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authorshmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
committershmel1k <shmel1k@ydb.tech>2022-09-02 12:44:59 +0300
commit90d450f74722da7859d6f510a869f6c6908fd12f (patch)
tree538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/cppequ.c
parent01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff)
downloadydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz
[] add metering mode to CLI
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+/* cppequ.f -- translated by f2c (version 20061008).
+ You must link the resulting object file with libf2c:
+ on Microsoft Windows system, link with libf2c.lib;
+ on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+ or, if you install libf2c.a in a standard place, with -lf2c -lm
+ -- in that order, at the end of the command line, as in
+ cc *.o -lf2c -lm
+ Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+ http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Subroutine */ int cppequ_(char *uplo, integer *n, complex *ap, real *s,
+ real *scond, real *amax, integer *info)
+{
+ /* System generated locals */
+ integer i__1, i__2;
+ real r__1, r__2;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ integer i__, jj;
+ real smin;
+ extern logical lsame_(char *, char *);
+ logical upper;
+ extern /* Subroutine */ int xerbla_(char *, integer *);
+
+
+/* -- LAPACK routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CPPEQU computes row and column scalings intended to equilibrate a */
+/* Hermitian 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) COMPLEX array, dimension (N*(N+1)/2) */
+/* The upper or lower triangle of the Hermitian 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. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters. */
+
+ /* Parameter adjustments */
+ --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_("CPPEQU", &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].r;
+ 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__;
+ i__2 = jj;
+ s[i__] = ap[i__2].r;
+/* 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;
+ i__2 = jj;
+ s[i__] = ap[i__2].r;
+/* 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 CPPEQU */
+
+} /* cppequ_ */