
double[,] a;
public Matrix(int n, int m)
{
if (n <= 0 || m <= 0)
throw new ArgumentException("Matrix dimensions must be positive");
this.n = n;
this.m = m;
a = new double[n, m];
}
//indices start from one
public double this[int i, int j]
{
get { return a[i - 1, j - 1]; }
set { a[i - 1, j - 1] = value; }
}
public int N { get { return n; } }
public int M { get { return m; } }
public static Matrix operator*(Matrix _a, Matrix b)
{
int n = _a.N;
int m = b.M;
int l = _a.M;
if (l != b.N)
throw new ArgumentException("Illegal matrix dimensions for multiplication. _a.M must be equal b.N");
Matrix result = new Matrix(_a.N, b.M);
for(int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
{
double sum = 0.0;
for (int k = 0; k < l; k++)
sum += _a.a[i, k]*b.a[k, j];
result.a[i, j] = sum;
}
return result;
}
}
C++
{{works with|Visual C++ 2010}}
{{libheader|Blitz++}}
#include <iostream>
#include <blitz/tinymat.h>
int main()
{
using namespace blitz;
TinyMatrix<double,3,3> A, B, C;
A = 1, 2, 3,
4, 5, 6,
7, 8, 9;
B = 1, 0, 0,
0, 1, 0,
0, 0, 1;
C = product(A, B);
std::cout << C << std::endl;
}
{{out}} (3,3): [ 1 2 3 ] [ 4 5 6 ] [ 7 8 9 ]
Generic solution
main.cpp
#include <iostream>
#include "matrix.h"
#if !defined(ARRAY_SIZE)
#define ARRAY_SIZE(x) (sizeof((x)) / sizeof((x)[0]))
#endif
int main() {
int am[2][3] = {
{1,2,3},
{4,5,6},
};
int bm[3][2] = {
{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]));
Matrix<int> b(ARRAY_SIZE(bm), ARRAY_SIZE(bm[0]), bm[0], ARRAY_SIZE(bm)*ARRAY_SIZE(bm[0]));
Matrix<int> c;
try {
c = a * b;
for (unsigned int i = 0; i < c.rowNum(); i++) {
for (unsigned int j = 0; j < c.colNum(); j++) {
std::cout << c[i][j] << " ";
}
std::cout << std::endl;
}
} catch (MatrixException& e) {
std::cerr << e.message() << std::endl;
return e.errorCode();
}
} /* main() */
matrix.h
#ifndef _MATRIX_H
#define _MATRIX_H
#include <sstream>
#include <string>
#include <vector>
#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&);
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;
}
#endif /* _MATRIX_H */
{{out}}
22 28
49 64
Ceylon
Integer[][];
void printMatrix(Matrix m) {
value strings = m.collect((row) => row.collect(Integer.string));
value maxLength = max(expand(strings).map(String.size)) else 0;
value padded = strings.collect((row) => row.collect((s) => s.padLeading(maxLength)));
for (row in padded) {
print("[``", ".join(row)``]");
}
}
Matrix? multiplyMatrices(Matrix a, Matrix b) {
function rectangular(Matrix m) =>
if (exists firstRow = m.first)
then m.every((row) => row.size == firstRow.size)
else false;
function rowCount(Matrix m) => m.size;
function columnCount(Matrix m) => m[0]?.size else 0;
if (!rectangular(a) || !rectangular(b) || columnCount(a) != rowCount(b)) {
return null;
}
function getNumber(Matrix m, Integer x, Integer y) {
assert (exists number = m[y]?.get(x));
return number;
}
function getRow(Matrix m, Integer rowIndex) {
assert (exists row = m[rowIndex]);
return row;
}
function getColumn(Matrix m, Integer columnIndex) => {
for (y in 0:rowCount(m))
getNumber(m, columnIndex, y)
};
return [
for (y in 0:rowCount(a)) [
for (x in 0:columnCount(b))
sum { 0, for ([a1, b1] in zipPairs(getRow(a, y), getColumn(b, x))) a1 * b1 }
]
];
}
shared void run() {
value m = [[1, 2, 3], [4, 5, 6]];
printMatrix(m);
print("---------");
print("multiplied by");
value m2 = [[7, 8], [9, 10], [11, 12]];
printMatrix(m2);
print("---------");
print("equals:");
value result = multiplyMatrices(m, m2);
if (exists result) {
printMatrix(result);
}
else {
print("something went wrong!");
}
}
{{out}}
[1, 2, 3]
[4, 5, 6]
---------
multiplied by
[ 7, 8]
[ 9, 10]
[11, 12]
---------
equals:
[ 58, 64]
[139, 154]
Clojure
(defn transpose
[s]
(apply map vector s))
(defn nested-for
[f x y]
(map (fn [a]
(map (fn [b]
(f a b)) y))
x))
(defn matrix-mult
[a b]
(nested-for (fn [x y] (reduce + (map * x y))) a (transpose b)))
(def ma [[1 1 1 1] [2 4 8 16] [3 9 27 81] [4 16 64 256]])
(def mb [[4 -3 4/3 -1/4] [-13/3 19/4 -7/3 11/24] [3/2 -2 7/6 -1/4] [-1/6 1/4 -1/6 1/24]])
{{out}}
=> (matrix-mult ma mb)
((1 0 0 0) (0 1 0 0) (0 0 1 0) (0 0 0 1))
Common Lisp
(defun matrix-multiply (a b)
(flet ((col (mat i) (mapcar #'(lambda (row) (elt row i)) mat))
(row (mat i) (elt mat i)))
(loop for row from 0 below (length a)
collect (loop for col from 0 below (length (row b 0))
collect (apply #'+ (mapcar #'* (row a row) (col b col)))))))
;; example use:
(matrix-multiply '((1 2) (3 4)) '((-3 -8 3) (-2 1 4)))
(defun matrix-multiply (matrix1 matrix2)
(mapcar
(lambda (row)
(apply #'mapcar
(lambda (&rest column)
(apply #'+ (mapcar #'* row column))) matrix2)) matrix1))
The following version uses 2D arrays as inputs.
(defun mmul (A B)
(let* ((m (car (array-dimensions A)))
(n (cadr (array-dimensions A)))
(l (cadr (array-dimensions B)))
(C (make-array `(,m ,l) :initial-element 0)))
(loop for i from 0 to (- m 1) do
(loop for k from 0 to (- l 1) do
(setf (aref C i k)
(loop for j from 0 to (- n 1)
sum (* (aref A i j)
(aref B j k))))))
C))
Example use:
(mmul #2a((1 2) (3 4)) #2a((-3 -8 3) (-2 1 4)))
#2A((-7 -6 11) (-17 -20 25))
Another version:
(defun mmult (a b)
(loop
with m = (array-dimension a 0)
with n = (array-dimension a 1)
with l = (array-dimension b 1)
with c = (make-array (list m l) :initial-element 0)
for i below m do
(loop for k below l do
(setf (aref c i k)
(loop for j below n
sum (* (aref a i j)
(aref b j k)))))
finally (return c)))
Chapel
Overload the '*' operator for arrays
proc *(a:[], b:[]) {
if (a.eltType != b.eltType) then
writeln("type mismatch: ", a.eltType, " ", b.eltType);
var ad = a.domain.dims();
var bd = b.domain.dims();
var (arows, acols) = ad;
var (brows, bcols) = bd;
if (arows != bcols) then
writeln("dimension mismatch: ", ad, " ", bd);
var c:[{arows, bcols}] a.eltType = 0;
for i in arows do
for j in bcols do
for k in acols do
c(i,j) += a(i,k) * b(k,j);
return c;
}
example usage (I could not figure out the syntax for multi-dimensional array literals)
var m1:[{1..2, 1..2}] int;
m1(1,1) = 1; m1(1,2) = 2;
m1(2,1) = 3; m1(2,2) = 4;
writeln(m1);
var m2:[{1..2, 1..2}] int;
m2(1,1) = 2; m2(1,2) = 3;
m2(2,1) = 4; m2(2,2) = 5;
writeln(m2);
var m3 = m1 * m2;
writeln(m3);
var m4:[{1..2, 1..3}] int;
m4(1, 1) = 1; m4(1, 2) = 2; m4(1, 3) = 3;
m4(2, 1) = 4; m4(2, 2) = 5; m4(2, 3) = 6;
writeln(m4);
var m5:[{1..3, 1..2}] int;
m5(1, 1) = 6; m5(1, 2) = -1;
m5(2, 1) = 3; m5(2, 2) = 2;
m5(3, 1) = 0; m5(3, 2) = -3;
writeln(m5);
writeln(m4 * m5);
D
Basic Version
import std.stdio, std.string, std.conv, std.numeric,
std.array, std.algorithm;
bool isRectangular(T)(in T[][] M) pure nothrow {
return M.all!(row => row.length == M[0].length);
}
T[][] matrixMul(T)(in T[][] A, in T[][] B) pure nothrow
in {
assert(A.isRectangular && B.isRectangular &&
!A.empty && !B.empty && A[0].length == B.length);
} body {
auto result = new T[][](A.length, B[0].length);
auto aux = new T[B.length];
foreach (immutable j; 0 .. B[0].length) {
foreach (immutable k, const row; B)
aux[k] = row[j];
foreach (immutable i, const ai; A)
result[i][j] = dotProduct(ai, aux);
}
return result;
}
void main() {
immutable a = [[1, 2], [3, 4], [3, 6]];
immutable b = [[-3, -8, 3,], [-2, 1, 4]];
immutable form = "[%([%(%d, %)],\n %)]]";
writefln("A = \n" ~ form ~ "\n", a);
writefln("B = \n" ~ form ~ "\n", b);
writefln("A * B = \n" ~ form, matrixMul(a, b));
}
{{out}}
A =
[[1, 2],
[3, 4],
[3, 6]]
B =
[[-3, -8, 3],
[-2, 1, 4]]
A * B =
[[-7, -6, 11],
[-17, -20, 25],
[-21, -18, 33]]
Short Version
import std.stdio, std.range, std.array, std.numeric, std.algorithm;
T[][] matMul(T)(in T[][] A, in T[][] B) pure nothrow /*@safe*/ {
const Bt = B[0].length.iota.map!(i=> B.transversal(i).array).array;
return A.map!(a => Bt.map!(b => a.dotProduct(b)).array).array;
}
void main() {
immutable a = [[1, 2], [3, 4], [3, 6]];
immutable b = [[-3, -8, 3,], [-2, 1, 4]];
immutable form = "[%([%(%d, %)],\n %)]]";
writefln("A = \n" ~ form ~ "\n", a);
writefln("B = \n" ~ form ~ "\n", b);
writefln("A * B = \n" ~ form, matMul(a, b));
}
The output is the same.
Pure Short Version
import std.stdio, std.range, std.numeric, std.algorithm;
T[][] matMul(T)(immutable T[][] A, immutable T[][] B) pure nothrow {
immutable Bt = B[0].length.iota.map!(i=> B.transversal(i).array)
.array;
return A.map!((in a) => Bt.map!(b => a.dotProduct(b)).array).array;
}
void main() {
immutable a = [[1, 2], [3, 4], [3, 6]];
immutable b = [[-3, -8, 3,], [-2, 1, 4]];
immutable form = "[%([%(%d, %)],\n %)]]";
writefln("A = \n" ~ form ~ "\n", a);
writefln("B = \n" ~ form ~ "\n", b);
writefln("A * B = \n" ~ form, matMul(a, b));
}
The output is the same.
Stronger Statically Typed Version
All array sizes are verified at compile-time (and no matrix is copied). Same output.
import std.stdio, std.string, std.numeric, std.algorithm, std.traits;
alias TMMul_helper(M1, M2) = Unqual!(ForeachType!(ForeachType!M1))
[M2.init[0].length][M1.length];
void matrixMul(T, T2, size_t k, size_t m, size_t n)
(in ref T[m][k] A, in ref T[n][m] B,
/*out*/ ref T2[n][k] result) pure nothrow /*@safe*/ @nogc
if (is(T2 == Unqual!T)) {
static if (hasIndirections!T)
T2[m] aux;
else
T2[m] aux = void;
foreach (immutable j; 0 .. n) {
foreach (immutable i, const ref bi; B)
aux[i] = bi[j];
foreach (immutable i, const ref ai; A)
result[i][j] = dotProduct(ai, aux);
}
}
void main() {
immutable int[2][3] a = [[1, 2], [3, 4], [3, 6]];
immutable int[3][2] b = [[-3, -8, 3,], [-2, 1, 4]];
enum form = "[%([%(%d, %)],\n %)]]";
writefln("A = \n" ~ form ~ "\n", a);
writefln("B = \n" ~ form ~ "\n", b);
TMMul_helper!(typeof(a), typeof(b)) result = void;
matrixMul(a, b, result);
writefln("A * B = \n" ~ form, result);
}
Ela
open list
mmult a b = [ [ sum $ zipWith (*) ar bc \\ bc <- (transpose b) ] \\ ar <- a ]
[[1, 2],
[3, 4]] `mmult` [[-3, -8, 3],
[-2, 1, 4]]
ELLA
Sample originally from ftp://ftp.dra.hmg.gb/pub/ella (a now dead link) - Public release.
Code for matrix multiplication hardware design verification:
MAC ZIP = ([INT n]TYPE t: vector1 vector2) -> [n][2]t:
[INT k = 1..n](vector1[k], vector2[k]).
MAC TRANSPOSE = ([INT n][INT m]TYPE t: matrix) -> [m][n]t:
[INT i = 1..m] [INT j = 1..n] matrix[j][i].
MAC INNER_PRODUCT{FN * = [2]TYPE t -> TYPE s, FN + = [2]s -> s}
= ([INT n][2]t: vector) -> s:
IF n = 1 THEN *vector[1]
ELSE *vector[1] + INNER_PRODUCT {*,+} vector[2..n]
FI.
