1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
<html lang="en">
<head>
<title>Level 1 GSL BLAS Interface - GNU Scientific Library -- Reference Manual</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="GNU Scientific Library -- Reference Manual">
<meta name="generator" content="makeinfo 4.8">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="GSL-BLAS-Interface.html" title="GSL BLAS Interface">
<link rel="next" href="Level-2-GSL-BLAS-Interface.html" title="Level 2 GSL BLAS Interface">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<!--
Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 or
any later version published by the Free Software Foundation; with the
Invariant Sections being ``GNU General Public License'' and ``Free Software
Needs Free Documentation'', the Front-Cover text being ``A GNU Manual'',
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled ``GNU Free Documentation
License''.
(a) The Back-Cover Text is: ``You have freedom to copy and modify this
GNU Manual, like GNU software.''-->
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
pre.display { font-family:inherit }
pre.format { font-family:inherit }
pre.smalldisplay { font-family:inherit; font-size:smaller }
pre.smallformat { font-family:inherit; font-size:smaller }
pre.smallexample { font-size:smaller }
pre.smalllisp { font-size:smaller }
span.sc { font-variant:small-caps }
span.roman { font-family:serif; font-weight:normal; }
span.sansserif { font-family:sans-serif; font-weight:normal; }
--></style>
</head>
<body>
<div class="node">
<p>
<a name="Level-1-GSL-BLAS-Interface"></a>
Next: <a rel="next" accesskey="n" href="Level-2-GSL-BLAS-Interface.html">Level 2 GSL BLAS Interface</a>,
Up: <a rel="up" accesskey="u" href="GSL-BLAS-Interface.html">GSL BLAS Interface</a>
<hr>
</div>
<h4 class="subsection">12.1.1 Level 1</h4>
<div class="defun">
— Function: int <b>gsl_blas_sdsdot</b> (<var>float alpha, const gsl_vector_float * x, const gsl_vector_float * y, float * result</var>)<var><a name="index-gsl_005fblas_005fsdsdot-1077"></a></var><br>
<blockquote><p><a name="index-DOT_002c-Level_002d1-BLAS-1078"></a>This function computes the sum \alpha + x^T y for the vectors
<var>x</var> and <var>y</var>, returning the result in <var>result</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_sdot</b> (<var>const gsl_vector_float * x, const gsl_vector_float * y, float * result</var>)<var><a name="index-gsl_005fblas_005fsdot-1079"></a></var><br>
— Function: int <b>gsl_blas_dsdot</b> (<var>const gsl_vector_float * x, const gsl_vector_float * y, double * result</var>)<var><a name="index-gsl_005fblas_005fdsdot-1080"></a></var><br>
— Function: int <b>gsl_blas_ddot</b> (<var>const gsl_vector * x, const gsl_vector * y, double * result</var>)<var><a name="index-gsl_005fblas_005fddot-1081"></a></var><br>
<blockquote><p>These functions compute the scalar product x^T y for the vectors
<var>x</var> and <var>y</var>, returning the result in <var>result</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_cdotu</b> (<var>const gsl_vector_complex_float * x, const gsl_vector_complex_float * y, gsl_complex_float * dotu</var>)<var><a name="index-gsl_005fblas_005fcdotu-1082"></a></var><br>
— Function: int <b>gsl_blas_zdotu</b> (<var>const gsl_vector_complex * x, const gsl_vector_complex * y, gsl_complex * dotu</var>)<var><a name="index-gsl_005fblas_005fzdotu-1083"></a></var><br>
<blockquote><p>These functions compute the complex scalar product x^T y for the
vectors <var>x</var> and <var>y</var>, returning the result in <var>result</var>
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_cdotc</b> (<var>const gsl_vector_complex_float * x, const gsl_vector_complex_float * y, gsl_complex_float * dotc</var>)<var><a name="index-gsl_005fblas_005fcdotc-1084"></a></var><br>
— Function: int <b>gsl_blas_zdotc</b> (<var>const gsl_vector_complex * x, const gsl_vector_complex * y, gsl_complex * dotc</var>)<var><a name="index-gsl_005fblas_005fzdotc-1085"></a></var><br>
<blockquote><p>These functions compute the complex conjugate scalar product x^H
y for the vectors <var>x</var> and <var>y</var>, returning the result in
<var>result</var>
</p></blockquote></div>
<div class="defun">
— Function: float <b>gsl_blas_snrm2</b> (<var>const gsl_vector_float * x</var>)<var><a name="index-gsl_005fblas_005fsnrm2-1086"></a></var><br>
— Function: double <b>gsl_blas_dnrm2</b> (<var>const gsl_vector * x</var>)<var><a name="index-gsl_005fblas_005fdnrm2-1087"></a></var><br>
<blockquote><p><a name="index-NRM2_002c-Level_002d1-BLAS-1088"></a>These functions compute the Euclidean norm
<!-- {$||x||_2 = \sqrt{\sum x_i^2}$} -->
||x||_2 = \sqrt {\sum x_i^2} of the vector <var>x</var>.
