In a scan of a vector, each element of the result is a function of the
elements of the vector that precede it (for a prefix scan) or that follow it
(for a suffix scan). These functions provide scan operations on arrays
and subarrays.
The functions
all have the form
XXX_PREFIX(ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE)
XXX_SUFFIX(ARRAY, DIM, MASK, SEGMENT, EXCLUSIVE)
The allowed values of XXX are
ALL,
ANY,
COPY,
COUNT,
IALL,
IANY,
IPARITY,
MAXVAL,
MINVAL,
PARITY,
PRODUCT, and
SUM.
When comments below apply to both prefix and suffix forms of the
routines, we will refer to them as YYYFIX functions.
The arguments DIM, MASK, SEGMENT, and EXCLUSIVE are optional. The COPY_YYYFIX functions do not
have MASK or EXCLUSIVE arguments. The ALL_YYYFIX,
ANY_YYYFIX, COUNT_YYYFIX,
and PARITY_YYYFIX functions do not have MASK arguments. Their ARRAY argument must be of type logical;
it is denoted MASK in their specifications in Section .
The arguments MASK and SEGMENT must be of type logical.
SEGMENT must have the same shape as ARRAY.
MASK must be conformable with ARRAY.
EXCLUSIVE is a logical scalar.
DIM is a scalar integer between one and the rank of ARRAY.
Result Value.
The result has the same shape as ARRAY, and, with the exception of
COUNT_YYYFIX, the same type and kind type parameter as ARRAY.
(The result of COUNT_YYYFIX is default integer.)
In every case, every element of the result is determined by the values
of certain selected elements of ARRAY in a way that is specific
to the particular function and is described in its specification. The
optional arguments affect the selection of elements of ARRAY for
each element of the result; the selected elements of ARRAY are
said to contribute to the result element. This section describes
fully which elements of ARRAY contribute to a given element of the
result.
If no elements of ARRAY are selected
for a given element of the result, that result element is set to a default value
that is specific to the particular function and is described in its specification.
For any given element of the result, let be the
corresponding element of ARRAY. Every element of ARRAY contributes
to unless disqualified by one of the following rules.
These general rules lead to the following important cases:
(i): If ARRAY has rank one, element of the result of
XXX_PREFIX(ARRAY) is determined by
the first elements of ARRAY;
element of the result of
XXX_SUFFIX(ARRAY) is determined by
the last elements of ARRAY.
(ii): If ARRAY has rank greater than one, then each
element of the result of XXX_PREFIX(ARRAY) has a
value determined by the corresponding element
of the ARRAY and all elements of ARRAY that
precede in array element order. For XXX_SUFFIX, is determined by the elements of
ARRAY that correspond to or follow in array
element order.
(iii): Each element of the result of XXX_PREFIX(ARRAY,MASK=MASK)
is determined by selected elements of ARRAY, namely the
corresponding element of the ARRAY and all elements of
ARRAY that precede in array element order, but an
element of ARRAY may contribute to the result only if the
corresponding
element of MASK is true. If this restriction results in
selecting no array elements to contribute to some element of the
result, then that element of the result is set to the default
value for the given function.
(iv): Each element of the result of XXX_PREFIX(ARRAY,DIM=DIM)
is determined by selected elements of ARRAY,
namely the corresponding element of the ARRAY and all elements of ARRAY that precede along dimension DIM;
for example, in SUM_PREFIX(A(1:N,1:N), DIM=2), result element
could be computed as SUM(A(,)).
More generally, in SUM_PREFIX(ARRAY, DIM), result element
could be computed
as SUM(ARRAY( )) . (Note the colon before i_DIM in that
last expression.)
(v): If ARRAY has rank one, then element of the result of
XXX_PREFIX(ARRAY, EXCLUSIVE=.TRUE.) is determined by the first
elements of ARRAY.
(vi): The options may be used in any combination.
(/T,T,T,F,T,F,F,F,T,F,F,T/)
-- - - -- - - - seven segments
(End of advice to users.)
(End of rationale.)
Examples.
The examples below illustrate all possible combinations of optional
arguments for SUM_PREFIX. The default value for SUM_YYYFIX is zero.
(i): SUM_PREFIX((/1,3,5,7/)) is ,1,4,9,16,, plus 1filll
-1;1,4,9,16,; plus 1filll
-1:1,4,9,16,: plus 1filll
-1.1,4,9,16,. plus 1filll
-11,4,9,16, plus 1filll-1.
