aboutsummaryrefslogtreecommitdiffstats
path: root/contrib/libs/clapack/cgebal.c
diff options
context:
space:
mode:
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/cgebal.c
parent01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff)
downloadydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/cgebal.c')
-rw-r--r--contrib/libs/clapack/cgebal.c414
1 files changed, 414 insertions, 0 deletions
diff --git a/contrib/libs/clapack/cgebal.c b/contrib/libs/clapack/cgebal.c
new file mode 100644
index 0000000000..435e9a72c5
--- /dev/null
+++ b/contrib/libs/clapack/cgebal.c
@@ -0,0 +1,414 @@
+/* cgebal.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"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* Subroutine */ int cgebal_(char *job, integer *n, complex *a, integer *lda,
+ integer *ilo, integer *ihi, real *scale, integer *info)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3;
+ real r__1, r__2;
+
+ /* Builtin functions */
+ double r_imag(complex *), c_abs(complex *);
+
+ /* Local variables */
+ real c__, f, g;
+ integer i__, j, k, l, m;
+ real r__, s, ca, ra;
+ integer ica, ira, iexc;
+ extern logical lsame_(char *, char *);
+ extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
+ complex *, integer *);
+ real sfmin1, sfmin2, sfmax1, sfmax2;
+ extern integer icamax_(integer *, complex *, integer *);
+ extern doublereal slamch_(char *);
+ extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
+ *), xerbla_(char *, integer *);
+ logical noconv;
+
+
+/* -- LAPACK routine (version 3.2) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* CGEBAL balances a general complex matrix A. This involves, first, */
+/* permuting A by a similarity transformation to isolate eigenvalues */
+/* in the first 1 to ILO-1 and last IHI+1 to N elements on the */
+/* diagonal; and second, applying a diagonal similarity transformation */
+/* to rows and columns ILO to IHI to make the rows and columns as */
+/* close in norm as possible. Both steps are optional. */
+
+/* Balancing may reduce the 1-norm of the matrix, and improve the */
+/* accuracy of the computed eigenvalues and/or eigenvectors. */
+
+/* Arguments */
+/* ========= */
+
+/* JOB (input) CHARACTER*1 */
+/* Specifies the operations to be performed on A: */
+/* = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0 */
+/* for i = 1,...,N; */
+/* = 'P': permute only; */
+/* = 'S': scale only; */
+/* = 'B': both permute and scale. */
+
+/* N (input) INTEGER */
+/* The order of the matrix A. N >= 0. */
+
+/* A (input/output) COMPLEX array, dimension (LDA,N) */
+/* On entry, the input matrix A. */
+/* On exit, A is overwritten by the balanced matrix. */
+/* If JOB = 'N', A is not referenced. */
+/* See Further Details. */
+
+/* LDA (input) INTEGER */
+/* The leading dimension of the array A. LDA >= max(1,N). */
+
+/* ILO (output) INTEGER */
+/* IHI (output) INTEGER */
+/* ILO and IHI are set to integers such that on exit */
+/* A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N. */
