132 lines
8.6 KiB
Factor
132 lines
8.6 KiB
Factor
USING: alien byte-arrays help.markup help.syntax sequences ;
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IN: math.blas.vectors
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ARTICLE: "math.blas.vectors" "BLAS interface vector operations"
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"Slicing vectors:"
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{ $subsection Vsub }
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"Taking the norm (magnitude) of a vector:"
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{ $subsection Vnorm }
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"Summing and taking the maximum of elements:"
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{ $subsection Vasum }
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{ $subsection Viamax }
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{ $subsection Vamax }
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"Scalar-vector products:"
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{ $subsection n*V-in-place }
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{ $subsection n*V }
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{ $subsection V*n }
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{ $subsection V/n }
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{ $subsection Vneg }
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"Vector addition:"
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{ $subsection n*V+V-in-place }
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{ $subsection n*V+V }
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{ $subsection V+ }
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{ $subsection V- }
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"Vector inner products:"
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{ $subsection V. }
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{ $subsection V.conj } ;
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ABOUT: "math.blas.vectors"
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HELP: blas-vector-base
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{ $class-description "The base class for all BLAS vector types. Objects of this type should not be created directly; instead, instantiate one of the typed subclasses:"
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{ $list
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{ { $link float-blas-vector } }
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{ { $link double-blas-vector } }
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{ { $link float-complex-blas-vector } }
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{ { $link double-complex-blas-vector } }
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}
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"All of these subclasses share the same tuple layout:"
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{ $list
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{ { $snippet "data" } " contains an alien pointer referencing or byte-array containing a packed array of float, double, float complex, or double complex values;" }
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{ { $snippet "length" } " indicates the length of the vector;" }
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{ "and " { $snippet "inc" } " indicates the distance, in elements, between elements." }
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} } ;
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HELP: float-blas-vector
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{ $class-description "A vector of single-precision floating-point values. For details on the tuple layout, see " { $link blas-vector-base } "." } ;
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HELP: double-blas-vector
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{ $class-description "A vector of double-precision floating-point values. For details on the tuple layout, see " { $link blas-vector-base } "." } ;
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HELP: float-complex-blas-vector
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{ $class-description "A vector of single-precision floating-point complex values. Complex values are stored in memory as two consecutive float values, real part then imaginary part. For details on the tuple layout, see " { $link blas-vector-base } "." } ;
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HELP: double-complex-blas-vector
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{ $class-description "A vector of single-precision floating-point complex values. Complex values are stored in memory as two consecutive float values, real part then imaginary part. For details on the tuple layout, see " { $link blas-vector-base } "." } ;
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HELP: n*V+V-in-place
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{ $values { "alpha" "a number" } { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the vector sum " { $snippet "αx + y" } " and replace the existing contents of y with the result. Corresponds to the xAXPY routines in BLAS." }
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{ $side-effects "y" } ;
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HELP: n*V-in-place
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{ $values { "alpha" "a number" } { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the scalar-vector product " { $snippet "αx" } " and replace the existing contents of x with the result. Corresponds to the xSCAL routines in BLAS." }
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{ $side-effects "x" } ;
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HELP: V.
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the inner product " { $snippet "x⋅y" } ". Corresponds to the xDOT and xDOTU routines in BLAS." } ;
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HELP: V.conj
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{ $values { "x" "a complex BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a complex BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the conjugate inner product " { $snippet "x̅⋅y" } ". Corresponds to the xDOTC routines in BLAS." } ;
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HELP: Vnorm
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the norm-2, i.e., the magnitude or absolute value, of " { $snippet "x" } " (" { $snippet "‖x‖₂" } "). Corresponds to the xNRM2 routines in BLAS." } ;
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HELP: Vasum
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the sum of the norm-1s of the elements of " { $snippet "x" } " (" { $snippet "Σ ‖xᵢ‖₁" } "). Corresponds to the xASUM routines in BLAS." } ;
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HELP: Vswap
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Swap the contents of " { $snippet "x" } " and " { $snippet "y" } " in place. Corresponds to the xSWAP routines in BLAS." }
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{ $side-effects "x" "y" } ;
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HELP: Viamax
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Return the index of the element in " { $snippet "x" } " with the largest norm-1. If more than one element has the same norm-1, returns the smallest index. Corresponds to the IxAMAX routines in BLAS." } ;
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HELP: Vamax
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Return the value of the element in " { $snippet "x" } " with the largest norm-1. If more than one element has the same norm-1, returns the first element. Corresponds to the IxAMAX routines in BLAS." } ;
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{ Viamax Vamax } related-words
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HELP: <zero-vector>
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{ $values { "exemplar" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Return a vector of zeros with the same length and element type as " { $snippet "v" } ". The vector is constructed with an " { $snippet "inc" } " of zero, so it is not suitable for receiving results from BLAS functions; it is intended to be used as a term in other vector calculations. To construct an empty vector that can be used to receive results, see " { $link <empty-vector> } "." } ;
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HELP: n*V+V
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{ $values { "alpha" "a number" } { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the vector sum " { $snippet "αx + y" } " and return a freshly-allocated vector with the same length as " { $snippet "x" } " and " { $snippet "y" } " containing the result. Corresponds to the xAXPY routines in BLAS." } ;
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HELP: n*V
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{ $values { "alpha" "a number" } { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the scalar-vector product " { $snippet "αx" } " and return a freshly-allocated vector with the same length as " { $snippet "x" } " containing the result. Corresponds to the xSCAL routines in BLAS." } ;
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HELP: V+
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the vector sum " { $snippet "x + y" } " and return a freshly-allocated vector with the same length as " { $snippet "x" } " and " { $snippet "y" } " containing the result. Corresponds to the xAXPY routines in BLAS." } ;
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HELP: V-
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Calculate the vector difference " { $snippet "x – y" } " and return a freshly-allocated vector with the same length as " { $snippet "x" } " and " { $snippet "y" } " containing the result. Corresponds to the xAXPY routines in BLAS." } ;
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HELP: Vneg
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "y" "a BLAS vector inheriting from " { $link blas-vector-base } } }
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{ $description "Negate the elements of " { $snippet "x" } " and return a freshly-allocated vector with the same length as " { $snippet "x" } " and " { $snippet "y" } " containing the result." } ;
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HELP: V*n
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "alpha" "a number" } }
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{ $description "Calculate the scalar-vector product " { $snippet "αx" } " and return a freshly-allocated vector with the same length as " { $snippet "x" } " containing the result. Corresponds to the xSCAL routines in BLAS." } ;
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HELP: V/n
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{ $values { "x" "a BLAS vector inheriting from " { $link blas-vector-base } } { "alpha" "a number" } }
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{ $description "Calculate the scalar-vector product " { $snippet "(1/α)x" } " and return a freshly-allocated vector with the same length as " { $snippet "x" } " containing the result. Corresponds to the xSCAL routines in BLAS." } ;
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{ n*V+V-in-place n*V-in-place n*V+V n*V V+ V- Vneg V*n V/n } related-words
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HELP: Vsub
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{ $values { "v" "a BLAS vector inheriting from " { $link blas-vector-base } } { "start" "The index of the first element of the slice" } { "length" "The length of the slice" } }
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{ $description "Slice a subvector out of " { $snippet "v" } " with the given length. The subvector will share storage with the parent vector." } ;
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