/* slasq3.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 "clapack.h" /* Subroutine */ int slasq3_(integer *i0, integer *n0, real *z__, integer *pp, real *dmin__, real *sigma, real *desig, real *qmax, integer *nfail, integer *iter, integer *ndiv, logical *ieee, integer *ttype, real * dmin1, real *dmin2, real *dn, real *dn1, real *dn2, real *g, real * tau) { /* System generated locals */ integer i__1; real r__1, r__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ real s, t; integer j4, nn; real eps, tol; integer n0in, ipn4; real tol2, temp; extern /* Subroutine */ int slasq4_(integer *, integer *, real *, integer *, integer *, real *, real *, real *, real *, real *, real *, real *, integer *, real *), slasq5_(integer *, integer *, real *, integer *, real *, real *, real *, real *, real *, real *, real *, logical *), slasq6_(integer *, integer *, real *, integer *, real *, real *, real *, real *, real *, real *); extern doublereal slamch_(char *); extern logical sisnan_(real *); /* -- LAPACK routine (version 3.2) -- */ /* -- Contributed by Osni Marques of the Lawrence Berkeley National -- */ /* -- Laboratory and Beresford Parlett of the Univ. of California at -- */ /* -- Berkeley -- */ /* -- November 2008 -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. */ /* In case of failure it changes shifts, and tries again until output */ /* is positive. */ /* Arguments */ /* ========= */ /* I0 (input) INTEGER */ /* First index. */ /* N0 (input) INTEGER */ /* Last index. */ /* Z (input) REAL array, dimension ( 4*N ) */ /* Z holds the qd array. */ /* PP (input/output) INTEGER */ /* PP=0 for ping, PP=1 for pong. */ /* PP=2 indicates that flipping was applied to the Z array */ /* and that the initial tests for deflation should not be */ /* performed. */ /* DMIN (output) REAL */ /* Minimum value of d. */ /* SIGMA (output) REAL */ /* Sum of shifts used in current segment. */ /* DESIG (input/output) REAL */ /* Lower order part of SIGMA */ /* QMAX (input) REAL */ /* Maximum value of q. */ /* NFAIL (output) INTEGER */ /* Number of times shift was too big. */ /* ITER (output) INTEGER */ /* Number of iterations. */ /* NDIV (output) INTEGER */ /* Number of divisions. */ /* IEEE (input) LOGICAL */ /* Flag for IEEE or non IEEE arithmetic (passed to SLASQ5). */ /* TTYPE (input/output) INTEGER */ /* Shift type. */ /* DMIN1, DMIN2, DN, DN1, DN2, G, TAU (input/output) REAL */ /* These are passed as arguments in order to save their values */ /* between calls to SLASQ3. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. External Function .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ --z__; /* Function Body */ n0in = *n0; eps = slamch_("Precision"); tol = eps * 100.f; /* Computing 2nd power */ r__1 = tol; tol2 = r__1 * r__1; /* Check for deflation. */ L10: if (*n0 < *i0) { return 0; } if (*n0 == *i0) { goto L20; } nn = (*n0 << 2) + *pp; if (*n0 == *i0 + 1) { goto L40; } /* Check whether E(N0-1) is negligible, 1 eigenvalue. */ if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - 4] > tol2 * z__[nn - 7]) { goto L30; } L20: z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma; --(*n0); goto L10; /* Check whether E(N0-2) is negligible, 2 eigenvalues. */ L30: if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[ nn - 11]) { goto L50; } L40: if (z__[nn - 3] > z__[nn - 7]) { s = z__[nn - 3]; z__[nn - 