#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int sppequ_(char *uplo, integer *n, real *ap, real *s, real *
	scond, real *amax, integer *info)
{
/*  -- LAPACK routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    Purpose   
    =======   

    SPPEQU computes row and column scalings intended to equilibrate a   
    symmetric positive definite matrix A in packed storage 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   
    =========   

    UPLO    (input) CHARACTER*1   
            = 'U':  Upper triangle of A is stored;   
            = 'L':  Lower triangle of A is stored.   

    N       (input) INTEGER   
            The order of the matrix A.  N >= 0.   

    AP      (input) REAL array, dimension (N*(N+1)/2)   
            The upper or lower triangle of the symmetric matrix A, packed   
            columnwise in a linear array.  The j-th column of A is stored   
            in the array AP as follows:   
            if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;   
            if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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.   

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


       Test the input parameters.   

       Parameter adjustments */
    /* System generated locals */
    integer i__1;
    real r__1, r__2;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer i__, jj;
    static real smin;
    extern logical lsame_(char *, char *);
    static logical upper;
    extern /* Subroutine */ int xerbla_(char *, integer *);

    --s;
    --ap;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SPPEQU", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	*scond = 1.f;
	*amax = 0.f;
	return 0;
    }

/*     Initialize SMIN and AMAX. */

    s[1] = ap[1];
    smin = s[1];
    *amax = s[1];

    if (upper) {

/*        UPLO = 'U':  Upper triangle of A is stored.   
          Find the minimum and maximum diagonal elements. */

	jj = 1;
	i__1 = *n;
	for (i__ = 2; i__ <= i__1; ++i__) {
	    jj += i__;
	    s[i__] = ap[jj];
/* 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: */
	}

    } else {

/*        UPLO = 'L':  Lower triangle of A is stored.   
          Find the minimum and maximum diagonal elements. */

	jj = 1;
	i__1 = *n;
	for (i__ = 2; i__ <= i__1; ++i__) {
	    jj = jj + *n - i__ + 2;
	    s[i__] = ap[jj];
/* 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);
/* L20: */
	}
    }

    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;
	    }
/* L30: */
	}
    } 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__]);
/* L40: */
	}

/*        Compute SCOND = min(S(I)) / max(S(I)) */

	*scond = sqrt(smin) / sqrt(*amax);
    }
    return 0;

/*     End of SPPEQU */

} /* sppequ_ */