(octave.info)Element-by-element Boolean Operators

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8.5.1 Element-by-element Boolean Operators
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An “element-by-element boolean expression” is a combination of
comparison expressions using the boolean operators “or” (‘|’), “and”
(‘&’), and “not” (‘!’), along with parentheses to control nesting.  The
truth of the boolean expression is computed by combining the truth
values of the corresponding elements of the component expressions.  A
value is considered to be false if it is zero, and true otherwise.

   Element-by-element boolean expressions can be used wherever
comparison expressions can be used.  They can be used in ‘if’ and
‘while’ statements.  However, a matrix value used as the condition in an
‘if’ or ‘while’ statement is only true if _all_ of its elements are
nonzero.

   Like comparison operations, each element of an element-by-element
boolean expression also has a numeric value (1 if true, 0 if false) that
comes into play if the result of the boolean expression is stored in a
variable, or used in arithmetic.

   Here are descriptions of the three element-by-element boolean
operators.

‘BOOLEAN1 & BOOLEAN2’
     Elements of the result are true if both corresponding elements of
     BOOLEAN1 and BOOLEAN2 are true.

‘BOOLEAN1 | BOOLEAN2’
     Elements of the result are true if either of the corresponding
     elements of BOOLEAN1 or BOOLEAN2 is true.

‘! BOOLEAN’
‘~ BOOLEAN’
     Each element of the result is true if the corresponding element of
     BOOLEAN is false.

   These operators work on an element-by-element basis.  For example,
the expression

     [1, 0; 0, 1] & [1, 0; 2, 3]

returns a two by two identity matrix.

   For the binary operators, broadcasting rules apply.  Note:
Broadcasting.  In particular, if one of the operands is a scalar and
the other a matrix, the operator is applied to the scalar and each
element of the matrix.

   For the binary element-by-element boolean operators, both
subexpressions BOOLEAN1 and BOOLEAN2 are evaluated before computing the
result.  This can make a difference when the expressions have side
effects.  For example, in the expression

     a & b++

the value of the variable B is incremented even if the variable A is
zero.

   This behavior is necessary for the boolean operators to work as
described for matrix-valued operands.

 -- : Z = and (X, Y)
 -- : Z = and (X1, X2, ...)
     Return the logical AND of X and Y.

     This function is equivalent to the operator syntax ‘X & Y’.  If
     more than two arguments are given, the logical AND is applied
     cumulatively from left to right:

          (...((X1 & X2) & X3) & ...)

     At least one argument is required.

     See also: Note: or, Note: not, Note: xor.

 -- : Z = not (X)
     Return the logical NOT of X.

     This function is equivalent to the operator syntax ‘! X’.

     See also: Note: and, Note: or, Note: xor.

 -- : Z = or (X, Y)
 -- : Z = or (X1, X2, ...)
     Return the logical OR of X and Y.

     This function is equivalent to the operator syntax ‘X | Y’.  If
     more than two arguments are given, the logical OR is applied
     cumulatively from left to right:

          (...((X1 | X2) | X3) | ...)

     At least one argument is required.

     See also: Note: and, Note: not, *note xor:
     XREFxor.