An introduction to arrays. Introduction In scientific and engineering computing, it is very common...
-
Upload
roy-bennett-dorsey -
Category
Documents
-
view
221 -
download
0
Transcript of An introduction to arrays. Introduction In scientific and engineering computing, it is very common...
An introduction to arrays
IntroductionIn scientific and engineering computing, it is very common to need to manipulate ordered sets of values, such as vectors and matrices.
There is a common requirement in many applications to repeat the same sequence of operations on successive sets of data.
In order to handle both of these requirements, F provides extensive facilities for grouping a set of items of the same type into an array which can be operated on
Either as an object in its own right
Or by reference to each of its individual elements.
The array concept
1 2 3 4 5 6
A
The array concept
A set with n (=6) object, named A In mathematical terms, we can call A, a
vector And we refer to its elements as
A1, A2, A3, …
The array concept
In F, we call such an ordered set of related variables an array
Individual items within an arrayarray elements
A(1), A(2), A(3), …, A(n)
Array ConceptIn all the programs we have used one name to refer to one location in the computer’s memory.
It is possible to refer a complete set of data obtained for example from repeating statements, etc.
To do this is to define a group called “array” with locations in the memory so that its all elements are identified by an index or subscript of integer type.
An array element is designated by the name of the array along with a parenthesized list of subscript expressions.
The array concept
Subscripts can be:x(10)
y(i+4)
z(3*i+max(i, j, k))
x(int(y(i)*z(j)+x(k)))
x(1)=x(2)+x(4)+1
print*,x(5)
The array concept
A
1
2
3
4
-1 0 1 2 3
A20
A31
Array declarations
type, dimension(subscript bounds) :: list_of_array_names
type, dimension(n:m) :: variable_name_list
real, dimension(0:4) :: gravity, pressure
integer, dimension(1:100) :: scores
logical, dimension(-1, 3) :: table
An integer showing the array subscript lower bound
An integer showing the array subcript upper bound
Type can be integer, real, complex, logical, character
Examples for Shape Arrays
real, dimension ( 0 : 49 ) : : z
! the array “z” has 50 elements
real, dimension ( 11 : 60 ) : : a, b, c
! a,b,c has 50 elements
real, dimension ( -20 : -1 ) : : x
! the array “x” has 20 elements
real, dimension ( -9 : 10 ) : : y
! the array “y” has 20 elements
Array declarations real, dimension ( 2,3,4,3,4,5,2) : : a
Number of permissible subscripts:rank
Number of elements in a particular dimension:extent
Total number of elements of an array:size
Shape of an array is determined by its rank and the extent of each dimension
1………….…7 Up to 7 dimensions
2*3*4*3*4*5*2=
Array constants and initial values
Since an array consists of a number of array elements, it is necessary to provide values for each of these elements by means of an “ array constructor “.
In its simplest form, an array constructor consists of a list of values enclosed between special delimiters :
the first of which consists of the 2 characters : ( /
the second of the 2 characters : / )
(/ value_1, value_2, ……………………., value_n /)
Examples
integer, dimension ( 10 ) : : arr
arr = (/ 3, 5, 7, 3, 27, 8, 12, 31, 4, 22 /)
arr ( 1 ) = 3
arr ( 5 ) = 27
! the value 27 is storen in the 5th location of the array “arr”
arr ( 7 ) = 12
arr ( 10 ) = 22
Array constructors
(/ value_1, value_2, … /) arr = (/ 123, 234, 567, 987 /)
Regular patterns are common:implied do(/ value_list, implied_do_control /)
arr = (/ (i, i = 1, 10) /) arr = (/ -1, (0, i = 1, 48), 1 /) arr = (/ (i*4, i = 1, 10) /)
4,8,12,16….
Initialization
You can declare and initialize an array at the same time:
integer,dimension(50)::my_array=(/(0,i=1,50)/)
Input and output
Array elements treated as scalar variables
Array name may appear: whole array Subarrays can be referred too
EXAMPLE :
integer, dimension ( 5 ) : : value
read *, value
read *, value(3)
real, dimension(5) :: p, qinteger, dimension(4) :: rprint *, p, q(3), rread *, p(3), r(1), qprint *, p, q (3), q (4), rprint *, q (2)
! displays the value in the 2nd location of the array “q”
print *, p! displays all the values storen in the array “p”
Examples
Using arrays and array elements... The use of array variables within a loop , therefore, greatly increases the power and flexibility of a program. F enables an array to be treated as a single object in its own right, in much the same way as a scalar object. Assignment of an array constant to an array variable will be performed as is seen below : array_name = (/ list_of_values /) array_name = (/ value_1, value_2, ….., value_n /) An array element can be used anywhere that a scalar variable can be useda(2) = t(5) - t(3)*q(2) a(i) = t(j) - f(k)
Using arrays and array elements...