3] = z__[nn - 7]; z__[nn - 7] = s; } if (z__[nn - 5] > z__[nn - 3] * tol2) { t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5f; s = z__[nn - 3] * (z__[nn - 5] / t); if (s <= t) { s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.f) + 1.f))); } else { s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s))); } t = z__[nn - 7] + (s + z__[nn - 5]); z__[nn - 3] *= z__[nn - 7] / t; z__[nn - 7] = t; } z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma; z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma; *n0 += -2; goto L10; L50: if (*pp == 2) { *pp = 0; } /* Reverse the qd-array, if warranted. */ if (*dmin__ <= 0.f || *n0 < n0in) { if (z__[(*i0 << 2) + *pp - 3] * 1.5f < z__[(*n0 << 2) + *pp - 3]) { ipn4 = *i0 + *n0 << 2; i__1 = *i0 + *n0 - 1 << 1; for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { temp = z__[j4 - 3]; z__[j4 - 3] = z__[ipn4 - j4 - 3]; z__[ipn4 - j4 - 3] = temp; temp = z__[j4 - 2]; z__[j4 - 2] = z__[ipn4 - j4 - 2]; z__[ipn4 - j4 - 2] = temp; temp = z__[j4 - 1]; z__[j4 - 1] = z__[ipn4 - j4 - 5]; z__[ipn4 - j4 - 5] = temp; temp = z__[j4]; z__[j4] = z__[ipn4 - j4 - 4]; z__[ipn4 - j4 - 4] = temp; /* L60: */ } if (*n0 - *i0 <= 4) { z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1]; z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp]; } /* Computing MIN */ r__1 = *dmin2, r__2 = z__[(*n0 << 2) + *pp - 1]; *dmin2 = dmin(r__1,r__2); /* Computing MIN */ r__1 = z__[(*n0 << 2) + *pp - 1], r__2 = z__[(*i0 << 2) + *pp - 1] , r__1 = min(r__1,r__2), r__2 = z__[(*i0 << 2) + *pp + 3]; z__[(*n0 << 2) + *pp - 1] = dmin(r__1,r__2); /* Computing MIN */ r__1 = z__[(*n0 << 2) - *pp], r__2 = z__[(*i0 << 2) - *pp], r__1 = min(r__1,r__2), r__2 = z__[(*i0 << 2) - *pp + 4]; z__[(*n0 << 2) - *pp] = dmin(r__1,r__2); /* Computing MAX */ r__1 = *qmax, r__2 = z__[(*i0 << 2) + *pp - 3], r__1 = max(r__1, r__2), r__2 = z__[(*i0 << 2) + *pp + 1]; *qmax = dmax(r__1,r__2); *dmin__ = -0.f; } } /* Choose a shift. */ slasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g); /* Call dqds until DMIN > 0. */ L70: slasq5_(i0, n0, &z__[1], pp, tau, dmin__, dmin1, dmin2, dn, dn1, dn2, ieee); *ndiv += *n0 - *i0 + 2; ++(*iter); /* Check status. */ if (*dmin__ >= 0.f && *dmin1 > 0.f) { /* Success. */ goto L90; } else if (*dmin__ < 0.f && *dmin1 > 0.f && z__[(*n0 - 1 << 2) - *pp] < tol * (*sigma + *dn1) && dabs(*dn) < tol * *sigma) { /* Convergence hidden by negative DN. */ z__[(*n0 - 1 << 2) - *pp + 2] = 0.f; *dmin__ = 0.f; goto L90; } else if (*dmin__ < 0.f) { /* TAU too big. Select new TAU and try again. */ ++(*nfail); if (*ttype < -22) { /* Failed twice. Play it safe. */ *tau = 0.f; } else if (*dmin1 > 0.f) { /* Late failure. Gives excellent shift. */ *tau = (*tau + *dmin__) * (1.f - eps * 2.f); *ttype += -11; } else { /* Early failure. Divide by 4. */ *tau *= .25f; *ttype += -12; } goto L70; } else if (sisnan_(dmin__)) { /* NaN. */ if (*tau == 0.f) { goto L80; } else { *tau = 0.f; goto L70; } } else { /* Possible underflow. Play it safe. */ goto L80; } /* Risk of underflow. */ L80: slasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2); *ndiv += *n0 - *i0 + 2; ++(*iter); *tau = 0.f; L90: if (*tau < *sigma) { *desig += *tau; t = *sigma + *desig; *desig -= t - *sigma; } else { t = *sigma + *tau; *desig = *sigma - (t - *tau) + *desig; } *sigma = t; return 0; /* End of SLASQ3 */ } /* slasq3_ */