194 lines
18 KiB
Factor
194 lines
18 KiB
Factor
USING: alien byte-arrays help.markup help.syntax math.blas.vectors sequences ;
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IN: math.blas.matrices
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ARTICLE: "math.blas" "Basic Linear Algebra Subroutines (BLAS) interface"
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"Factor provides an interface to high-performance vector and matrix math routines available in the system's BLAS library. A set of specialized types are provided for handling packed, unboxed vector data:"
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{ $subsection float-blas-vector }
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{ $subsection double-blas-vector }
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{ $subsection float-complex-blas-vector }
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{ $subsection double-complex-blas-vector }
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"These vector types all follow the " { $link sequence } " protocol. In addition, there are corresponding types for matrix data:"
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{ $subsection float-blas-matrix }
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{ $subsection double-blas-matrix }
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{ $subsection float-complex-blas-matrix }
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{ $subsection double-complex-blas-matrix }
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"Matrices can be transposed, broken down into sequences of row or column vectors, or sliced into rectangular submatrices:"
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{ $subsection Mtranspose }
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{ $subsection Mrows }
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{ $subsection Mcols }
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{ $subsection Msub }
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"Scalar-vector and vector-vector operations are available in the " { $vocab-link "math.blas.vectors" } " vocabulary:"
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{ $subsection Vnorm }
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{ $subsection Vasum }
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{ $subsection Viamax }
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{ $subsection n*V }
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{ $subsection V+ }
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{ $subsection V- }
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{ $subsection V. }
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{ $subsection V.conj }
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"Vector-matrix and matrix-matrix operations are available in the " { $vocab-link "math.blas.matrices" } " vocabulary:"
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{ $subsection M.V }
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{ $subsection V(*) }
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{ $subsection V(*)conj }
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{ $subsection M. }
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{ $subsection n*M }
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"The above operations only operate on the BLAS vector and matrix types. You cannot mix element types in a BLAS operation; for example, you can't use " { $link V. } " to take the dot product of a " { $link float-blas-vector } " and " { $link double-blas-vector } "."
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$nl
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"The low-level BLAS C interface can be accessed directly through the " { $vocab-link "math.blas.cblas" } " vocabulary." ;
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HELP: blas-matrix-base
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{ $class-description "The base class for all BLAS matrix 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-matrix } }
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{ { $link double-blas-matrix } }
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{ { $link float-complex-blas-matrix } }
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{ { $link double-complex-blas-matrix } }
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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, column-major array of float, double, float complex, or double complex values;" }
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{ { $snippet "ld" } " indicates the distance, in elements, between matrix columns;" }
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{ { $snippet "rows" } " and " { $snippet "cols" } " indicate the number of significant rows and columns in the matrix;" }
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{ "and " { $snippet "transpose" } ", if set to a true value, indicates that the matrix should be treated as transposed relative to its in-memory representation." }
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} } ;
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{ blas-vector-base blas-matrix-base } related-words
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HELP: float-blas-matrix
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{ $class-description "A matrix of single-precision floating-point values. For details on the tuple layout, see " { $link blas-matrix-base } "." } ;
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HELP: double-blas-matrix
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{ $class-description "A matrix of double-precision floating-point values. For details on the tuple layout, see " { $link blas-matrix-base } "." } ;
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HELP: float-complex-blas-matrix
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{ $class-description "A matrix 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-matrix-base } "." } ;
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HELP: double-complex-blas-matrix
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{ $class-description "A matrix of double-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-matrix-base } "." } ;
