1 USING: alien byte-arrays help.markup help.syntax math math.blas.vectors sequences strings multiline ;
4 ARTICLE: "math.blas-summary" "Basic Linear Algebra Subroutines (BLAS) interface"
5 "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:"
6 { $subsection "math.blas-types" }
7 "Scalar-vector and vector-vector operations are available in the " { $vocab-link "math.blas.vectors" } " vocabulary:"
8 { $subsection "math.blas.vectors" }
9 "Vector-matrix and matrix-matrix operations are available in the " { $vocab-link "math.blas.matrices" } " vocabulary:"
10 { $subsection "math.blas.matrices" }
11 "The low-level BLAS C interface can be accessed directly through the " { $vocab-link "math.blas.cblas" } " vocabulary." ;
13 ARTICLE: "math.blas-types" "BLAS interface types"
14 "BLAS vectors come in single- and double-precision, real and complex flavors:"
15 { $subsection float-blas-vector }
16 { $subsection double-blas-vector }
17 { $subsection float-complex-blas-vector }
18 { $subsection double-complex-blas-vector }
19 "These vector types all follow the " { $link sequence } " protocol. In addition, there are corresponding types for matrix data:"
20 { $subsection float-blas-matrix }
21 { $subsection double-blas-matrix }
22 { $subsection float-complex-blas-matrix }
23 { $subsection double-complex-blas-matrix }
24 "There are BOA constructors for all vector and matrix types, which provide the most flexibility in specifying memory layout:"
25 { $subsection <float-blas-vector> }
26 { $subsection <double-blas-vector> }
27 { $subsection <float-complex-blas-vector> }
28 { $subsection <double-complex-blas-vector> }
29 { $subsection <float-blas-matrix> }
30 { $subsection <double-blas-matrix> }
31 { $subsection <float-complex-blas-matrix> }
32 { $subsection <double-complex-blas-matrix> }
33 "For the simple case of creating a dense, zero-filled vector or matrix, simple empty object constructors are provided:"
34 { $subsection <empty-vector> }
35 { $subsection <empty-matrix> }
36 "BLAS vectors and matrices can also be constructed from other Factor sequences:"
37 { $subsection >float-blas-vector }
38 { $subsection >double-blas-vector }
39 { $subsection >float-complex-blas-vector }
40 { $subsection >double-complex-blas-vector }
41 { $subsection >float-blas-matrix }
42 { $subsection >double-blas-matrix }
43 { $subsection >float-complex-blas-matrix }
44 { $subsection >double-complex-blas-matrix } ;
46 ARTICLE: "math.blas.matrices" "BLAS interface matrix operations"
47 "Transposing and slicing matrices:"
48 { $subsection Mtranspose }
52 "Matrix-vector products:"
53 { $subsection n*M.V+n*V! }
54 { $subsection n*M.V+n*V }
57 "Vector outer products:"
58 { $subsection n*V(*)V+M! }
59 { $subsection n*V(*)Vconj+M! }
60 { $subsection n*V(*)V+M }
61 { $subsection n*V(*)Vconj+M }
62 { $subsection n*V(*)V }
63 { $subsection n*V(*)Vconj }
65 { $subsection V(*)conj }
67 { $subsection n*M.M+n*M! }
68 { $subsection n*M.M+n*M }
71 "Scalar-matrix products:"
77 { $subsection POSTPONE: smatrix{ }
78 { $subsection POSTPONE: dmatrix{ }
79 { $subsection POSTPONE: cmatrix{ }
80 { $subsection POSTPONE: zmatrix{ } ;
83 ABOUT: "math.blas.matrices"
85 HELP: blas-matrix-base
86 { $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:"
88 { { $link float-blas-matrix } }
89 { { $link double-blas-matrix } }
90 { { $link float-complex-blas-matrix } }
91 { { $link double-complex-blas-matrix } }
93 "All of these subclasses share the same tuple layout:"
95 { { $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;" }
96 { { $snippet "ld" } " indicates the distance, in elements, between matrix columns;" }
97 { { $snippet "rows" } " and " { $snippet "cols" } " indicate the number of significant rows and columns in the matrix;" }
98 { "and " { $snippet "transpose" } ", if set to a true value, indicates that the matrix should be treated as transposed relative to its in-memory representation." }
101 { blas-vector-base blas-matrix-base } related-words
103 HELP: float-blas-matrix
104 { $class-description "A matrix of single-precision floating-point values. For details on the tuple layout, see " { $link blas-matrix-base } "." } ;
105 HELP: double-blas-matrix
106 { $class-description "A matrix of double-precision floating-point values. For details on the tuple layout, see " { $link blas-matrix-base } "." } ;
107 HELP: float-complex-blas-matrix
108 { $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 } "." } ;
109 HELP: double-complex-blas-matrix
110 { $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 } "." } ;
113 float-blas-matrix double-blas-matrix float-complex-blas-matrix double-complex-blas-matrix
114 float-blas-vector double-blas-vector float-complex-blas-vector double-complex-blas-vector
118 { $values { "matrix" blas-matrix-base } { "width" integer } }
119 { $description "Returns the number of columns in " { $snippet "matrix" } "." } ;
122 { $values { "matrix" blas-matrix-base } { "height" integer } }
123 { $description "Returns the number of rows in " { $snippet "matrix" } "." } ;
125 { Mwidth Mheight } related-words
128 { $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 } }
129 { $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." }
130 { $side-effects "y" } ;
133 { $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "A=alpha*x(*)y+A" blas-matrix-base } }
134 { $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." }
135 { $side-effects "A" } ;
138 { $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "A=alpha*x(*)yconj+A" blas-matrix-base } }
139 { $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." }
140 { $side-effects "A" } ;
143 { $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 } }
144 { $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." }
145 { $side-effects "C" } ;
