spoequb.c
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00001 /* spoequb.f -- translated by f2c (version 20061008).
00002    You must link the resulting object file with libf2c:
00003         on Microsoft Windows system, link with libf2c.lib;
00004         on Linux or Unix systems, link with .../path/to/libf2c.a -lm
00005         or, if you install libf2c.a in a standard place, with -lf2c -lm
00006         -- in that order, at the end of the command line, as in
00007                 cc *.o -lf2c -lm
00008         Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
00009 
00010                 http://www.netlib.org/f2c/libf2c.zip
00011 */
00012 
00013 #include "f2c.h"
00014 #include "blaswrap.h"
00015 
00016 /* Subroutine */ int spoequb_(integer *n, real *a, integer *lda, real *s, 
00017         real *scond, real *amax, integer *info)
00018 {
00019     /* System generated locals */
00020     integer a_dim1, a_offset, i__1, i__2;
00021     real r__1, r__2;
00022 
00023     /* Builtin functions */
00024     double log(doublereal), pow_ri(real *, integer *), sqrt(doublereal);
00025 
00026     /* Local variables */
00027     integer i__;
00028     real tmp, base, smin;
00029     extern doublereal slamch_(char *);
00030     extern /* Subroutine */ int xerbla_(char *, integer *);
00031 
00032 
00033 /*     -- LAPACK routine (version 3.2)                                 -- */
00034 /*     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
00035 /*     -- Jason Riedy of Univ. of California Berkeley.                 -- */
00036 /*     -- November 2008                                                -- */
00037 
00038 /*     -- LAPACK is a software package provided by Univ. of Tennessee, -- */
00039 /*     -- Univ. of California Berkeley and NAG Ltd.                    -- */
00040 
00041 /*     .. */
00042 /*     .. Scalar Arguments .. */
00043 /*     .. */
00044 /*     .. Array Arguments .. */
00045 /*     .. */
00046 
00047 /*  Purpose */
00048 /*  ======= */
00049 
00050 /*  SPOEQU computes row and column scalings intended to equilibrate a */
00051 /*  symmetric positive definite matrix A and reduce its condition number */
00052 /*  (with respect to the two-norm).  S contains the scale factors, */
00053 /*  S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with */
00054 /*  elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This */
00055 /*  choice of S puts the condition number of B within a factor N of the */
00056 /*  smallest possible condition number over all possible diagonal */
00057 /*  scalings. */
00058 
00059 /*  Arguments */
00060 /*  ========= */
00061 
00062 /*  N       (input) INTEGER */
00063 /*          The order of the matrix A.  N >= 0. */
00064 
00065 /*  A       (input) REAL array, dimension (LDA,N) */
00066 /*          The N-by-N symmetric positive definite matrix whose scaling */
00067 /*          factors are to be computed.  Only the diagonal elements of A */
00068 /*          are referenced. */
00069 
00070 /*  LDA     (input) INTEGER */
00071 /*          The leading dimension of the array A.  LDA >= max(1,N). */
00072 
00073 /*  S       (output) REAL array, dimension (N) */
00074 /*          If INFO = 0, S contains the scale factors for A. */
00075 
00076 /*  SCOND   (output) REAL */
00077 /*          If INFO = 0, S contains the ratio of the smallest S(i) to */
00078 /*          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too */
00079 /*          large nor too small, it is not worth scaling by S. */
00080 
00081 /*  AMAX    (output) REAL */
00082 /*          Absolute value of largest matrix element.  If AMAX is very */
00083 /*          close to overflow or very close to underflow, the matrix */
00084 /*          should be scaled. */
00085 
00086 /*  INFO    (output) INTEGER */
00087 /*          = 0:  successful exit */
00088 /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
00089 /*          > 0:  if INFO = i, the i-th diagonal element is nonpositive. */
00090 
00091 /*  ===================================================================== */
00092 
00093 /*     .. Parameters .. */
00094 /*     .. */
00095 /*     .. Local Scalars .. */
00096 /*     .. */
00097 /*     .. External Functions .. */
00098 /*     .. */
00099 /*     .. External Subroutines .. */
00100 /*     .. */
00101 /*     .. Intrinsic Functions .. */
00102 /*     .. */
00103 /*     .. Executable Statements .. */
00104 
00105 /*     Test the input parameters. */
00106 
00107 /*     Positive definite only performs 1 pass of equilibration. */
00108 
00109     /* Parameter adjustments */
00110     a_dim1 = *lda;
00111     a_offset = 1 + a_dim1;
00112     a -= a_offset;
00113     --s;
00114 
00115     /* Function Body */
00116     *info = 0;
00117     if (*n < 0) {
00118         *info = -1;
00119     } else if (*lda < max(1,*n)) {
00120         *info = -3;
00121     }
00122     if (*info != 0) {
00123         i__1 = -(*info);
00124         xerbla_("SPOEQUB", &i__1);
00125         return 0;
00126     }
00127 
00128 /*     Quick return if possible. */
00129 
00130     if (*n == 0) {
00131         *scond = 1.f;
00132         *amax = 0.f;
00133         return 0;
00134     }
00135     base = slamch_("B");
00136     tmp = -.5f / log(base);
00137 
00138 /*     Find the minimum and maximum diagonal elements. */
00139 
00140     s[1] = a[a_dim1 + 1];
00141     smin = s[1];
00142     *amax = s[1];
00143     i__1 = *n;
00144     for (i__ = 2; i__ <= i__1; ++i__) {
00145         s[i__] = a[i__ + i__ * a_dim1];
00146 /* Computing MIN */
00147         r__1 = smin, r__2 = s[i__];
00148         smin = dmin(r__1,r__2);
00149 /* Computing MAX */
00150         r__1 = *amax, r__2 = s[i__];
00151         *amax = dmax(r__1,r__2);
00152 /* L10: */
00153     }
00154 
00155     if (smin <= 0.f) {
00156 
00157 /*        Find the first non-positive diagonal element and return. */
00158 
00159         i__1 = *n;
00160         for (i__ = 1; i__ <= i__1; ++i__) {
00161             if (s[i__] <= 0.f) {
00162                 *info = i__;
00163                 return 0;
00164             }
00165 /* L20: */
00166         }
00167     } else {
00168 
00169 /*        Set the scale factors to the reciprocals */
00170 /*        of the diagonal elements. */
00171 
00172         i__1 = *n;
00173         for (i__ = 1; i__ <= i__1; ++i__) {
00174             i__2 = (integer) (tmp * log(s[i__]));
00175             s[i__] = pow_ri(&base, &i__2);
00176 /* L30: */
00177         }
00178 
00179 /*        Compute SCOND = min(S(I)) / max(S(I)). */
00180 
00181         *scond = sqrt(smin) / sqrt(*amax);
00182     }
00183 
00184     return 0;
00185 
00186 /*     End of SPOEQUB */
00187 
00188 } /* spoequb_ */


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autogenerated on Sat Jun 8 2019 18:56:12