#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dppequ_(char *uplo, integer *n, doublereal *ap, doublereal *s, doublereal *scond, doublereal *amax, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= DPPEQU 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static doublereal smin; static integer i__; extern logical lsame_(char *, char *); static logical upper; static integer jj; 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_("DPPEQU", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { *scond = 1.; *amax = 0.; 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 */ d__1 = smin, d__2 = s[i__]; smin = min(d__1,d__2); /* Computing MAX */ d__1 = *amax, d__2 = s[i__]; *amax = max(d__1,d__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 */ d__1 = smin, d__2 = s[i__]; smin = min(d__1,d__2); /* Computing MAX */ d__1 = *amax, d__2 = s[i__]; *amax = max(d__1,d__2); /* L20: */ } } if (smin <= 0.) { /* Find the first non-positive diagonal element and return. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] <= 0.) { *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. / sqrt(s[i__]); /* L40: */ } /* Compute SCOND = min(S(I)) / max(S(I)) */ *scond = sqrt(smin) / sqrt(*amax); } return 0; /* End of DPPEQU */ } /* dppequ_ */