(ii): If B is the array , 1, 2, 3 4, 5, 6 7, 8, 9 ,, plus 1filll
-1; 1, 2, 3 4, 5, 6 7, 8, 9 ,; plus 1filll
-1: 1, 2, 3 4, 5, 6 7, 8, 9 ,: plus 1filll
-1.plus 1filll
1, 2, 3 4, 5, 6 7, 8, 9 ,.-50 1, 2, 3 4, 5, 6 7, 8, 9 , plus 1filll-1,
SUM_PREFIX(B) is the array , 1, 14, 30 5, 19, 36 12, 27, 45 ,, plus 1filll
-1; 1, 14, 30 5, 19, 36 12, 27, 45 ,; plus 1filll
-1: 1, 14, 30 5, 19, 36 12, 27, 45 ,: plus 1filll
-1.plus 1filll
1, 14, 30 5, 19, 36 12, 27, 45 ,.-50 1, 14, 30 5, 19, 36 12, 27, 45 , plus 1filll-1.
(iii): If A is the array ,3, 5, -2, -1, 7, 4, 8,, plus 1filll
-1;3, 5, -2, -1, 7, 4, 8,; plus 1filll
-1:3, 5, -2, -1, 7, 4, 8,: plus 1filll
-1.3, 5, -2, -1, 7, 4, 8,. plus 1filll
-13, 5, -2, -1, 7, 4, 8, plus 1filll-1, then
SUM_PREFIX(A, MASK = A .LT. 6) is ,3, 8, 6, 5, 5, 9, 9,, plus 1filll
-1;3, 8, 6, 5, 5, 9, 9,; plus 1filll
-1:3, 8, 6, 5, 5, 9, 9,: plus 1filll
-1.3, 8, 6, 5, 5, 9, 9,. plus 1filll
-13, 8, 6, 5, 5, 9, 9, plus 1filll-1.
(iv): If B is the array , 1, 2, 3 4, 5, 6 7, 8, 9 ,, plus 1filll
-1; 1, 2, 3 4, 5, 6 7, 8, 9 ,; plus 1filll
-1: 1, 2, 3 4, 5, 6 7, 8, 9 ,: plus 1filll
-1.plus 1filll
1, 2, 3 4, 5, 6 7, 8, 9 ,.-50 1, 2, 3 4, 5, 6 7, 8, 9 , plus 1filll-1,
then SUM_PREFIX(B, DIM=1) is the array
, 1, 2, 3 5, 7, 9 12, 15, 18 ,, plus 1filll
-1; 1, 2, 3 5, 7, 9 12, 15, 18 ,; plus 1filll
-1: 1, 2, 3 5, 7, 9 12, 15, 18 ,: plus 1filll
-1.plus 1filll
1, 2, 3 5, 7, 9 12, 15, 18 ,.-50 1, 2, 3 5, 7, 9 12, 15, 18 , plus 1filll-1
and SUM_PREFIX(B, DIM=2) is the array
, 1, 3, 6 4, 9, 15 7, 15, 24 ,, plus 1filll
-1; 1, 3, 6 4, 9, 15 7, 15, 24 ,; plus 1filll
-1: 1, 3, 6 4, 9, 15 7, 15, 24 ,: plus 1filll
-1.plus 1filll
1, 3, 6 4, 9, 15 7, 15, 24 ,.-50 1, 3, 6 4, 9, 15 7, 15, 24 , plus 1filll-1.
(v): SUM_PREFIX((/1,3,5,7/), EXCLUSIVE=.TRUE.)
is ,0,1,4,9,, plus 1filll
-1;0,1,4,9,; plus 1filll
-1:0,1,4,9,: plus 1filll
-1.0,1,4,9,. plus 1filll
-10,1,4,9, plus 1filll-1.