An array can be treated as a single object– Two arrays are conformable if they have
the same shape– A scalar, including a constant, is
conformable with any array– All intrinsic operations are defined between
two conformable objects
Using arrays and array elements...
.real, dimension(20) :: a, b, c..a = b*c
do i = 1, 20 a(i) = b(i)*c(i)end do
Arrays having the same number of elements may be applied to arrays and simple expressions. In this case, operation applied to an array are carried out element wise.
integer, dimension ( 4 ) : : a, b
integer, dimension ( 0 : 3 ) : : c
integer, dimension ( 6 : 9 ) : : d
a = (/ 1, 2, 3, 4 /)
b = (/ 5, 6, 7, 8 /)
c = (/ -1, 3, -5, 7 /)
c(0) c(1) c(2) c(3)
a = a + b ! will result a = (/ 6, 8, 10, 12 /)
d = 2 * abs ( c ) + 1 ! will result d = (/ 3, 7, 11, 15 /)
d(6) d(7) d(8) d(9)
Example
Intrinsic procedures with arrays
Elemental intrinsic procedures with arrays
array_1 = sin(array_2)
arr_max = max(100.0, a, b, c, d, e)
Some special intrinsic functions:maxval(arr)
maxloc(arr)
minval(arr)
minloc(arr)
size(arr)
sum(arr)
Sub-arrays
Array sections can be extracted from a parent array in a rectangular grid usinf subscript triplet notation or using vector subscript notation
Subscript triplet:subscript_1 : subscript_2 : stride
Similar to the do – loops, a subscript triplet defines an ordered set of subscripts
beginning with subscript_1, ending with subscript_2 and
considering a seperation of stride between the consecutive subscripts. The value of stride must not be “zero”.
Sub-arrays
Subscript triplet:subscript_1 : subscript_2 : stride
Simpler forms:subscript_1 : subscript_2
subscript_1 :
subscript_1 : : stride
: subscript_2
: subscript_2 : stride
: : stride
:
Examplereal, dimension ( 10 ) : : arr
arr ( 1 : 10 ) ! rank-one array containing all the elements of arr.
arr ( : ) ! rank-one array containing all the elements of arr.
arr ( 3 : 5 ) ! rank-one array containing the elements arr (3), arr(4), arr(5).
arr ( : 9 ! rank-one array containing the elements arr (1), arr(2),…., arr(9).
arr ( : : 4 ) ! rank-one array containing the elements arr (1), arr(5),arr(9).
Exampleinteger, dimension ( 10 ) : : a
integer, dimension ( 5 ) : : b, i
integer : : j
a = (/ 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 /)
i = (/ 6, 5, 3, 9, 1 /)
b = a ( i ) ! will result b = ( 66, 55, 33, 99, 11 /)
a ( 2 : 10 : 2 ) ! will result a = ( 22, 44, 66, 88, 110 /)
a ( 1 : 10 : 2 ) = (/ j ** 2, ( j = 1, 5 ) /)
! will result a = ( 1, 4, 9, 16, 25 /)
a(1) a(3) a(5) a(7) a(9)
Type of printing sub-arrayswork = ( / 3, 7, 2 /)print *, work (1), work (2), work (3)! orprint *, work ( 1 : 3 )! orprint *, work ( : : 1 )! orinteger : : ido i = 1, 3, 1print *, work (i)end do! or another exampleprint *, sum ( work (1: 3) )! or another exampleprint *, sum ( work (1: 3 : 2) )
Type of INPUT of sub-arraysinteger, dimension ( 10 ) : : a
integer, dimension ( 3 ) : : b .
b = a ( 4 : 6 ) ! b (1 ) = a (4)
! b (2 ) = a (5)
! b (3 ) = a (6)
a ( 1 : 3 ) = 0 ! a(1) = a(2) = a(3) = 0
a ( 1 : : 2 ) = 1 ! a(1) = a(3) =…….= a(9) = 1
a ( 1 : : 2 ) = a ( 2 : : 2 ) + 1
» ! a(1) = a(2) +1
! a(3) = a(4) +1
! a(5) = a(6) +1
! etc.
