I want to run m*n matrix to do QR decomposition in fortran
PROGRAM SUBDEM
INTEGER key, n, m, loopA
REAL resq
REAL A(3,2)
REAL B(3)
REAL X(2)
key = 0
n = 2
m = 3
resq = 0
CALL QR(m, n, A, B, X, resq)
END
The QR routine is:
subroutine QR(m, n, a, b, x, resq)
implicit double precision (a-h, o-z)
dimension a(m,n),b(m),x(n)
double precision sum, dot
resq=-2.0
if (m .lt. n) then
return
endif
resq=-1.0
! Loop ending on 1800 rotates a into upper triangular form.
do 1800 j=1, n
! Find constants for rotation and diagonal entry.
sq=0.0
do 1100 i=j, m
sq=a(i,j)**2 + sq
1100 continue
if (sq .eq. 0.0) then
return
endif
qv1=-sign(sqrt(sq), a(j,j))
u1=a(j,j) - qv1
a(j,j)=qv1
j1=j + 1
! Rotate remaining columns of sub-matrix.
do 1400 jj=j1, n
dot=u1*a(j,jj)
do 1200 i=j1, m
dot=a(i,jj)*a(i,j) + dot
1200 continue
const=dot/abs(qv1*u1)
do 1300 i=j1, m
a(i,jj)=a(i,jj) - const*a(i,j)
1300 continue
a(j,jj)=a(j,jj) - const*u1
1400 continue
! Rotate b vector.
dot=u1*b(j)
do 1600 i=j1, m
dot=b(i)*a(i,j) + dot
1600 continue
const=dot/abs(qv1*u1)
b(j)=b(j) - const*u1
do 1700 i=j1, m
b(i)=b(i) - const*a(i,j)
1700 continue
1800 continue
! Solve triangular system by back-substitution.
do 2200 ii=1, n
i=n-ii+1
sum=b(i)
do 2100 j=i+1, n
sum=sum - a(i,j)*x(j)
2100 continue
if (a(i,i).eq. 0.0) then
return
endif
x(i)=sum/a(i,i)
2200 continue
! Find residual in overdetermined case.
resq=0.0
do 2300 i=n+1, m
resq=b(i)**2 + resq
2300 continue
return
end subroutine
However I am getting:
Error 1 error #6633: The type of the actual argument differs from the
type of the dummy argument. [A] Error 2 error #6633: The type of
the actual argument differs from the type of the dummy argument.
[B] Error 3 error #6633: The type of the actual argument differs
from the type of the dummy argument. [X] Error 4 error #6633: The
type of the actual argument differs from the type of the dummy
argument. [RESQ]
What Am I doing wrong?
I will sum the comments of #george and #M.S.B.
The types and kinds of dummy arguments of procedures must match the actual arguments used by the calling code. The compiler can check this when having an explicit interface, when the procedure is in a module, for example, and some compilers can do that also for external procedures, which is your case.
Placing the subroutines in modules is the preferred way for making this check possible at all conditions and all compilers.
By using implicit double precision (a-h, o-z) you declare all variables with name beginning with a-h or o-z as being double precision. In your main program you are using real for calling the procedure. This is the error, the types have to match.
It is strongly discouraged to use any other form of the implicit other than implicit none, which is the form that should be present at the beginning of every compilation unit (program, module, external procedures).
Related
I am declaring a variable with inline declaration 50 * ( 2 / 5 ). The problem is that output result is 0 instead of expected 20.
DATA(exact_result) = 50 * ( 2 / 5 ) .
cl_demo_output=>display( exact_result ).
Can anyone suggest why the result is zero where as 50 * (2/5) = 20.
regards,
Umar Abdullah
The inline declaration assigns a data type depending on the type from the Right-Hand Side (RHS) expression. With an arithmetic expression, the compiler determines a data type based on the overall calculation type.
First, 2 and 5 are considered as type I (4 bytes integer), so the result is also of type I even if the operator is a division (integer division in that precise case).
Then, 50 is also considered as type I, and because it's used with another I-type data object (result of subexpression 2 / 5 which is of type I) the result is also of type I.
So, in your example, EXACT_RESULT is assigned the type I.
At run time, because both LHS and RHS data objects are of type I, then the calculation type is I too. Consequently, 2 / 5 equals 0.4 which is rounded to 0 because it's an integer division and the default ABAP rounding is "half up" (rounding of 0.4 gives 0, but 0.5 gives 1).