MAC MATRIX_MULT {FN * = [2]TYPE t->TYPE s, FN + = [2]s->s} =
([INT n][INT m]t: matrix1, [m][INT p]t: matrix2) -> [n][p]s:
BEGIN
LET transposed_matrix2 = TRANSPOSE matrix2.
OUTPUT [INT i = 1..n][INT j = 1..p]
INNER_PRODUCT{*,+}ZIP(matrix1[i],transposed_matrix2[j])
END.
TYPE element = NEW elt/(1..20),
product = NEW prd/(1..1200).
FN PLUS = (product: integer1 integer2) -> product:
ARITH integer1 + integer2.
FN MULT = (element: integer1 integer2) -> product:
ARITH integer1 * integer2.
FN MULT_234 = ([2][3]element:matrix1, [3][4]element:matrix2) ->
[2][4]product:
MATRIX_MULT{MULT,PLUS}(matrix1, matrix2).
FN TEST = () -> [2][4]product:
( LET m1 = ((elt/2, elt/1, elt/1),
(elt/3, elt/6, elt/9)),
m2 = ((elt/6, elt/1, elt/3, elt/4),
(elt/9, elt/2, elt/8, elt/3),
(elt/6, elt/4, elt/1, elt/2)).
OUTPUT
MULT_234 (m1, m2)
).
COM test: just displaysignal MOC
Euphoria
function matrix_mul(sequence a, sequence b)
sequence c
if length(a[1]) != length(b) then
return 0
else
c = repeat(repeat(0,length(b[1])),length(a))
for i = 1 to length(a) do
for j = 1 to length(b[1]) do
for k = 1 to length(a[1]) do
c[i][j] += a[i][k]*b[k][j]
end for
end for
end for
return c
end if
end function
EGL
program Matrix_multiplication type BasicProgram {}
function main()
a float[][] = [[1,2,3],[4,5,6]];
b float[][] = [[1,2],[3,4],[5,6]];
c float[][] = mult(a, b);
end
function mult(a float[][], b float[][]) returns(float[][])
if(a.getSize() == 0)
return (new float[0][0]);
end
if(a[1].getSize() != b.getSize())
return (null); //invalid dims
end
n int = a[1].getSize();
m int = a.getSize();
p int = b[1].getSize();
ans float[0][0];
ans.resizeAll([m, p]);
// Calculate dot product.
for(i int from 1 to m)
for(j int from 1 to p)
for(k int from 1 to n)
ans[i][j] += a[i][k] * b[k][j];
end
end
end
return (ans);
end
end
Elixir
def mult(m1, m2) do
Enum.map m1, fn (x) -> Enum.map t(m2), fn (y) -> Enum.zip(x, y)
|> Enum.map(fn {x, y} -> x * y end)
|> Enum.sum
end
end
end
def t(m) do # transpose
List.zip(m) |> Enum.map(&Tuple.to_list(&1))
end
Erlang
%% Multiplies two matrices. Usage example:
%% $ matrix:multiply([[1,2,3],[4,5,6]], [[4,4],[0,0],[1,4]])
%% If the dimentions are incompatible, an error is thrown.
%%
%% The erl shell may encode the lists output as strings. In order to prevent such
%% behaviour, BEFORE running matrix:multiply, run shell:strings(false) to disable
%% auto-encoding. When finished, run shell:strings(true) to reset the defaults.
-module(matrix).
-export([multiply/2]).
transpose([[]|_]) ->
[];
transpose(B) ->
[lists:map(fun hd/1, B) | transpose(lists:map(fun tl/1, B))].
red(Pair, Sum) ->
X = element(1, Pair), %gets X
Y = element(2, Pair), %gets Y
X * Y + Sum.
%% Mathematical dot product. A x B = d
%% A, B = 1-dimension vector
%% d = scalar
dot_product(A, B) ->
lists:foldl(fun red/2, 0, lists:zip(A, B)).
%% Exposed function. Expected result is C = A x B.
multiply(A, B) ->
%% First transposes B, to facilitate the calculations (It's easier to fetch
%% row than column wise).
multiply_internal(A, transpose(B)).
%% This function does the actual multiplication, but expects the second matrix
%% to be transposed.
multiply_internal([Head | Rest], B) ->
% multiply each row by Y
Element = multiply_row_by_col(Head, B),
% concatenate the result of this multiplication with the next ones
[Element | multiply_internal(Rest, B)];
multiply_internal([], B) ->
% concatenating and empty list to the end of a list, changes nothing.
[].
multiply_row_by_col(Row, [Col_Head | Col_Rest]) ->
Scalar = dot_product(Row, Col_Head),
[Scalar | multiply_row_by_col(Row, Col_Rest)];
multiply_row_by_col(Row, []) ->
[].
{{out}}
[[7,16],[22,40]]
ERRE
PROGRAM MAT_PROD
DIM A[3,1],B[1,2],ANS[3,2]
BEGIN
DATA(1,2,3,4,5,6,7,8)
DATA(1,2,3,4,5,6)
FOR I=0 TO 3 DO
FOR J=0 TO 1 DO
READ(A[I,J])
END FOR
END FOR
FOR I=0 TO 1 DO
FOR J=0 TO 2 DO
READ(B[I,J])
END FOR
END FOR
FOR I=0 TO UBOUND(ANS,1) DO
FOR J=0 TO UBOUND(ANS,2) DO
FOR K=0 TO UBOUND(A,2) DO
ANS[I,J]=ANS[I,J]+(A[I,K]*B[K,J])
END FOR
END FOR
END FOR
! print answer
FOR I=0 TO UBOUND(ANS,1) DO
FOR J=0 TO UBOUND(ANS,2) DO
PRINT(ANS[I,J],)
END FOR
PRINT
END FOR
END PROGRAM
{{out}}
9 12 15
19 26 33
29 40 51
39 54 69
F#
let MatrixMultiply (matrix1 : _[,] , matrix2 : _[,]) =
let result_row = (matrix1.GetLength 0)
let result_column = (matrix2.GetLength 1)
let ret = Array2D.create result_row result_column 0
for x in 0 .. result_row - 1 do
for y in 0 .. result_column - 1 do
let mutable acc = 0
for z in 0 .. (matrix1.GetLength 1) - 1 do
acc <- acc + matrix1.[x,z] * matrix2.[z,y]
ret.[x,y] <- acc
ret
Factor
The built-in word m. multiplies matrices:
( scratchpad ) USE: math.matrices { { 1 2 } { 3 4 } } { { -3 -8 3 } { -2 1 4 } } m. . { { -7 -6 11 } { -17 -20 25 } }
Fantom
Using a list of lists representation. The multiplication is done using three nested loops.
class Main
{
// multiply two matrices (with no error checking)
public static Int[][] multiply (Int[][] m1, Int[][] m2)
{
Int[][] result := [,]
m1.each |Int[] row1|
{
Int[] row := [,]
m2[0].size.times |Int colNumber|
{
Int value := 0
m2.each |Int[] row2, Int index|
{
value += row1[index] * row2[colNumber]
}
row.add (value)
}
result.add (row)
}
return result
}
public static Void main ()
{
m1 := [[1,2,3],[4,5,6]]
m2 := [[1,2],[3,4],[5,6]]
echo ("${m1} times ${m2} = ${multiply(m1,m2)}")
}
}
{{out}}
[[1, 2, 3], [4, 5, 6]] times [[1, 2], [3, 4], [5, 6]] = [[22, 28], [49, 64]]
Forth
{{libheader|Forth Scientific Library}} {{works with|gforth|0.7.9_20170308}}
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
3 3 float matrix A{{
1e 2e 3e 4e 5e 6e 7e 8e 9e 3 3 A{{ }}fput
3 3 float matrix B{{
3e 3e 3e 2e 2e 2e 1e 1e 1e 3 3 B{{ }}fput
float dmatrix C{{ \ result
A{{ 3 3 B{{ 3 3 & C{{ mat*
3 3 C{{ }}fprint
Fortran
In ISO Fortran 90 or later, use the MATMUL intrinsic function to perform Matrix Multiply; use RESHAPE and SIZE intrinsic functions to form the matrices themselves:
real, dimension(n,m) :: a = reshape( [ (i, i=1, n*m) ], [ n, m ] )
real, dimension(m,k) :: b = reshape( [ (i, i=1, m*k) ], [ m, k ] )
real, dimension(size(a,1), size(b,2)) :: c ! C is an array whose first dimension (row) size
! is the same as A's first dimension size, and
! whose second dimension (column) size is the same
! as B's second dimension size.
c = matmul( a, b )
print *, 'A'
do i = 1, n
print *, a(i,:)
end do
print *,
print *, 'B'
do i = 1, m
print *, b(i,:)
end do
print *,
print *, 'C = AB'
do i = 1, n
print *, c(i,:)
end do
For Intel 14.x or later (with compiler switch -assume realloc_lhs)
program mm
real , allocatable :: a(:,:),b(:,:)
integer :: l=5,m=6,n=4
a = reshape([1:l*m],[l,m])
b = reshape([1:m*n],[m,n])
print'(<n>f15.7)',transpose(matmul(a,b))
end program
Frink
matprod[a is array, b is array] :=
{
c = makeArray[[length[a], length[b@0]], 0]
a_row = length[a]-1
a_col = length[a@0]-1
b_col = length[b]-1
for row = 0 to a_row
for col = 0 to b_col
for inc = 0 to a_col
c@row@col = c@row@col + (a@row@inc * b@inc@col)
return c
}
Futhark
{{incorrect|Futhark|Futhark's syntax has changed, so this example will not compile}}
Note that the transposition need not be manifested, but is merely a change of indexing.
fun main(x: [n][m]int, y: [m][p]int): [n][p]int =
map (fn xr => map (fn yc => reduce (+) 0 (zipWith (*) xr yc))
(transpose y))
x
GAP
# Built-in
A := [[1, 2], [3, 4], [5, 6], [7, 8]];
B := [[1, 2, 3], [4, 5, 6]];
PrintArray(A);
# [ [ 1, 2 ],
# [ 3, 4 ],
# [ 5, 6 ],
# [ 7, 8 ] ]
PrintArray(B);
# [ [ 1, 2, 3 ],
# [ 4, 5, 6 ] ]
PrintArray(A * B);
# [ [ 9, 12, 15 ],
# [ 19, 26, 33 ],
# [ 29, 40, 51 ],
# [ 39, 54, 69 ] ]
Go
Library gonum/mat
package main
import (
"fmt"
"gonum.org/v1/gonum/mat"
)
func main() {
a := mat.NewDense(2, 4, []float64{
1, 2, 3, 4,
5, 6, 7, 8,
})
b := mat.NewDense(4, 3, []float64{
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
})
var m mat.Dense
m.Mul(a, b)
fmt.Println(mat.Formatted(&m))
}
{{out}}
⎡ 70 80 90⎤
⎣158 184 210⎦
Library go.matrix
package main
import (
"fmt"
mat "github.com/skelterjohn/go.matrix"
)
func main() {
a := mat.MakeDenseMatrixStacked([][]float64{
{1, 2, 3, 4},
{5, 6, 7, 8},
})
b := mat.MakeDenseMatrixStacked([][]float64{
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12},
})
fmt.Printf("Matrix A:\n%v\n", a)
fmt.Printf("Matrix B:\n%v\n", b)
p, err := a.TimesDense(b)
if err != nil {
fmt.Println(err)
return
}
fmt.Printf("Product of A and B:\n%v\n", p)
}
{{out}}
Matrix A:
{1, 2, 3, 4,
5, 6, 7, 8}
Matrix B:
{ 1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12}
Product of A and B:
{ 70, 80, 90,
158, 184, 210}
2D representation
package main
import "fmt"
type Value float64
type Matrix [][]Value
func Multiply(m1, m2 Matrix) (m3 Matrix, ok bool) {
rows, cols, extra := len(m1), len(m2[0]), len(m2)
if len(m1[0]) != extra {
return nil, false
}
m3 = make(Matrix, rows)
for i := 0; i < rows; i++ {
m3[i] = make([]Value, cols)
for j := 0; j < cols; j++ {
for k := 0; k < extra; k++ {
m3[i][j] += m1[i][k] * m2[k][j]
}
}
}
return m3, true
}
func (m Matrix) String() string {
rows := len(m)
cols := len(m[0])
out := "["
for r := 0; r < rows; r++ {
if r > 0 {
out += ",\n "
}
out += "[ "
for c := 0; c < cols; c++ {
if c > 0 {
out += ", "
}
out += fmt.Sprintf("%7.3f", m[r][c])
}
out += " ]"
}
out += "]"
return out
}
func main() {
A := Matrix{[]Value{1, 2, 3, 4},
[]Value{5, 6, 7, 8}}
B := Matrix{[]Value{1, 2, 3},
[]Value{4, 5, 6},
[]Value{7, 8, 9},
[]Value{10, 11, 12}}
P, ok := Multiply(A, B)
if !ok {
panic("Invalid dimensions")
}
fmt.Printf("Matrix A:\n%s\n\n", A)
fmt.Printf("Matrix B:\n%s\n\n", B)
fmt.Printf("Product of A and B:\n%s\n\n", P)
}
{{out}}
Matrix A:
[[ 1.000, 2.000, 3.000, 4.000 ],
[ 5.000, 6.000, 7.000, 8.000 ]]
Matrix B:
[[ 1.000, 2.000, 3.000 ],
[ 4.000, 5.000, 6.000 ],
[ 7.000, 8.000, 9.000 ],
[ 10.000, 11.000, 12.000 ]]
Product of A and B:
[[ 70.000, 80.000, 90.000 ],
[ 158.000, 184.000, 210.000 ]]
Flat representation
package main
import "fmt"
type matrix struct {
stride int
ele []float64
}
func (m *matrix) print(heading string) {
if heading > "" {
fmt.Print("\n", heading, "\n")
}
for e := 0; e < len(m.ele); e += m.stride {
fmt.Printf("%8.3f ", m.ele[e:e+m.stride])
fmt.Println()
}
}
func (m1 *matrix) multiply(m2 *matrix) (m3 *matrix, ok bool) {
if m1.stride*m2.stride != len(m2.ele) {
return nil, false
}
m3 = &matrix{m2.stride, make([]float64, (len(m1.ele)/m1.stride)*m2.stride)}
for m1c0, m3x := 0, 0; m1c0 < len(m1.ele); m1c0 += m1.stride {
for m2r0 := 0; m2r0 < m2.stride; m2r0++ {
for m1x, m2x := m1c0, m2r0; m2x < len(m2.ele); m2x += m2.stride {
m3.ele[m3x] += m1.ele[m1x] * m2.ele[m2x]
m1x++
}
m3x++
}
}
return m3, true
}
func main() {
a := matrix{4, []float64{
1, 2, 3, 4,
5, 6, 7, 8,
}}
b := matrix{3, []float64{
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
}}
p, ok := a.multiply(&b)
a.print("Matrix A:")
b.print("Matrix B:")
if !ok {
fmt.Println("not conformable for matrix multiplication")
return
}
p.print("Product of A and B:")
}
Output is similar to 2D version.