PROBLEM : Write a function that takes 2 real arrays as its arguments returns an array in which each element is the maximum of the 2 corresponding elements in the input array
function max_array ( array_1, array_2 ) result (maximum_array)
! this function returns the maximum of 2 arrays on an element-by- element basis
! dummy arguments
real, dimension ( : ) , intent (in) : : array_1, array_2
! result variable
real, dimension ( size (array_1) ) : : maximum_array
! use the intrinsic function “max” to compare elements
maximum_array = max ( array_1, array_2)
! or use a do-loop instead of the intrinsic function max to compare elements
! do i = 1, size (array_2)
! maximum_array ( i ) = max ( array_1 ( i ), array_2 ( i ) )
! end do
end function max_array
program normal_probabilityinteger, parameter :: ndim = 100real, parameter :: pi = 3.1415927, two_pi = 2.0*pireal, dimension(ndim) :: phi_x, xreal :: del_x integer :: i, n , stepstep = 5! use do constructi = 1x(i) = -3.0del_x = 0.2
do if (x(i) > 3.0 + del_x) thenexitend ifphi_x(i) = exp(-x(i)**2/2.0)/sqrt(two_pi)i = i + 1x(i) = x(i-1) + del_xend do n = i-1do i = 1 , nwrite(unit=*,fmt="(1x,i3,2x,f8.5,2x,f8.5)") i,x(i),phi_x(i)end dodo i = 1 , n , stepprint "(5f8.5)", phi_x(i:i+step-1)end doend program normal_probability
program vector_manipulationUse matris1real, dimension(3) :: a, b, creal :: dot_proa = (/1., -1., 0./)b =(/2., 3., 5./)dot_pro = dots_product(a,b)call vector_product(a,b,c)print *, "the dot product of two vectors is:",dot_proprint *, "the vector product of two vectors is:",cend program vector_manipulation
module matris1Public::dots_product, vector_productcontains
function dots_product(a,b) result(result)real, dimension(3),intent(in):: a, b
result = a(1)*b(1) + a(2)*b(2) + a(3)*b(3)end function dots_productsubroutine vector_product(a,b,c)real, dimension(3),intent(in):: a, breal, dimension(3),intent(out) :: c
c(1) = a(2)*b(3) - a(3)*b(2) c(2) = a(3)*b(1) - a(1)*b(3) c(3) = a(1)*b(2) - a(2)*b(1)
end subroutine vector_product
!Write a program to order from min to the max value of a vector.program orderingreal,dimension(10)::ainteger::i,jreal::tempa=(/6.3,2.4,7.6,8.0,2.4,10.5,12.2,13.1,3.1,1.2/)minval1=minval(a)do i=1,9 do j=i+1,10 if (a(j)<a(i))then temp=a(j) a(j)=a(i) a(i)=temp endif enddoenddoprint*,a end program ordering
Arrays and procedures
Example
main program unit: real, dimension ( b : 40 ) : : a
subprogram: real, dimension ( d : ) : : x
x ( d ) ----------------------a ( b )
x ( d + 1 ) ----------------------a ( b + 1 )
x ( d + 2 ) ----------------------a ( b + 2 )
x ( d + 3 ) ----------------------a ( b + 3 )
.
.
Examplemain program unit:
real, dimension ( 10 : 40 ) : : a, b
.
call array_example_l (a,b)
subroutine array_example_1 ( dummy_array_1, dummy_array_2)
real, intent (inout), dimension : : dummy_array_1, dummy_array_2
.
.
subprogram:
Exampleinteger , dimension ( 4 ) : : section = (/ 5, 1, 2, 3 /)
real , dimension ( 9 ) : : a
call array_example_3 ( a ( 4 : 8 : 2 ), a ( section ) )
dummy_array_1 = (/ a (4), a (6), a (8) /)
dummy_array_2 = (/ a (5), a (1), a (2), a (3) /)
dummy_argument_2 (4) dummy_argument_2 (3)
dummy_argument_2 (2)
dummy_argument_2 (1)
ExamplePROBLEM : Write a subroutine that will sort a set of names into alphabetic order.