</p></blockquote></div>
<div class="defun">
— Function: float <b>gsl_blas_scnrm2</b> (<var>const gsl_vector_complex_float * x</var>)<var><a name="index-gsl_005fblas_005fscnrm2-1089"></a></var><br>
— Function: double <b>gsl_blas_dznrm2</b> (<var>const gsl_vector_complex * x</var>)<var><a name="index-gsl_005fblas_005fdznrm2-1090"></a></var><br>
<blockquote><p>These functions compute the Euclidean norm of the complex vector <var>x</var>,
<pre class="example"> ||x||_2 = \sqrt {\sum (\Re(x_i)^2 + \Im(x_i)^2)}.
</pre>
</blockquote></div>
<div class="defun">
— Function: float <b>gsl_blas_sasum</b> (<var>const gsl_vector_float * x</var>)<var><a name="index-gsl_005fblas_005fsasum-1091"></a></var><br>
— Function: double <b>gsl_blas_dasum</b> (<var>const gsl_vector * x</var>)<var><a name="index-gsl_005fblas_005fdasum-1092"></a></var><br>
<blockquote><p><a name="index-ASUM_002c-Level_002d1-BLAS-1093"></a>These functions compute the absolute sum \sum |x_i| of the
elements of the vector <var>x</var>.
</p></blockquote></div>
<div class="defun">
— Function: float <b>gsl_blas_scasum</b> (<var>const gsl_vector_complex_float * x</var>)<var><a name="index-gsl_005fblas_005fscasum-1094"></a></var><br>
— Function: double <b>gsl_blas_dzasum</b> (<var>const gsl_vector_complex * x</var>)<var><a name="index-gsl_005fblas_005fdzasum-1095"></a></var><br>
<blockquote><p>These functions compute the sum of the magnitudes of the real and
imaginary parts of the complex vector <var>x</var>,
<!-- {$\sum \left( |\Re(x_i)| + |\Im(x_i)| \right)$} -->
\sum |\Re(x_i)| + |\Im(x_i)|.
