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kaz:blas [2014/02/17 16:00] – [Level1 BLAS Interfaces] kazkaz:blas [2014/12/29 13:09] (現在) – 削除 kaz
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-====== BLAS Interface for Racket ====== 
-[[.:|Go back]] 
  
-|''(require math/blas)''|package: blas| 
-|Author: K. Hishinuma|| 
- 
-The ''math/blas'' library ([[https://github.com/kazh98/blas|git://github.com/kazh98/blas]] package) provides BLAS interfaces for Racket using a ''libcblas'' or ''libgslcblas'' FFI. 
-To install ''math/blas'' library, enter the following command in terminal. 
-<code> 
-% raco pkg install github://github.com/kazh98/blas/master 
-</code> 
-If your operating system isn't MacOS X, you are required to install [[https://www.gnu.org/software/gsl/|GNU Scientific Library]] in your computer to use this library. 
-===== "vect" Object and its Operations ===== 
-<code scheme> 
-; [PROCEDURE] exact-nonnegative-integer? -> vect? 
-(make-vect len) 
- 
-; [PROCEDURE] real? ... -> vect? 
-(vect val ...) 
- 
-; [PROCEDURE] any/c -> boolean? 
-(vect? v) 
- 
-; [PROCEDURE] vect? -> exact-nonnegative-integer? 
-(vect-length vec) 
- 
-; [PROCEDURE] vect? exact-nonnegative-integer? -> real? 
-(vect-ref vec k) 
- 
-; [PROCEDURE] vect? exact-nonnegative-integer? real? -> void? 
-(vect-set! vec k val) 
- 
-; [PROCEDURE] (listof real?) -> vect? 
-(list->vect lst) 
- 
-; [PROCEDURE] vect? -> (listof real?) 
-(vect->list vec) 
-</code> 
-They are like [[http://docs.racket-lang.org/reference/vectors.html#%28def._%28%28quote._~23~25kernel%29._make-vector%29%29|make-vector]], etc. 
- 
-===== Level1 BLAS (Vector-Vector Operations) Interfaces ===== 
-<code scheme> 
-; [PROCEDURE] vect? vect? -> void? 
-(SWAP x y) 
-</code> 
-$x\in\mathbb{R}^n,y\in\mathbb{R}^n,$\\ 
-$$x \leftrightarrow y.$$ 
- 
-<code scheme> 
-; [PROCEDURE] real? vect? -> void? 
-(SCAL a x) 
-</code> 
-$a\in\mathbb{R},x\in\mathbb{R}^n,$\\ 
-$$x \leftarrow ax.$$ 
- 
-<code scheme> 
-; [PROCEDURE] vect? vect? -> void? 
-(COPY x y) 
-</code> 
-$x\in\mathbb{R}^n,y\in\mathbb{R}^n,$\\ 
-$$y \leftarrow x.$$ 
- 
-<code scheme> 
-; [PROCEDURE] real? vect? vect? -> void? 
-(AXPY a x y) 
-</code> 
-$a\in\mathbb{R},x\in\mathbb{R}^n,y\in\mathbb{R}^n,$\\ 
-$$y \leftarrow ax+y.$$ 
- 
-<code scheme> 
-; [PROCEDURE] vect? vect? -> real? 
-(DOT_ x y) 
-</code> 
-$x\in\mathbb{R}^n,y\in\mathbb{R}^n,$\\ 
-$$\langle x,y \rangle=\sum_{i=1}^nx_iy_i.$$ 
- 
-<code scheme> 
-; [PROCEDURE] vect? -> (and/c real? (not/c negative?)) 
-(NRM2 x) 
-</code> 
-$x\in\mathbb{R}^n,$\\ 
-$$\|x\|_2=\sqrt{\langle x,x \rangle}.$$ 
- 
-<code scheme> 
-; [PROCEDURE] vect? -> (and/c real? (not/c negative?)) 
-(ASUM x) 
-</code> 
-$x\in\mathbb{R}^n,$\\ 
-$$\|x\|_1=\sum_{i=1}^n\left|x_i\right|.$$ 
- 
-<code scheme> 
-; [PROCEDURE] vect? -> exact-nonnegative-integer? 
-(IAMX x) 
-</code> 
-$x\in\mathbb{R}^n,$\\ 
-$$k\in\mathbb{N}:\left|x_k\right|\ge{}\left|x_i\right|\hspace{1em}(\forall{}i\in\mathbb{Z}:0\le{}i<n).$$ 
- 
-===== References ===== 
-  - Numerical Algorithms Group Ltd.: [[http://www.netlib.org/blas/blasqr.pdf|Basic Linear Algebra Subprograms: A Quick Reference Guide]]. Oak Ridge National Laboratory, University of Tennessee: (1997). 
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