(vi): If B is the array , 1, 2, 3, 4, 5 6, 7, 8, 9, 10 11, 12, 13, 14, 15 ,, plus 1filll
-1; 1, 2, 3, 4, 5 6, 7, 8, 9, 10 11, 12, 13, 14, 15 ,; plus 1filll
-1: 1, 2, 3, 4, 5 6, 7, 8, 9, 10 11, 12, 13, 14, 15 ,: plus 1filll
-1.plus 1filll
1, 2, 3, 4, 5 6, 7, 8, 9, 10 11, 12, 13, 14, 15 ,.-50 1, 2, 3, 4, 5 6, 7, 8, 9, 10 11, 12, 13, 14, 15 , plus 1filll-1,
M is the array , T, T, T, T, T F, F, T, T, T T, F, T, F, F ,, plus 1filll
-1; T, T, T, T, T F, F, T, T, T T, F, T, F, F ,; plus 1filll
-1: T, T, T, T, T F, F, T, T, T T, F, T, F, F ,: plus 1filll
-1.plus 1filll
T, T, T, T, T F, F, T, T, T T, F, T, F, F ,.-50 T, T, T, T, T F, F, T, T, T T, F, T, F, F , plus 1filll-1,
and S is the array , T, T, F, F, F F, T, T, F, F T, T, T, T, T ,, plus 1filll
-1; T, T, F, F, F F, T, T, F, F T, T, T, T, T ,; plus 1filll
-1: T, T, F, F, F F, T, T, F, F T, T, T, T, T ,: plus 1filll
-1.plus 1filll
T, T, F, F, F F, T, T, F, F T, T, T, T, T ,.-50 T, T, F, F, F F, T, T, F, F T, T, T, T, T , plus 1filll-1,
then:
SUM_PREFIX(B, DIM=2, MASK=M, SEGMENT=S, EXCLUSIVE=.FALSE.) is
, 1, 3, 3, 7, 12 0, 0, 8, 9, 19 11, 11, 24, 24, 24 ,, plus 1filll
-1; 1, 3, 3, 7, 12 0, 0, 8, 9, 19 11, 11, 24, 24, 24 ,; plus 1filll
-1: 1, 3, 3, 7, 12 0, 0, 8, 9, 19 11, 11, 24, 24, 24 ,: plus 1filll
-1.plus 1filll
1, 3, 3, 7, 12 0, 0, 8, 9, 19 11, 11, 24, 24, 24 ,.-50 1, 3, 3, 7, 12 0, 0, 8, 9, 19 11, 11, 24, 24, 24 , plus 1filll-1.
SUM_PREFIX(B, DIM=2, MASK=M, EXCLUSIVE=.TRUE.) is
, 0, 1, 3, 6, 10 0, 0, 0, 8, 17 0, 11, 11, 24, 24 ,, plus 1filll
-1; 0, 1, 3, 6, 10 0, 0, 0, 8, 17 0, 11, 11, 24, 24 ,; plus 1filll
-1: 0, 1, 3, 6, 10 0, 0, 0, 8, 17 0, 11, 11, 24, 24 ,: plus 1filll
-1.plus 1filll
0, 1, 3, 6, 10 0, 0, 0, 8, 17 0, 11, 11, 24, 24 ,.-50 0, 1, 3, 6, 10 0, 0, 0, 8, 17 0, 11, 11, 24, 24 , plus 1filll-1.
SUM_PREFIX(B, DIM=2, MASK=M, EXCLUSIVE=.FALSE.) is
, 1, 3, 6, 10, 15 0, 0, 8, 17, 27 11, 11, 24, 24, 24 ,, plus 1filll
-1; 1, 3, 6, 10, 15 0, 0, 8, 17, 27 11, 11, 24, 24, 24 ,; plus 1filll
-1: 1, 3, 6, 10, 15 0, 0, 8, 17, 27 11, 11, 24, 24, 24 ,: plus 1filll
-1.plus 1filll
1, 3, 6, 10, 15 0, 0, 8, 17, 27 11, 11, 24, 24, 24 ,.-50 1, 3, 6, 10, 15 0, 0, 8, 17, 27 11, 11, 24, 24, 24 , plus 1filll-1.
SUM_PREFIX(B, DIM=2, SEGMENT=S, EXCLUSIVE=.TRUE.) is
, 0, 1, 0, 3, 7 0, 0, 7, 0, 9 0, 11, 23, 36, 50 ,, plus 1filll
-1; 0, 1, 0, 3, 7 0, 0, 7, 0, 9 0, 11, 23, 36, 50 ,; plus 1filll
-1: 0, 1, 0, 3, 7 0, 0, 7, 0, 9 0, 11, 23, 36, 50 ,: plus 1filll
-1.plus 1filll
0, 1, 0, 3, 7 0, 0, 7, 0, 9 0, 11, 23, 36, 50 ,.-50 0, 1, 0, 3, 7 0, 0, 7, 0, 9 0, 11, 23, 36, 50 , plus 1filll-1.
