Conjugate transpose: Difference between revisions
Added Algol 68
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Normal?: TRUE
Unitary?: TRUE</pre>
=={{header|ALGOL 68}}==
Uses the same test cases as the Ada sample.
<lang algol68>BEGIN # find and classify the complex conjugate transpose of a complex matrix #
# returns the conjugate transpose of m #
OP CONJUGATETRANSPOSE = ( [,]COMPL m )[,]COMPL:
BEGIN
[ 2 LWB m : 2 UPB m, 1 LWB m : 1 UPB m ]COMPL result;
FOR i FROM 1 LWB m TO 1 UPB m DO
FOR j FROM 2 LWB m TO 2 UPB m DO
result[ j, i ] := CONJ m[ i, j ]
OD
OD;
result
END # CONJUGATETRANSPOSE # ;
# returns TRUE if m is an identity matrix, FALSE otherwise #
OP ISIDENTITY = ( [,]COMPL m )BOOL:
IF 1 LWB m /= 2 LWB m OR 1 UPB m /= 2 UPB m THEN
# non-square matrix #
FALSE
ELSE
# the matrix is square #
# returns TRUE IF v - e is nearly 0, FALSE Otherwise #
PROC nearly equal = ( COMPL v, REAL e )BOOL: ABS re OF v - e < 1e-14 AND ABS im OF v < 1e-14;
BOOL result := TRUE;
FOR i FROM 1 LWB m TO 1 UPB m WHILE result DO
IF result := nearly equal( m[ i, i ], 1 ) THEN
# the diagonal element is 1 - test the non-diagonals #
FOR j FROM 1 LWB m TO 1 UPB m WHILE result DO
IF i /= j THEN result := nearly equal( m[ i, j ], 0 ) FI
OD
FI
OD;
result
FI # ISIDENTITY # ;
# returns m multiplied by n #
PRIO X = 7;
OP X = ( [,]COMPL m, n )[,]COMPL:
BEGIN
[ 1 : 1 UPB m, 1 : 2 UPB n ]COMPL r;
FOR i FROM 1 LWB m TO 1 UPB m DO
FOR j FROM 2 LWB n TO 2 UPB n DO
r[ i, j ] := 0;
FOR k TO 2 UPB n DO
r[ i, j ] +:= m[ i, k ] * n[ k, j ]
OD
OD
OD;
r
END # X # ;
# prints the complex matris m #
PROC show matrix = ( [,]COMPL m )VOID:
FOR i FROM 1 LWB m TO 1 UPB m DO
print( ( " " ) );
FOR j FROM 2 LWB m TO 2 UPB m DO
print( ( "( ", fixed( re OF m[ i, j ], -8, 4 )
, ", ", fixed( im OF m[ i, j ], -8, 4 )
, "i )"
)
)
OD;
print( ( newline ) )
OD # show matrix # ;
# display the matrix m, its conjugate transpose and whether it is Hermitian, Normal and Unitary #
PROC show = ( [,]COMPL m )VOID:
BEGIN
[,]COMPL c = CONJUGATETRANSPOSE m;
[,]COMPL cm = c X m;
[,]COMPL mc = m X c;
print( ( "Matrix:", newline ) );
show matrix( m );
print( ( "Conjugate Transpose:", newline ) );
show matrix( c );
BOOL is normal = cm = mc;
BOOL is unitary = IF NOT is normal THEN FALSE
ELIF NOT ISIDENTITY cm THEN FALSE
ELSE ISIDENTITY mc
FI;
print( ( IF c = m THEN "" ELSE "not " FI, "Hermitian; "
, IF is normal THEN "" ELSE "not " FI, "Normal; "
, IF is unitary THEN "" ELSE "not " FI, "Unitary"
, newline
)
);
print( ( newline ) )
END # show # ;
# test some matrices for Hermitian, Normal and Unitary #
show( ( ( ( 3.0000 I 0.0000 ), ( 2.0000 I 1.0000 ) )
, ( ( 2.0000 I -1.0000 ), ( 1.0000 I 0.0000 ) )
)
);
show( ( ( ( 1.0000 I 0.0000 ), ( 1.0000 I 0.0000 ), ( 0.0000 I 0.0000 ) )
, ( ( 0.0000 I 0.0000 ), ( 1.0000 I 0.0000 ), ( 1.0000 I 0.0000 ) )
, ( ( 1.0000 I 0.0000 ), ( 0.0000 I 0.0000 ), ( 1.0000 I 0.0000 ) )
)
);
REAL rh = sqrt( 0.5 );
show( ( ( ( rh I 0.0000 ), ( rh I 0.0000 ), ( 0.0000 I 0.0000 ) )
, ( ( 0.0000 I rh ), ( 0.0000 I - rh ), ( 0.0000 I 0.0000 ) )
, ( ( 0.0000 I 0.0000 ), ( 0.0000 I 0.0000 ), ( 0.0000 I 1.0000 ) )
)
)
END</lang>
{{out}}
<pre>
Matrix:
( 3.0000, 0.0000i )( 2.0000, 1.0000i )
( 2.0000, -1.0000i )( 1.0000, 0.0000i )
Conjugate Transpose:
( 3.0000, 0.0000i )( 2.0000, 1.0000i )
( 2.0000, -1.0000i )( 1.0000, 0.0000i )
Hermitian; Normal; not Unitary
Matrix:
( 1.0000, 0.0000i )( 1.0000, 0.0000i )( 0.0000, 0.0000i )
( 0.0000, 0.0000i )( 1.0000, 0.0000i )( 1.0000, 0.0000i )
( 1.0000, 0.0000i )( 0.0000, 0.0000i )( 1.0000, 0.0000i )
Conjugate Transpose:
( 1.0000, 0.0000i )( 0.0000, 0.0000i )( 1.0000, 0.0000i )
( 1.0000, 0.0000i )( 1.0000, 0.0000i )( 0.0000, 0.0000i )
( 0.0000, 0.0000i )( 1.0000, 0.0000i )( 1.0000, 0.0000i )
not Hermitian; Normal; not Unitary
Matrix:
( 0.7071, 0.0000i )( 0.7071, 0.0000i )( 0.0000, 0.0000i )
( 0.0000, 0.7071i )( 0.0000, -0.7071i )( 0.0000, 0.0000i )
( 0.0000, 0.0000i )( 0.0000, 0.0000i )( 0.0000, 1.0000i )
Conjugate Transpose:
( 0.7071, 0.0000i )( 0.0000, -0.7071i )( 0.0000, 0.0000i )
( 0.7071, 0.0000i )( 0.0000, 0.7071i )( 0.0000, 0.0000i )
( 0.0000, 0.0000i )( 0.0000, 0.0000i )( 0.0000, -1.0000i )
not Hermitian; Normal; Unitary</pre>
=={{header|C}}==
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