Groovy
Without Indexed Loops
Uses transposition to avoid indirect element access via ranges of indexes. "assertConformable()" asserts that a & b are both rectangular lists of lists, and that row-length (number of columns) of a is equal to the column-length (number of rows) of b.
def assertConformable = { a, b ->
assert a instanceof List
assert b instanceof List
assert a.every { it instanceof List && it.size() == b.size() }
assert b.every { it instanceof List && it.size() == b[0].size() }
}
def matmulWOIL = { a, b ->
assertConformable(a, b)
def bt = b.transpose()
a.collect { ai ->
bt.collect { btj ->
[ai, btj].transpose().collect { it[0] * it[1] }.sum()
}
}
}
Without Transposition
Uses ranges of indexes, the way that matrix multiplication is typically defined. Not as elegant, but it avoids expensive transpositions. Reuses "assertConformable()" from above.
def matmulWOT = { a, b ->
assertConformable(a, b)
(0..<a.size()).collect { i ->
(0..<b[0].size()).collect { j ->
(0..<b.size()).collect { k -> a[i][k] * b[k][j] }.sum()
}
}
}
Test:
def m4by2 = [ [ 1, 2 ],
[ 3, 4 ],
[ 5, 6 ],
[ 7, 8 ] ]
def m2by3 = [ [ 1, 2, 3 ],
[ 4, 5, 6 ] ]
matmulWOIL(m4by2, m2by3).each { println it }
println()
matmulWOT(m4by2, m2by3).each { println it }
{{out}}
[9, 12, 15]
[19, 26, 33]
[29, 40, 51]
[39, 54, 69]
[9, 12, 15]
[19, 26, 33]
[29, 40, 51]
[39, 54, 69]
Haskell
With List and transpose
A somewhat inefficient version with lists (''transpose'' is expensive):
import Data.List
mmult :: Num a => [[a]] -> [[a]] -> [[a]]
mmult a b = [ [ sum $ zipWith (*) ar bc | bc <- (transpose b) ] | ar <- a ]
-- Example use:
test = [[1, 2],
[3, 4]] `mmult` [[-3, -8, 3],
[-2, 1, 4]]
With Array
A more efficient version, based on arrays:
import Data.Array
mmult :: (Ix i, Num a) => Array (i,i) a -> Array (i,i) a -> Array (i,i) a
mmult x y
| x1 /= y0 || x1' /= y0' = error "range mismatch"
| otherwise = array ((x0,y1),(x0',y1')) l
where
((x0,x1),(x0',x1')) = bounds x
((y0,y1),(y0',y1')) = bounds y
ir = range (x0,x0')
jr = range (y1,y1')
kr = range (x1,x1')
l = [((i,j), sum [x!(i,k) * y!(k,j) | k <- kr]) | i <- ir, j <- jr]
With List and without transpose
multiply:: Num a => [[a]] -> [[a]] -> [[a]]
multiply [] _ = error "left matrix is empty"
multiply _ [] = error "right matrix is empty"
multiply us vs = map (mult [] vs) us
where
mult xs [] _ = xs
mult xs _ [] = xs
mult [] (zs:zss) (y:ys) = mult (map (\v -> v*y) zs) zss ys
mult xs (zs:zss) (y:ys) = mult (zipWith (\u v -> u+v*y) xs zs) zss ys
main = mapM_ print $ multiply [[1, 2],[3, 4]] [[-3, -8, 3],[-2, 1, 4]]
{{out}}
[-7,-6,11]
[-17,-20,25]
foldlZipWith::(a -> b -> c) -> (d -> c -> d) -> d -> [a] -> [b] -> d
foldlZipWith _ _ u [] _ = u
foldlZipWith _ _ u _ [] = u
foldlZipWith f g u (x:xs) (y:ys) = foldlZipWith f g (g u (f x y)) xs ys
foldl1ZipWith::(a -> b -> c) -> (c -> c -> c) -> [a] -> [b] -> c
foldl1ZipWith _ _ [] _ = error "First list is empty"
foldl1ZipWith _ _ _ [] = error "Second list is empty"
foldl1ZipWith f g (x:xs) (y:ys) = foldlZipWith f g (f x y) xs ys
multAdd::(a -> b -> c) -> (c -> c -> c) -> [[a]] -> [[b]] -> [[c]]
multAdd f g xs ys = map (\us -> foldl1ZipWith (\u vs -> map (f u) vs) (zipWith g) us ys) xs
mult:: Num a => [[a]] -> [[a]] -> [[a]]
mult xs ys = multAdd (*) (+) xs ys
test a b = do
let c = mult a b
putStrLn "a ="
mapM_ print a
putStrLn "b ="
mapM_ print b
putStrLn "c = a * b = mult a b ="
mapM_ print c
main = test [[1, 2],[3, 4]] [[-3, -8, 3],[-2, 1, 4]]
{{out}}
a =
[1,2]
[3,4]
b =
[-3,-8,3]
[-2,1,4]
c = a * b = mult a b =
[-7,-6,11]
[-17,-20,25]
HicEst
REAL :: m=4, n=2, p=3, a(m,n), b(n,p), res(m,p)
a = $ ! initialize to 1, 2, ..., m*n
b = $ ! initialize to 1, 2, ..., n*p
res = 0
DO i = 1, m
DO j = 1, p
DO k = 1, n
res(i,j) = res(i,j) + a(i,k) * b(k,j)
ENDDO
ENDDO
ENDDO
DLG(DefWidth=4, Text=a, Text=b,Y=0, Text=res,Y=0)
a b res
1 2 1 2 3 9 12 15
3 4 4 5 6 19 26 33
5 6 29 40 51
7 8 39 54 69
=={{header|Icon}} and {{header|Unicon}}==
Using the provided matrix library:
link matrix
procedure main ()
m1 := [[1,2,3], [4,5,6]]
m2 := [[1,2],[3,4],[5,6]]
m3 := mult_matrix (m1, m2)
write ("Multiply:")
write_matrix ("", m1) # first argument is filename, or "" for stdout
write ("by:")
write_matrix ("", m2)
write ("Result: ")
write_matrix ("", m3)
end
And a hand-crafted multiply procedure:
procedure multiply_matrix (m1, m2)
result := [] # to hold the final matrix
every row1 := !m1 do { # loop through each row in the first matrix
row := []
every colIndex := 1 to *m1 do { # and each column index of the result
value := 0
every rowIndex := 1 to *m2 do {
value +:= row1[rowIndex] * m2[rowIndex][colIndex]
}
put (row, value)
}
put (result, row) # add each row as it is complete
}
return result
end
{{out}}
Multiply:
1 2 3
4 5 6
by:
1 2
3 4
5 6
Result:
22 28
49 64
IDL
## Idris
```idris
import Data.Vect
Matrix : Nat -> Nat -> Type -> Type
Matrix m n t = Vect m (Vect n t)
multiply : Num t => Matrix m1 n t -> Matrix n m2 t -> Matrix m1 m2 t
multiply a b = multiply' a (transpose b)
where
dot : Num t => Vect n t -> Vect n t -> t
dot v1 v2 = sum $ map (\(s1, s2) => (s1 * s2)) (zip v1 v2)
multiply' : Num t => Matrix m1 n t -> Matrix m2 n t -> Matrix m1 m2 t
multiply' (a::as) b = map (dot a) b :: multiply' as b
multiply' [] _ = []
J
Matrix multiply in J is +/ .*. For example:
mp =: +/ .* NB. Matrix product
A =: ^/~>:i. 4 NB. Same A as in other examples (1 1 1 1, 2 4 8 16, 3 9 27 81,:4 16 64 256)
B =: %.A NB. Matrix inverse of A
'6.2' 8!:2 A mp B
1.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00
0.00 0.00 1.00 0.00
0.00 0.00 0.00 1.00
The notation is for a generalized inner product so that
x ~:/ .*. y NB. boolean inner product ( ~: is "not equal" (exclusive or) and *. is "and")
x *./ .= y NB. which rows of x are the same as vector y?
x + / .= y NB. number of places where a value in row x equals the corresponding value in y
[[Floyd-Warshall_algorithm#J|etc.]]
The general inner product extends to multidimensional arrays, requiring only that x and y be conformable (trailing dimension of array x equals the leading dimension of array y). For example, the matrix multiplication of two dimensional arrays requires x to have the same numbers of rows as y has columns, as you would expect.
Note also that mp=: +/@:*"1 _ functions identically.
Perhaps it would have made more sense to define something more like dot=: conjunction def 'u/@:v"1 _' so that matrix multiplication would be +dot* -- this would also correspond to the original [[Matrix_multiplication#APL|APL]] implementation.
Java
public static double[][] mult(double a[][], double b[][]){//a[m][n], b[n][p]
if(a.length == 0) return new double[0][0];
if(a[0].length != b.length) return null; //invalid dims
int n = a[0].length;
int m = a.length;
int p = b[0].length;
double ans[][] = new double[m][p];
for(int i = 0;i < m;i++){
for(int j = 0;j < p;j++){
for(int k = 0;k < n;k++){
ans[i][j] += a[i][k] * b[k][j];
}
}
}
return ans;
}
JavaScript
ES5
=Iterative=
{{works with|SpiderMonkey}} for the print() function
Extends [[Matrix Transpose#JavaScript]]
// returns a new matrix
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);
}
var a = new Matrix([[1,2],[3,4]])
var b = new Matrix([[-3,-8,3],[-2,1,4]]);
print(a.mult(b));
{{out}}
-7,-6,11
-17,-20,25
=Functional=
(function () {
'use strict';
// matrixMultiply:: [[n]] -> [[n]] -> [[n]]
function matrixMultiply(a, b) {
var bCols = transpose(b);
return a.map(function (aRow) {
return bCols.map(function (bCol) {
return dotProduct(aRow, bCol);
});
});
}
// [[n]] -> [[n]] -> [[n]]
function dotProduct(xs, ys) {
return sum(zipWith(product, xs, ys));
}
return matrixMultiply(
[[-1, 1, 4],
[ 6, -4, 2],
[-3, 5, 0],
[ 3, 7, -2]],
[[-1, 1, 4, 8],
[ 6, 9, 10, 2],
[11, -4, 5, -3]]
);
// --> [[51, -8, 26, -18], [-8, -38, -6, 34],
// [33, 42, 38, -14], [17, 74, 72, 44]]
// GENERIC LIBRARY FUNCTIONS
// (a -> b -> c) -> [a] -> [b] -> [c]
function zipWith(f, xs, ys) {
return xs.length === ys.length ? (
xs.map(function (x, i) {
return f(x, ys[i]);
})
) : undefined;
}
// [[a]] -> [[a]]
function transpose(lst) {
return lst[0].map(function (_, iCol) {
return lst.map(function (row) {
return row[iCol];
});
});
}
// sum :: (Num a) => [a] -> a
function sum(xs) {
return xs.reduce(function (a, x) {
return a + x;
}, 0);
}
// product :: n -> n -> n
function product(a, b) {
return a * b;
}
})();
{{Out}}
[[51, -8, 26, -18], [-8, -38, -6, 34],
[33, 42, 38, -14], [17, 74, 72, 44]]
ES6
((() => {
'use strict';
// matrixMultiply :: Num a => [[a]] -> [[a]] -> [[a]]
const matrixMultiply = (a, b) => {
const bCols = transpose(b);
return a.map(aRow => bCols.map(bCol => dotProduct(aRow, bCol)));
}
// dotProduct :: Num a => [[a]] -> [[a]] -> [[a]]
const dotProduct = (xs, ys) => sum(zipWith(product, xs, ys));
// GENERIC
// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = (f, xs, ys) =>
xs.length === ys.length ? (
xs.map((x, i) => f(x, ys[i]))
) : undefined;
// transpose :: [[a]] -> [[a]]
const transpose = xs =>
xs[0].map((_, iCol) => xs.map(row => row[iCol]));
// sum :: (Num a) => [a] -> a
const sum = xs =>
xs.reduce((a, x) => a + x, 0);
// product :: Num a => a -> a -> a
const product = (a, b) => a * b;
// TEST
return matrixMultiply(
[
[-1, 1, 4],
[6, -4, 2],
[-3, 5, 0],
[3, 7, -2]
],
[
[-1, 1, 4, 8],
[6, 9, 10, 2],
[11, -4, 5, -3]
]
);
// --> [[51, -8, 26, -18], [-8, -38, -6, 34],
// [33, 42, 38, -14], [17, 74, 72, 44]]
}))();
{{Out}}
[[51, -8, 26, -18], [-8, -38, -6, 34],
[33, 42, 38, -14], [17, 74, 72, 44]]
jq
In the following, an m by n matrix is represented by an array of m arrays, each of which is of length n.