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{
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float-blas-matrix double-blas-matrix float-complex-blas-matrix double-complex-blas-matrix
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float-blas-vector double-blas-vector float-complex-blas-vector double-complex-blas-vector
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} related-words
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HELP: Mwidth
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{ $values { "matrix" "a BLAS matrix inherited from " { $link blas-matrix-base } } { "width" "The number of columns" } }
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{ $description "Returns the number of columns in " { $snippet "matrix" } "." } ;
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HELP: Mheight
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{ $values { "matrix" "a BLAS matrix inherited from " { $link blas-matrix-base } } { "width" "The number of columns" } }
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{ $description "Returns the number of rows in " { $snippet "matrix" } "." } ;
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{ Mwidth Mheight } related-words
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HELP: n*M.V+n*V-in-place
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{ $values { "alpha" "a number" } { "A" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } { "x" "an N-element BLAS vector inherited from " { $link blas-vector-base } } { "beta" "a number" } { "y" "an M-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the matrix-vector product " { $snippet "αAx + βy" } ", and overwrite the current contents of " { $snippet "y" } " with the result. The width of " { $snippet "A" } " must match the length of " { $snippet "x" } ", and the height must match the length of " { $snippet "y" } ". Corresponds to the xGEMV routines in BLAS." }
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{ $side-effects "The memory used by " { $snippet "y" } " is overwritten with the result." } ;
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HELP: n*V(*)V+M-in-place
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{ $values { "alpha" "a number" } { "x" "an M-element BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element BLAS vector inherited from " { $link blas-vector-base } } { "A" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the outer product " { $snippet "αx⊗y + A" } " and overwrite the current contents of A with the result. The width of " { $snippet "A" } " must match the length of " { $snippet "y" } ", and its height must match the length of " { $snippet "x" } ". Corresponds to the xGER and xGERU routines in BLAS." }
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{ $side-effects "The memory used by " { $snippet "A" } " is overwritten with the result." } ;
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HELP: n*V(*)Vconj+M-in-place
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{ $values { "alpha" "a number" } { "x" "an M-element complex BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element complex BLAS vector inherited from " { $link blas-vector-base } } { "A" "an M-row, N-column complex BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the conjugate outer product " { $snippet "αx⊗y̅ + A" } " and overwrite the current contents of A with the result. The width of " { $snippet "A" } " must match the length of " { $snippet "y" } ", and its height must match the length of " { $snippet "x" } ". Corresponds to the xGERC routines in BLAS." }
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{ $side-effects "The memory used by " { $snippet "A" } " is overwritten with the result." } ;
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HELP: n*M.M+n*M-in-place
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{ $values { "alpha" "a number" } { "A" "an M-row, K-column BLAS matrix inherited from " { $link blas-matrix-base } } { "B" "a K-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } { "beta" "a number" } { "C" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the matrix product " { $snippet "αAB + βC" } " and overwrite the current contents of C with the result. The width of " { $snippet "A" } " and the height of " { $snippet "B" } " must match, as must the heights of " { $snippet "A" } " and " { $snippet "C" } ", and the widths of " { $snippet "B" } " and " { $snippet "C" } ". Corresponds to the xGEMM routines in BLAS." } ;
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HELP: <empty-matrix>
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{ $values { "rows" "the number of rows the new matrix will have" } { "cols" "the number of columns the new matrix will have" } { "exemplar" "A BLAS vector inherited from " { $link blas-vector-base } " or BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Create a matrix of all zeros with the given dimensions and the same element type as " { $snippet "exemplar" } "." } ;
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{ <zero-vector> <empty-vector> <empty-matrix> } related-words
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HELP: n*M.V+n*V
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{ $values { "alpha" "a number" } { "A" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } { "x" "an N-element BLAS vector inherited from " { $link blas-vector-base } } { "beta" "a number" } { "y" "an M-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the matrix-vector product " { $snippet "αAx + βy" } " and return a freshly allocated vector containing the result. The width of " { $snippet "A" } " must match the length of " { $snippet "x" } ", and the height must match the length of " { $snippet "y" } ". The returned vector will have the same length as " { $snippet "y" } ". Corresponds to the xGEMV routines in BLAS." } ;
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HELP: n*V(*)V+M
