![]() Putf(stand error, $x"Exception: index error. Matrix c = a × b ¢ actual multiplication example of A x B ¢ Proc real matrix printf= ( format real fmt, matrix m) void:(įormat vector fmt = $"("n(2 ⌈m-1)(f(real fmt)",")f(real fmt)")"$ įormat matrix fmt = $x"("n(⌈m-1)(f(vector fmt)","lxx)f(vector fmt)") "$ ![]() ( required →schedule | ↓idle cpus thread →schedule ↑idle cpus)įormat real fmt = $g(-6,2)$ ¢ width of 6, with no '+' sign, 2 decimals ¢ ¢ try to do opposite corners of matrix in parallel if CPUs are limited ¢ ( required →schedule | ↓idle cpus thread →schedule ↑idle cpus), Thread →schedule, ¢ thread is always required, and assume parent CPU ¢ Creating a matrix is as easy as making a vector, using semicolons ( ) to separate the rows of a matrix. Void: out := a × b)įor thread to ⌈schedule do (required →schedule | thread →schedule ) od else par ( ¢ run vector in parallel ¢ One area in which MATLAB excels is matrix computation. ( (⌊a, 2 ⌊b) ≠ (⌈a, 2 ⌈b), ¢ calculate bottom right corner ¢ ( 2 ⌊b ≠ 2 ⌈b, ¢ calculate top right corner ¢ ( ⌊a ≠ ⌈a, ¢ calculate bottom left corner ¢ struct( bool required, proc void thread) schedule = ( If (2 ⌊a, 2 ⌈a) ≠ (⌊b, ⌈b) then raise index error fi Op × = ( matrix a, b) matrix: ¢ matrix multiply ¢ Even a single number is stored as a matrix. The elements can be numbers, logical values (true or false), dates and times, strings, categorical values, or some other MATLAB data type. A matrix is a two-dimensional, rectangular array of data elements arranged in rows and columns. In the case of a scalar (1-by-1 matrix), the brackets are not required. Within the brackets, use a semicolon to denote the end of a row. To define a matrix manually, use square brackets to denote the beginning and end of the array. ![]() If level idle cpus = 0 then ¢ use current CPU ¢įor thread to ⌈schedule do schedule od else par ( ¢ run vector in parallel ¢ The most basic MATLAB® data structure is the matrix. A column vector is an m-by-1 matrix, a row vector is a 1-by-n matrix, and a scalar is a 1-by-1 matrix. How to concatenate matrix row wise to get a. If (⌊a, ⌈a) ≠ (⌊b, ⌈b) then raise index error fi Op × = ( vector a, b) field: ( ¢ dot product ¢ Prio top = 8, bot = 8, left = 8, right = 8 ¢ Operator priority - same as LWB & UPB ¢ Op top = ( matrix m) int: ( ⌊m + ⌈m ) %2, ¢ define an operator to slice array into quarters ¢ Sema idle cpus = level ( 8 - 1 ) ¢ 8 = number of CPU cores minus parent CPU ¢ Proc void raise index error := void: goto exception index error The next step might be to augment with Strassen's O(n^log2(7)) recursive matrix multiplication algorithm: Putf(stand error, $x"Exception: index error."l$)Īlternatively - for multicore CPUs - use the following parallel code. Print(("Product of a and b: ",new line)) ![]() PROC real matrix printf= (FORMAT real fmt, MATRIX m)VOID:(įORMAT vector fmt = $"("n(2 UPB m-1)(f(real fmt)",")f(real fmt)")"$ įORMAT matrix fmt = $x"("n(UPB m-1)(f(vector fmt)","lxx)f(vector fmt)") "$ MATRIX prod = a * b # actual multiplication example of A x B #įORMAT real fmt = $g(-6,2)$ # width of 6, with no '+' sign, 2 decimals # IF 2 LWB a/=LWB b OR 2 UPB a/=UPB b THEN raise index error FI įOR k FROM LWB result TO UPB result DO result:=a*b OD OP * = (MATRIX a, b)MATRIX: ( # overload matrix times matrix #įIELD result Syntax x A./B x rdivide (A,B) Description example x A./B divides each element of A by the corresponding element of B. OP * = (VECTOR a, MATRIX b)VECTOR: ( # overload vector times matrix #įOR j FROM 2 LWB b TO 2 UPB b DO result:=a*b OD IF LWB a/=LWB b OR UPB a/=UPB b THEN raise index error FI įOR i FROM LWB a TO UPB a DO result+:= a*b OD OP * = (VECTOR a,b)FIELD: ( # basically the dot product # PROC VOID raise index error := VOID: GOTO exception index error MODE FIELD = LONG REAL # field type is LONG REAL # Print("Invalid size of matrices for multiplication!") PROC Create(MATRIX POINTER m BYTE w,h INT ARRAY a) INCLUDE "D2:PRINTF.ACT" from the Action! Tool Kit We can multiply the transpose of the matrix with the vector and then take the transpose of that multiplication this will result in the multiplication by rows.A DC F'1',F'2',F'3',F'4',F'5',F'6',F'7',F'8' a(4,2)ī DC F'1',F'2',F'3',F'4',F'5',F'6' b(2,3) When we multiple a matrix with a vector in R, the multiplication is done by column but if we want to do it with rows then we can use transpose function.
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