İnitial order 7 1 8 4 6 3 5 2
After 1st exc. 1 7 8 4 6 3 5 2
After 2nd exc. 1 2 8 4 6 3 5 7
After 3rd exc. 1 2 3 4 6 8 5 7
After 4th exc. 1 2 3 4 6 8 5 7
After 5th exc. 1 2 3 4 5 8 6 7
After 6th exc. 1 2 3 4 5 6 8 7
After 7th exc. 1 2 3 4 5 6 7 8
Array-valued functionsAs is well known, arrays can be passed to procedures as arguments and a subroutine can return information by means of an array.
It is convenient for a function to return its result in the form of an array of values rather than as a single scalar value ------------array-valued function, as can be seen below :
function name ( ……………………..) result (arr)
real, dimension ( dim ) : : arr
.
.
end function name
Array-valued functions
A function can return an array Such a function is called an
array-valued function
function name(…..) result(arr)real, dimension(dim) :: arr...
end function nameExplicit-shape
ExampleConsider a trivial subroutine that simply adds 2 arrays together, returning the result through a third dummy argument array.
subroutine trivial_fun ( x, y ) result (sumxy)
real, dimension ( : ) , intent (in) : : x, y
real, dimension ( size (x) ) : : sumxy
end subroutine trivial_fun
Matrices and 2-d arrays
In mathematics, a matrix is a two-dimensional rectangular array of elements (that obeys to certain rules!)
[A1,1 A1,2 A1,3 A1,4
A2,1 A2,2 A2,3 A2,4
A3,1 A3,2 A3,3 A3,4
A4,1 A4,2 A4,3 A2,1]A=
Row number Column number
F extends the concept of a one-dimensional array in a natural manner, by means of the “dimension” attribute.
Thus, to define a two-dimensional array that could hold the elements of the matrix A, we would write :
real, dimension ( 3, 4 ) : : A
numbers of rows numbers of columns
Matrices and 2-d arrays
Similarly, a vector is (given a basis) a one-dimensional array of elements (that obeys to certain rules!)
[A1 A 2 A 3 A 4 ]
[A1
A2
A3
A4]
2-d arrays
dimension attribute:real, dimension(3, 4) :: alogical, dimension(10,4) :: b, c, d
You can refer to a particular element of a 2-d array by specifing the row and column numbers:
a(2,3)b(9,3)
Intrinsic functions
matmul(array, array)dot_product(array, array)transpose(array)maxval(array[,dim,mask])maxloc(array[,dim]) minval(array[,dim,mask]) minloc(array[,dim]) product(array[,dim,mask])sum(array[,dim,mask])
program vectors_and_matrices integer, dimension(2,3) :: matrix_a integer, dimension(3,2) :: matrix_b integer, dimension(2,2) :: matrix_ab integer, dimension(2) :: vector_c integer, dimension(3) :: vector_bc! Set initial value for vector_c vector_c = (/1, 2/)! Set initial value for matrix_a matrix_a(1,1) = 1 ! matrix_a is the matrix: matrix_a(1,2) = 2 matrix_a(1,3) = 3 ! [1 2 3] matrix_a(2,1) = 2 ! [2 3 4] matrix_a(2,2) = 3 matrix_a(2,3) = 4! Set matrix_b as the transpose of matrix_a matrix_b = transpose(matrix_a)! Calculate matrix products matrix_ab = matmul(matrix_a, matrix_b) vector_bc = matmul(matrix_b, vector_c) do i=1,2 print*,matrix_ab(i,1:2) end doend program vectors_and_matrices
Some basic array concepts...
Ranknumber of its dimensions
Examples:real, dimension(8) :: ainteger, dimension(3, 100, 5) :: blogical, dimension(2,5,3,100,5) :: c
1
35
Some basic array concepts...
Extentnumber of elements in each dimension
Examples:real, dimension(8) :: areal, dimension(-4:3) :: b
integer, dimension(3,-50:50,40:44) :: cinteger, dimension(0:2, 101, -1:3) :: d
Some basic array concepts...
Sizetotal number of elements
Examples:real, dimension(8) :: a
integer, dimension(3, 100, 5) :: b
logical, dimension(2,5,4,10,5) :: c
8
1500
2000
Some basic array concepts... Shape
– Rank– Extent in each dimension
Shape of an array is representable as a rank-one integer array whose elements are the extents
Examplelogical, dimension(2,-3:3,4,0:9,5) :: c
shape_c = (/ 2,7,4,10,5 /)
Some basic array concepts...
Array element orderfirst index of the element specification is varying most rapidly, …
Exampleinteger, dimension(3,4) :: a
a(1,1), a(2,1), a(3,1) a(1,2), a(2,2), a(3,2) ...