The workaround is to define explicitly the data type of EXACT_RESULT as having digits after the decimal point (DECFLOAT16, DECFLOAT34, P type with decimals, F and even C because then the calculation type is P !), because the type of the LHS will have a higher priority than the type of the RHS (I), so the calculation will be deduced from the type of the LHS variable.
DATA(exact_result) = CONV decfloat16( 50 * ( 2 / 5 ) ).
Be careful with this next solution : as I said, C leads to a calculation with type P and many decimals, so we could think this example is a good solution :
DATA(exact_result) = '50' * ( 2 / 5 ). " equals 20
But with inline declarations, a P calculation type leads to a data object of type P but with 0 digits after the decimal point, so the result is truncated with other numbers (8 instead of 50 here) :
DATA(exact_result) = '8' * ( 2 / 5 ). " rounded ! (3 instead of 3.2)
What is the time Complexity for below code:
1)
function(values,xlist,ylist):
sum =0
n=0
for r from 0 to xlist:
for c from 0 to ylist:
sum+= values[r][c]
n+1
return sum/n
2)
function PrintCharacters():
characters= {"a","b","c","d"}
foreach character in characters
print(character)
According to me the 1st code has O(xlist*ylist) complexity and 2nd code has O(n).
Is this right?
Big O notation to describe the asymptotic behavior of functions. Basically, it tells you how fast a function grows or declines
For example, when analyzing some algorithm, one might find that the time (or the number of steps) it takes to complete a problem of size n is given by
T(n) = 4 n^2 - 2 n + 2
If we ignore constants (which makes sense because those depend on the particular hardware the program is run on) and slower growing terms, we could say "T(n)" grows at the order of n^2 " and write:T(n) = O(n^2)
For the formal definition, suppose f(x) and g(x) are two functions defined on some subset of the real numbers. We write
f(x) = O(g(x))
(or f(x) = O(g(x)) for x -> infinity to be more precise) if and only if there exist constants N and C such that
|f(x)| <= C|g(x)| for all x>N
Intuitively, this means that f does not grow faster than g
If a is some real number, we write
f(x) = O(g(x)) for x->a
if and only if there exist constants d > 0 and C such that
|f(x)| <= C|g(x)| for all x with |x-a| < d
So for your case it would be
O(n) as |f(x)| > C|g(x)|
Reference from http://web.mit.edu/16.070/www/lecture/big_o.pdf
for r from 0 to xlist: // --> n time
for c from 0 to ylist: // n time
sum+= values[r][c]
n+1
}
function PrintCharacters():
characters= {"a","b","c","d"}
foreach character in characters --> # This loop will run as many time as there are characters suppose n characters than it will run time so O(n)
print(character)
Big O Notation gives an assumption when value is very big outer loop
will run n times and inner loop is running n times
Assume n -> 100 than total n^2 10000 run times
As title says, I don't understand why f^:proposition^:_ y is a while loop. I have actually used it a couple times, but I don't understand how it works. I get that ^: repeats functions, but I'm confused by its double use in that statement.
I also can't understand why f^:proposition^:a: y works. This is the same as the previous one but returns the values from all the iterations, instead of only the last one as did the one above.
a: is an empty box and I get that has a special meaning used with ^: but even after having looked into the dictionary I couldn't understand it.
Thanks.
Excerpted and adapted from a longer writeup I posted to the J forums in 2009:
while =: ^:break_clause^:_
Here's an adverb you can apply to any code (which would equivalent of the
loop body) to create a while loop. In case you haven't seen it before, ^: is the power conjunction. More specifically, the phrase f^:n y applies the function f to the argument y exactly n times. The count n maybe be an integer or a function which applied to y produces an integer¹.
In the adverb above, we see the power conjunction twice, once in ^:break_clause and again in ^:_ . Let's first discuss the latter. That _ is J's notation for infinity. So, read literally, ^:_ is "apply the function an infinite number of times" or "keep reapplying forever". This is related to a while-loop's function, but it's not very useful if applied literally.
So, instead, ^:_ and its kin were defined to mean "apply a function to its limit", that is, "keep applying the function until its output matches its input". In that case, applying the function again would have no effect, because the next iteration would have the same input as the previous (remember that J is a functional language). So there's
no point in applying the function even once more: it has reached its limit.
