slaev2.c

来自「NIST Handwriting OCR Testbed」· C语言 代码 · 共 175 行

/*
* ======================================================================
* NIST Guide to Available Math Software.
* Fullsource for module SSYEVX.C from package CLAPACK.
* Retrieved from NETLIB on Fri Mar 10 14:23:44 2000.
* ======================================================================
*/
#include <f2c.h>

/* Subroutine */ int slaev2_(real *a, real *b, real *c, real *rt1, real *rt2, 
	real *cs1, real *sn1)
{
/*  -- LAPACK auxiliary routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1992   


    Purpose   
    =======   

    SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix   
       [  A   B  ]   
       [  B   C  ].   
    On return, RT1 is the eigenvalue of larger absolute value, RT2 is the 
  
    eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right 
  
    eigenvector for RT1, giving the decomposition   

       [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]   
       [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].   

    Arguments   
    =========   

    A       (input) REAL   
            The (1,1) element of the 2-by-2 matrix.   

    B       (input) REAL   
            The (1,2) element and the conjugate of the (2,1) element of   
            the 2-by-2 matrix.   

    C       (input) REAL   
            The (2,2) element of the 2-by-2 matrix.   

    RT1     (output) REAL   
            The eigenvalue of larger absolute value.   

    RT2     (output) REAL   
            The eigenvalue of smaller absolute value.   

    CS1     (output) REAL   
    SN1     (output) REAL   
            The vector (CS1, SN1) is a unit right eigenvector for RT1.   

    Further Details   
    ===============   

    RT1 is accurate to a few ulps barring over/underflow.   

    RT2 may be inaccurate if there is massive cancellation in the   
    determinant A*C-B*B; higher precision or correctly rounded or   
    correctly truncated arithmetic would be needed to compute RT2   
    accurately in all cases.   

    CS1 and SN1 are accurate to a few ulps barring over/underflow.   

    Overflow is possible only if RT1 is within a factor of 5 of overflow. 
  
    Underflow is harmless if the input data is 0 or exceeds   
       underflow_threshold / macheps.   

   ===================================================================== 
  


       Compute the eigenvalues */
    /* System generated locals */
    real r__1;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static real acmn, acmx, ab, df, cs, ct, tb, sm, tn, rt, adf, acs;
    static integer sgn1, sgn2;


    sm = *a + *c;
    df = *a - *c;
    adf = dabs(df);
    tb = *b + *b;
    ab = dabs(tb);
    if (dabs(*a) > dabs(*c)) {
	acmx = *a;
	acmn = *c;
    } else {
	acmx = *c;
	acmn = *a;
    }
    if (adf > ab) {
/* Computing 2nd power */
	r__1 = ab / adf;
	rt = adf * sqrt(r__1 * r__1 + 1.f);
    } else if (adf < ab) {
/* Computing 2nd power */
	r__1 = adf / ab;
	rt = ab * sqrt(r__1 * r__1 + 1.f);
    } else {

/*        Includes case AB=ADF=0 */

	rt = ab * sqrt(2.f);
    }
    if (sm < 0.f) {
	*rt1 = (sm - rt) * .5f;
	sgn1 = -1;

/*        Order of execution important.   
          To get fully accurate smaller eigenvalue,   
          next line needs to be executed in higher precision. */

	*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
    } else if (sm > 0.f) {
	*rt1 = (sm + rt) * .5f;
	sgn1 = 1;

/*        Order of execution important.   
          To get fully accurate smaller eigenvalue,   
          next line needs to be executed in higher precision. */

	*rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
    } else {

/*        Includes case RT1 = RT2 = 0 */

	*rt1 = rt * .5f;
	*rt2 = rt * -.5f;
	sgn1 = 1;
    }

/*     Compute the eigenvector */

    if (df >= 0.f) {
	cs = df + rt;
	sgn2 = 1;
    } else {
	cs = df - rt;
	sgn2 = -1;
    }
    acs = dabs(cs);
    if (acs > ab) {
	ct = -(doublereal)tb / cs;
	*sn1 = 1.f / sqrt(ct * ct + 1.f);
	*cs1 = ct * *sn1;
    } else {
	if (ab == 0.f) {
	    *cs1 = 1.f;
	    *sn1 = 0.f;
	} else {
	    tn = -(doublereal)cs / tb;
	    *cs1 = 1.f / sqrt(tn * tn + 1.f);
	    *sn1 = tn * *cs1;
	}
    }
    if (sgn1 == sgn2) {
	tn = *cs1;
	*cs1 = -(doublereal)(*sn1);
	*sn1 = tn;
    }
    return 0;

/*     End of SLAEV2 */

} /* slaev2_ */