290 lines
18 KiB
Factor
290 lines
18 KiB
Factor
USING: alien byte-arrays help.markup help.syntax math math.blas.vectors sequences strings multiline ;
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IN: math.blas.matrices
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ARTICLE: "math.blas-summary" "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 "math.blas-types" }
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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 "math.blas.vectors" }
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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 "math.blas.matrices" }
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"The low-level BLAS Fortran interface can be accessed directly through the " { $vocab-link "math.blas.ffi" } " vocabulary." ;
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ARTICLE: "math.blas-types" "BLAS interface types"
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"BLAS vectors come in single- and double-precision, real and complex flavors:"
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{ $subsection float-blas-vector }
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{ $subsection double-blas-vector }
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{ $subsection complex-float-blas-vector }
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{ $subsection complex-double-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 complex-float-blas-matrix }
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{ $subsection complex-double-blas-matrix }
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"There are BOA constructors for all vector and matrix types, which provide the most flexibility in specifying memory layout:"
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{ $subsection <float-blas-vector> }
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{ $subsection <double-blas-vector> }
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{ $subsection <complex-float-blas-vector> }
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{ $subsection <complex-double-blas-vector> }
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{ $subsection <float-blas-matrix> }
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{ $subsection <double-blas-matrix> }
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{ $subsection <complex-float-blas-matrix> }
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{ $subsection <complex-double-blas-matrix> }
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"For the simple case of creating a dense, zero-filled vector or matrix, simple empty object constructors are provided:"
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{ $subsection <empty-vector> }
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{ $subsection <empty-matrix> }
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"BLAS vectors and matrices can also be constructed from other Factor sequences:"
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{ $subsection >float-blas-vector }
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{ $subsection >double-blas-vector }
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{ $subsection >complex-float-blas-vector }
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{ $subsection >complex-double-blas-vector }
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{ $subsection >float-blas-matrix }
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{ $subsection >double-blas-matrix }
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{ $subsection >complex-float-blas-matrix }
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{ $subsection >complex-double-blas-matrix } ;
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ARTICLE: "math.blas.matrices" "BLAS interface matrix operations"
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"Transposing and slicing matrices:"
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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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"Matrix-vector products:"
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{ $subsection n*M.V+n*V! }
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{ $subsection n*M.V+n*V }
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{ $subsection n*M.V }
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{ $subsection M.V }
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"Vector outer products:"
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{ $subsection n*V(*)V+M! }
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{ $subsection n*V(*)Vconj+M! }
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{ $subsection n*V(*)V+M }
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{ $subsection n*V(*)Vconj+M }
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{ $subsection n*V(*)V }
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{ $subsection n*V(*)Vconj }
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{ $subsection V(*) }
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{ $subsection V(*)conj }
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"Matrix products:"
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{ $subsection n*M.M+n*M! }
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{ $subsection n*M.M+n*M }
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{ $subsection n*M.M }
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{ $subsection M. }
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"Scalar-matrix products:"
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{ $subsection n*M! }
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{ $subsection n*M }
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{ $subsection M*n }
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{ $subsection M/n }
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"Literal syntax:"
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{ $subsection POSTPONE: smatrix{ }
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{ $subsection POSTPONE: dmatrix{ }
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{ $subsection POSTPONE: cmatrix{ }
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{ $subsection POSTPONE: zmatrix{ } ;
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ABOUT: "math.blas.matrices"
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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 complex-float-blas-matrix } }
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{ { $link complex-double-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 "underlying" } " 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: complex-float-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: complex-double-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 complex-float-blas-matrix complex-double-blas-matrix
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float-blas-vector double-blas-vector complex-float-blas-vector complex-double-blas-vector
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} related-words
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HELP: Mwidth
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{ $values { "matrix" blas-matrix-base } { "width" integer } }
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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" blas-matrix-base } { "height" integer } }
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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!
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{ $values { "alpha" number } { "A" blas-matrix-base } { "x" blas-vector-base } { "beta" number } { "y" blas-vector-base } { "y=alpha*A.x+b*y" 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 "y" } ;
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HELP: n*V(*)V+M!
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{ $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "A=alpha*x(*)y+A" 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 "A" } ;
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HELP: n*V(*)Vconj+M!
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{ $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "A=alpha*x(*)yconj+A" 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 "A" } ;
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HELP: n*M.M+n*M!