SUM_PREFIX(B, DIM=2, SEGMENT=S, EXCLUSIVE=.FALSE.) is
, 1, 3, 3, 7, 12 6, 7, 15, 9, 19 11, 23, 36, 50, 65 ,, plus 1filll
-1; 1, 3, 3, 7, 12 6, 7, 15, 9, 19 11, 23, 36, 50, 65 ,; plus 1filll
-1: 1, 3, 3, 7, 12 6, 7, 15, 9, 19 11, 23, 36, 50, 65 ,: plus 1filll
-1.plus 1filll
1, 3, 3, 7, 12 6, 7, 15, 9, 19 11, 23, 36, 50, 65 ,.-50 1, 3, 3, 7, 12 6, 7, 15, 9, 19 11, 23, 36, 50, 65 , plus 1filll-1.
SUM_PREFIX(B, DIM=2, EXCLUSIVE=.TRUE.) is
, 0, 1, 3, 6, 10 0, 6, 13, 21, 30 0, 11, 23, 36, 50 ,, plus 1filll
-1; 0, 1, 3, 6, 10 0, 6, 13, 21, 30 0, 11, 23, 36, 50 ,; plus 1filll
-1: 0, 1, 3, 6, 10 0, 6, 13, 21, 30 0, 11, 23, 36, 50 ,: plus 1filll
-1.plus 1filll
0, 1, 3, 6, 10 0, 6, 13, 21, 30 0, 11, 23, 36, 50 ,.-50 0, 1, 3, 6, 10 0, 6, 13, 21, 30 0, 11, 23, 36, 50 , plus 1filll-1.
SUM_PREFIX(B, DIM=2, EXCLUSIVE=.FALSE.) is
, 1, 3, 6, 10, 15 6, 13, 21, 30, 40 11, 23, 36, 50, 65 ,, plus 1filll
-1; 1, 3, 6, 10, 15 6, 13, 21, 30, 40 11, 23, 36, 50, 65 ,; plus 1filll
-1: 1, 3, 6, 10, 15 6, 13, 21, 30, 40 11, 23, 36, 50, 65 ,: plus 1filll
-1.plus 1filll
1, 3, 6, 10, 15 6, 13, 21, 30, 40 11, 23, 36, 50, 65 ,.-50 1, 3, 6, 10, 15 6, 13, 21, 30, 40 11, 23, 36, 50, 65 , plus 1filll-1.
SUM_PREFIX(B, MASK=M, SEGMENT=S, EXCLUSIVE=.TRUE.) is
, 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 13, 8, 0, 0 ,, plus 1filll
-1; 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 13, 8, 0, 0 ,; plus 1filll
-1: 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 13, 8, 0, 0 ,: plus 1filll
-1.plus 1filll
0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 13, 8, 0, 0 ,.-50 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 13, 8, 0, 0 , plus 1filll-1.
SUM_PREFIX(B, MASK=M, SEGMENT=S, EXCLUSIVE=.FALSE.) is
, 1, 13, 3, 4, 5 0, 13, 8, 13, 15 11, 13, 21, 0, 0 ,, plus 1filll
-1; 1, 13, 3, 4, 5 0, 13, 8, 13, 15 11, 13, 21, 0, 0 ,; plus 1filll
-1: 1, 13, 3, 4, 5 0, 13, 8, 13, 15 11, 13, 21, 0, 0 ,: plus 1filll
-1.plus 1filll
1, 13, 3, 4, 5 0, 13, 8, 13, 15 11, 13, 21, 0, 0 ,.-50 1, 13, 3, 4, 5 0, 13, 8, 13, 15 11, 13, 21, 0, 0 , plus 1filll-1.
SUM_PREFIX(B, MASK=M, EXCLUSIVE=.TRUE.) is
, 0, 12, 14, 38, 51 1, 14, 17, 42, 56 1, 14, 25, 51, 66 ,, plus 1filll
-1; 0, 12, 14, 38, 51 1, 14, 17, 42, 56 1, 14, 25, 51, 66 ,; plus 1filll
-1: 0, 12, 14, 38, 51 1, 14, 17, 42, 56 1, 14, 25, 51, 66 ,: plus 1filll
-1.plus 1filll
0, 12, 14, 38, 51 1, 14, 17, 42, 56 1, 14, 25, 51, 66 ,.-50 0, 12, 14, 38, 51 1, 14, 17, 42, 56 1, 14, 25, 51, 66 , plus 1filll-1.