The function multiply(A;B) assumes its arguments are numeric matrices of the proper dimensions. Note that preallocating the resultant matrix would actually slow things down.
def dot_product(a; b):
a as $a | b as $b
| reduce range(0;$a|length) as $i (0; . + ($a[$i] * $b[$i]) );
# transpose/0 expects its input to be a rectangular matrix (an array of equal-length arrays)
def transpose:
if (.[0] | length) == 0 then []
else [map(.[0])] + (map(.[1:]) | transpose)
end ;
# A and B should both be numeric matrices, A being m by n, and B being n by p.
def multiply(A; B):
A as $A | B as $B
| ($B[0]|length) as $p
| ($B|transpose) as $BT
| reduce range(0; $A|length) as $i
([]; reduce range(0; $p) as $j
(.; .[$i][$j] = dot_product( $A[$i]; $BT[$j] ) )) ;
'''Example''' ((2|sqrt)/2) as $r | [ [$r, $r], [(-($r)), $r]] as $R | multiply($R;$R) {{Out}} [[0,1.0000000000000002],[-1.0000000000000002,0]]
Jsish
Based on Javascript matrix entries.
Uses module listed in [[Matrix Transpose#Jsish]]
/* Matrix multiplication, in Jsish */
require('Matrix');
if (Interp.conf('unitTest')) {
var a = new Matrix([[1,2],[3,4]]);
var b = new Matrix([[-3,-8,3],[-2,1,4]]);
; a;
; b;
; a.mult(b);
}
/*
=!EXPECTSTART!=
a ==> { height:2, mtx:[ [ 1, 2 ], [ 3, 4 ] ], width:2 }
b ==> { height:2, mtx:[ [ -3, -8, 3 ], [ -2, 1, 4 ] ], width:3 }
a.mult(b) ==> { height:2, mtx:[ [ -7, -6, 11 ], [ -17, -20, 25 ] ], width:3 }
=!EXPECTEND!=
*/
{{out}}
prompt$ jsish -u matrixMultiplication.jsi
[PASS] matrixMultiplication.jsi
Julia
The multiplication is denoted by *
[1 2 3 ; 4 5 6] * [1 2 ; 3 4 ; 5 6] # product of a 2x3 by a 3x2
2x2 Array{Int64,2}:
22 28
49 64
julia> [1 2 3] * [1,2,3] # product of a row vector by a column vector
1-element Array{Int64,1}:
14
K
(1 2;3 4)_mul (5 6;7 8)
(19 22
43 50)
Klong
mul::{[a b];b::+y;{a::x;+/'{a*x}'b}'x}
[[1 2] [3 4]] mul [[5 6] [7 8]]
[[19 22]
[43 50]]
Kotlin
// version 1.1.3
typealias Vector = DoubleArray
typealias Matrix = Array<Vector>
operator fun Matrix.times(other: Matrix): Matrix {
val rows1 = this.size
val cols1 = this[0].size
val rows2 = other.size
val cols2 = other[0].size
require(cols1 == rows2)
val result = Matrix(rows1) { Vector(cols2) }
for (i in 0 until rows1) {
for (j in 0 until cols2) {
for (k in 0 until rows2) {
result[i][j] += this[i][k] * other[k][j]
}
}
}
return result
}
fun printMatrix(m: Matrix) {
for (i in 0 until m.size) println(m[i].contentToString())
}
fun main(args: Array<String>) {
val m1 = arrayOf(
doubleArrayOf(-1.0, 1.0, 4.0),
doubleArrayOf( 6.0, -4.0, 2.0),
doubleArrayOf(-3.0, 5.0, 0.0),
doubleArrayOf( 3.0, 7.0, -2.0)
)
val m2 = arrayOf(
doubleArrayOf(-1.0, 1.0, 4.0, 8.0),
doubleArrayOf( 6.0, 9.0, 10.0, 2.0),
doubleArrayOf(11.0, -4.0, 5.0, -3.0)
)
printMatrix(m1 * m2)
}
{{out}}
[51.0, -8.0, 26.0, -18.0]
[-8.0, -38.0, -6.0, 34.0]
[33.0, 42.0, 38.0, -14.0]
[17.0, 74.0, 72.0, 44.0]
Lang5
[[1 2 3] [4 5 6]] 'm dress
[[1 2] [3 4] [5 6]] 'm dress * .
{{out}}
[
[ 22 28 ]
[ 49 64 ]
]
LFE
Use the LFE transpose/1 function from [[Matrix transposition]].
(defun matrix* (matrix-1 matrix-2)
(list-comp
((<- a matrix-1))
(list-comp
((<- b (transpose matrix-2)))
(lists:foldl #'+/2 0
(lists:zipwith #'*/2 a b)))))
Usage example in the LFE REPL:
> (set ma '((1 2)
(3 4)
(5 6)
(7 8)))
((1 2) (3 4) (5 6) (7 8))
> (set mb (transpose ma))
((1 3 5 7) (2 4 6 8))
> (matrix* ma mb)
((5 11 17 23) (11 25 39 53) (17 39 61 83) (23 53 83 113))
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.
MatrixA$ ="4, 4, 1, 1, 1, 1, 2, 4, 8, 16, 3, 9, 27, 81, 4, 16, 64, 256"
MatrixB$ ="4, 4, 4, -3, 4/3, -1/4 , -13/3, 19/4, -7/3, 11/24, 3/2, -2, 7/6, -1/4, -1/6, 1/4, -1/6, 1/24"
print "Product of two matrices"
call DisplayMatrix MatrixA$
print " *"
call DisplayMatrix MatrixB$
print " ="
MatrixP$ =MatrixMultiply$( MatrixA$, MatrixB$)
call DisplayMatrix MatrixP$
{{out}}
Product of two matrices
| 1.00000 1.00000 1.00000 1.00000 |
| 2.00000 4.00000 8.00000 16.00000 |
| 3.00000 9.00000 27.00000 81.00000 |
| 4.00000 16.00000 64.00000 256.00000 |
*
| 4.00000 -3.00000 1.33333 -0.25000 |
| -4.33333 4.75000 -2.33333 0.45833 |
| 1.50000 -2.00000 1.16667 -0.25000 |
| -0.16667 0.25000 -0.16667 0.04167 |
=
| 1.00000 0.00000 0.00000 0.00000 |
| 0.00000 1.00000 0.00000 0.00000 |
| 0.00000 0.00000 1.00000 0.00000 |
| 0.00000 0.00000 0.00000 1.00000 |
Logo
TO LISTVMD :A :F :C :NV
;PROCEDURE LISTVMD
;A = LIST
;F = ROWS
;C = COLS
;NV = NAME OF MATRIX / VECTOR NEW
;this procedure transform a list in matrix / vector square or rect
(LOCAL "CF "CC "NV "T "W)
MAKE "CF 1
MAKE "CC 1
MAKE "NV (MDARRAY (LIST :F :C) 1)
MAKE "T :F * :C
FOR [Z 1 :T][MAKE "W ITEM :Z :A
MDSETITEM (LIST :CF :CC) :NV :W
MAKE "CC :CC + 1
IF :CC = :C + 1 [MAKE "CF :CF + 1 MAKE "CC 1]]
OUTPUT :NV
END
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
TO XX
; MAIN PROGRAM
;LRCVS 10.04.12
; THIS PROGRAM multiplies two "square" matrices / vector ONLY!!!
; THE RECTANGULAR NOT WORK!!!
CT CS HT
; FIRST DATA MATRIX / VECTOR
MAKE "A [1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49]
MAKE "FA 5 ;"ROWS
MAKE "CA 5 ;"COLS
; SECOND DATA MATRIX / VECTOR
MAKE "B [2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50]
MAKE "FB 5 ;"ROWS
MAKE "CB 5 ;"COLS
IF (OR :FA <> :CA :FB <>:CB) [PRINT "Las_matrices/vector_no_son_cuadradas THROW
"TOPLEVEL ]
IFELSE (OR :CA <> :FB :FA <> :CB) [PRINT
"Las_matrices/vector_no_son_compatibles THROW "TOPLEVEL ][MAKE "MA LISTVMD :A
:FA :CA "MA MAKE "MB LISTVMD :B :FB :CB "MB] ;APPLICATION <<< "LISTVMD"
PRINT (LIST "THIS_IS: "ROWS "X "COLS)
PRINT []
PRINT (LIST :MA "=_M1 :FA "ROWS "X :CA "COLS)
PRINT []
PRINT (LIST :MB "=_M2 :FA "ROWS "X :CA "COLS)
PRINT []
MAKE "T :FA * :CB
MAKE "RE (ARRAY :T 1)
MAKE "CO 0
FOR [AF 1 :CA][
FOR [AC 1 :CA][
MAKE "TEMP 0
FOR [I 1 :CA ][
MAKE "TEMP :TEMP + (MDITEM (LIST :I :AF) :MA) * (MDITEM (LIST :AC :I) :MB)]
MAKE "CO :CO + 1
SETITEM :CO :RE :TEMP]]
PRINT []
PRINT (LIST "THIS_IS: :FA "ROWS "X :CB "COLS)
SHOW LISTVMD :RE :FA :CB "TO ;APPLICATION <<< "LISTVMD"
END
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::\
M1 * M2 RESULT / SOLUTION
1 3 5 7 9 2 4 6 8 10 830 1880 2930 3980 5030
11 13 15 17 19 12 14 16 18 20 890 2040 3190 4340 5490
21 23 25 27 29 X 22 24 26 28 30 = 950 2200 3450 4700 5950
31 33 35 37 39 32 34 36 38 40 1010 2360 3710 5060 6410
41 43 45 47 49 42 44 46 48 50 1070 2520 3970 5420 6870
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::\
NOW IN LOGO!!!!
THIS_IS: ROWS X COLS
{{1 3 5 7 9} {11 13 15 17 19} {21 23 25 27 29} {31 33 35 37 39} {41 43 45 47
49}} =_M1 5 ROWS X 5 COLS
{{2 4 6 8 10} {12 14 16 18 20} {22 24 26 28 30} {32 34 36 38 40} {42 44 46 48
50}} =_M2 5 ROWS X 5 COLS
THIS_IS: 5 ROWS X 5 COLS
{{830 1880 2930 3980 5030} {890 2040 3190 4340 5490} {950 2200 3450 4700 5950}
{1010 2360 3710 5060 6410} {1070 2520 3970 5420 6870}}
Lua
function MatMul( m1, m2 )
if #m1[1] ~= #m2 then -- inner matrix-dimensions must agree
return nil
end
local res = {}
for i = 1, #m1 do
res[i] = {}
for j = 1, #m2[1] do
res[i][j] = 0
for k = 1, #m2 do
res[i][j] = res[i][j] + m1[i][k] * m2[k][j]
end
end
end
return res
end
-- Test for MatMul
mat1 = { { 1, 2, 3 }, { 4, 5, 6 } }
mat2 = { { 1, 2 }, { 3, 4 }, { 5, 6 } }
erg = MatMul( mat1, mat2 )
for i = 1, #erg do
for j = 1, #erg[1] do
io.write( erg[i][j] )
io.write(" ")
end
io.write("\n")
end
SciLua
Using the sci.alg library from scilua.org
local alg = require("sci.alg")
mat1 = alg.tomat{{1, 2, 3}, {4, 5, 6}}
mat2 = alg.tomat{{1, 2}, {3, 4}, {5, 6}}
mat3 = mat1[] ** mat2[]
print(mat3)
{{out}}
+22.00000,+28.00000
+49.00000,+64.00000
M2000 Interpreter
Module CheckMatMult {
\\ Matrix Multiplication
\\ we use array pointers so we pass arrays byvalue but change this by reference
\\ this can be done because always arrays passed by reference,
\\ and Read statement decide if this goes to a pointer of array or copied to a local array
\\ the first line of code for MatMul is: Read a as array, b as array
\\ interpreter insert this at function construction.
\\ if a pointer inside function change to point to a new array, the this has no reflect to the passed array.
Function MatMul(a as array, b as array) {
if dimension(a)<>2 or dimension(b)<>2 then Error "Need two 2D arrays "
let a2=dimension(a,2), b1=dimension(b,1)
if a2<>b1 then Error "Need columns of first array equal to rows of second array"
let a1=dimension(a,1), b2=dimension(b,2)
let aBase=dimension(a,1,0)-1, bBase=dimension(b,1,0)-1
let aBase1=dimension(a,2,0)-1, bBase1=dimension(b,2,0)-1
link a,b to a(), b() ' change interface for arrays
dim base 1, c(a1, b2)
for i=1 to a1 : let ia=i+abase : for j=1 to b2 : let jb=j+bBase1 : for k=1 to a2
c(i,j)+=a(ia,k+aBase1)*b(k+bBase,jb)
next k : next j : next i
\\ redim to base 0
dim base 0, c(a1, b2)
=c()
}
\\ define arrays with different base per dimension
\\ res() defined as empty array
dim a(10 to 13, 4), b(4, 2 to 5), res()
\\ numbers from ADA task
a(10,0)= 1, 1, 1, 1, 2, 4, 8, 16, 3, 9, 27, 81, 4, 16, 64, 256
b(0,2)= 4, -3, 4/3, -1/4, -13/3, 19/4, -7/3, 11/24, 3/2, -2, 7/6, -1/4, -1/6, 1/4, -1/6, 1/24
res()=MatMul(a(), b())
for i=0 to 3 :for j=0 to 3
Print res(i,j),
next j : Print : next i
}
CheckMatMult
Module CheckMatMult2 {
\\ Matrix Multiplication
\\ pass arrays by reference
\\ if we change a passed array here, to a new array then this change also the reference array.