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{ $values { "alpha" number } { "A" blas-matrix-base } { "B" blas-matrix-base } { "beta" number } { "C" blas-matrix-base } { "C=alpha*A.B+beta*C" 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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{ $side-effects "C" } ;
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HELP: <empty-matrix>
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{ $values { "rows" integer } { "cols" integer } { "exemplar" blas-vector-base blas-matrix-base } { "matrix" 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" number } { "A" blas-matrix-base } { "x" blas-vector-base } { "beta" number } { "y" blas-vector-base } { "alpha*A.x+b*y" 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" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "alpha*x(*)y+A" 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" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "alpha*x(*)yconj+A" 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" number } { "A" blas-matrix-base } { "B" blas-matrix-base } { "beta" number } { "C" blas-matrix-base } { "alpha*A.B+beta*C" 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" number } { "A" blas-matrix-base } { "x" blas-vector-base } { "alpha*A.x" 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" blas-matrix-base } { "x" blas-vector-base } { "A.x" 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! 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" number } { "x" blas-vector-base } { "y" blas-vector-base } { "alpha*x(*)y" blas-matrix-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" number } { "x" blas-vector-base } { "y" blas-vector-base } { "alpha*x(*)yconj" blas-matrix-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" blas-vector-base } { "y" blas-vector-base } { "x(*)y" blas-matrix-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" blas-vector-base } { "y" blas-vector-base } { "x(*)yconj" blas-matrix-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! n*V(*)Vconj+M! 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" number } { "A" blas-matrix-base } { "B" blas-matrix-base } { "alpha*A.B" 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" blas-matrix-base } { "B" blas-matrix-base } { "A.B" 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! n*M.M+n*M n*M.M M. } related-words
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HELP: Msub
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{ $values { "matrix" blas-matrix-base } { "row" integer } { "col" integer } { "height" integer } { "width" integer } { "sub" blas-matrix-base } }
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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 { "A" blas-matrix-base } { "rows" sequence } }
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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 { "A" blas-matrix-base } { "cols" sequence } }
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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!
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{ $values { "n" number } { "A" blas-matrix-base } { "A=n*A" 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 "A" } ;
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HELP: n*M
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{ $values { "n" number } { "A" blas-matrix-base } { "n*A" 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" blas-matrix-base } { "n" number } { "A*n" 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" blas-matrix-base } { "n" number } { "A/n" blas-matrix-base } }
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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! n*M M*n M/n } related-words
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HELP: Mtranspose
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{ $values { "matrix" blas-matrix-base } { "matrix^T" 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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HELP: element-type
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{ $values { "v" blas-vector-base blas-matrix-base } { "type" string } }
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{ $description "Return the C type of the elements in the given BLAS vector or matrix." } ;
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HELP: <empty-vector>
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{ $values { "length" "The length of the new vector" } { "exemplar" blas-vector-base blas-matrix-base } { "vector" blas-vector-base } }
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{ $description "Return a vector of zeros with the given " { $snippet "length" } " and the same element type as " { $snippet "v" } "." } ;
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HELP: smatrix{
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{ $syntax <" smatrix{
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{ 1.0 0.0 0.0 1.0 }
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{ 0.0 1.0 0.0 2.0 }
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{ 0.0 0.0 1.0 3.0 }
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{ 0.0 0.0 0.0 1.0 }
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} "> }
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{ $description "Construct a literal " { $link float-blas-matrix } ". Note that although BLAS matrices are stored in column-major order, the literal is specified in row-major order." } ;
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HELP: dmatrix{
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{ $syntax <" dmatrix{
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{ 1.0 0.0 0.0 1.0 }
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{ 0.0 1.0 0.0 2.0 }
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{ 0.0 0.0 1.0 3.0 }
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{ 0.0 0.0 0.0 1.0 }
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} "> }
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{ $description "Construct a literal " { $link double-blas-matrix } ". Note that although BLAS matrices are stored in column-major order, the literal is specified in row-major order." } ;
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HELP: cmatrix{
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{ $syntax <" cmatrix{
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{ 1.0 0.0 0.0 1.0 }
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{ 0.0 C{ 0.0 1.0 } 0.0 2.0 }
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{ 0.0 0.0 -1.0 3.0 }
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{ 0.0 0.0 0.0 C{ 0.0 -1.0 } }
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} "> }
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{ $description "Construct a literal " { $link complex-float-blas-matrix } ". Note that although BLAS matrices are stored in column-major order, the literal is specified in row-major order." } ;
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HELP: zmatrix{
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{ $syntax <" zmatrix{
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{ 1.0 0.0 0.0 1.0 }
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{ 0.0 C{ 0.0 1.0 } 0.0 2.0 }
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{ 0.0 0.0 -1.0 3.0 }
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{ 0.0 0.0 0.0 C{ 0.0 -1.0 } }
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} "> }
|
||
{ $description "Construct a literal " { $link complex-double-blas-matrix } ". Note that although BLAS matrices are stored in column-major order, the literal is specified in row-major order." } ;
|
||
|
||
{
|
||
POSTPONE: smatrix{ POSTPONE: dmatrix{
|
||
POSTPONE: cmatrix{ POSTPONE: zmatrix{
|
||
} related-words
|