+/* If JOB = 'N' or 'S', ILO = 1 and IHI = N. */
+
+/* SCALE (output) REAL array, dimension (N) */
+/* Details of the permutations and scaling factors applied to */
+/* A. If P(j) is the index of the row and column interchanged */
+/* with row and column j and D(j) is the scaling factor */
+/* applied to row and column j, then */
+/* SCALE(j) = P(j) for j = 1,...,ILO-1 */
+/* = D(j) for j = ILO,...,IHI */
+/* = P(j) for j = IHI+1,...,N. */
+/* The order in which the interchanges are made is N to IHI+1, */
+/* then 1 to ILO-1. */
+
+/* INFO (output) INTEGER */
+/* = 0: successful exit. */
+/* < 0: if INFO = -i, the i-th argument had an illegal value. */
+
+/* Further Details */
+/* =============== */
+
+/* The permutations consist of row and column interchanges which put */
+/* the matrix in the form */
+
+/* ( T1 X Y ) */
+/* P A P = ( 0 B Z ) */
+/* ( 0 0 T2 ) */
+
+/* where T1 and T2 are upper triangular matrices whose eigenvalues lie */
+/* along the diagonal. The column indices ILO and IHI mark the starting */
+/* and ending columns of the submatrix B. Balancing consists of applying */
+/* a diagonal similarity transformation inv(D) * B * D to make the */
+/* 1-norms of each row of B and its corresponding column nearly equal. */
+/* The output matrix is */
+
+/* ( T1 X*D Y ) */
+/* ( 0 inv(D)*B*D inv(D)*Z ). */
+/* ( 0 0 T2 ) */
+
+/* Information about the permutations P and the diagonal matrix D is */
+/* returned in the vector SCALE. */
+
+/* This subroutine is based on the EISPACK routine CBAL. */
+
+/* Modified by Tzu-Yi Chen, Computer Science Division, University of */
+/* California at Berkeley, USA */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. External Functions .. */
+/* .. */
+/* .. External Subroutines .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Statement Functions .. */
+/* .. */
+/* .. Statement Function definitions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --scale;
+
+ /* Function Body */
+ *info = 0;
+ if (! lsame_(job, "N") && ! lsame_(job, "P") && ! lsame_(job, "S")
+ && ! lsame_(job, "B")) {
+ *info = -1;
+ } else if (*n < 0) {
+ *info = -2;
+ } else if (*lda < max(1,*n)) {
+ *info = -4;
+ }
+ if (*info != 0) {
+ i__1 = -(*info);
+ xerbla_("CGEBAL", &i__1);
+ return 0;
+ }
+
+ k = 1;
+ l = *n;
+
+ if (*n == 0) {
+ goto L210;
+ }
+
+ if (lsame_(job, "N")) {
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ scale[i__] = 1.f;
+/* L10: */
+ }
+ goto L210;
+ }
+
+ if (lsame_(job, "S")) {
+ goto L120;
+ }
+
+/* Permutation to isolate eigenvalues if possible */
+
+ goto L50;
+
+/* Row and column exchange. */
+
+L20:
+ scale[m] = (real) j;
+ if (j == m) {
+ goto L30;
+ }
+
+ cswap_(&l, &a[j * a_dim1 + 1], &c__1, &a[m * a_dim1 + 1], &c__1);
+ i__1 = *n - k + 1;
+ cswap_(&i__1, &a[j + k * a_dim1], lda, &a[m + k * a_dim1], lda);
+
+L30:
+ switch (iexc) {
+ case 1: goto L40;
+ case 2: goto L80;
+ }
+
+/* Search for rows isolating an eigenvalue and push them down. */
+
+L40:
+ if (l == 1) {
+ goto L210;
+ }
+ --l;