Function MatMul(&a(),&b()) {
if dimension(a())<>2 or dimension(b())<>2 then Error "Need two 2D arrays "
let a2=dimension(a(),2), b1=dimension(b(),1)
if a2<>b1 then Error "Need columns of first array equal to rows of second array"
let a1=dimension(a(),1), b2=dimension(b(),2)
let aBase=dimension(a(),1,0)-1, bBase=dimension(b(),1,0)-1
let aBase1=dimension(a(),2,0)-1, bBase1=dimension(b(),2,0)-1
dim base 1, c(a1, b2)
for i=1 to a1 : let ia=i+abase : for j=1 to b2 : let jb=j+bBase1 : for k=1 to a2
c(i,j)+=a(ia,k+aBase1)*b(k+bBase,jb)
next k : next j : next i
\\ redim to base 0
dim base 0, c(a1, b2)
=c()
}
\\ define arrays with different base per dimension
\\ res() defined as empty array
dim a(10 to 13, 4), b(4, 2 to 5), res()
\\ numbers from ADA task
a(10,0)= 1, 1, 1, 1, 2, 4, 8, 16, 3, 9, 27, 81, 4, 16, 64, 256
b(0,2)= 4, -3, 4/3, -1/4, -13/3, 19/4, -7/3, 11/24, 3/2, -2, 7/6, -1/4, -1/6, 1/4, -1/6, 1/24
res()=MatMul(&a(), &b())
for i=0 to 3 :for j=0 to 3
Print res(i,j),
next j : Print : next i
}
CheckMatMult2
{{out}}
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Maple
A := <<1|2|3>,<4|5|6>>;
B := <<1,2,3>|<4,5,6>|<7,8,9>|<10,11,12>>;
A . B;
{{out}}
[1 2 3]
A := [ ]
[4 5 6]
[1 4 7 10]
[ ]
B := [2 5 8 11]
[ ]
[3 6 9 12]
[14 32 50 68]
[ ]
[32 77 122 167]
MathCortex
>> A = [2,3; -2,1]
2 3
-2 1
>> B = [1,2;4,2]
1 2
4 2
>> A * B
14 10
2 -2
Mathematica
The Wolfram Language supports both dot products and element-wise multiplication of matrices.
This computes a dot product:
Dot[{{a, b}, {c, d}}, {{w, x}, {y, z}}]
With the following output:
{{a w + b y, a x + b z}, {c w + d y, c x + d z}}
This also computes a dot product, using the infix . notation:
{{a, b}, {c, d}} . {{w, x}, {y, z}}
This does element-wise multiplication of matrices:
Times[{{a, b}, {c, d}}, {{w, x}, {y, z}}]
With the following output:
{{a w, b x}, {c y, d z}}
Alternative infix notations '*' and ' ' (space, indicating multiplication):
{{a, b}, {c, d}}*{{w, x}, {y, z}}
{{a, b}, {c, d}} {{w, x}, {y, z}}
In all cases matrices can be fully symbolic or numeric or mixed symbolic and numeric. Numeric matrices support arbitrary numerical magnitudes, arbitrary precision as well as complex numbers:
Dot[{{85, 60, 65}, {54, 99, 33}, {46, 52, 87}}, {{89, 77, 98}, {55, 27, 25}, {80, 68, 85}}]
With the following output:
{{16065, 12585, 15355}, {12891, 9075, 10572}, {13914, 10862, 13203}}
MATLAB
Matlab contains two methods of multiplying matrices: by using the "mtimes(matrix,matrix)" function, or the "*" operator.
A = [1 2;3 4]
A =
1 2
3 4
>> B = [5 6;7 8]
B =
5 6
7 8
>> A * B
ans =
19 22
43 50
>> mtimes(A,B)
ans =
19 22
43 50
Maxima
a: matrix([1, 2],
[3, 4],
[5, 6],
[7, 8])$
b: matrix([1, 2, 3],
[4, 5, 6])$
a . b;
/* matrix([ 9, 12, 15],
[19, 26, 33],
[29, 40, 51],
[39, 54, 69]) */
Nial
|A := 4 4 reshape 1 1 1 1 2 4 8 16 3 9 27 81 4 16 64 256
=1 1 1 1
=2 4 8 16
=3 9 27 81
=4 16 64 256
|B := inverse A
|A innerproduct B
=1. 0. 8.3e-17 -2.9e-16
=1.3e-15 1. -4.4e-16 -3.3e-16
=0. 0. 1. 4.4e-16
=0. 0. 0. 1.
Nim
import strfmt
type Matrix[M,N: static[int]] = array[M, array[N, float]]
let a = [[1.0, 1.0, 1.0, 1.0],
[2.0, 4.0, 8.0, 16.0],
[3.0, 9.0, 27.0, 81.0],
[4.0, 16.0, 64.0, 256.0]]
let b = [[ 4.0 , -3.0 , 4/3.0, -1/4.0 ],
[-13/3.0, 19/4.0, -7/3.0, 11/24.0],
[ 3/2.0, -2.0 , 7/6.0, -1/4.0 ],
[ -1/6.0, 1/4.0, -1/6.0, 1/24.0]]
proc `$`(m: Matrix): string =
result = "(["
for r in m:
if result.len > 2: result.add "]\n ["
for val in r: result.add val.format("8.2f")
result.add "])"
proc `*`[M,P,N](a: Matrix[M,P]; b: Matrix[P,N]): Matrix[M,N] =
for i in result.low .. result.high:
for j in result[0].low .. result[0].high:
for k in a[0].low .. a[0].high:
result[i][j] += a[i][k] * b[k][j]
echo a
echo b
echo a * b
echo b * a
OCaml
This version works on arrays of arrays of ints:
let matrix_multiply x y =
let x0 = Array.length x
and y0 = Array.length y in
let y1 = if y0 = 0 then 0 else Array.length y.(0) in
let z = Array.make_matrix x0 y1 0 in
for i = 0 to x0-1 do
for j = 0 to y1-1 do
for k = 0 to y0-1 do
z.(i).(j) <- z.(i).(j) + x.(i).(k) * y.(k).(j)
done
done
done;
z
matrix_multiply [|[|1;2|];[|3;4|]|] [|[|-3;-8;3|];[|-2;1;4|]|];;
- : int array array = [|[|-7; -6; 11|]; [|-17; -20; 25|]|]
{{trans|Scheme}} This version works on lists of lists of ints:
(* equivalent to (apply map ...) *)
let rec mapn f lists =
assert (lists <> []);
if List.mem [] lists then
[]
else
f (List.map List.hd lists) :: mapn f (List.map List.tl lists)
let matrix_multiply m1 m2 =
List.map
(fun row ->
mapn
(fun column ->
List.fold_left (+) 0
(List.map2 ( * ) row column))
m2)
m1
matrix_multiply [[1;2];[3;4]] [[-3;-8;3];[-2;1;4]];;
- : int list list = [[-7; -6; 11]; [-17; -20; 25]]
Octave
a = zeros(4);
% prepare the matrix
% 1 1 1 1
% 2 4 8 16
% 3 9 27 81
% 4 16 64 256
for i = 1:4
for j = 1:4
a(i, j) = i^j;
endfor
endfor
b = inverse(a);
a * b
Ol
{{trans|Scheme}} This version works on lists of lists:
(define (matrix-multiply matrix1 matrix2)
(map
(lambda (row)
(apply map
(lambda column
(apply + (map * row column)))
matrix2))
matrix1))
(matrix-multiply '((1 2) (3 4)) '((-3 -8 3) (-2 1 4))) ((-7 -6 11) (-17 -20 25))
OxygenBasic
When using matrices in Video graphics, speed is important. Here is a matrix multiplier written in OxygenBasics's x86 Assembly code.
'Example of matrix layout mapped to an array of 4x4 cells
'
' 0 4 8 C
' 1 5 9 D
' 2 6 A E
' 3 7 B F
'
% MatrixType double
sub MatrixMul(MatrixType *A,*B,*C, sys n)
'
### ==================================
'
'
#if leftmatch matrixtype single
% OneStep 4
% mtype single
#endif
'
#if leftmatch matrixtype double
% OneStep 8
% mtype double
#endif
sys pa=@A, pb=@B, pc=@C
sys ColStep=OneStep*n
mov ecx,pa
mov edx,pb
mov eax,pc
mov esi,n
(
call column : dec esi : jg repeat
)
exit sub
column:
'======
mov edi,n
(
call cell : dec edi : jg repeat
)
add edx,ColStep
sub ecx,ColStep
ret
cell: ' row A * column B
'
### =================
'matrix data is stored ascending vertically then horizontally
'thus rows are minor, columns are major
'
push ecx
push edx
push eax
mov eax,4
fldz
(
fld mtype [ecx]
fmul mtype [edx]
faddp st1
add ecx,ColStep 'next column of matrix A
add edx,OneStep 'next row of matrix B
dec eax
jnz repeat
)
pop eax
fstp mtype [eax] 'assign to next row of matrix C
'
pop edx
pop ecx
add eax,OneStep 'next cell in column of matrix C (columns then rows)
add ecx,OneStep 'next row of matrix A
ret
'
end sub
function ShowMatrix(MatrixType*A,sys n) as string
'
### ==========================================
string cr=chr(13)+chr(10), tab=chr(9)
function="MATRIX " n "x" n cr cr
sys i,j,m
'
for i=1 to n
m=0
for j=1 to n
function+=str( A[m+i] ) tab
m+=n
next
function+=cr
next
end function
'TEST
'====
% n 4
MatrixType A[n*n],B[n*n],C[n*n]
'reading vertically (minor) then left to right (major)
A <= 4,0,0,1, 0,4,0,0, 0,0,4,0, 0,0,0,4
B <= 2,0,0,2, 0,2,0,0, 0,0,2,0, 0,0,0,2
MatrixMul A,B,C,n
Print ShowMatrix C,n
PARI/GP
M*N
Perl
For most applications involving extensive matrix arithmetic, using the CPAN module called "PDL" (that stands for "Perl Data Language") would probably be the easiest and most efficient approach. That said, here's an implementation of matrix multiplication in plain Perl.
This function takes two references to arrays of arrays and returns the product as a reference to a new anonymous array of arrays.
sub mmult
{
our @a; local *a = shift;
our @b; local *b = shift;
my @p = [];
my $rows = @a;
my $cols = @{ $b[0] };
my $n = @b - 1;
for (my $r = 0 ; $r < $rows ; ++$r)
{
for (my $c = 0 ; $c < $cols ; ++$c)
{
$p[$r][$c] += $a[$r][$_] * $b[$_][$c]
foreach 0 .. $n;
}
}
return [@p];
}
sub display { join("\n" => map join(" " => map(sprintf("%4d", $_), @$_)), @{+shift})."\n" }
@a =
(
[1, 2],
[3, 4]
);
@b =
(
[-3, -8, 3],
[-2, 1, 4]
);
$c = mmult(\@a,\@b);
display($c)
{{out}}
-7 -6 11
-17 -20 25
Perl 6
{{trans|Perl 5}}
{{works with|Rakudo|2015-09-22}}
There are three ways in which this example differs significantly from the original Perl 5 code. These are not esoteric differences; all three of these features typically find heavy use in Perl 6.
First, we can use a real signature that can bind two arrays as arguments, because the default in Perl 6 is not to flatten arguments unless the signature specifically requests it. We don't need to pass the arrays with backslashes because the binding choice is made lazily by the signature itself at run time; in Perl 5 this choice must be made at compile time. Also, we can bind the arrays to formal parameters that are really lexical variable names; in Perl 5 they can only be bound to global array objects (via a typeglob assignment).
Second, we use the X cross operator in conjunction with a two-parameter closure to avoid writing nested loops. The X cross operator, along with Z, the zip operator, is a member of a class of operators that expect lists on both sides, so we call them "list infix" operators. We tend to define these operators using capital letters so that they stand out visually from the lists on both sides. The cross operator makes every possible combination of the one value from the first list followed by one value from the second. The right side varies most rapidly, just like an inner loop. (The X and Z operators may both also be used as meta-operators, Xop or Zop, distributing some other operator "op" over their generated list. All metaoperators in Perl 6 may be applied to user-defined operators as well.)
Third is the use of prefix ^ to generate a list of numbers in a range. Here it is used on an array to generate all the indexes of the array. We have a way of indicating a range by the infix .. operator, and you can put a ^ on either end to exclude that endpoint. We found ourselves writing 0 ..^ @a so often that we made ^@a a shorthand for that. It's pronounced "upto". The array is evaluated in a numeric context, so it returns the number of elements it contains, which is exactly what you want for the exclusive limit of the range.
sub mmult(@a,@b) {
my @p;
for ^@a X ^@b[0] -> ($r, $c) {
@p[$r][$c] += @a[$r][$_] * @b[$_][$c] for ^@b;
}
@p;
}
my @a = [1, 1, 1, 1],
[2, 4, 8, 16],
[3, 9, 27, 81],
[4, 16, 64, 256];
my @b = [ 4 , -3 , 4/3, -1/4 ],
[-13/3, 19/4, -7/3, 11/24],
[ 3/2, -2 , 7/6, -1/4 ],
[ -1/6, 1/4, -1/6, 1/24];
.say for mmult(@a,@b);
{{out}}
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
Note that these are not rounded values, but exact, since all the math was done in rationals. Hence we need not rely on format tricks to hide floating-point inaccuracies.
