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Size and Shape of Arrays

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• Obtaining information on the size and shape of an array
  • F90 (but not F77) is one of the few programming languages where programmers can determine the size of an array

    This feature is useful for writing functions that can manipulate array (matrices and vectors) of arbitrary size in a flexible manner

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  • If you CANNOT determine the array size (and shape) , the function must include size parameters

    Example:

    C++ style: int func( double *A, int nrows, int ncols) { // dimension of matrix is passed as parameters // because array A does not contain information // about its size and shape... ... }

  • If you CAN determine the array size (and shape) , the function becomes:

    Example:

    C++ style: int func( double *A ) { ... A contains information on its size and shape ... The function can handle any size and shape of matrices }

  • One important advantage of encoding the array size and shape information into the array variable is:

    The function can be very general The function can be written in such a way that it can manipulate any size and shape of matrices

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  • Obtaining information on an array:

    SHAPE(A): return the "shape" (dimensions) of array A SIZE(A): return the "size" (# elements) of array A

    A more detailed discussion follows....

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• The shape of an array
  • The intrinsic function (See: click here)

    SHAPE(A)

    returns the shape of array A in the form of an array of integer.

    Each integer represents the number of rows in one dimension of the array

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    Examples:

    REAL, DIMENSION(5) :: A1 !! One-dim array (vector) REAL, DIMENSION(4,3) :: A2 !! Two-dim array (matrix) REAL, DIMENSION(3,2,2) :: A3 !! 3-dim array (tensor) REAL, DIMENSION(1:2, 2:3) :: A4 print *, "shape(A1) = ", shape(A1) --> 5 print *, "shape(A2) = ", shape(A2) --> 4 3 print *, "shape(A3) = ", shape(A3) --> 3 2 2 print *, "shape(A4) = ", shape(A4) --> 2 2

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  • Example Program: (Demo above code)                                                
    • Prog file: click here

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• The size of an array
  • The intrinsic function (See: click here)

    SIZE(A) // total number of elements in A

    returns the total size (number of elements) of array A in the form of an integer scalar.

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  • The intrinsic function

    SIZE(A, k) // number of elements in dimension k in A

    returns the size (number of elements) of the k^th dimension of the array A in the form of an integer scalar.

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    Examples:

    REAL, DIMENSION(5) :: A1 !! One-dim array (vector) REAL, DIMENSION(4,3) :: A2 !! Two-dim array (matrix) REAL, DIMENSION(3,2,2) :: A3 !! 3-dim array (tensor) REAL, DIMENSION(1:2, 2:3) :: A4 print *, "size(A1) = ", size(A1) --> 5 print *, "size(A2) = ", size(A2) --> 12 (= 4*3) print *, "size(A3) = ", size(A3) --> 12 (= 3*2*2) print *, "size(A4) = ", size(A4) --> 4 (2*2) print *, "size(A3,1) = ", size(A3,1) --> 3 print *, "size(A3,2) = ", size(A3,2) --> 2 print *, "size(A3,3) = ", size(A3,3) --> 2

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  • Example Program: (Demo above code)                                                
    • Prog file: click here

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• Attention: difference between an array and a scalar
  • Recall that:

    SHAPE(.) returns an array , and SIZE(.) returns a scalar

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  • An array is a serie (sequence) of values

  • An scalar is a solitairy value

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  • NOTE:

    An array of a single value is not the same as a scalar

    Example:

    REAL, DIMENSION(5) :: A1 SHAPE(A1) ---------> 5 .... it is an ARRAY of 1 element SIZE(A1) ---------> 5 .... it is a SCALAR

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  • You can see the difference between an array (of one element) and scalar in the following examples:

    Example 1:

    REAL, DIMENSION(5) :: A1 SHAPE ( SHAPE(A1) ) ----> 1 (it's an ARRAY again) SHAPE ( SIZE(A1) ) ----> undefined (SIZE(A1) is not an array)

    Example Program: (Demo above code)                                                

    • Prog file: click here

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    Example 2:

    REAL, DIMENSION(5) :: A1 REAL, DIMENSION(SHAPE(A1)):: B ---------> Illegal, SHAPE(A1) is not a sacaler REAL, DIMENSION(SIZE(A1)):: B ---------> Legal

    Example Program: (Demo above code)                                                

    • Prog file: click here