Array constructors for rank-n arrays
An array constructor always creates a rank-one array of values
Solution? reshape functionreshape((/ (i, i=1,6) /), (/ 2, 3 /))
1 2 3
4 5 6
Example : The implied-do loop given below provides the following matrix
integer : : i, j
real, save, dimension ( 2,2 ) : : a = &
reshape ( ( / (10*i + j, i = 1,2 ), j = 1, 2) / ), (/ 2, 2 /) )
1 12
21 22
Matrix a is given as follows. Write a program calculate Matrix b as transpose of matrix a and matrix n as multiplication of matrices a and b.
2 4
1 5
a =
program mat_cal
integer,dimension(2,2)::a,b,n
integer::i
a(1,1)=2
a(1,2)=4
a(2,1)=1
a(2,2)=5
b=transpose (a)
n=matmul(a,b)
print*,"Martix_a=",a,"Matrix_b=",b,"Matrix_n=",n
do i=1,2
print "(3(2i3,a))",a(i,1:2)," ",b(i,1:2)," ",n(i,1:2)," "
end do
endprogram mat_cal
Matrix a and b are given as follows. Write a program calculate and print Matrix a, b, c and d. (Write same program using reshape function also).
-1 2 2
4 3 1
1 1 1
1 1 1
1 1 1
1 1 1
a=
b=
e=transpose(a)
c=matmul(e,b)
d=a+c
program mat1
integer,dimension(3,3)::a,b,c,d,e
integer::i,j
a(1,1)=-1
a(1,2)=2
a(1,3)=2
a(2,1)=4
a(2,2)=3
a(2,3)=1
a(1,3)=2
a(3,1)=1
a(3,2)=1
a(3,3)=1
do i=1,3
do j=1,3
b(i,j)=1
e=transpose(a)
c=matmul(e,b)
d=a+c
end do
end do
print*,"a=",a," b=",b," c=",c," d=",d
end program mat1
print*," "
do i=1,3
print "(4(3i3,a))",a(i,1:3)," ",b(i,1:3)," ",c(i,1:3)," ",d(i,1:3)
end do
program mat2integer,dimension(3,3)::a,b,c,d,einteger::i,ja=reshape((/-1,4,1,2,3,1,2,1,1/),(/3,3/))do i=1,3do j=1,3b(i,j)=1e=transpose(a)c=matmul(e,b)d=a+cend doend doprint*," "do i=1,3print "(4(3i3,a))",a(i,1:3)," ",b(i,1:3)," ",c(i,1:3)," ",d(i,1:3)end doend program mat2
Write down a program that calculates each rows and columns and print the elements of given matrix using do loop.
program mat3integer,dimension(5,5)::ainteger::i,jdo i=1,5do j=1,5if (i==j) thena(i,j)=i**2elsea(i,j)=(i+j)-1end ifend doend dodo i=1,5print"(3(5i4))",a(i,1:5)end doend program mat3
Array I/O
As a list of individual array elements:a(1,1), a(4,3), …
As the complete array:real, dimension(2,4) :: aprint *, a
a(1,1), a(2,1), a(1,2), a(2,2), ...
As an array section
Could be handled in three different ways
The four classes of arrays
Explicit-shape arrays Assumed-shape arrays Allocatable (deferred-shape) arrays Automatic arrays
Explicit-shape arrays
Arrays whose index bounds for each dimension are specified when the array is declared in a type declaration statement
real, dimension(35, 0:26, 3) :: a
Assumed-shape arrays
Only assumed shape arrays can be procedure dummy arguments
Extents of such arrays is defined implicitly when an actual array is associated with an assumed-shape dummy argument
subroutine example(a, b) integer, dimension(:,:), intent(in) :: a integer, dimension(:), intent(out) :: b
Automatic arrays
A special type of explicit-shape array It can only be declared in a procedure It is not a dummy argument At least one index bound is not constant The space for the elements of an automatic
array is created dynamically when the procedure is entered and is removed upon exit from the procedure
Automatic arrays
subroutine abc(x)
! Dummy arguments
real, dimension(:), intent(inout):: x
! Assumed shape
! Local variables
real, dimension(size(x)) :: e !Automatic
real, dimension(size(x), size(x)) :: f !Automatic
real, dimension(10) :: !Explicit shape
.