Just for the fun of it, here's a functional version that uses no temp variables or side effects. Some people will find this more readable and elegant, and others will, well, not.
sub mmult(\a,\b) {
[
for ^a -> \r {
[
for ^b[0] -> \c {
[+] a[r;^b] Z* b[^b;c]
}
]
}
]
}
Here we use Z with an "op" of *, which is a zip with multiply. This, along with the [+] reduction operator, replaces the inner loop. We chose to split the outer X loop back into two loops to make it convenient to collect each subarray value in [...]. It just collects all the returned values from the inner loop and makes an array of them. The outer loop simply returns the outer array.
Phix
Copy of [[Matrix_multiplication#Euphoria|Euphoria]]
function matrix_mul(sequence a, sequence b)
sequence c
if length(a[1]) != length(b) then
return 0
else
c = repeat(repeat(0,length(b[1])),length(a))
for i=1 to length(a) do
for j=1 to length(b[1]) do
for k=1 to length(a[1]) do
c[i][j] += a[i][k]*b[k][j]
end for
end for
end for
return c
end if
end function
PicoLisp
(de matMul (Mat1 Mat2)
(mapcar
'((Row)
(apply mapcar Mat2
'(@ (sum * Row (rest))) ) )
Mat1 ) )
(matMul
'((1 2 3) (4 5 6))
'((6 -1) (3 2) (0 -3)) )
{{out}}
-> ((12 -6) (39 -12))
PL/I
/* Matrix multiplication of A by B, yielding C */
MMULT: procedure (a, b, c);
declare (a, b, c)(*,*) float controlled;
declare (i, j, m, n, p) fixed binary;
if hbound(a,2) ^= hbound(b,1) then
do;
put skip list
('Matrices are incompatible for matrix multiplication');
signal error;
end;
m = hbound(a, 1); p = hbound(b, 2);
if allocation(c) > 0 then free c;
allocate c(m,p);
do i = 1 to m;
do j = 1 to p;
c(i,j) = sum(a(i,*) * b(*,j) );
end;
end;
end MMULT;
Pop11
define matmul(a, b) -> c;
lvars ba = boundslist(a), bb = boundslist(b);
lvars i, i0 = ba(1), i1 = ba(2);
lvars j, j0 = bb(1), j1 = bb(2);
lvars k, k0 = bb(3), k1 = bb(4);
if length(ba) /= 4 then
throw([need_2d_array ^a])
endif;
if length(bb) /= 4 then
throw([need_2d_array ^b])
endif;
if ba(3) /= j0 or ba(4) /= j1 then
throw([dimensions_do_not_match ^a ^b]);
endif;
newarray([^i0 ^i1 ^k0 ^k1], 0) -> c;
for i from i0 to i1 do
for k from k0 to k1 do
for j from j0 to j1 do
c(i, k) + a(i, j)*b(j, k) -> c(i, k);
endfor;
endfor;
endfor;
enddefine;
PowerShell
function multarrays($a, $b) {
$n,$m,$p = ($a.Count - 1), ($b.Count - 1), ($b[0].Count - 1)
if ($a[0].Count -ne $b.Count) {throw "Multiplication impossible"}
$c = @(0)*($a[0].Count)
foreach ($i in 0..$n) {
$c[$i] = foreach ($j in 0..$p) {
$sum = 0
foreach ($k in 0..$m){$sum += $a[$i][$k]*$b[$k][$j]}
$sum
}
}
$c
}
function show($a) { $a | foreach{"$_"}}
$a = @(@(1,2),@(3,4))
$b = @(@(5,6),@(7,8))
$c = @(5,6)
"`$a ="
show $a
""
"`$b ="
show $b
""
"`$c ="
$c
""
"`$a * `$b ="
show (multarrays $a $b)
" "
"`$a * `$c ="
show (multarrays $a $c)
Output:
$a =
1 2
3 4
$b =
5 6
7 8
$c =
5
6
$a * $b =
19 22
43 50
$a * $c =
17
39
Prolog
{{trans|Scheme}} {{works with|SWI Prolog|5.9.9}}
% SWI-Prolog has transpose/2 in its clpfd library
:- use_module(library(clpfd)).
% N is the dot product of lists V1 and V2.
dot(V1, V2, N) :- maplist(product,V1,V2,P), sumlist(P,N).
product(N1,N2,N3) :- N3 is N1*N2.
% Matrix multiplication with matrices represented
% as lists of lists. M3 is the product of M1 and M2
mmult(M1, M2, M3) :- transpose(M2,MT), maplist(mm_helper(MT), M1, M3).
mm_helper(M2, I1, M3) :- maplist(dot(I1), M2, M3).
PureBasic
Matrices represented as integer arrays with rows in the first dimension and columns in the second.
Procedure multiplyMatrix(Array a(2), Array b(2), Array prd(2))
Protected ar = ArraySize(a()) ;#rows for matrix a
Protected ac = ArraySize(a(), 2) ;#cols for matrix a
Protected br = ArraySize(b()) ;#rows for matrix b
Protected bc = ArraySize(b(), 2) ;#cols for matrix b
If ac = br
Dim prd(ar, bc)
Protected i, j, k
For i = 0 To ar
For j = 0 To bc
For k = 0 To br ;ac
prd(i, j) = prd(i, j) + (a(i, k) * b(k, j))
Next
Next
Next
ProcedureReturn #True ;multiplication performed, product in prd()
Else
ProcedureReturn #False ;multiplication not performed, dimensions invalid
EndIf
EndProcedure
Additional code to demonstrate use.
DataSection
Data.i 2,3 ;matrix a (#rows, #cols)
Data.i 1,2,3, 4,5,6 ;elements by row
Data.i 3,1 ;matrix b (#rows, #cols)
Data.i 1, 5, 9 ;elements by row
EndDataSection
Procedure displayMatrix(Array a(2), text.s)
Protected i, j
Protected columns = ArraySize(a(), 2), rows = ArraySize(a(), 1)
PrintN(text + ": (" + Str(rows + 1) + ", " + Str(columns + 1) + ")")
For i = 0 To rows
For j = 0 To columns
Print(LSet(Str(a(i, j)), 4, " "))
Next
PrintN("")
Next
PrintN("")
EndProcedure
Procedure loadMatrix(Array a(2))
Protected rows, columns, i, j
Read.i rows
Read.i columns
Dim a(rows - 1, columns - 1)
For i = 0 To rows - 1
For j = 0 To columns - 1
Read.i a(i, j)
Next
Next
EndProcedure
Dim a(0,0)
Dim b(0,0)
Dim c(0,0)
If OpenConsole()
loadMatrix(a()): displayMatrix(a(), "matrix a")
loadMatrix(b()): displayMatrix(b(), "matrix b")
If multiplyMatrix(a(), b(), c())
displayMatrix(c(), "product of a * b")
Else
PrintN("product of a * b is undefined")
EndIf
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
EndIf
{{out}}
matrix a: (2, 3)
1 2 3
4 5 6
matrix b: (3, 1)
1
5
9
product of a * b: (2, 1)
38
83
Python
a=((1, 1, 1, 1), # matrix A #
(2, 4, 8, 16),
(3, 9, 27, 81),
(4, 16, 64, 256))
b=(( 4 , -3 , 4/3., -1/4. ), # matrix B #
(-13/3., 19/4., -7/3., 11/24.),
( 3/2., -2. , 7/6., -1/4. ),
( -1/6., 1/4., -1/6., 1/24.))
def MatrixMul( mtx_a, mtx_b):
tpos_b = zip( *mtx_b)
rtn = [[ sum( ea*eb for ea,eb in zip(a,b)) for b in tpos_b] for a in mtx_a]
return rtn
v = MatrixMul( a, b )
print 'v = ('
for r in v:
print '[',
for val in r:
print '%8.2f '%val,
print ']'
print ')'
u = MatrixMul(b,a)
print 'u = '
for r in u:
print '[',
for val in r:
print '%8.2f '%val,
print ']'
print ')'
Another one, {{trans|Scheme}}
from operator import mul
def matrixMul(m1, m2):
return map(
lambda row:
map(
lambda *column:
sum(map(mul, row, column)),
*m2),
m1)
Using list comprehensions, multiplying matrices represented as lists of lists. (Input is not validated):
def mm(A, B):
return [[sum(x * B[i][col] for i,x in enumerate(row)) for col in range(len(B[0]))] for row in A]
Another one, use numpy the most popular array package for python
import numpy as np
np.dot(a,b)
#or if a is an array
a.dot(b)
R
a %*% b
Racket
{{trans|Scheme}}
#lang racket
(define (m-mult m1 m2)
(for/list ([r m1])
(for/list ([c (apply map list m2)])
(apply + (map * r c)))))
(m-mult '((1 2) (3 4)) '((5 6) (7 8)))
;; -> '((19 22) (43 50))
Alternative:
#lang racket
(require math)
(matrix* (matrix [[1 2] [3 4]]) (matrix [[5 6] [7 8]]))
;; -> (array #[#[19 22] #[43 50]])
Rascal
public rel[real, real, real] matrixMultiplication(rel[real x, real y, real v] matrix1, rel[real x, real y, real v] matrix2){
if (max(matrix1.x) == max(matrix2.y)){
p = {<x1,y1,x2,y2, v1*v2> | <x1,y1,v1> <- matrix1, <x2,y2,v2> <- matrix2};
result = {};
for (y <- matrix1.y){
for (x <- matrix2.x){
v = (0.0 | it + v | <x1, y1, x2, y2, v> <- p, x==x2 && y==y1, x1==y2 && y2==x1);
result += <x,y,v>;
}
}
return result;
}
else throw "Matrix sizes do not match.";
//a matrix, given by a relation of the x-coordinate, y-coordinate and value.
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>
};
REXX
/*REXX program multiplies two matrices together, displays the matrices and the results. */
x.=; x.1=1 2 /*╔═══════════════════════════════════╗*/
x.2=3 4 /*║ As none of the matrix values have ║*/
x.3=5 6 /*║ a sign, quotes aren't needed. ║*/
x.4=7 8 /*╚═══════════════════════════════════╝*/
do r=1 while x.r\=='' /*build the "A" matrix from X. numbers.*/
do c=1 while x.r\==''; parse var x.r a.r.c x.r; end /*c*/
end /*r*/
Arows=r-1 /*adjust the number of rows (DO loop).*/
Acols=c-1 /* " " " " cols " " .*/
y.=; y.1=1 2 3
y.2=4 5 6
do r=1 while y.r\=='' /*build the "B" matrix from Y. numbers.*/
do c=1 while y.r\==''; parse var y.r b.r.c y.r; end /*c*/
end /*r*/
Brows=r-1 /*adjust the number of rows (DO loop).*/
Bcols=c-1 /* " " " " cols " " */
c.=0; w=0 /*W is max width of an matrix element.*/
do i=1 for Arows /*multiply matrix A and B ───► C */
do j=1 for Bcols
do k=1 for Acols; c.i.j=c.i.j + a.i.k * b.k.j
w=max(w, length(c.i.j))
end /*k*/ /* ↑ */
end /*j*/ /* └──◄─── maximum width of elements. */
end /*i*/
call showMatrix 'A', Arows, Acols /*display matrix A ───► the terminal.*/
call showMatrix 'B', Brows, Bcols /* " " B ───► " " */
call showMatrix 'C', Arows, Bcols /* " " C ───► " " */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
showMatrix: parse arg mat,rows,cols; say; say center(mat 'matrix', cols*(w+1) +4, "─")
do r=1 for rows; _=
do c=1 for cols; _=_ right(value(mat'.'r"."c), w); end; say _
end /*r*/
return
'''output'''
─A matrix─
1 2
3 4
5 6
7 8
──B matrix───
1 2 3
4 5 6
──C matrix───
9 12 15
19 26 33
29 40 51
39 54 69
Ring
load "stdlib.ring"
n = 3
C = newlist(n,n)
A = [[1,2,3], [4,5,6], [7,8,9]]
B = [[1,0,0], [0,1,0], [0,0,1]]
for i = 1 to n
for j = 1 to n
for k = 1 to n
C[i][k] += A[i][j] * B[j][k]
next
next
next
for i = 1 to n
for j = 1 to n
see C[i][j] + " "
next
see nl
next
Output:
123
456
789
Ruby
Using 'matrix' from the standard library:
require 'matrix'
Matrix[[1, 2],
[3, 4]] * Matrix[[-3, -8, 3],
[-2, 1, 4]]
{{out}} Matrix[[-7, -6, 11], [-17, -20, 25]]
Version for lists: {{trans|Haskell}}
def matrix_mult(a, b)
a.map do |ar|
b.transpose.map do |bc|
ar.zip(bc).map(&:*).inject(&:+)
end
end
end
Rust
struct Matrix {
dat: [[f32; 3]; 3]
}
impl Matrix {
pub fn mult_m(a: Matrix, b: 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 {
for k in 0..3 {
out.dat[i][j] += a.dat[i][k] * b.dat[k][j];
}
}
}
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 b = Matrix {
dat: [[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]]
};
let c = Matrix::mult_m(a, b);
c.print();
}
Scala
{{works with|Scala|2.8}} Assuming an array of arrays representation:
def mult[A](a: Array[Array[A]], b: Array[Array[A]])(implicit n: Numeric[A]) = {
import n._
for (row <- a)
yield for(col <- b.transpose)
yield row zip col map Function.tupled(_*_) reduceLeft (_+_)
}
For any subclass of Seq (which does not include Java-specific arrays):
def mult[A, CC[X] <: Seq[X], DD[Y] <: Seq[Y]](a: CC[DD[A]], b: CC[DD[A]])
(implicit n: Numeric[A]): CC[DD[A]] = {
import n._
for (row <- a)
yield for(col <- b.transpose)
yield row zip col map Function.tupled(_*_) reduceLeft (_+_)
}
Examples:
scala> Array(Array(1, 2), Array(3, 4))
res0: Array[Array[Int]] = Array(Array(1, 2), Array(3, 4))
scala> Array(Array(-3, -8, 3), Array(-2, 1, 4))
res1: Array[Array[Int]] = Array(Array(-3, -8, 3), Array(-2, 1, 4))
scala> mult(res0, res1)
res2: Array[scala.collection.mutable.GenericArray[Int]] = Array(GenericArray(-7, -6, 11), GenericArray(-17, -20, 25))
scala> res0.map(_.toList).toList
res5: List[List[Int]] = List(List(1, 2), List(3, 4))
scala> res1.map(_.toList).toList
res6: List[List[Int]] = List(List(-3, -8, 3), List(-2, 1, 4))
scala> mult(res5, res6)
res7: Seq[Seq[Int]] = List(List(-7, -6, 11), List(-17, -20, 25))
A fully generic multiplication that returns the same collection as received is possible, but much more verbose.