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{ $values { "alpha" "a number" } { "x" "an M-element BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element BLAS vector inherited from " { $link blas-vector-base } } { "A" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the outer product " { $snippet "αx⊗y + A" } " and return a freshly allocated matrix containing the result. The width of " { $snippet "A" } " must match the length of " { $snippet "y" } ", and its height must match the length of " { $snippet "x" } ". The returned matrix will have the same dimensions as " { $snippet "A" } ". Corresponds to the xGER and xGERU routines in BLAS." } ;
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HELP: n*V(*)Vconj+M
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{ $values { "alpha" "a number" } { "x" "an M-element complex BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element complex BLAS vector inherited from " { $link blas-vector-base } } { "A" "an M-row, N-column complex BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the conjugate outer product " { $snippet "αx⊗y̅ + A" } " and return a freshly allocated matrix containing the result. The width of " { $snippet "A" } " must match the length of " { $snippet "y" } ", and its height must match the length of " { $snippet "x" } ". The returned matrix will have the same dimensions as " { $snippet "A" } ". Corresponds to the xGERC routines in BLAS." } ;
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HELP: n*M.M+n*M
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{ $values { "alpha" "a number" } { "A" "an M-row, K-column BLAS matrix inherited from " { $link blas-matrix-base } } { "B" "a K-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } { "beta" "a number" } { "C" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the matrix product " { $snippet "αAB + βC" } " and overwrite the current contents of C with the result. The width of " { $snippet "A" } " and the height of " { $snippet "B" } " must match, as must the heights of " { $snippet "A" } " and " { $snippet "C" } ", and the widths of " { $snippet "B" } " and " { $snippet "C" } ". Corresponds to the xGEMM routines in BLAS." } ;
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HELP: n*M.V
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{ $values { "alpha" "a number" } { "A" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } { "x" "an N-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the matrix-vector product " { $snippet "αAx" } " and return a freshly allocated vector containing the result. The width of " { $snippet "A" } " must match the length of " { $snippet "x" } ". The length of the returned vector will match the height of " { $snippet "A" } ". Corresponds to the xGEMV routines in BLAS." } ;
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HELP: M.V
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{ $values { "A" "an M-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } { "x" "an N-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the matrix-vector product " { $snippet "Ax" } " and return a freshly allocated vector containing the result. The width of " { $snippet "A" } " must match the length of " { $snippet "x" } ". The length of the returned vector will match the height of " { $snippet "A" } ". Corresponds to the xGEMV routines in BLAS." } ;
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{ n*M.V+n*V-in-place n*M.V+n*V n*M.V M.V } related-words
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HELP: n*V(*)V
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{ $values { "alpha" "a number" } { "x" "an M-element BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the outer product " { $snippet "αx⊗y" } " and return a freshly allocated matrix containing the result. The returned matrix's height will match the length of " { $snippet "x" } ", and its width will match the length of " { $snippet "y" } ". Corresponds to the xGER and xGERU routines in BLAS." } ;
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HELP: n*V(*)Vconj
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{ $values { "alpha" "a number" } { "x" "an M-element BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the outer product " { $snippet "αx⊗y̅" } " and return a freshly allocated matrix containing the result. The returned matrix's height will match the length of " { $snippet "x" } ", and its width will match the length of " { $snippet "y" } ". Corresponds to the xGERC routines in BLAS." } ;
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HELP: V(*)
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{ $values { "x" "an M-element BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the outer product " { $snippet "x⊗y" } " and return a freshly allocated matrix containing the result. The returned matrix's height will match the length of " { $snippet "x" } ", and its width will match the length of " { $snippet "y" } ". Corresponds to the xGER and xGERU routines in BLAS." } ;
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HELP: V(*)conj
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{ $values { "x" "an M-element BLAS vector inherited from " { $link blas-vector-base } } { "y" "an N-element BLAS vector inherited from " { $link blas-vector-base } } }
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{ $description "Calculate the conjugate outer product " { $snippet "x⊗y̅" } " and return a freshly allocated matrix containing the result. The returned matrix's height will match the length of " { $snippet "x" } ", and its width will match the length of " { $snippet "y" } ". Corresponds to the xGERC routines in BLAS." } ;
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{ n*V(*)V+M-in-place n*V(*)Vconj+M-in-place n*V(*)V+M n*V(*)Vconj+M n*V(*)V n*V(*)Vconj V(*) V(*)conj V. V.conj } related-words
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HELP: n*M.M
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{ $values { "alpha" "a number" } { "A" "an M-row, K-column BLAS matrix inherited from " { $link blas-matrix-base } } { "B" "a K-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the matrix product " { $snippet "αAB" } " and return a freshly allocated matrix containing the result. The width of " { $snippet "A" } " and the height of " { $snippet "B" } " must match. The returned matrix's height will be the same as " { $snippet "A" } "'s, and its width will match " { $snippet "B" } "'s. Corresponds to the xGEMM routines in BLAS." } ;
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HELP: M.
