3.5. Tensor Operations

3.5. Tensor Operations
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VSIPL++ Tensor objects represent three-dimensional sets of data. The type of values stored in the tensor is given by the first template argument.

3.5.1. Tensor Generation Functions

A = 0: Clears tensor to value 0.
A = value: Fills tensor with scalar value value.

3.5.2. Tensor Copy

Z = A: Copies value from tensor A into tensor Z.

3.5.3. Tensor Arithmetic Elementwise Unary Operations and Functions

The following elementwise unary operations can be performed on tensors, producing a tensor result:

acos(A): Trigonometric arc cosine (section 4.2.1)
arg(A): Phase angle of complex (section 4.2.4)
asin(A): Trigonometric arc sine (section 4.2.5)
atan(A): Trigonometric arc tangent (section 4.2.6)
bnot(A): Boolean not (section 4.2.35)
ceil(A): Round floating-point value up to next integral value (section 4.2.12)
conj(A): Complex conjugate (section 4.2.13)
cos(A): Trigonometric cosine (section 4.2.14)
cosh(A): Hyperbolic cosine (section 4.2.15)
euler(A): Rotate complex unit vector by angle (section 4.2.18)
exp(A): Natural exponential (section 4.2.19)
exp10(A): Base-10 exponential (section 4.2.20)
floor(A): Round floating-point value down to next integral value (section 4.2.22)
imag(A): Imaginary part of complex (section 4.2.27)
is_finite(A): Is floating-point value finite (section 4.2.29)
is_nan(A): Is floating-point value not a number (NaN) (section 4.2.29)
is_normal(A): Is floating-point value normal (section 4.2.30)
lnot(A): Logical not (section 4.2.35)
log(A): Base-e logarithm (section 4.2.36)
log10(A): Base-10 logarithm (section 4.2.37)
mag(A): Magnitude (section 4.2.42)
magsq(A): Magnitude squared (section 4.2.43)
neg(A): Negation (section 4.2.53)
real(A): Real part of complex (section 4.2.55)
recip(A): Recipricol (section 4.2.56)
rsqrt(A): Recipricol square root (section 4.2.57)
sin(A): Trigonometric sine (section 4.2.59)
sinh(A): Hyperbolic sine (section 4.2.60)
sq(A): Square (section 4.2.61)
sqrt(A): Square root (section 4.2.62)
tan(A): Trigonometric tangent (section 4.2.64)
tanh(A): Hyperbolic tangent (section 4.2.65)

3.5.4. Tensor Arithmetic Elementwise Binary Operations and Functions

The following elementwise binary operations can be performed on tensors, producing a tensor result:

add(A): Addition (section 4.2.2)
atan2(A): Arc tangent of quotient (section 4.2.7)
band(A): Bitwise and (section 4.2.8)
bor(A): Bitwise or (section 4.2.9)
bxor(A): Bitwise exclusive or (section 4.2.11)
div(A): Division (section 4.2.16)
eq(A): Equality comparison (section 4.2.17)
fmod(A): Floating-point modulo (remainder after division) (section 4.2.23)
ge(A): Greater-than or equal comparison (section 4.2.24)
gt(A): Greater-than comparison (section 4.2.25)
hypot(A): Hypotenuse of right triangle (section 4.2.26)
jmul(A): Conjugate multiply (section 4.2.32)
land(A): Logical and (section 4.2.33)
le(A): Less-than or equal comparison (section 4.2.34)
lor(A): Logical or (section 4.2.38)
lt(A): Less-than comparison (section 4.2.39)
lxor(A): Logical exclusive or (section 4.2.40)
max(A): Maxima (section 4.2.44)
maxmg(A): Magnitude maxima (section 4.2.45)
maxmgsq(A): Magnitude squared maxima (section 4.2.46)
min(A): Minima (section 4.2.47)
minmg(A): Magnitude minima (section 4.2.48)
minmgsq(A): Magnitude squared minima (section 4.2.49)
mul(A): Multiplication (section 4.2.51)
ne(A): Not equal comparison (section 4.2.52)
pow(A): Raise to power (section 4.2.54)
sub(A): Subtract (section 4.2.63)

3.5.5. Tensor Arithmetic Elementwise Ternary Operations and Functions

The following elementwise ternary operations can be performed on tensors, producing a tensor result:

am(A): Fused addition-multiplication (section 4.2.3)
expoavg(A): Exponential average (section 4.2.21)
ite(A): Addition (section 4.2.31)
ma(A): Fused multiplication-addition (section 4.2.41)
msb(A): Fused multiplication-subtraction (section 4.2.50)
sbm(A): Fused subtraction-multiplication (section 4.2.58)

3.5.6. Tensor Type Conversions

A tensor with one type of values can be converted a tensor with another type of values using view_cast.

