void test023 ( )
/******************************************************************************/
/*
Purpose:
TEST023 tests R4_SIGN and R4_SIGN3.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
28 September 2014
Author:
John Burkardt
*/
{
float r4;
float r4_test[5] = { -1.25E+00, -0.25E+00, 0.0E+00, +0.5E+00, +9.0E+00 };
float s1;
float s2;
int test;
const int test_num = 5;
printf ( "\n" );
printf ( "TEST023\n" );
printf ( " R4_SIGN returns the sign of an R4.\n" );
printf ( " R4_SIGN3 returns the three-way sign of an R4.\n" );
printf ( "\n" );
printf ( " R4 R4_SIGN(R4) R4_SIGN3(R4)\n" );
printf ( "\n" );
for ( test = 0; test < test_num; test++ )
{
r4 = r4_test[test];
s1 = r4_sign ( r4 );
s2 = r4_sign3 ( r4 );
printf ( " %8.4f %8.0f %8.0f\n", r4, s1, s2 );
}
return;
}
void srotg ( float *sa, float *sb, float *c, float *s )
/******************************************************************************/
/*
Purpose:
SROTG constructs a Givens plane rotation.
Discussion:
Given values A and B, this routine computes
SIGMA = sign ( A ) if abs ( A ) > abs ( B )
= sign ( B ) if abs ( A ) <= abs ( B );
R = SIGMA * ( A * A + B * B );
C = A / R if R is not 0
= 1 if R is 0;
S = B / R if R is not 0,
0 if R is 0.
The computed numbers then satisfy the equation
( C S ) ( A ) = ( R )
( -S C ) ( B ) = ( 0 )
The routine also computes
Z = S if abs ( A ) > abs ( B ),
= 1 / C if abs ( A ) <= abs ( B ) and C is not 0,
= 1 if C is 0.
The single value Z encodes C and S, and hence the rotation:
If Z = 1, set C = 0 and S = 1;
If abs ( Z ) < 1, set C = sqrt ( 1 - Z * Z ) and S = Z;
if abs ( Z ) > 1, set C = 1/ Z and S = sqrt ( 1 - C * C );
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
29 March 2007
Author:
C version by John Burkardt
Reference:
Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart,
LINPACK User's Guide,
SIAM, 1979,
ISBN13: 978-0-898711-72-1,
LC: QA214.L56.
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,
Algorithm 539:
Basic Linear Algebra Subprograms for Fortran Usage,
ACM Transactions on Mathematical Software,
Volume 5, Number 3, September 1979, pages 308-323.
Parameters:
Input/output, float *SA, *SB, On input, SA and SB are the values
A and B. On output, SA is overwritten with R, and SB is
overwritten with Z.
Output, float *C, *S, the cosine and sine of the Givens rotation.
*/
{
float r;
float roe;
float scale;
float z;
if ( r4_abs ( *sb ) < r4_abs ( *sa ) )
{
roe = *sa;
}
else
{
roe = *sb;
}
scale = r4_abs ( *sa ) + r4_abs ( *sb );
if ( scale == 0.0 )
{
*c = 1.0;
*s = 0.0;
r = 0.0;
}
else
{
r = scale * sqrt ( ( *sa / scale ) * ( *sa / scale )
+ ( *sb / scale ) * ( *sb / scale ) );
r = r4_sign ( roe ) * r;
*c = *sa / r;
*s = *sb / r;
}
if ( 0.0 < r4_abs ( *c ) && r4_abs ( *c ) <= *s )
{
z = 1.0 / *c;
}
else
{
z = *s;
}
*sa = r;
*sb = z;
return;
}
