Mat
See Also: Mat for Beginners
The Mat (M) statement performs several array (or Matrix) operations. It can change the number of dimensions or elements, assign new values, and apply an expression to all elements. Each element is an individual variable.
MAT subarray operator
Arrays may now be subscripted with a starting and ending element number to process a portion of an array. This works much the same as Business Rules sub-string feature, except it works with elements instead of characters.
00100 MAT A(6:10)=B ! copies B(1)..B(5) into A(6)..A(10); 00110 MAT B=A(6:10) ! B dimensioned for 5 elements. 00120 MAT B(1:5)=A(6:10) ! Copy part of 1 array to part of another 00130 READ MAT A(1:5) ! only read elements 1-5 00140 PRINT FIELDS SF$:MAT A$(F:F+9) ! 10 elements starting at "F" are displayed
Multi-dimensional matrixes are not supported for sub-array processing.
Comments and Examples
Arrays and matrices are manipulated using the MAT statement. An array is a one-dimensional matrix. The MAT statement can be used to assign values to all elements of a matrix in a single statement. For example, MAT can be used to initialize all elements of an array to a constant as follows:
00100 MAT A = (0)
00200 MAT A$ = ("")
In the next example, values in one array are copied to another array:
00300 MAT A$ = B$ 00400 MAT A = B
The MAT statement also handles mathematical operations on numeric arrays. Two arrays may be added or subtracted as follows:
00100 MAT A = B + C 00200 MAT A = B - C
Line 100 adds each element of matrix B to the corresponding element of matrix C and stores the result in the corresponding element of matrix A. The dimensions of A, B and C must be the same.
Another form of matrix arithmetic involves combining a matrix and a scalar. Business Rules adding, subtracting, multiplying, and dividing a number by all elements of a matrix. It is important to note that the scalar (X in the following examples) must be the left operand, and the matrix (B) must be the right operand. Due to these restrictions, subtraction and division must be accomplished in the manner illustrated in lines 500 and 600 below:
00300 MAT A=(X)+B 00400 MAT A=(X)*B 00500 MAT A=(-X)+B 00600 MAT A=(1/X)*B
In line 300, the numeric expression inside the parentheses is added to every element of matrix B; the result is stored in matrix A.
Array sorting is another feature of the MAT statement. Both string and numeric arrays can be sorted in ascending (AIDX) or descending (DIDX) order. The following is an example of using MAT AIDX to sort an array of names. The names are stored in array N$ and the number of names used is stored in L. See AIDX in the Functions chapter for another example.
00100 DIM A(100), N$(100)*30 00200 MAT N$(L) 00300 MAT A(L)=AIDX(N$) 00400 FOR I=1 TO L 00500 PRINT N$(A(I)) 00600 NEXT I
Array A contains the indexed order of array N$, similar to the way an address-out sort file contains pointers to the original data. Lines 400 to 600 print the names in ascending order.
Lines 200 and 300 above illustrate another MAT function -redimensioning. The number of elements in an array or matrix can be increased or decreased. For example:
00100 DIM A(100), B(100) 00200 NA=200 00300 MAT A(NA) 00400 NB=50 00500 MAT B(NB) 00600 MAT A(NB)=B
Line 300 increases the number of elements of A to 200, and line 500 decreases the number of elements of B to 50. Line 600 illustrates copying array B into array A, while at the same time re-dimensioning A to have NB elements.
Re-dimensioning also allows you to change the number of dimensions. The following example changes matrix A from a 10 x 10 matrix to a one-dimensional array of 100 elements without changing the values of the elements of the matrix.
00100 DIM A(10,10) 00200 MAT A(100)=A
Syntax
Defaults
- No re-dimension.
- No assignment.
- Set the value of all elements to the expression.
Parameters
"Array-name" is a required parameter that represents a numeric or string array name. The optional "dimension" parameter is used to change the dimensions of the array mentioned in "array-name". Each dimension specification identifies the maximum size for that dimension. The dimension parameter is exactly the same as a combination of the "rows" and "columns" parameters described with the DIM statement, with the important distinction that any type of numeric expression may be used -not just integer constants.
"String-expr" can be used to set all the elements of an array to the same character string.
"Num-expr" represents expressions to be evaluated to a single value, which are used to make assignments to the matrix elements. It may be followed by one of four allowable "math-op" (math operator) parameters: +, -, * or /. The math-op must then be followed by a "num-array".
"Num-array" is used in varieties of the MAT statement that perform arithmetic on arrays.
"AIDX" and "DIDX" are keywords used to invoke array functions for sorting an array in ascending (AIDX)D5095W or descending (DIDX)1MFUSOL order. Both must be followed by an "array-name" within parentheses. Both create an index array, which is a numeric array containing numbers to be used as subscripts for accessing the original array in a sorted order. AIDX and DIDX can be used to sort either numeric or string arrays.
Technical Considerations
- Using re-dimensioning to decrease the number of elements saves memory and speeds up the AIDX and DIDX functions.
- When one matrix is assigned to another (via arithmetic or the AIDX/DIDX functions) the assigned-to matrix must be the same size as the assigned-from matrix. In the case of string matrices, the assigned-to matrix must have the same string length dimension as the assigned-from matrix; a SOFLOW condition will occur if the assigned-to string is too short.
- The expression to the right of the equal sign must be the same type (either numeric or string) as the array named on the left side.
- Re-dimensioning can increase or decrease the number of elements or the number of dimensions, but it cannot change the maximum lengths of string arrays.
- Use PRINT with the MAT keyword to print a matrix.
- Use READ with the MAT keyword to read data into an entire array.
- When matrixes are re-dimensioned, data is always preserved. When the size of a matrix is increased, the added elements are set to zero or null.
- Use CHAIN with the MAT keyword to chain an array assignment. (See the CHAIN statement for more information.)
- See the AIDX and DIDX Functions for more information.