For example, to convert a tensor of floats A into a tensor of ints Z:

Tensor<float> A(size);
Tensor<int>   Z(size);
Z = view_cast<int>(A)

3.5.7. Tensor Arithmetic Elementwise Binary Operations and Functions

The following arithmetic elementwise binary operations and functions are available on tensors:

Z = add(A, B): Addition, Z(n) = A(n) + B(n)(section 4.2.2)
Z = div(A, B): Division, Z(n) = A(n) / B(n)(section 4.2.16)
Z = max(A, B): Maximum of A(n) and B(n)
Z = min(A, B): Minimum of A(n) and B(n)
Z = mul(A, B): Multiplication, Z(n) = A(n) * B(n)(section 4.2.51)
Z = sub(A, B): Subtraction, Z(n) = A(n) - B(n)(section 4.2.63)

Addition, subtraction, multiplication, and division can also be written in operator form:

Z = A + B: equivalent to Z = add(A, B)
Z = A - B: equivalent to Z = sub(A, B)
Z = A * B: equivalent to Z = mul(A, B)
Z = A / B: equivalent to Z = div(A, B)

In all the preceding functions and operations, either of the tensor operands can be replaced with scalar operands.

For example, to perform a scalar-tensor multiply:

Z = a * B;

Z = mul(a, B);

3.5.8. Tensor Logical Elementwise Binary Operations and Functions

Z = eq(A, B): Z(n) = A(n) == B(n)
Z = gt(A, B): Z(n) = A(n) > B(n)
Z = gte(A, B): Z(n) = A(n) >= B(n)
Z = lt(A, B): Z(n) = A(n) < B(n)
Z = lte(A, B): Z(n) = A(n) <= B(n)
Z = ne(A, B): Z(n) = A(n) != B(n)

3.5.9. Tensor Arithmetic Elementwise Ternary Operations and Functions

The following arithmetic elementwise ternary operations and functions are available on tensors:

Z = ma(A, B, C): Multiply-add, Z(n) = A(n) * B(n) + C(n)
Z = am(A, B, C): Add-multiply, Z(n) = A(n) + B(n) * C(n)

In all the preceding functions and operations, one or more of the tensor operands can be replaced with scalar operands.

For example, to scale a tensor, then apply an offset:

Z = scale * A + offset;

Z = ma(scale, A, offset);

(where scale and offset are scalar values)

3.5.10. Tensor Non-Arithmetic Elementwise Ternary Operations and Functions

Z = ite(bool_tensor, A, B): For the m,n,pth element of Z, sets value to nth element ofA if m,n,pth element of bool_tensor is true, otherwise sets value to the m,n,pth element of B. Notionally equivalent to C ?: operator. (Foreach n) Z[m, n, p] = bool_tensor[m, n, p] ? A[m, n, p] : B[m, n, p]

In all the preceding functions and operations, one or more of the tensor operands can be replaced with scalar operands.

For example, the apply a scalar threshold b to a tensor:

Z = ite(A > b, A, b);

3.5.11. Tensor Reductions

The following functions reduce a tensor to a single value:

z = alltrue(A): When the element type of A is bool, the function returns true if all the elements are true; otherwise false. When the element type is something else, see (section 4.3.1) for more information.
z = anytrue(A): When the element type of A is bool, the function returns true if any elements are true; otherwise false. When the element type is something else, see (section 4.3.2) for more information.
z = sumval(A): Return the sum of A's values.
z = sumsqval(A): Return the sum of the squares of A's values.
z = meanval(A): Return the mean of A's values.
z = meansqval(A): Return the mean of the squares of A's values.

The following functions reduce a tensor to a single value that corresponds to an element within the vector.

z = maxval(A, idx): return the maximum value of A. Set idx to the index of this element (A.get(idx[0], idx[1], idx[2]) == z).
z = maxmgval(A, idx): return the maximum value of the magnitude of A. Set idx to the index of this element (mag(A.get(idx[0], idx[1], idx[2])) == z).
z = maxmgsqval(A, idx): return the maximum value of the magnitude squared of A. Set idx to the index of this element (magsq(A.get(idx[0], idx[1], idx[2])) == z).
z = minval(A, idx): return the minimum value of A. Set idx to the index of this element (A.get(idx[0], idx[1], idx[2]) == z).
z = minmgval(A, idx): return the minimum value of the magnitude of A. Set idx to the index of this element (mag(A.get(idx[0], idx[1], idx[2])) == z).
z = minmgsqval(A, idx): return the minimum value of the magnitude squared of A. Set idx to the index of this element (magsq(A.get(idx[0], idx[1], idx[2])) == z).

3.5.12. Tensor Random Number Generation

VSIPL++ provides facilities to generate tensors of random number through the class template Rand. Once constructed with compile-time selections, a Rand object can generate a tensor of random numbers through the invocation of one of its member functions.

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