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A = A + B
in lieu of:
DO J=1,M
DO I=1,NA(I,J) = A(I,J) + B(I,J)
END DOEND DO
Naturally, when you want to combine two arrays in an operation, their shapes have to be compatible. Adding a seven-element vector to an eight-element vector doesn't make sense. Neither would multiplying a 2×4 array by a 3×4 array. When the two arrays have compatible shapes, relative to the operation being performed upon them, we say they are in shape conformance , as in the following code:
DOUBLE PRECISION A(8), B(8)
...A = A + B
Scalars are always considered to be in shape conformance with arrays (and other scalars). In a binary operation with an array, a scalar is treated as an array of the same size with a single element duplicated throughout.
Still, we are limited. When you reference a particular array, A, for example, you reference the whole thing, from the first element to the last. You can imagine cases where you might be interested in specifying a subset of an array. This could be either a group of consecutive elements or something like "every eighth element" (i.e., a non-unit stride through the array). Parts of arrays, possibly noncontiguous, are called array sections .
FORTRAN 90 array sections can be specified by replacing traditional subscripts with triplets of the form
a:b:c , meaning "elements
a through
b , taken with an increment of
c ." You can omit parts of the triplet, provided the meaning remains clear. For example,
a:b means "elements a through
b ;"
a: means "elements from
a to the upper bound with an increment of 1." Remember that a triplet replaces a single subscript, so an
n -dimension array can have
n triplets.
You can use triplets in expressions, again making sure that the parts of the expression are in conformance. Consider these statements:
REAL X(10,10), Y(100)
...X(10,1:10) = Y(91:100)
X(10,:) = Y(91:100)
The first statement above assigns the last 10 elements of
Y to the 10th row of
X . The second statement expresses the same thing slightly differently. The lone " : " tells the compiler that the whole range (1 through 10) is implied.
FORTRAN 90 extends the functionality of FORTRAN 77 intrinsics, and adds many new ones as well, including some intrinsic subroutines. Most can be
array-valued : they can return arrays sections or scalars, depending on how they are invoked. For example, here's a new, array-valued use of the
SIN intrinsic:
REAL A(100,10,2)
...A = SIN(A)
Each element of array A is replaced with its sine. FORTRAN 90 intrinsics work with array sections too, as long as the variable receiving the result is in shape conformance with the one passed:
REAL A(100,10,2)
REAL B(10,10,100)...
B(:,:,1) = COS(A(1:100:10,:,1))
Other intrinsics, such as
SQRT ,
LOG , etc., have been extended as well. Among the new intrinsics are:
MAXVAL ,
MINVAL , and
SUM . For higher-order arrays (anything more than a vector) these functions can perform a reduction along a particular dimension. Additionally, there is a
DOT_PRODUCT function for the vectors.MATMUL and
TRANSPOSE can manipulate whole matrices.RESHAPE allows you to create a new array from elements of an old one with a different shape.
SPREAD replicates an array along a new dimension.
MERGE copies portions of one array into another under control of a mask.
CSHIFT allows an array to be shifted in one or more dimensions.SHAPE ,
SIZE ,
LBOUND , and
UBOUND let you ask questions about how an array is constructed.ANY and
ALL , are for testing many array elements in parallel.
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