Data Types in fastmat¶
To achieve high performance, fastmat is designed to support common data types only, namely
Floating point with single and double precision (float32 and float64)
Complex floating point with single and double precision (complex64 and complex128)
Signed integer of selected fixed sizes (int8, int16, int32, int64)
Some implementation of fastmat matrices use numpy under the hood. Although
those could technically be able to deal with other data types offered by
numpy as well, using other types than those listed above is disencouraged.
This is important to ensure consistency throughout the intestines of
fastmat, which is important for being able to reliably test the package.
The following sections detail the organization and handling of types in
fastmat and explain the mechanisms how fastmat handles type promotion. The
final section references the internal type API of fastmat.
Type handling¶
ftype
To distinguish between the supported data types fastmat uses the ftype
internally as type identifier. All data type checks within the package as well
as the type promotion logic is internally handled via these type numbers, that
correspond directly to the associated numpy.dtype given in this table:
Data Type |
|
fastmat |
Short |
Signed Integer 8 bit Signed Integer 16 bit Signed Integer 32 bit Signed Integer 64 bit Single-precision Float Double-Precision Float Single-Precision Complex Double-Precision Complex |
|
0 1 2 3 4 5 6 7 |
i8 i16 i32 i64 f32 f64 c64 c128 |
Type promotion¶
Type promotion matrix of binary operators of kind f(A, B) as used
throughout fastmat:
Type promotion |
B |
||||||||
int |
float |
complex |
|||||||
i8 |
i16 |
i32 |
i64 |
f32 |
f64 |
c64 |
c128 |
||
A |
int 8 |
i8 |
i16 |
i32 |
i64 |
f32 |
f64 |
c64 |
c128 |
int 16 |
i16 |
i16 |
i32 |
i64 |
f32 |
f64 |
c64 |
c128 |
|
int 32 |
i32 |
i32 |
i32 |
i64 |
f64 |
f64 |
c128 |
c128 |
|
int 64 |
i64 |
i64 |
i64 |
i64 |
f64 |
f64 |
c128 |
c128 |
|
float 32 |
f32 |
f32 |
f64 |
f64 |
f64 |
f64 |
c128 |
c128 |
|
float 64 |
f64 |
f64 |
f64 |
f64 |
f64 |
f64 |
c128 |
c128 |
|
complex 64 |
c64 |
c64 |
c128 |
c128 |
c64 |
c128 |
c64 |
c128 |
|
complex 128 |
c128 |
c128 |
c128 |
c128 |
c128 |
c128 |
c128 |
c128 |
|
- Example:
The forward operator of a
fastmat.Matrixof type float 32 will, if provided with an int 32 input vector, yield an output vector of type float 64.
Note
The output data type will be expanded to fit the mantissa of any of the operands best. As int 32 has a wider mantissa than float 32 offers, the example type promotion will yield float 64 to maintain accuracy.
Note
Data types will not be expanded automatically to the next larger data
type for the sake of preventing overflows. You’ll need to specifically
expand the data type – where necessary – by specifying minType=?
during the generation of your fastmat.Matrix instance.
fastmat.core.types¶
- fastmat.core.types.getFusedType()¶
Return fastmat type number for a given data type (or array).
- Parameters
- objobject
The object type or numpy.ndarray to query for.
- Returns
- ftype
The fastmat type number for that type.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.getNumpyType()¶
Return numpy type number for a given data type (or array).
- Parameters
- objobject
The object type or numpy.ndarray to query for.
- Returns
- ntype
The numpy type number for that type.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.getTypeEps()¶
Return eps for a given data type (or array).
- Parameters
- objobject
The object type or numpy.ndarray to query for.
- Returns
- np.float64_t
The epsilon value for that type.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.getTypeMax()¶
Return the maximum representable value for a given data type (or array).
- Parameters
- objobject
The object type or numpy.ndarray to query for.
- Returns
- np.float64_t
The maximum representable value for that type.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.getTypeMin()¶
Return the minimum representable value for a given data type (or array).
- Parameters
- objobject
The object type or numpy.ndarray to query for.
- Returns
- np.float64_t
The minimum representable value for that type.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.isComplex()¶
Return whether a given data type or an array’s data type is complex.
- Parameters
- objobject
The object type to query for.
- Returns
- bool
True if the data type is of complex kind.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.isFloat()¶
Return whether a given data type or an array’s data type is floating point.
- Parameters
- objobject
The object type to query for.
- Returns
- type
True if the data type is of floating point kind.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.isInteger()¶
Return whether a given data type or an array’s data type is integer.
- Parameters
- objobject
The object type to query for.
- Returns
- type
True if the data type is of integer kind.
- Raises
- TypeError
When the type is not supported by fastmat.
- fastmat.core.types.safeTypeExpansion()¶
Return a floating type expanding the given type with full accuracy.
- Parameters
- dtypeobject
A type object to be expanded to float without numerical accuracy loss.
- Returns
- object
The safely expanded datatype