text: #include "f2c.h"
  #include "blaswrap.h"
  
  /* Subroutine */ int spoequ_(integer *n, real *a, integer *lda, real *s, real 
  	*scond, real *amax, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1;
      real r__1, r__2;
  
      /* Builtin functions */
      double sqrt(doublereal);
  
      /* Local variables */
      integer i__;
      real smin;
      extern /* Subroutine */ int xerbla_(char *, integer *);
  
  
  /*  -- LAPACK routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  SPOEQU computes row and column scalings intended to equilibrate a */
  /*  symmetric positive definite matrix A and reduce its condition number */
  /*  (with respect to the two-norm).  S contains the scale factors, */
  /*  S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with */
  /*  elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This */
  /*  choice of S puts the condition number of B within a factor N of the */
  /*  smallest possible condition number over all possible diagonal */
  /*  scalings. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  N       (input) INTEGER */
  /*          The order of the matrix A.  N >= 0. */
  
  /*  A       (input) REAL array, dimension (LDA,N) */
  /*          The N-by-N symmetric positive definite matrix whose scaling */
  /*          factors are to be computed.  Only the diagonal elements of A */
  /*          are referenced. */
  
  /*  LDA     (input) INTEGER */
  /*          The leading dimension of the array A.  LDA >= max(1,N). */
  
  /*  S       (output) REAL array, dimension (N) */
  /*          If INFO = 0, S contains the scale factors for A. */
  
  /*  SCOND   (output) REAL */
  /*          If INFO = 0, S contains the ratio of the smallest S(i) to */
  /*          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too */
  /*          large nor too small, it is not worth scaling by S. */
  
  /*  AMAX    (output) REAL */
  /*          Absolute value of largest matrix element.  If AMAX is very */
  /*          close to overflow or very close to underflow, the matrix */
  /*          should be scaled. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0:  successful exit */
  /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
  /*          > 0:  if INFO = i, the i-th diagonal element is nonpositive. */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input parameters. */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --s;
  
      /* Function Body */
      *info = 0;
      if (*n < 0) {
  	*info = -1;
      } else if (*lda < max(1,*n)) {
  	*info = -3;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("SPOEQU", &i__1);
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*n == 0) {
  	*scond = 1.f;
  	*amax = 0.f;
  	return 0;
      }
  
  /*     Find the minimum and maximum diagonal elements. */
  
      s[1] = a[a_dim1 + 1];
      smin = s[1];
      *amax = s[1];
      i__1 = *n;
      for (i__ = 2; i__ <= i__1; ++i__) {
  	s[i__] = a[i__ + i__ * a_dim1];
  /* Computing MIN */
  	r__1 = smin, r__2 = s[i__];
  	smin = dmin(r__1,r__2);
  /* Computing MAX */
  	r__1 = *amax, r__2 = s[i__];
  	*amax = dmax(r__1,r__2);
  /* L10: */
      }
  
      if (smin <= 0.f) {
  
  /*        Find the first non-positive diagonal element and return. */
  
  	i__1 = *n;
  	for (i__ = 1; i__ <= i__1; ++i__) {
  	    if (s[i__] <= 0.f) {
  		*info = i__;
  		return 0;
  	    }
  /* L20: */
  	}
      } else {
  
  /*        Set the scale factors to the reciprocals */
  /*        of the diagonal elements. */
  
  	i__1 = *n;
  	for (i__ = 1; i__ <= i__1; ++i__) {
  	    s[i__] = 1.f / sqrt(s[i__]);
  /* L30: */
  	}
  
  /*        Compute SCOND = min(S(I)) / max(S(I)) */
  
  	*scond = sqrt(smin) / sqrt(*amax);
      }
      return 0;
  
  /*     End of SPOEQU */
  
  } /* spoequ_ */
  