148 { $values { "rows" integer } { "cols" integer } { "exemplar" blas-vector-base blas-matrix-base } { "matrix" blas-matrix-base } }
149 { $description "Create a matrix of all zeros with the given dimensions and the same element type as " { $snippet "exemplar" } "." } ;
151 { <zero-vector> <empty-vector> <empty-matrix> } related-words
154 { $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 } }
155 { $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." } ;
158 { $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "alpha*x(*)y+A" blas-matrix-base } }
159 { $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." } ;
162 { $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "A" blas-matrix-base } { "alpha*x(*)yconj+A" blas-matrix-base } }
163 { $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." } ;
166 { $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 } }
167 { $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." } ;
170 { $values { "alpha" number } { "A" blas-matrix-base } { "x" blas-vector-base } { "alpha*A.x" blas-vector-base } }
171 { $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." } ;
174 { $values { "A" blas-matrix-base } { "x" blas-vector-base } { "A.x" blas-vector-base } }
175 { $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." } ;
177 { n*M.V+n*V! n*M.V+n*V n*M.V M.V } related-words
180 { $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "alpha*x(*)y" blas-matrix-base } }
181 { $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." } ;
184 { $values { "alpha" number } { "x" blas-vector-base } { "y" blas-vector-base } { "alpha*x(*)yconj" blas-matrix-base } }
185 { $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." } ;
188 { $values { "x" blas-vector-base } { "y" blas-vector-base } { "x(*)y" blas-matrix-base } }
189 { $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." } ;
192 { $values { "x" blas-vector-base } { "y" blas-vector-base } { "x(*)yconj" blas-matrix-base } }
193 { $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." } ;
195 { 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
198 { $values { "alpha" number } { "A" blas-matrix-base } { "B" blas-matrix-base } { "alpha*A.B" blas-matrix-base } }
199 { $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." } ;
202 { $values { "A" blas-matrix-base } { "B" blas-matrix-base } { "A.B" blas-matrix-base } }
203 { $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." } ;
205 { n*M.M+n*M! n*M.M+n*M n*M.M M. } related-words
208 { $values { "matrix" blas-matrix-base } { "row" integer } { "col" integer } { "height" integer } { "width" integer } { "sub" blas-matrix-base } }
209 { $description "Select a rectangular submatrix of " { $snippet "matrix" } " with the given dimensions. The returned submatrix will share the parent matrix's storage." } ;
212 { $values { "A" blas-matrix-base } { "rows" sequence } }
213 { $description "Return a sequence of BLAS vectors representing the rows of " { $snippet "matrix" } ". Each vector will share the parent matrix's storage." } ;
216 { $values { "A" blas-matrix-base } { "cols" sequence } }
217 { $description "Return a sequence of BLAS vectors representing the columns of " { $snippet "matrix" } ". Each vector will share the parent matrix's storage." } ;
220 { $values { "n" number } { "A" blas-matrix-base } { "A=n*A" blas-matrix-base } }
221 { $description "Calculate the scalar-matrix product " { $snippet "nA" } " and overwrite the current contents of A with the result." }
222 { $side-effects "A" } ;
225 { $values { "n" number } { "A" blas-matrix-base } { "n*A" blas-matrix-base } }
226 { $description "Calculate the scalar-matrix product " { $snippet "nA" } " and return a freshly allocated matrix with the same dimensions as " { $snippet "A" } " containing the result." } ;
229 { $values { "A" blas-matrix-base } { "n" number } { "A*n" blas-matrix-base } }
230 { $description "Calculate the scalar-matrix product " { $snippet "nA" } " and return a freshly allocated matrix with the same dimensions as " { $snippet "A" } " containing the result." } ;
233 { $values { "A" blas-matrix-base } { "n" number } { "A/n" blas-matrix-base } }
234 { $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." } ;
236 { n*M! n*M M*n M/n } related-words
239 { $values { "matrix" blas-matrix-base } { "matrix^T" blas-matrix-base } }
240 { $description "Returns the transpose of " { $snippet "matrix" } ". The returned matrix shares storage with the original matrix." } ;
243 { $values { "v" blas-vector-base blas-matrix-base } { "type" string } }
244 { $description "Return the C type of the elements in the given BLAS vector or matrix." } ;
247 { $values { "length" "The length of the new vector" } { "exemplar" blas-vector-base blas-matrix-base } { "vector" blas-vector-base } }
248 { $description "Return a vector of zeros with the given " { $snippet "length" } " and the same element type as " { $snippet "v" } "." } ;
251 { $syntax <" smatrix{
257 { $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." } ;
260 { $syntax <" dmatrix{
266 { $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." } ;
269 { $syntax <" cmatrix{
271 { 0.0 C{ 0.0 1.0 } 0.0 2.0 }
273 { 0.0 0.0 0.0 C{ 0.0 -1.0 } }
275 { $description "Construct a literal " { $link float-complex-blas-matrix } ". Note that although BLAS matrices are stored in column-major order, the literal is specified in row-major order." } ;
278 { $syntax <" zmatrix{
280 { 0.0 C{ 0.0 1.0 } 0.0 2.0 }
282 { 0.0 0.0 0.0 C{ 0.0 -1.0 } }
284 { $description "Construct a literal " { $link double-complex-blas-matrix } ". Note that although BLAS matrices are stored in column-major order, the literal is specified in row-major order." } ;
287 POSTPONE: smatrix{ POSTPONE: dmatrix{
288 POSTPONE: cmatrix{ POSTPONE: zmatrix{