</p></blockquote></div>
<div class="defun">
— Function: CBLAS_INDEX_t <b>gsl_blas_isamax</b> (<var>const gsl_vector_float * x</var>)<var><a name="index-gsl_005fblas_005fisamax-1096"></a></var><br>
— Function: CBLAS_INDEX_t <b>gsl_blas_idamax</b> (<var>const gsl_vector * x</var>)<var><a name="index-gsl_005fblas_005fidamax-1097"></a></var><br>
— Function: CBLAS_INDEX_t <b>gsl_blas_icamax</b> (<var>const gsl_vector_complex_float * x</var>)<var><a name="index-gsl_005fblas_005ficamax-1098"></a></var><br>
— Function: CBLAS_INDEX_t <b>gsl_blas_izamax</b> (<var>const gsl_vector_complex * x</var>)<var><a name="index-gsl_005fblas_005fizamax-1099"></a></var><br>
<blockquote><p><a name="index-AMAX_002c-Level_002d1-BLAS-1100"></a>These functions return the index of the largest element of the vector
<var>x</var>. The largest element is determined by its absolute magnitude for
real vectors and by the sum of the magnitudes of the real and imaginary
parts |\Re(x_i)| + |\Im(x_i)| for complex vectors. If the
largest value occurs several times then the index of the first
occurrence is returned.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_sswap</b> (<var>gsl_vector_float * x, gsl_vector_float * y</var>)<var><a name="index-gsl_005fblas_005fsswap-1101"></a></var><br>
— Function: int <b>gsl_blas_dswap</b> (<var>gsl_vector * x, gsl_vector * y</var>)<var><a name="index-gsl_005fblas_005fdswap-1102"></a></var><br>
— Function: int <b>gsl_blas_cswap</b> (<var>gsl_vector_complex_float * x, gsl_vector_complex_float * y</var>)<var><a name="index-gsl_005fblas_005fcswap-1103"></a></var><br>
— Function: int <b>gsl_blas_zswap</b> (<var>gsl_vector_complex * x, gsl_vector_complex * y</var>)<var><a name="index-gsl_005fblas_005fzswap-1104"></a></var><br>
<blockquote><p><a name="index-SWAP_002c-Level_002d1-BLAS-1105"></a>These functions exchange the elements of the vectors <var>x</var> and <var>y</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_scopy</b> (<var>const gsl_vector_float * x, gsl_vector_float * y</var>)<var><a name="index-gsl_005fblas_005fscopy-1106"></a></var><br>
— Function: int <b>gsl_blas_dcopy</b> (<var>const gsl_vector * x, gsl_vector * y</var>)<var><a name="index-gsl_005fblas_005fdcopy-1107"></a></var><br>
— Function: int <b>gsl_blas_ccopy</b> (<var>const gsl_vector_complex_float * x, gsl_vector_complex_float * y</var>)<var><a name="index-gsl_005fblas_005fccopy-1108"></a></var><br>
— Function: int <b>gsl_blas_zcopy</b> (<var>const gsl_vector_complex * x, gsl_vector_complex * y</var>)<var><a name="index-gsl_005fblas_005fzcopy-1109"></a></var><br>
<blockquote><p><a name="index-COPY_002c-Level_002d1-BLAS-1110"></a>These functions copy the elements of the vector <var>x</var> into the vector
<var>y</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_saxpy</b> (<var>float alpha, const gsl_vector_float * x, gsl_vector_float * y</var>)<var><a name="index-gsl_005fblas_005fsaxpy-1111"></a></var><br>
— Function: int <b>gsl_blas_daxpy</b> (<var>double alpha, const gsl_vector * x, gsl_vector * y</var>)<var><a name="index-gsl_005fblas_005fdaxpy-1112"></a></var><br>
— Function: int <b>gsl_blas_caxpy</b> (<var>const gsl_complex_float alpha, const gsl_vector_complex_float * x, gsl_vector_complex_float * y</var>)<var><a name="index-gsl_005fblas_005fcaxpy-1113"></a></var><br>
— Function: int <b>gsl_blas_zaxpy</b> (<var>const gsl_complex alpha, const gsl_vector_complex * x, gsl_vector_complex * y</var>)<var><a name="index-gsl_005fblas_005fzaxpy-1114"></a></var><br>
<blockquote><p><a name="index-AXPY_002c-Level_002d1-BLAS-1115"></a><a name="index-DAXPY_002c-Level_002d1-BLAS-1116"></a><a name="index-SAXPY_002c-Level_002d1-BLAS-1117"></a>These functions compute the sum y = \alpha x + y for the vectors
<var>x</var> and <var>y</var>.