SUM_PREFIX(B, MASK=M, EXCLUSIVE=.FALSE.) is
, 1, 14, 17, 42, 56 1, 14, 25, 51, 66 12, 14, 38, 51, 66 ,, plus 1filll
-1; 1, 14, 17, 42, 56 1, 14, 25, 51, 66 12, 14, 38, 51, 66 ,; plus 1filll
-1: 1, 14, 17, 42, 56 1, 14, 25, 51, 66 12, 14, 38, 51, 66 ,: plus 1filll
-1.plus 1filll
1, 14, 17, 42, 56 1, 14, 25, 51, 66 12, 14, 38, 51, 66 ,.-50 1, 14, 17, 42, 56 1, 14, 25, 51, 66 12, 14, 38, 51, 66 , plus 1filll-1.
SUM_PREFIX(B, SEGMENT=S, EXCLUSIVE=.TRUE.) is
, 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 20, 8, 0, 0 ,, plus 1filll
-1; 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 20, 8, 0, 0 ,; plus 1filll
-1: 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 20, 8, 0, 0 ,: plus 1filll
-1.plus 1filll
0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 20, 8, 0, 0 ,.-50 0, 11, 0, 0, 0 0, 13, 0, 4, 5 0, 20, 8, 0, 0 , plus 1filll-1.
SUM_PREFIX(B, SEGMENT=S, EXCLUSIVE=.FALSE.) is
, 1, 13, 3, 4, 5 6, 20, 8, 13, 15 11, 32, 21, 14, 15 ,, plus 1filll
-1; 1, 13, 3, 4, 5 6, 20, 8, 13, 15 11, 32, 21, 14, 15 ,; plus 1filll
-1: 1, 13, 3, 4, 5 6, 20, 8, 13, 15 11, 32, 21, 14, 15 ,: plus 1filll
-1.plus 1filll
1, 13, 3, 4, 5 6, 20, 8, 13, 15 11, 32, 21, 14, 15 ,.-50 1, 13, 3, 4, 5 6, 20, 8, 13, 15 11, 32, 21, 14, 15 , plus 1filll-1.
SUM_PREFIX(B, EXCLUSIVE=.TRUE.) is
, 0, 18, 39, 63, 90 1, 20, 42, 67, 95 7, 27, 50, 76, 105 ,, plus 1filll
-1; 0, 18, 39, 63, 90 1, 20, 42, 67, 95 7, 27, 50, 76, 105 ,; plus 1filll
-1: 0, 18, 39, 63, 90 1, 20, 42, 67, 95 7, 27, 50, 76, 105 ,: plus 1filll
-1.plus 1filll
0, 18, 39, 63, 90 1, 20, 42, 67, 95 7, 27, 50, 76, 105 ,.-50 0, 18, 39, 63, 90 1, 20, 42, 67, 95 7, 27, 50, 76, 105 , plus 1filll-1.
SUM_PREFIX(B, EXCLUSIVE=.FALSE.) is
, 1, 20, 42, 67, 95 7, 27, 50, 76, 105 18, 39, 63, 90, 120 ,, plus 1filll
-1; 1, 20, 42, 67, 95 7, 27, 50, 76, 105 18, 39, 63, 90, 120 ,; plus 1filll
-1: 1, 20, 42, 67, 95 7, 27, 50, 76, 105 18, 39, 63, 90, 120 ,: plus 1filll
-1.plus 1filll
1, 20, 42, 67, 95 7, 27, 50, 76, 105 18, 39, 63, 90, 120 ,.-50 1, 20, 42, 67, 95 7, 27, 50, 76, 105 18, 39, 63, 90, 120 , plus 1filll-1.
*
*
SUM_PREFIX(B, DIM=2, MASK=M, SEGMENT=S, EXCLUSIVE=.TRUE.) is
, 0, 1, 0, 3, 7 0, 0, 0, 0, 9 0, 11, 11, 24, 24 ,, plus 1filll
-1; 0, 1, 0, 3, 7 0, 0, 0, 0, 9 0, 11, 11, 24, 24 ,; plus 1filll
-1: 0, 1, 0, 3, 7 0, 0, 0, 0, 9 0, 11, 11, 24, 24 ,: plus 1filll
-1.plus 1filll
0, 1, 0, 3, 7 0, 0, 0, 0, 9 0, 11, 11, 24, 24 ,.-50 0, 1, 0, 3, 7 0, 0, 0, 0, 9 0, 11, 11, 24, 24 , plus 1filll-1.
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