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    This subchapter looks at matrices or two dimensional arrays.

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stub section

    This subchapter is a stub section. It will be filled in with instructional material later. For now it serves the purpose of a place holder for the order of instruction.

    Professors are invited to give feedback on both the proposed contents and the propsed order of this text book. Send commentary to Milo, PO Box 1361, Tustin, California, 92781, USA.

matrix

    This subchapter looks at matrices or two dimensional arrays.

declaring an array

LISP

    All arrays in LISP must be declared before they are used.

LISP    ARRAY(x) — LISP function that takes three or more arguments of type name, type, and dimnsions, and creates an array of that name, type, and dimensions.

    (ARRAY TWODIMENSIONS FIXNUM 1024 1024)

    The example creates a LISP array named TWODIMENSIONS that can contain fixed point numbers. The array elements are numbered by two indices, both in the range of 0 to 1,023.

order of multi-dimensional arrays

    The storage of a signle dimension array in memory is obvious: a linear sequence of memory locations (possibly with padding for instruction alignment purposes).

    When an array has two or more dimensions, it is still ultimately stored in a linear sequence of memory locations (possibly with padding for instruction alignment purposes), but the dimensions must be lined up sequentially as well.

    The two major choices are either row major (rows are stored one after another) or column major (columns are stored one after another). These either group the linear representation of the array by the row or by the column.

1,1   1   0x1000   1
1,3   13   0x1008   13
2,2   10,000   0x1010   10,000
3,1   -25   0x1018   -25
3,3   1,024   0x1020   1,024

    Ada uses a row-major order.

    ALGOL 60 does not specify an order, but many ALGOL 60 compilers use row-major order.

    C uses a row-major order.

    C++ uses a row-major order.

    COBOL uses a row-major order.

    FORTRAN explicitly requires a column-major order.

    Java uses a row-major order.

    Matlab uses a column-major order.

    Modula-2 uses a row-major order.

    Pascal implicitly requires a row-major order.

    PL/I uses a row-major order.

C

Stanford C essentials

    Stanford CS Education Library This [the following section until marked as end of Stanford University items] is document #101, Essential C, in the Stanford CS Education Library. This and other educational materials are available for free at http://cslibrary.stanford.edu/. This article is free to be used, reproduced, excerpted, retransmitted, or sold so long as this notice is clearly reproduced at its beginning. Copyright 1996-2003, Nick Parlante, nick.parlante@cs.stanford.edu.

Multidimensional Arrays

    The following declares a two-dimensional 10 by 10 array of integers and sets the first and last elements to be 13.

    int board [10][10];

    board[0][0] = 13;
    board[9][9] = 13;

    The implementation of the array stores all the elements in a single contiguous block of memory. The other possible implementation would be a combination of several distinct one dimensional arrays -- that’s not how C does it. In memory, the array is arranged with the elements of the rightmost index next to each other. In other words, board[1][8] comes right before board[1][9] in memory.

    (highly optional efficiency point) It’s typically efficient to access memory which is near other recently accessed memory. This means that the most efficient way to read through a chunk of the array is to vary the rightmost index the most frequently since that will access elements that are near each other in memory.

    Stanford CS Education Library This [the above section] is document #101, Essential C, in the Stanford CS Education Library. This and other educational materials are available for free at http://cslibrary.stanford.edu/. This article is free to be used, reproduced, excerpted, retransmitted, or sold so long as this notice is clearly reproduced at its beginning. Copyright 1996-2003, Nick Parlante, nick.parlante@cs.stanford.edu.

end of Stanford C essentials

matrix operations in APL

    ABSOLUTE VALUE |B. APL monadic function that when applied to a vector returns a matrix with each element having the absolute value of the corresponding element of the source matrix.

    ADDITION A+B. APL dyadic function that adds all of the corresponding element of the matrices A and B and places the results into matrix A. If B is a scalar, this fucntion adds the scalar B to every element in matrix A and places the results into matrix A.

    AND (x) — APL dyadic function that returns the logical AND of two matrices. Form is AB. This function can be used with two matrices to logically AND all of the corresponding elements of the two matrices; or with a matrix and a vector or scalar to logically AND the scalar to every element of the matrix with the value of the vector or scalar. Each element of the operation must intiially have the value of one (1) or zero (0). One is TRUE and zero is FALSE.

functions

PostScript    aload(x) — PosScript array operator that places on the stack all of the elements of an array followed by the array itself.
LISP    ARRAY(x) — LISP function that takes three or more arguments of type name, type, and dimnsions, and creates an array of that name, type, and dimensions.

PL/I    DIM(x, n) — Pl/I built-in function that returns the size of an array. The data item x is the name of the array to be examined. The data item n is the number of the dimension of the specififed array for which the extent is to be returned. The function is most efficient if data item n is of type FIXED BINARY (15). It is an error if the array has less than n dimensions or if n is zero or less or if the array x is not currently allocated. For a matrix the value of n should be either 1 or 2.

PL/I    LBOUND(x, n) — Pl/I built-in function that returns the lower bound for the specififed dimension of an array. The data item x is the name of the array to be examined. The data item n is the number of the dimension of the specififed array for which the extent is to be returned. The function is most efficient if data item n is of type FIXED BINARY (15). It is an error if the array has less than n dimensions or if n is zero or less or if the array x is not currently allocated. For a matrix, the value of n should be 1 or 2.

PL/I    HBOUND(x, n) — Pl/I built-in function that returns the upper bound for the specififed dimension of an array. The data item x is the name of the array to be examined. The data item n is the number of the dimension of the specififed array for which the extent is to be returned. The function is most efficient if data item n is of type FIXED BINARY (15). It is an error if the array has less than n dimensions or if n is zero or less or if the array x is not currently allocated. For a matrix, the value of n should be 1 or 2.

PL/I    SUM(x) — Pl/I built-in function that returns the total sum of all of the values of the elements in an arithmetic array x. Note that the IBM PL/I-F compiler converts all array values to floating point to perform the operation and returns a result in floating point. This may create small rounding errors for commercial programmers needing dollar and cents accuracy.

PL/I    PROD(x) — Pl/I built-in function that returns the total product of all of the values of the elements in an arithmetic array x. The PROD function is always carried out in floating point arithmetic. This may create small rounding errors for commercial programmers needing dollar and cents accuracy.

other

   “Ah, variable names.╩Length is not a virtue in a name; clarity of expression is.╩A global variable rarely used may deserve a long name, maxphysaddr say.╩An array index used on every line of a loop needn’t be named any more elaborately than i.╩ Saying index or elementnumber is more to type (or calls upon your text editor) and obscures the details of the computation.╩When the variable names are huge, it’s harder to see what’s going on.╩This is partly a typographic issue; consider
        for(i=0 to 100)
            array[i]=0 ;
   “vs.
        for(elementnumber=0 to 100)
            array[elementnumber]=0;
   “The problem gets worse fast with real examples.╩Indices are just notation, so treat them as such.” —Rob Pike, Notes on Programming in C, February 21, 1989


free music player coding example

    Coding example: I am making heavily documented and explained open source code for a method to play music for free — almost any song, no subscription fees, no download costs, no advertisements, all completely legal. This is done by building a front-end to YouTube (which checks the copyright permissions for you).

    View music player in action: www.musicinpublic.com/.

    Create your own copy from the original source code/ (presented for learning programming).


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    Created: December 8, 2010

    Last Updated: February 26, 2011


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