Conjugate transpose: Difference between revisions
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Compilation finished at Fri Jun 7 16:31:38
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=={{header|FreeBASIC}}==
<lang freebasic>'complex type and operators for it
type complex
real as double
imag as double
end type
operator + ( a as complex, b as complex ) as complex
dim as complex r
r.real = a.real + b.real
r.imag = a.imag + b.imag
return r
end operator
operator * ( a as complex, b as complex ) as complex
dim as complex r
r.real = a.real*b.real - a.imag*b.imag
r.imag = a.real*b.imag + b.real*a.imag
return r
end operator
operator = ( a as complex, b as complex ) as boolean
if not a.real = b.real then return false
if not a.imag = b.imag then return false
return true
end operator
function complex_conjugate( a as complex ) as complex
dim as complex r
r.real = a.real
r.imag = -a.imag
return r
end function
'matrix type and operations for it
'reuses code from the matrix multiplication task
type Matrix
dim as complex m( any , any )
declare constructor ( )
declare constructor ( byval x as uinteger )
end type
constructor Matrix ( )
end constructor
constructor Matrix ( byval x as uinteger )
redim this.m( x - 1 , x - 1 )
end constructor
operator * ( byref a as Matrix , byref b as Matrix ) as Matrix
dim as Matrix ret
dim as uinteger i, j, k
redim ret.m( ubound( a.m , 1 ) , ubound( a.m , 1 ) )
for i = 0 to ubound( a.m , 1 )
for j = 0 to ubound( b.m , 2 )
for k = 0 to ubound( b.m , 1 )
ret.m( i , j ) += a.m( i , k ) * b.m( k , j )
next k
next j
next i
return ret
end operator
function conjugate_transpose( byref a as Matrix ) as Matrix
dim as Matrix ret
dim as uinteger i, j
redim ret.m( ubound( a.m , 1 ) , ubound( a.m , 1 ) )
for i = 0 to ubound( a.m , 1 )
for j = 0 to ubound( a.m , 2 )
ret.m( i, j ) = complex_conjugate(a.m( j, i ))
next j
next i
return ret
end function
'tests if matrices are unitary, hermitian, or normal
operator = (byref a as Matrix, byref b as matrix) as boolean
dim as integer i, j
if ubound(a.m, 1) <> ubound(b.m, 1) then return false
for i = 0 to ubound( a.m , 1 )
for j = 0 to ubound( a.m , 2 )
if not a.m(i,j)=b.m(i,j) then return false
next j
next i
return true
end operator
function is_identity( byref a as Matrix ) as boolean
dim as integer i, j
for i = 0 to ubound( a.m , 1 )
for j = 0 to ubound( a.m , 2 )
if i = j and ( not a.m(i,j).real = 1.0 or not a.m(i,j).imag = 0.0 ) then return false
if i <> j and ( not a.m(i,j).real = 0.0 or not a.m(i,j).imag = 0.0 ) then return false
next j
next i
return true
end function
function is_hermitian( byref a as Matrix ) as boolean
if a = conjugate_transpose(a) then return true
return false
end function
function is_normal( byref a as Matrix ) as boolean
dim as Matrix aa = conjugate_transpose(a)
if a*aa = aa*a then return true else return false
end function
function is_unitary( byref a as Matrix ) as boolean
dim as Matrix aa = conjugate_transpose(a)
if not is_identity( a*aa ) or not is_identity( aa*a ) then return false
return true
end function
'''now some example matrices
dim as Matrix A = Matrix(2) 'an identity matrix
A.m(0,0).real = 1.0 : A.m(0,0).imag = 0.0 : A.m(0,1).real = 0.0 : A.m(0,1).imag = 0.0
A.m(1,0).real = 0.0 : A.m(1,0).imag = 0.0 : A.m(1,1).real = 1.0 : A.m(1,1).imag = 0.0
dim as Matrix B = Matrix(2) 'a hermitian matrix
B.m(0,0).real = 1.0 : B.m(0,0).imag = 0.0 : B.m(0,1).real = 1.0 : B.m(0,1).imag = -1.0
B.m(1,0).real = 1.0 : B.m(1,0).imag = 1.0 : B.m(1,1).real = 1.0 : B.m(1,1).imag = 0.0
dim as Matrix C = Matrix(2) 'a random matrix
C.m(0,0).real = rnd : C.m(0,0).imag = rnd : C.m(0,1).real = rnd : C.m(0,1).imag = rnd
C.m(1,0).real = rnd : C.m(1,0).imag = rnd : C.m(1,1).real = rnd : C.m(1,1).imag = rnd
print is_hermitian(A), is_normal(A), is_unitary(A)
print is_hermitian(B), is_normal(B), is_unitary(B)
print is_hermitian(C), is_normal(C), is_unitary(C)</lang>
{{out}}
<pre>true true true
true true false
false false false</pre>
=={{header|Go}}==
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