Scheme
{{trans|Common Lisp}} This version works on lists of lists:
(define (matrix-multiply matrix1 matrix2)
(map
(lambda (row)
(apply map
(lambda column
(apply + (map * row column)))
matrix2))
matrix1))
(matrix-multiply '((1 2) (3 4)) '((-3 -8 3) (-2 1 4))) ((-7 -6 11) (-17 -20 25))
Seed7
const type: matrix is array array float;
const func matrix: (in matrix: left) * (in matrix: right) is func
result
var matrix: result is matrix.value;
local
var integer: i is 0;
var integer: j is 0;
var integer: k is 0;
var float: accumulator is 0.0;
begin
if length(left[1]) <> length(right) then
raise RANGE_ERROR;
else
result := length(left) times length(right[1]) times 0.0;
for i range 1 to length(left) do
for j range 1 to length(right) do
accumulator := 0.0;
for k range 1 to length(left) do
accumulator +:= left[i][k] * right[k][j];
end for;
result[i][j] := accumulator;
end for;
end for;
end if;
end func;
Original source: [http://seed7.sourceforge.net/algorith/math.htm#mmult]
SequenceL
:The product of the ''m''×''p'' matrix ''A'' with the ''p''×''n'' matrix ''B'' is the ''m''×''n'' matrix whose (''i'',''j'')'th entry is ::
The SequenceL definition mirrors that definition more or less exactly:
matmul(A(2), B(2)) [i,j] :=
let k := 1...size(B);
in sum( A[i,k] * B[k,j] );
//Example Use
a := [[1, 2],
[3, 4]];
b := [[-3, -8, 3],
[-2, 1, 4]];
test := matmul(a, b);
It can be written a little more simply using the all keyword:
matmul(A(2), B(2)) [i,j] := sum( A[i,all] * B[all,j] );
Sidef
func matrix_multi(a, b) {
var m = [[]]
for r in ^a {
for c in ^b[0] {
for i in ^b {
m[r][c] := 0 += (a[r][i] * b[i][c])
}
}
}
return m
}
var a = [
[1, 2],
[3, 4],
[5, 6],
[7, 8]
]
var b = [
[1, 2, 3],
[4, 5, 6]
]
for line in matrix_multi(a, b) {
say line.map{|i|'%3d' % i }.join(', ')
}
{{out}}
9, 12, 15
19, 26, 33
29, 40, 51
39, 54, 69
SPAD
{{works with|FriCAS}} {{works with|OpenAxiom}} {{works with|Axiom}}
(1) -> A:=matrix [[1,2],[3,4],[5,6],[7,8]]
+1 2+
| |
|3 4|
(1) | |
|5 6|
| |
+7 8+
Type: Matrix(Integer)
(2) -> B:=matrix [[1,2,3],[4,5,6]]
+1 2 3+
(2) | |
+4 5 6+
Type: Matrix(Integer)
(3) -> A*B
+9 12 15+
| |
|19 26 33|
(3) | |
|29 40 51|
| |
+39 54 69+
Type: Matrix(Integer)
Domain:[http://fricas.github.io/api/Matrix.html?highlight=matrix Matrix(R)]
SQL
CREATE TABLE a (x integer, y integer, e real);
CREATE TABLE b (x integer, y integer, e real);
-- test data
-- A is a 2x2 matrix
INSERT INTO a VALUES(0,0,1); INSERT INTO a VALUES(1,0,2);
INSERT INTO a VALUES(0,1,3); INSERT INTO a VALUES(1,1,4);
-- B is a 2x3 matrix
INSERT INTO b VALUES(0,0,-3); INSERT INTO b VALUES(1,0,-8); INSERT INTO b VALUES(2,0,3);
INSERT INTO b VALUES(0,1,-2); INSERT INTO b VALUES(1,1, 1); INSERT INTO b VALUES(2,1,4);
-- C is 2x2 * 2x3 so will be a 2x3 matrix
SELECT rhs.x, lhs.y, (SELECT sum(a.e*b.e) FROM a, b
WHERE a.y = lhs.y
AND b.x = rhs.x
AND a.x = b.y)
INTO TABLE c
FROM a AS lhs, b AS rhs
WHERE lhs.x = 0 AND rhs.y = 0;
Standard ML
structure Matrix = struct
local
open Array2
fun dot(x,y) = Vector.foldli (fn (i,xi,agg) => agg+xi*Vector.sub(y,i)) 0 x
in
val fromList = fromList
fun x*y = tabulate ColMajor (nRows x, nCols y, fn (i,j) => dot(row(x,i),column(y,j)))
(* for display *)
fun toList a =
List.tabulate(nRows a, fn i => List.tabulate(nCols a, fn j => sub(a,i,j)))
end
end;
(* example *)
let open Matrix
val m1 = fromList [[1,2],[3,4]]
val m2 = fromList [[~3,~8,3],[~2,1,4]]
in
toList (m1*m2)
end;
'''Output:'''
val it = [[~7,~6,11],[~17,~20,25]] : int list list
Stata
Stata matrices
. mat a=1,2,3\4,5,6
. mat b=1,1,0,0\1,0,0,1\0,0,1,1
. mat c=a*b
. mat list c
c[2,4]
c1 c2 c3 c4
r1 3 1 3 5
r2 9 4 6 11
Mata
: a=1,2,3\4,5,6
: b=1,1,0,0\1,0,0,1\0,0,1,1
: a*b
1 2 3 4
+---------------------+
1 | 3 1 3 5 |
2 | 9 4 6 11 |
+---------------------+
Swift
@inlinable
public func matrixMult<T: Numeric>(_ m1: [[T]], _ m2: [[T]]) -> [[T]] {
let n = m1[0].count
let m = m1.count
let p = m2[0].count
guard m != 0 else {
return []
}
precondition(n == m2.count)
var ret = Array(repeating: Array(repeating: T.zero, count: p), count: m)
for i in 0..<m {
for j in 0..<p {
for k in 0..<n {
ret[i][j] += m1[i][k] * m2[k][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 = [
[6.5, 2, 3],
[4.5, 1, 5]
]
let m2 = [
[10.0, 16, 23, 50],
[12, -8, 16, -4],
[70, 60, -1, -2]
]
let m3 = matrixMult(m1, m2)
printMatrix(m3)
{{out}}
299.0 268.0 178.5 311.0
407.0 364.0 114.5 211.0
Tailspin
templates matmul@{B:}
$ -> [i](def r: $;
[1..$B(1)::length -> (def j: $; @: 0;
1..$r::length -> @: $@ + $r($) * $B($;$j);
$@ !)] !
) !
end matmul
templates printMatrix@{w:}
templates formatN
@: [];
$ -> #
'$@ -> $::length~..$w -> ' ';$@(-1..1:-1)...;' !
<1..> ..|@: $ mod 10; $ / 10 -> #
<0?($@ <[](0)>)> ..|@: 0;
end formatN
$... -> '|$(1) -> formatN;$(2..-1)... -> ', $ -> formatN;';|
' !
end printMatrix
def a: [[1, 2, 3], [4, 5, 6]];
'a:
' -> !OUT::write
$a -> printMatrix@{w:2} -> !OUT::write
def b: [[0, 1], [2, 3], [4, 5]];
'
b:
' -> !OUT::write
$b -> printMatrix@{w:2} -> !OUT::write
'
axb:
' -> !OUT::write
$a -> matmul@{B: $b} -> printMatrix@{w:2} -> !OUT::write
{{out}}
a:
| 1, 2, 3|
| 4, 5, 6|
b:
| 0, 1|
| 2, 3|
| 4, 5|
axb:
|16, 22|
|34, 49|
Tcl
{{works with|Tcl|8.5}}
package require Tcl 8.5
namespace path ::tcl::mathop
proc matrix_multiply {a b} {
lassign [size $a] a_rows a_cols
lassign [size $b] b_rows b_cols
if {$a_cols != $b_rows} {
error "incompatible sizes: a($a_rows, $a_cols), b($b_rows, $b_cols)"
}
set temp [lrepeat $a_rows [lrepeat $b_cols 0]]
for {set i 0} {$i < $a_rows} {incr i} {
for {set j 0} {$j < $b_cols} {incr j} {
set sum 0
for {set k 0} {$k < $a_cols} {incr k} {
set sum [+ $sum [* [lindex $a $i $k] [lindex $b $k $j]]]
}
lset temp $i $j $sum
}
}
return $temp
}
Using the print_matrix procedure defined in [[Matrix Transpose#Tcl]]
% print_matrix [matrix_multiply {{1 2} {3 4}} {{-3 -8 3} {-2 1 4}}]
-7 -6 11
-17 -20 25
=={{header|TI-83 BASIC}}== Store your matrices in [A] and [B].
Disp [A]*[B]
An error will show if the matrices have invalid dimensions for multiplication.
'''Other way:''' enter directly your matrices:
[[1,2][3,4][5,6][7,8]]*[[1,2,3][4,5,6]]
{{out}} [[9 12 15] [19 26 33] [29 40 51] [39 54 69]]]
=={{header|TI-89 BASIC}}==
{{trans|Mathematica}}
[1,2; 3,4; 5,6; 7,8] → m1
[1,2,3; 4,5,6] → m2
m1 * m2
Or without the variables:
[1,2; 3,4; 5,6; 7,8] * [1,2,3; 4,5,6]
The result (without prettyprinting) is:
[[9,12,15][19,26,33][29,40,51][39,54,69]]
UNIX Shell
#!/bin/bash
DELAY=0 # increase this if printing of matrices should be slower
echo "This script takes two matrices, henceforth called A and B,
and returns their product, AB.
For the time being, matrices can have integer components only.
"
read -p "Number of rows of matrix A: " arows
read -p "Number of columns of matrix A: " acols
brows="$acols"
echo
echo "Number of rows of matrix B: "$brows
read -p "Number of columns of matrix B: " bcols
crows="$arows"
ccols="$bcols"
echo
echo "Number of rows of matrix AB: " $crows
echo "Number of columns of matrix AB: " $ccols
echo
echo
matrixa=( )
matrixb=( )
# input matrix A
maxlengtha=0
for ((row=1; row<=arows; row++)); do
for ((col=1; col<=acols; col++)); do
checkentry="false"
while [ "$checkentry" != "true" ]; do
read -p "Enter component A[$row, $col]: " number
index=$(((row-1)*acols+col))
matrixa[$index]="$number"
[ "${matrixa[$index]}" -eq "$number" ] && checkentry="true"
echo
done
entry="${matrixa[$index]}"
[ "${#entry}" -gt "$maxlengtha" ] && maxlengtha="${#entry}"
done
echo
done
# print matrix A to guard against errors
if [ "$maxlengtha" -le "5" ]; then
width=8
else
width=$((maxlengtha + 3))
fi
echo "This is matrix A:
"
for ((row=1; row<=arows; row++)); do
for ((col=1; col<=acols; col++)); do
index=$(((row-1)*acols+col))
printf "%${width}d" "${matrixa[$index]}"
sleep "$DELAY"
done
echo; echo # printf %s "\n\n" does not work...
done
echo
echo
# input matrix B
maxlengthb=0
for ((row=1; row<=brows; row++)); do
for ((col=1; col<=bcols; col++)); do
checkentry="false"
while [ "$checkentry" != "true" ]; do
read -p "Enter component B[$row, $col]: " number
index=$(((row-1)*bcols+col))
matrixb[$index]="$number"
[ "${matrixb[$index]}" -eq "$number" ] && checkentry="true"
echo
done
entry="${matrixb[$index]}"
[ "${#entry}" -gt "$maxlengthb" ] && maxlengthb="${#entry}"
done
echo
done
# print matrix B to guard against errors
if [ "$maxlengthb" -le "5" ]; then
width=8
else
width=$((maxlengthb + 3))
fi
echo "This is matrix B:
"
for ((row=1; row<=brows; row++)); do
for ((col=1; col<=bcols; col++)); do
index=$(((row-1)*bcols+col))
printf "%${width}d" "${matrixb[$index]}"
sleep "$DELAY"
done
echo; echo # printf %s "\n\n" does not work...
done
read -p "Hit enter to continue"
# calculate matrix C := AB
maxlengthc=0
time for ((row=1; row<=crows; row++)); do
for ((col=1; col<=ccols; col++)); do
# calculate component C[$row, $col]
runningtotal=0
for ((j=1; j<=acols; j++)); do
rowa="$row"
cola="$j"
indexa=$(((rowa-1)*acols+cola))
rowb="$j"
colb="$col"
indexb=$(((rowb-1)*bcols+colb))
entry_from_A=${matrixa[$indexa]}
entry_from_B=${matrixb[$indexb]}
subtotal=$((entry_from_A * entry_from_B))
((runningtotal+=subtotal))
done
number="$runningtotal"
# store component in the result array
index=$(((row-1)*ccols+col))
matrixc[$index]="$number"
entry="${matrixc[$index]}"
[ "${#entry}" -gt "$maxlengthc" ] && maxlengthc="${#entry}"
done
done
echo
read -p "Hit enter to continue"
echo
# print the matrix C
if [ "$maxlengthc" -le "5" ]; then
width=8
else
width=$((maxlengthc + 3))
fi
echo "The product matrix is:
"
for ((row=1; row<=crows; row++)); do
for ((col=1; col<=ccols; col++)); do
index=$(((row-1)*ccols+col))
printf "%${width}d" "${matrixc[$index]}"
sleep "$DELAY"
done
echo; echo # printf %s "\n\n" does not work...
done
echo
echo
Ursala
There is a library function for matrix multiplication of IEEE double precision floating point numbers. This example shows how to define and use a matrix multiplication function over any chosen field given only the relevant product and sum functions, in this case for the built in rational number type.