.
end subroutine abc
Allocatable arrays
Allocation and deallocation of space for their elements us completely under user control
Flexible: can be defined in main programs, procedures and modules
Allocatable arrays
Steps:– Array is specified in a type declaration
statement– Space is diynamically allocated for its
elements in a separate allocation statement
– The arrays is used (like any other array!)– Space for the elements is deallocated by a
deallocation statement
Allocatable arrays
Declaration
type, allocatable, dimension(:,:,:) :: allocatable array
real, allocatable, dimension(:,:,:) :: my_array
type(person), allocatable, dimension(:) :: personel_list
integer, allocatable, dimension(:,:) :: big_table
Allocatable arrays
Allocation
allocate(list_of_array_specs, [stat=status_variable])
allocate(my_array(1:10,-2:3,5:15), personel_list(1:10))
allocate(big_table(0:50000,1:100000), stat=check)
if (check /= 0) then
print *, "No space for big_table"
stop
end if
Allocatable arrays
Deallocation
deallocate(list_of_currently_allocated_arrays,
[stat=status variable])
deallocate(my_array, personel_list, big_table)
Whole-array operations
Whole array operations can be used with conformable arrays of any rank– Two arrays are conformable if they have
the same shape– A scalar, including a constant, is
conformable with any array– All intrinsic operations are defined between
conformable arrays
Whole-array operations
Relational operators follow the same rules:
Example:
A=[1 23 4] B=[−1 −5
6 2 ]A>B
[. true . . true .. false . . true .]
Masked array assignment
where (mask_expression)array_assignment_statements
end where where (my_array > 0)
my_array = exp(my_array)end where
Masked array assignment
where (mask_expression)array_assignment_statements
elsewherearray_assignment_statements
end where where (my_array > 0)
my_array = exp(my_array)elsewhere
my_array = 0.0end where
Sub-arrays
Array sections can be extracted from a parent array of any rank
Using subscript triplet notation:first_index, last_index, stride
Resulting array section is itself an array
Sub-arrays
integer, dimension(-2:2, 0:4) :: tablo
2 3 4 5 64 5 6 7 81 2 3 4 5 tablo(-1:2, 1:3)6 7 8 9 64 4 6 6 8
Rank-2
integer, dimension(-2:2, 0:4) :: tablo
2 3 4 5 64 5 6 7 81 2 3 4 5 tablo(2, 1:3)6 7 8 9 64 4 6 6 8
Sub-arrays
Rank-1
The pressure inside a can of carbonated drink is given by the expression0.0015xT2+0.0042xT+1.352 atmwhere ToC is the temperature of the drink. When the pressure exceeds 3.2atm, the can will explode. Write a program to print the pressure inside the can for the temperature rising in one degree steps from 25oC until the can explodes.
Write a program which produces a table of sin x and cos x for angles x from 0° to 90° in steps of 15°.
program home10integer,dimension(5,5)::A,B,C,Dinteger::i,jA=reshape((/1,2,3,4,5,2,4,4,5,6,3,4,9,6,7,4,5,6,16,8,5,6,7,8,25/),(/5,5/))do i=1,5do j=1,5if (i==j)thenB(i,j)=7else B(i,j)=0end ifend doend do
C=A+BD=5*A-3*Bprint*," Matrix A"," ","Matrix B"do i=1,5print"(2(5i4,a))",A(i,1:5)," ",B(i,1:5)end doprint*," "print*," Matrix C"," ","Matrix D"do i=1,5print"(2(5i4,a))",C(i,1:5)," ",D(i,1:5)end doend program home10
Write down a program that writes the results of the multiplication table as following.
program multi_square!-------------------------------------------------------------!This program shows the multipication square.!-------------------------------------------------------------!variable declerationsinteger::i,jinteger,dimension(12)::xprint*," 1 2 3 4 5 6 7 8 9 10 11 12"print*," x"!make the calculationsdo i=1,12do j=1,12x(j)=i*jend do !print the outputsprint "(i6,12i4)",i,x(1:12)end doend program multi_square
program mat2integer,dimension(3,3)::a,b,c,d,einteger::i,ja=reshape((/-1,4,1,2,3,1,2,1,1/),(/3,3/))do i=1,3do j=1,3b(i,j)=1e=transpose(a)c=matmul(e,b)d=a+cend doend doprint*," "do i=1,3print "(4(3i3,a))",a(i,1:3)," ",b(i,1:3)," ",c(i,1:3)," ",d(i,1:3)end doend program mat2
write a program finds the numbers which have integer square root of between 1 and 1000. Example:n=1 square=1n=4 square=2n=9 square=3