For example:
cos=: 2&o. NB. Cosine function
pi =: 1p1 NB. J's notation for 1*pi^1 analogous to scientific notation 1e1
cos pi
_1
cos cos cos pi
0.857553
cos^:3 pi
0.857553
cos^:10 pi
0.731404
cos^:_ pi NB. Fixed point of cosine
0.739085
Here, we keep applying cosine until the answer stops changing: cosine has reached its fixed point, and more applications are superfluous. We can visualize this by showing the
intermediate steps:
cos^:a: pi
3.1415926535897 _1 0.54030230586813 ...73 more... 0.73908513321512 0.73908513321
So ^:_ applies a function to its limit. OK, what about ^:break_condition? Again, it's the same concept: apply the function on the left the number of times specified by the function on the right. In the case of _ (or its function-equivalent, _: ) the output is "infinity", in the case of break_condition the output will be 0 or 1 depending on the input (a break condition is boolean).
So if the input is "right" (i.e. processing is done), then the break_condition will be 0, whence loop_body^:break_condition^:_ will become loop_body^:0^:_ . Obviously, loop_body^:0 applies the loop_body zero times, which has no effect.
To "have no effect" is to leave the input untouched; put another way, it copies the input to the output ... but if the input matches the output, then the function has reached its limit! Obviously ^:_: detects this fact and terminates. Voila, a while loop!
¹ Yes, including zero and negative integers, and "an integer" should be more properly read as "an arbitrary array of integers" (so the function can be applied at more than one power simultaneously).
f^:proposition^:_ is not a while loop. It's (almost) a while loop when proposition returns 1 or 0. It's some strange kind of while loop when proposition returns other results.
Let's take a simple monadic case.
f =: +: NB. Double
v =: 20 > ] NB. y less than 20
(f^:v^:_) 0 NB. steady case
0
(f^:v^:_) 1 NB. (f^:1) y, until (v y) = 0
32
(f^:v^:_) 2
32
(f^:v^:_) 5
20
(f^:v^:_) 21 NB. (f^:0) y
21
This is what's happening: every time that v y is 1, (f^:1) y is executed. The result of (f^:1) y is the new y and so on.
If y stays the same for two times in a row → output y and stop.
If v y is 0→ output y and stop.
So f^:v^:_ here, works like double while less than 20 (or until the result doesn't change)
Let's see what happens when v returns 2/0 instead of 1/0.
v =: 2 * 20 > ]
(f^:v^:_) 0 NB. steady state
0
(f^:v^:_) 1 NB. (f^:2) 1 = 4 -> (f^:2) 4 = 16 -> (f^:2) 16 = 64 [ -> (f^:0) 64 ]
64
(f^:v^:_) 2 NB. (f^:2) 2 = 8 -> (f^:2) 8 = 32 [ -> (f^:0) 32 ]
32
(f^:v^:_) 5 NB. (f^:2) 5 = 20 [ -> (f^:0) 20 ]
20
(f^:v^:_) 21 NB. [ (f^:0) 21 ]
21
You can have many kinds of "strange" loops by playing with v. (It can even return negative integers, to use the inverse of f).
I've coded a basic Mandelbrot explorer in C#, but I have those horrible bands of color, and it's all greyscale.
I have the equation for smooth coloring:
mu = N + 1 - log (log |Z(N)|) / log 2
Where N is the escape count, and |Z(N)| is the modulus of the complex number after the value has escaped, it's this value which I'm unsure of.
My code is based off the pseudo code given on the wikipedia page: http://en.wikipedia.org/wiki/Mandelbrot_set#For_programmers
The complex number is represented by the real values x and y, using this method, how would I calculate the value of |Z(N)| ?
|Z(N)| means the distance to the origin, so you can calculate it via sqrt(x*x + y*y).
If you run into an error with the logarithm: Check the iterations before. If it's part of the Mandelbrot set (iteration = max_iteration), the first logarithm will result 0 and the second will raise an error.
So just add this snippet instead of your old return code. .
if (i < iterations)
{
return i + 1 - Math.Log(Math.Log(Math.Sqrt(x * x + y * y))) / Math.Log(2);
}
return i;
Later, you should divide i by the max_iterations and multiply it with 255. This will give you a nice rgb-value.
I already checked similar posting. The solution is given by M. S. B. here Reading data file in Fortran with known number of lines but unknown number of entries in each line
So, the problem I am having is that from text file I am trying to read inputs. In one line there is supposed to be 3 variables. But sometimes the input file may have 2 variables. In that case I need to make the last variable zero. I tried using READ statement with IOSTAT but if there is only two values it goes to the next line and reads the next available value. I need to make it stop in the 1st line after reading 2 values when there is no 3rd value.
I found one way to do that is to have a comment/other than the type I am trying to read (in this case I am reading float while a comment is a char) which makes a IOSTAT>0 and I can use that as a check. But if in some cases I may not have that comment. I want to make sure it works even than.