</p></blockquote></div>
<div class="defun">
— Function: void <b>gsl_blas_sscal</b> (<var>float alpha, gsl_vector_float * x</var>)<var><a name="index-gsl_005fblas_005fsscal-1118"></a></var><br>
— Function: void <b>gsl_blas_dscal</b> (<var>double alpha, gsl_vector * x</var>)<var><a name="index-gsl_005fblas_005fdscal-1119"></a></var><br>
— Function: void <b>gsl_blas_cscal</b> (<var>const gsl_complex_float alpha, gsl_vector_complex_float * x</var>)<var><a name="index-gsl_005fblas_005fcscal-1120"></a></var><br>
— Function: void <b>gsl_blas_zscal</b> (<var>const gsl_complex alpha, gsl_vector_complex * x</var>)<var><a name="index-gsl_005fblas_005fzscal-1121"></a></var><br>
— Function: void <b>gsl_blas_csscal</b> (<var>float alpha, gsl_vector_complex_float * x</var>)<var><a name="index-gsl_005fblas_005fcsscal-1122"></a></var><br>
— Function: void <b>gsl_blas_zdscal</b> (<var>double alpha, gsl_vector_complex * x</var>)<var><a name="index-gsl_005fblas_005fzdscal-1123"></a></var><br>
<blockquote><p><a name="index-SCAL_002c-Level_002d1-BLAS-1124"></a>These functions rescale the vector <var>x</var> by the multiplicative factor
<var>alpha</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_srotg</b> (<var>float a</var>[]<var>, float b</var>[]<var>, float c</var>[]<var>, float s</var>[])<var><a name="index-gsl_005fblas_005fsrotg-1125"></a></var><br>
— Function: int <b>gsl_blas_drotg</b> (<var>double a</var>[]<var>, double b</var>[]<var>, double c</var>[]<var>, double s</var>[])<var><a name="index-gsl_005fblas_005fdrotg-1126"></a></var><br>
<blockquote><p><a name="index-ROTG_002c-Level_002d1-BLAS-1127"></a><a name="index-Givens-Rotation_002c-BLAS-1128"></a>These functions compute a Givens rotation (c,s) which zeroes the
vector (a,b),
<pre class="example"> [ c s ] [ a ] = [ r ]
[ -s c ] [ b ] [ 0 ]
</pre>
<p class="noindent">The variables <var>a</var> and <var>b</var> are overwritten by the routine.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_srot</b> (<var>gsl_vector_float * x, gsl_vector_float * y, float c, float s</var>)<var><a name="index-gsl_005fblas_005fsrot-1129"></a></var><br>
— Function: int <b>gsl_blas_drot</b> (<var>gsl_vector * x, gsl_vector * y, const double c, const double s</var>)<var><a name="index-gsl_005fblas_005fdrot-1130"></a></var><br>
<blockquote><p>These functions apply a Givens rotation (x', y') = (c x + s y, -s
x + c y) to the vectors <var>x</var>, <var>y</var>.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_srotmg</b> (<var>float d1</var>[]<var>, float d2</var>[]<var>, float b1</var>[]<var>, float b2, float P</var>[])<var><a name="index-gsl_005fblas_005fsrotmg-1131"></a></var><br>
— Function: int <b>gsl_blas_drotmg</b> (<var>double d1</var>[]<var>, double d2</var>[]<var>, double b1</var>[]<var>, double b2, double P</var>[])<var><a name="index-gsl_005fblas_005fdrotmg-1132"></a></var><br>
<blockquote><p><a name="index-Modified-Givens-Rotation_002c-BLAS-1133"></a><a name="index-Givens-Rotation_002c-Modified_002c-BLAS-1134"></a>These functions compute a modified Givens transformation. The modified
Givens transformation is defined in the original Level-1 <span class="sc">blas</span>
specification, given in the references.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_blas_srotm</b> (<var>gsl_vector_float * x, gsl_vector_float * y, const float P</var>[])<var><a name="index-gsl_005fblas_005fsrotm-1135"></a></var><br>
— Function: int <b>gsl_blas_drotm</b> (<var>gsl_vector * x, gsl_vector * y, const double P</var>[])<var><a name="index-gsl_005fblas_005fdrotm-1136"></a></var><br>
<blockquote><p>These functions apply a modified Givens transformation.
</p></blockquote></div>
<hr>The GNU Scientific Library - a free numerical library licensed under the GNU GPL<br>Back to the <a href="/software/gsl/">GNU Scientific Library Homepage</a></body></html>
|