+
+L50:
+ for (j = l; j >= 1; --j) {
+
+ i__1 = l;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+ if (i__ == j) {
+ goto L60;
+ }
+ i__2 = j + i__ * a_dim1;
+ if (a[i__2].r != 0.f || r_imag(&a[j + i__ * a_dim1]) != 0.f) {
+ goto L70;
+ }
+L60:
+ ;
+ }
+
+ m = l;
+ iexc = 1;
+ goto L20;
+L70:
+ ;
+ }
+
+ goto L90;
+
+/* Search for columns isolating an eigenvalue and push them left. */
+
+L80:
+ ++k;
+
+L90:
+ i__1 = l;
+ for (j = k; j <= i__1; ++j) {
+
+ i__2 = l;
+ for (i__ = k; i__ <= i__2; ++i__) {
+ if (i__ == j) {
+ goto L100;
+ }
+ i__3 = i__ + j * a_dim1;
+ if (a[i__3].r != 0.f || r_imag(&a[i__ + j * a_dim1]) != 0.f) {
+ goto L110;
+ }
+L100:
+ ;
+ }
+
+ m = k;
+ iexc = 2;
+ goto L20;
+L110:
+ ;
+ }
+
+L120:
+ i__1 = l;
+ for (i__ = k; i__ <= i__1; ++i__) {
+ scale[i__] = 1.f;
+/* L130: */
+ }
+
+ if (lsame_(job, "P")) {
+ goto L210;
+ }
+
+/* Balance the submatrix in rows K to L. */
+
+/* Iterative loop for norm reduction */
+
+ sfmin1 = slamch_("S") / slamch_("P");
+ sfmax1 = 1.f / sfmin1;
+ sfmin2 = sfmin1 * 2.f;
+ sfmax2 = 1.f / sfmin2;
+L140:
+ noconv = FALSE_;
+
+ i__1 = l;
+ for (i__ = k; i__ <= i__1; ++i__) {
+ c__ = 0.f;
+ r__ = 0.f;
+
+ i__2 = l;
+ for (j = k; j <= i__2; ++j) {
+ if (j == i__) {
+ goto L150;
+ }
+ i__3 = j + i__ * a_dim1;
+ c__ += (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[j + i__
+ * a_dim1]), dabs(r__2));
+ i__3 = i__ + j * a_dim1;
+ r__ += (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[i__ + j
+ * a_dim1]), dabs(r__2));
+L150:
+ ;
+ }
+ ica = icamax_(&l, &a[i__ * a_dim1 + 1], &c__1);
+ ca = c_abs(&a[ica + i__ * a_dim1]);
+ i__2 = *n - k + 1;
+ ira = icamax_(&i__2, &a[i__ + k * a_dim1], lda);
+ ra = c_abs(&a[i__ + (ira + k - 1) * a_dim1]);
+
+/* Guard against zero C or R due to underflow. */
+
+ if (c__ == 0.f || r__ == 0.f) {
+ goto L200;
+ }
+ g = r__ / 2.f;
+ f = 1.f;
+ s = c__ + r__;
+L160:
+/* Computing MAX */
+ r__1 = max(f,c__);
+/* Computing MIN */
+ r__2 = min(r__,g);
+ if (c__ >= g || dmax(r__1,ca) >= sfmax2 || dmin(r__2,ra) <= sfmin2) {
+ goto L170;
+ }
+ f *= 2.f;
+ c__ *= 2.f;
+ ca *= 2.f;
+ r__ /= 2.f;
+ g /= 2.f;
+ ra /= 2.f;
+ goto L160;
+
+L170:
+ g = c__ / 2.f;
+L180:
+/* Computing MIN */
+ r__1 = min(f,c__), r__1 = min(r__1,g);
+ if (g < r__ || dmax(r__,ra) >= sfmax2 || dmin(r__1,ca) <= sfmin2) {
+ goto L190;
+ }
+ f /= 2.f;
+ c__ /= 2.f;
+ g /= 2.f;
+ ca /= 2.f;
+ r__ *= 2.f;
+ ra *= 2.f;
+ goto L180;
+
+/* Now balance. */
+
+L190:
+ if (c__ + r__ >= s * .95f) {
+ goto L200;
+ }
+ if (f < 1.f && scale[i__] < 1.f) {
+ if (f * scale[i__] <= sfmin1) {
+ goto L200;
+ }
+ }
+ if (f > 1.f && scale[i__] > 1.f) {
+ if (scale[i__] >= sfmax1 / f) {
+ goto L200;
+ }
+ }
+ g = 1.f / f;
+ scale[i__] *= f;
+ noconv = TRUE_;
+
+ i__2 = *n - k + 1;
+ csscal_(&i__2, &g, &a[i__ + k * a_dim1], lda);
+ csscal_(&l, &f, &a[i__ * a_dim1 + 1], &c__1);
+
+L200:
+ ;
+ }
+
+ if (noconv) {
+ goto L140;
+ }
+
+L210:
+ *ilo = k;
+ *ihi = l;
+
+ return 0;
+
+/* End of CGEBAL */
+
+} /* cgebal_ */