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{ $values { "A" "an M-row, K-column BLAS matrix inherited from " { $link blas-matrix-base } } { "B" "a K-row, N-column BLAS matrix inherited from " { $link blas-matrix-base } } }
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{ $description "Calculate the matrix product " { $snippet "AB" } " and return a freshly allocated matrix containing the result. The width of " { $snippet "A" } " and the height of " { $snippet "B" } " must match. The returned matrix's height will be the same as " { $snippet "A" } "'s, and its width will match " { $snippet "B" } "'s. Corresponds to the xGEMM routines in BLAS." } ;
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{ n*M.M+n*M-in-place n*M.M+n*M n*M.M M. } related-words
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HELP: Msub
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{ $values { "matrix" "A BLAS matrix inheriting from " { $link blas-matrix-base } } { "row" "The topmost row of the slice" } { "col" "The leftmost column of the slice" } { "height" "The height of the slice" } { "width" "The width of the slice" } }
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{ $description "Select a rectangular submatrix of " { $snippet "matrix" } " with the given dimensions. The returned submatrix will share the parent matrix's storage." } ;
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HELP: Mrows
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{ $values { "matrix" "A BLAS matrix inheriting from " { $link blas-matrix-base } } }
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{ $description "Return a sequence of BLAS vectors representing the rows of " { $snippet "matrix" } ". Each vector will share the parent matrix's storage." } ;
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HELP: Mcols
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{ $values { "matrix" "A BLAS matrix inheriting from " { $link blas-matrix-base } } }
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{ $description "Return a sequence of BLAS vectors representing the columns of " { $snippet "matrix" } ". Each vector will share the parent matrix's storage." } ;
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HELP: n*M-in-place
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{ $values { "n" "a number" } { "A" "A BLAS matrix inheriting from " { $link blas-matrix-base } } }
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{ $description "Calculate the scalar-matrix product " { $snippet "nA" } " and overwrite the current contents of A with the result." }
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{ $side-effects "The memory used by " { $snippet "A" } " is overwritten with the result." } ;
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HELP: n*M
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{ $values { "n" "a number" } { "A" "A BLAS matrix inheriting from " { $link blas-matrix-base } } }
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{ $description "Calculate the scalar-matrix product " { $snippet "nA" } " and return a freshly allocated matrix with the same dimensions as " { $snippet "A" } " containing the result." } ;
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HELP: M*n
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{ $values { "A" "A BLAS matrix inheriting from " { $link blas-matrix-base } } { "n" "a number" } }
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{ $description "Calculate the scalar-matrix product " { $snippet "nA" } " and return a freshly allocated matrix with the same dimensions as " { $snippet "A" } " containing the result." } ;
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HELP: M/n
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{ $values { "A" "A BLAS matrix inheriting from " { $link blas-matrix-base } } { "n" "a number" } }
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{ $description "Calculate the scalar-matrix product " { $snippet "(1/n)A" } " and return a freshly allocated matrix with the same dimensions as " { $snippet "A" } " containing the result." } ;
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{ n*M-in-place n*M M*n M/n } related-words
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HELP: Mtranspose
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{ $values { "matrix" "A BLAS matrix inheriting from " { $link blas-matrix-base } } }
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{ $description "Returns the transpose of " { $snippet "matrix" } ". The returned matrix shares storage with the original matrix." } ;
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