#import rat
a =
<
<1/1, 1/1, 1/1, 1/1>,
<2/1, 4/1, 8/1, 16/1>,
<3/1, 9/1, 27/1, 81/1>,
<4/1, 16/1, 64/1, 256/1>>
b =
<
< 4/1, -3/1, 4/3, -1/4>,
<-13/3, 19/4, -7/3, 11/24>,
< 3/2, -2/1, 7/6, -1/4>,
< -1/6, 1/4, -1/6, 1/24>>
mmult = *rK7lD *rlD sum:-0.+ product*p
#cast %qLL
test = mmult(a,b)
{{out}}
<
<1/1,0/1,0/1,0/1>,
<0/1,1/1,0/1,0/1>,
<0/1,0/1,1/1,0/1>,
<0/1,0/1,0/1,1/1>>
VBA
Using Excel. The resulting matrix should be smaller than 5461 elements.
Function matrix_multiplication(a As Variant, b As Variant) As Variant
matrix_multiplication = WorksheetFunction.MMult(a, b)
End Function
VBScript
Dim matrix1(2,2)
matrix1(0,0) = 3 : matrix1(0,1) = 7 : matrix1(0,2) = 4
matrix1(1,0) = 5 : matrix1(1,1) = -2 : matrix1(1,2) = 9
matrix1(2,0) = 8 : matrix1(2,1) = -6 : matrix1(2,2) = -5
Dim matrix2(2,2)
matrix2(0,0) = 9 : matrix2(0,1) = 2 : matrix2(0,2) = 1
matrix2(1,0) = -7 : matrix2(1,1) = 3 : matrix2(1,2) = -10
matrix2(2,0) = 4 : matrix2(2,1) = 5 : matrix2(2,2) = -6
Call multiply_matrix(matrix1,matrix2)
Sub multiply_matrix(arr1,arr2)
For i = 0 To UBound(arr1)
For j = 0 To 2
WScript.StdOut.Write (arr1(i,j) * arr2(i,j)) & vbTab
Next
WScript.StdOut.WriteLine
Next
End Sub
{{Out}}
27 14 4
-35 -6 -90
32 -30 30
Visual FoxPro
LOCAL ARRAY a[4,2], b[2,3], c[4,3]
CLOSE DATABASES ALL
*!* The arrays could be created directly but I prefer to do this:
CREATE CURSOR mat1 (c1 I, c2 I)
CREATE CURSOR mat2 (c1 I, c2 I, c3 I)
*!* Since matrix multiplication of integer arrays
*!* involves only multiplication and addition,
*!* the result will contain integers
CREATE CURSOR result (c1 I, c2 I, c3 I)
INSERT INTO mat1 VALUES (1, 2)
INSERT INTO mat1 VALUES (3, 4)
INSERT INTO mat1 VALUES (5, 6)
INSERT INTO mat1 VALUES (7, 8)
SELECT * FROM mat1 INTO ARRAY a
INSERT INTO mat2 VALUES (1, 2, 3)
INSERT INTO mat2 VALUES (4, 5, 6)
SELECT * FROM mat2 INTO ARRAY b
STORE 0 TO c
MatMult(@a,@b,@c)
SELECT result
APPEND FROM ARRAY c
BROWSE
PROCEDURE MatMult(aa, bb, cc)
LOCAL n As Integer, m As Integer, p As Integer, i As Integer, j As Integer, k As Integer
IF ALEN(aa,2) = ALEN(bb,1)
n = ALEN(aa,2)
m = ALEN(aa,1)
p = ALEN(bb,2)
FOR i = 1 TO m
FOR j = 1 TO p
FOR k = 1 TO n
cc[i,j] = cc[i,j] + aa[i,k]*bb[k,j]
ENDFOR
ENDFOR
ENDFOR
ELSE
? "Invalid dimensions"
ENDIF
ENDPROC
XPL0
proc Mat4x1Mul(M, V); \Multiply matrix M times column vector V
real M, \4x4 matrix [M] * [V] -> [V]
V; \column vector
real W(4); \working copy of column vector
int R; \row
[for R:= 0 to 4-1 do
W(R):= M(R,0)*V(0) + M(R,1)*V(1) + M(R,2)*V(2) + M(R,3)*V(3);
for R:= 0 to 4-1 do V(R):= W(R);
];
proc Mat4x4Mul(M, N); \Multiply matrix M times matrix N
real M, N; \4x4 matrices [M] * [N] -> [N]
real W(4,4); \working copy of matrix N
int C; \column
[for C:= 0 to 4-1 do
[W(0,C):= M(0,0)*N(0,C) + M(0,1)*N(1,C) + M(0,2)*N(2,C) + M(0,3)*N(3,C);
W(1,C):= M(1,0)*N(0,C) + M(1,1)*N(1,C) + M(1,2)*N(2,C) + M(1,3)*N(3,C);
W(2,C):= M(2,0)*N(0,C) + M(2,1)*N(1,C) + M(2,2)*N(2,C) + M(2,3)*N(3,C);
W(3,C):= M(3,0)*N(0,C) + M(3,1)*N(1,C) + M(3,2)*N(2,C) + M(3,3)*N(3,C);
];
for C:= 0 to 4-1 do
[N(0,C):= W(0,C);
N(1,C):= W(1,C);
N(2,C):= W(2,C);
N(3,C):= W(3,C);
];
];
XSLT 1.0
With input document ...
<?xml-stylesheet href="matmul.templ.xsl" type="text/xsl"?>
<mult>
<A>
<r><c>1</c><c>2</c></r>
<r><c>3</c><c>4</c></r>
<r><c>5</c><c>6</c></r>
<r><c>7</c><c>8</c></r>
</A>
<B>
<r><c>1</c><c>2</c><c>3</c></r>
<r><c>4</c><c>5</c><c>6</c></r>
</B>
</mult>
... and this referenced stylesheet ...
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
>
<xsl:output method="html"/>
<xsl:template match="/mult">
<table>
<tr><td>╭</td><td colspan="{count(*[2]/*[1]/*)}"/><td>╮</td></tr>
<xsl:call-template name="prodMM">
<xsl:with-param name="A" select="*[1]/*"/>
<xsl:with-param name="B" select="*[2]/*"/>
</xsl:call-template>
<tr><td>╰</td><td colspan="{count(*[2]/*[1]/*)}"/><td>╯</td></tr>
</table>
</xsl:template>
<xsl:template name="prodMM">
<xsl:param name="A"/>
<xsl:param name="B"/>
<xsl:if test="$A/*">
<tr>
<td>│</td>
<xsl:call-template name="prodVM">
<xsl:with-param name="a" select="$A[1]/*"/>
<xsl:with-param name="B" select="$B"/>
</xsl:call-template>
<td>│</td>
</tr>
<xsl:call-template name="prodMM">
<xsl:with-param name="A" select="$A[position()>1]"/>
<xsl:with-param name="B" select="$B"/>
</xsl:call-template>
</xsl:if>
</xsl:template>
<xsl:template name="prodVM">
<xsl:param name="a"/>
<xsl:param name="B"/>
<xsl:param name="col" select="1"/>
<xsl:if test="$B/*[$col]">
<td align="right">
<xsl:call-template name="prod">
<xsl:with-param name="a" select="$a"/>
<xsl:with-param name="b" select="$B/*[$col]"/>
</xsl:call-template>
</td>
<xsl:call-template name="prodVM">
<xsl:with-param name="a" select="$a"/>
<xsl:with-param name="B" select="$B"/>
<xsl:with-param name="col" select="$col+1"/>
</xsl:call-template>
</xsl:if>
</xsl:template>
<xsl:template name="prod">
<xsl:param name="a"/>
<xsl:param name="b"/>
<xsl:if test="not($a)">0</xsl:if>
<xsl:if test="$a">
<xsl:variable name="res">
<xsl:call-template name="prod">
<xsl:with-param name="a" select="$a[position()>1]"/>
<xsl:with-param name="b" select="$b[position()>1]"/>
</xsl:call-template>
</xsl:variable>
<xsl:value-of select="$a[1] * $b[1] + $res"/>
</xsl:if>
</xsl:template>
</xsl:stylesheet>
{{out}} (in a browser):
╭ ╮
│ 9 12 15 │
│ 19 26 33 │
│ 29 40 51 │
│ 39 54 69 │
╰ ╯
You may try in your browser: [[http://www.stamm-wilbrandt.de/en/blog/matmul.templ.xml]]
A slightly smaller version of above stylesheet making use of (Non-"XSLT 1.0") EXSLT functions can be founde here: [[https://www.ibm.com/developerworks/mydeveloperworks/blogs/HermannSW/entry/matrix_multiplication30]]
zkl
Using the GNU Scientific Library:
var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)
A:=GSL.Matrix(4,2).set(1,2, 3,4, 5,6, 7,8);
B:=GSL.Matrix(2,3).set(1,2,3, 4,5,6);
(A*B).format().println(); // creates a new matrix
{{out}}
9.00, 12.00, 15.00
19.00, 26.00, 33.00
29.00, 40.00, 51.00
39.00, 54.00, 69.00
Or, using lists: {{trans|BASIC}}
fcn matMult(a,b){
n,m,p:=a[0].len(),a.len(),b[0].len();
ans:=(0).pump(m,List().write, (0).pump(p,List,0).copy); // matrix of zeros
foreach i,j,k in (m,p,n){ ans[i][j]+=a[i][k]*b[k][j]; }
ans
}
a:=L( L(1,2,), L(3,4,), L(5,6,), L(7,8) );
b:=L( L(1,2,3,), L(4,5,6) );
printM(matMult(a,b));
fcn printM(m){ m.pump(Console.println,rowFmt) }
fcn rowFmt(row){ ("%4d "*row.len()).fmt(row.xplode()) }
{{out}}
9 12 15
19 26 33
29 40 51
39 54 69
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 Multiplication;
var
a,b: Matrix;
begin
a := [[1,2],[3,4],[5,6],[7,8]];
b := [[1,2,3],[4,5,6]];
WriteMatrix(a * b);
end Multiplication;
begin
Multiplication;
end MatrixOps.
ZPL
program matmultSUMMA;
prototype GetSingleDim(infile:file):integer;
prototype GetInnerDim(infile1:file; infile2:file):integer;
config var
Afilename: string = "";
Bfilename: string = "";
Afile: file = open(Afilename,file_read);
Bfile: file = open(Bfilename,file_read);
default_size:integer = 4;
m:integer = GetSingleDim(Afile);
n:integer = GetInnerDim(Afile,Bfile);
p:integer = GetSingleDim(Bfile);
iters: integer = 1;
printinput: boolean = false;
verbose: boolean = true;
dotiming: boolean = false;
region
RA = [1..m,1..n];
RB = [1..n,1..p];
RC = [1..m,1..p];
FCol = [1..m,*];
FRow = [*,1..p];
var
A : [RA] double;
B : [RB] double;
C : [RC] double;
Aflood : [FCol] double;
Bflood : [FRow] double;
procedure ReadA();
var step:double;
[RA] begin
if (Afile != znull) then
read(Afile,A);
else
step := 1.0/(m*n);
A := ((Index1-1)*n + Index2)*step + 1.0;
end;
end;
procedure ReadB();
var step:double;
[RB] begin
if (Bfile != znull) then
read(Bfile,B);
else
step := 1.0/(n*p);
B := ((Index1-1)*p + Index2)*step + 1.0;
end;
end;
procedure matmultSUMMA();
var
i: integer;
it: integer;
runtime: double;
[RC] begin
ReadA();
ReadB();
if (printinput) then
[RA] writeln("A is:\n",A);
[RB] writeln("B is:\n",B);
end;
ResetTimer();
for it := 1 to iters do
C := 0.0; -- zero C
for i := 1 to n do
[FCol] Aflood := >>[,i] A; -- flood A col
[FRow] Bflood := >>[i,] B; -- flood B row
C += (Aflood * Bflood); -- multiply
end;
end;
runtime := CheckTimer();
if (verbose) then
writeln("C is:\n",C);
end;
if (dotiming) then
writeln("total runtime = %12.6f":runtime);
writeln("actual runtime = %12.6f":runtime/iters);
end;
end;
procedure GetSingleDim(infile:file):integer;
var dim:integer;
begin
if (infile != znull) then
read(infile,dim);
else
dim := default_size;
end;
return dim;
end;
procedure GetInnerDim(infile1:file; infile2:file):integer;
var
col:integer;
row:integer;
retval:integer;
begin
retval := -1;
if (infile1 != znull) then
read(infile1,col);
retval := col;
end;
if (infile2 != znull) then
read(infile2,row);
if (retval = -1) then
retval := row;
else
if (row != col) then
halt("ERROR: Inner dimensions don't match");
end;
end;
end;
if (retval = -1) then
retval := default_size;
end;
return retval;
end;