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author | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
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committer | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
commit | 90d450f74722da7859d6f510a869f6c6908fd12f (patch) | |
tree | 538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/ssterf.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/ssterf.c')
-rw-r--r-- | contrib/libs/clapack/ssterf.c | 460 |
1 files changed, 460 insertions, 0 deletions
diff --git a/contrib/libs/clapack/ssterf.c b/contrib/libs/clapack/ssterf.c new file mode 100644 index 0000000000..653dce04b3 --- /dev/null +++ b/contrib/libs/clapack/ssterf.c @@ -0,0 +1,460 @@ +/* ssterf.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__0 = 0; +static integer c__1 = 1; +static real c_b32 = 1.f; + +/* Subroutine */ int ssterf_(integer *n, real *d__, real *e, integer *info) +{ + /* System generated locals */ + integer i__1; + real r__1, r__2, r__3; + + /* Builtin functions */ + double sqrt(doublereal), r_sign(real *, real *); + + /* Local variables */ + real c__; + integer i__, l, m; + real p, r__, s; + integer l1; + real bb, rt1, rt2, eps, rte; + integer lsv; + real eps2, oldc; + integer lend, jtot; + extern /* Subroutine */ int slae2_(real *, real *, real *, real *, real *) + ; + real gamma, alpha, sigma, anorm; + extern doublereal slapy2_(real *, real *); + integer iscale; + real oldgam; + extern doublereal slamch_(char *); + real safmin; + extern /* Subroutine */ int xerbla_(char *, integer *); + real safmax; + extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, + real *, integer *, integer *, real *, integer *, integer *); + integer lendsv; + real ssfmin; + integer nmaxit; + real ssfmax; + extern doublereal slanst_(char *, integer *, real *, real *); + extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *); + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* SSTERF computes all eigenvalues of a symmetric tridiagonal matrix */ +/* using the Pal-Walker-Kahan variant of the QL or QR algorithm. */ + +/* Arguments */ +/* ========= */ + +/* N (input) INTEGER */ +/* The order of the matrix. N >= 0. */ + +/* D (input/output) REAL array, dimension (N) */ +/* On entry, the n diagonal elements of the tridiagonal matrix. */ +/* On exit, if INFO = 0, the eigenvalues in ascending order. */ + +/* E (input/output) REAL array, dimension (N-1) */ +/* On entry, the (n-1) subdiagonal elements of the tridiagonal */ +/* matrix. */ +/* On exit, E has been destroyed. */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > 0: the algorithm failed to find all of the eigenvalues in */ +/* a total of 30*N iterations; if INFO = i, then i */ +/* elements of E have not converged to zero. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --e; + --d__; + + /* Function Body */ + *info = 0; + +/* Quick return if possible */ + + if (*n < 0) { + *info = -1; + i__1 = -(*info); + xerbla_("SSTERF", &i__1); + return 0; + } + if (*n <= 1) { + return 0; + } + +/* Determine the unit roundoff for this environment. */ + + eps = slamch_("E"); +/* Computing 2nd power */ + r__1 = eps; + eps2 = r__1 * r__1; + safmin = slamch_("S"); + safmax = 1.f / safmin; + ssfmax = sqrt(safmax) / 3.f; + ssfmin = sqrt(safmin) / eps2; + +/* Compute the eigenvalues of the tridiagonal matrix. */ + + nmaxit = *n * 30; + sigma = 0.f; + jtot = 0; + +/* Determine where the matrix splits and choose QL or QR iteration */ +/* for each block, according to whether top or bottom diagonal */ +/* element is smaller. */ + + l1 = 1; + +L10: + if (l1 > *n) { + goto L170; + } + if (l1 > 1) { + e[l1 - 1] = 0.f; + } + i__1 = *n - 1; + for (m = l1; m <= i__1; ++m) { + if ((r__3 = e[m], dabs(r__3)) <= sqrt((r__1 = d__[m], dabs(r__1))) * + sqrt((r__2 = d__[m + 1], dabs(r__2))) * eps) { + e[m] = 0.f; + goto L30; + } +/* L20: */ + } + m = *n; + +L30: + l = l1; + lsv = l; + lend = m; + lendsv = lend; + l1 = m + 1; + if (lend == l) { + goto L10; + } + +/* Scale submatrix in rows and columns L to LEND */ + + i__1 = lend - l + 1; + anorm = slanst_("I", &i__1, &d__[l], &e[l]); + iscale = 0; + if (anorm > ssfmax) { + iscale = 1; + i__1 = lend - l + 1; + slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, + info); + i__1 = lend - l; + slascl_("G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, + info); + } else if (anorm < ssfmin) { + iscale = 2; + i__1 = lend - l + 1; + slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, + info); + i__1 = lend - l; + slascl_("G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, + info); + } + + i__1 = lend - 1; + for (i__ = l; i__ <= i__1; ++i__) { +/* Computing 2nd power */ + r__1 = e[i__]; + e[i__] = r__1 * r__1; +/* L40: */ + } + +/* Choose between QL and QR iteration */ + + if ((r__1 = d__[lend], dabs(r__1)) < (r__2 = d__[l], dabs(r__2))) { + lend = lsv; + l = lendsv; + } + + if (lend >= l) { + +/* QL Iteration */ + +/* Look for small subdiagonal element. */ + +L50: + if (l != lend) { + i__1 = lend - 1; + for (m = l; m <= i__1; ++m) { + if ((r__2 = e[m], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[ + m + 1], dabs(r__1))) { + goto L70; + } +/* L60: */ + } + } + m = lend; + +L70: + if (m < lend) { + e[m] = 0.f; + } + p = d__[l]; + if (m == l) { + goto L90; + } + +/* If remaining matrix is 2 by 2, use SLAE2 to compute its */ +/* eigenvalues. */ + + if (m == l + 1) { + rte = sqrt(e[l]); + slae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); + d__[l] = rt1; + d__[l + 1] = rt2; + e[l] = 0.f; + l += 2; + if (l <= lend) { + goto L50; + } + goto L150; + } + + if (jtot == nmaxit) { + goto L150; + } + ++jtot; + +/* Form shift. */ + + rte = sqrt(e[l]); + sigma = (d__[l + 1] - p) / (rte * 2.f); + r__ = slapy2_(&sigma, &c_b32); + sigma = p - rte / (sigma + r_sign(&r__, &sigma)); + + c__ = 1.f; + s = 0.f; + gamma = d__[m] - sigma; + p = gamma * gamma; + +/* Inner loop */ + + i__1 = l; + for (i__ = m - 1; i__ >= i__1; --i__) { + bb = e[i__]; + r__ = p + bb; + if (i__ != m - 1) { + e[i__ + 1] = s * r__; + } + oldc = c__; + c__ = p / r__; + s = bb / r__; + oldgam = gamma; + alpha = d__[i__]; + gamma = c__ * (alpha - sigma) - s * oldgam; + d__[i__ + 1] = oldgam + (alpha - gamma); + if (c__ != 0.f) { + p = gamma * gamma / c__; + } else { + p = oldc * bb; + } +/* L80: */ + } + + e[l] = s * p; + d__[l] = sigma + gamma; + goto L50; + +/* Eigenvalue found. */ + +L90: + d__[l] = p; + + ++l; + if (l <= lend) { + goto L50; + } + goto L150; + + } else { + +/* QR Iteration */ + +/* Look for small superdiagonal element. */ + +L100: + i__1 = lend + 1; + for (m = l; m >= i__1; --m) { + if ((r__2 = e[m - 1], dabs(r__2)) <= eps2 * (r__1 = d__[m] * d__[ + m - 1], dabs(r__1))) { + goto L120; + } +/* L110: */ + } + m = lend; + +L120: + if (m > lend) { + e[m - 1] = 0.f; + } + p = d__[l]; + if (m == l) { + goto L140; + } + +/* If remaining matrix is 2 by 2, use SLAE2 to compute its */ +/* eigenvalues. */ + + if (m == l - 1) { + rte = sqrt(e[l - 1]); + slae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); + d__[l] = rt1; + d__[l - 1] = rt2; + e[l - 1] = 0.f; + l += -2; + if (l >= lend) { + goto L100; + } + goto L150; + } + + if (jtot == nmaxit) { + goto L150; + } + ++jtot; + +/* Form shift. */ + + rte = sqrt(e[l - 1]); + sigma = (d__[l - 1] - p) / (rte * 2.f); + r__ = slapy2_(&sigma, &c_b32); + sigma = p - rte / (sigma + r_sign(&r__, &sigma)); + + c__ = 1.f; + s = 0.f; + gamma = d__[m] - sigma; + p = gamma * gamma; + +/* Inner loop */ + + i__1 = l - 1; + for (i__ = m; i__ <= i__1; ++i__) { + bb = e[i__]; + r__ = p + bb; + if (i__ != m) { + e[i__ - 1] = s * r__; + } + oldc = c__; + c__ = p / r__; + s = bb / r__; + oldgam = gamma; + alpha = d__[i__ + 1]; + gamma = c__ * (alpha - sigma) - s * oldgam; + d__[i__] = oldgam + (alpha - gamma); + if (c__ != 0.f) { + p = gamma * gamma / c__; + } else { + p = oldc * bb; + } +/* L130: */ + } + + e[l - 1] = s * p; + d__[l] = sigma + gamma; + goto L100; + +/* Eigenvalue found. */ + +L140: + d__[l] = p; + + --l; + if (l >= lend) { + goto L100; + } + goto L150; + + } + +/* Undo scaling if necessary */ + +L150: + if (iscale == 1) { + i__1 = lendsv - lsv + 1; + slascl_("G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], + n, info); + } + if (iscale == 2) { + i__1 = lendsv - lsv + 1; + slascl_("G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], + n, info); + } + +/* Check for no convergence to an eigenvalue after a total */ +/* of N*MAXIT iterations. */ + + if (jtot < nmaxit) { + goto L10; + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + if (e[i__] != 0.f) { + ++(*info); + } +/* L160: */ + } + goto L180; + +/* Sort eigenvalues in increasing order. */ + +L170: + slasrt_("I", n, &d__[1], info); + +L180: + return 0; + +/* End of SSTERF */ + +} /* ssterf_ */ |