Part of the code
read(15,*) x
read(15,*,IOSTAT=ioerr) y,z,w
if (ioerr.gt.0) then
write(*,*)'No value was found'
w=0.0;
goto 409
elseif (ioerr.eq.0) then
write(*,*)'Value found', w
endif
409 read(15,*) a,b
read(15,*) c,d
INPUT FILE is of the form
-1.000 abcd
12.460 28.000 8.00 efg
5.000 5.000 hijk
20.000 21.000 lmno
I need to make it work even when there is no "8.00 efg"
for this case
-1.000 abcd
12.460 28.000
5.000 5.000 hijk
20.000 21.000 lmno
I can not use the string method suggested by MSB. Is there any other way?
I seem to remember trying to do something similar in the past. If you know that the size of a line of the file won't exceed a certain number, you might be able to try something like:
...
character*(128) A
read(15,'(A128)') A !This now holds 1 line of text, padded on the right with spaces
read(A,*,IOSTAT=ioerror) x,y,z
if(IOSTAT.gt.0)then
!handle error here
endif
I'm not completely sure how portable this solution is from one compiler to the next and I don't have time right now to read up on it in the f77 standard...
I have a routine that counts the number of reals on a line. You could adapt this to your purpose fairly easily I think.
subroutine line_num_columns(iu,N,count)
implicit none
integer(4),intent(in)::iu,N
character(len=N)::line
real(8),allocatable::r(:)
integer(4)::r_size,count,i,j
count=0 !Set to zero in case of premature return
r_size=N/5 !Initially try out this max number of reals
allocate(r(r_size))
read(iu,'(a)') line
50 continue
do i=1,r_size
read(line,*,end=99) (r(j),j=1,i) !Try reading i reals
count=i
!write(*,*) count
enddo
r_size=r_size*2 !Need more reals
deallocate(r)
allocate(r(r_size))
goto 50
return
99 continue
write(*,*) 'I conclude that there are ',count,' reals on the first line'
end subroutine line_num_columns
If a Fortran 90 solution is fine, you can use the following procedure to parse a line with multiple real values:
subroutine readnext_r1(string, pos, value)
implicit none
character(len=*), intent(in) :: string
integer, intent(inout) :: pos
real, intent(out) :: value
integer :: i1, i2
i2 = len_trim(string)
! initial values:
if (pos > i2) then
pos = 0
value = 0.0
return
end if
! skip blanks:
i1 = pos
do
if (string(i1:i1) /= ' ') exit
i1 = i1 + 1
end do
! read real value and set pos:
read(string(i1:i2), *) value
pos = scan(string(i1:i2), ' ')
if (pos == 0) then
pos = i2 + 1
else
pos = pos + i1 - 1
end if
end subroutine readnext_r1
The subroutine reads the next real number from a string 'string' starting at character number 'pos' and returns the value in 'value'. If the end of the string has been reached, 'pos' is set to zero (and a value of 0.0 is returned), otherwise 'pos' is incremented to the character position behind the real number that was read.
So, for your case you would first read the line to a character string:
character(len=1024) :: line
...
read(15,'(A)') line
...
and then parse this string
real :: y, z, w
integer :: pos
...
pos = 1
call readnext_r1(line, pos, y)
call readnext_r1(line, pos, z)
call readnext_r1(line, pos, w)
if (pos == 0) w = 0.0
where the final 'if' is not even necessary (but this way it is more transparent imho).
Note, that this technique will fail if there is a third entry on the line that is not a real number.
I know the following simple solution:
w = 0.0
read(15,*,err=600)y, z, w
goto 610
600 read(15,*)y, z
610 do other stuff
But it contains "goto" operators
You might be able to use the wonderfully named colon edit descriptor. This allows you to skip the rest of a format if there are no further items in the I/O list:
Program test
Implicit None
Real :: a, b, c
Character( Len = 10 ) :: comment
Do
c = 0.0
comment = 'No comment'
Read( *, '( 2( f7.3, 1x ), :, f7.3, a )' ) a, b, c, comment
Write( *, * ) 'I read ', a, b, c, comment
End Do
End Program test
For instance with gfortran I get:
Wot now? gfortran -W -Wall -pedantic -std=f95 col.f90
Wot now? ./a.out
12.460 28.000 8.00 efg
I read 12.460000 28.000000 8.0000000 efg
12.460 28.000
I read 12.460000 28.000000 0.00000000E+00
^C
This works with gfortran, g95, the NAG compiler, Intel's compiler and the Sun/Oracle compiler. However I should say I'm not totally convinced I understand this - if c or comment are NOT read are they guaranteed to be 0 and all spaces respectively? Not sure, need to ask elsewhere.