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opencv/3rdparty/lapack/slagts.c

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#include "clapack.h"
/* Subroutine */ int slagts_(integer *job, integer *n, real *a, real *b, real
*c__, real *d__, integer *in, real *y, real *tol, integer *info)
{
/* System generated locals */
integer i__1;
real r__1, r__2, r__3, r__4, r__5;
/* Builtin functions */
double r_sign(real *, real *);
/* Local variables */
integer k;
real ak, eps, temp, pert, absak, sfmin;
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLAGTS may be used to solve one of the systems of equations */
/* (T - lambda*I)*x = y or (T - lambda*I)'*x = y, */
/* where T is an n by n tridiagonal matrix, for x, following the */
/* factorization of (T - lambda*I) as */
/* (T - lambda*I) = P*L*U , */
/* by routine SLAGTF. The choice of equation to be solved is */
/* controlled by the argument JOB, and in each case there is an option */
/* to perturb zero or very small diagonal elements of U, this option */
/* being intended for use in applications such as inverse iteration. */
/* Arguments */
/* ========= */
/* JOB (input) INTEGER */
/* Specifies the job to be performed by SLAGTS as follows: */
/* = 1: The equations (T - lambda*I)x = y are to be solved, */
/* but diagonal elements of U are not to be perturbed. */
/* = -1: The equations (T - lambda*I)x = y are to be solved */
/* and, if overflow would otherwise occur, the diagonal */
/* elements of U are to be perturbed. See argument TOL */
/* below. */
/* = 2: The equations (T - lambda*I)'x = y are to be solved, */
/* but diagonal elements of U are not to be perturbed. */
/* = -2: The equations (T - lambda*I)'x = y are to be solved */
/* and, if overflow would otherwise occur, the diagonal */
/* elements of U are to be perturbed. See argument TOL */
/* below. */
/* N (input) INTEGER */
/* The order of the matrix T. */
/* A (input) REAL array, dimension (N) */
/* On entry, A must contain the diagonal elements of U as */
/* returned from SLAGTF. */
/* B (input) REAL array, dimension (N-1) */
/* On entry, B must contain the first super-diagonal elements of */
/* U as returned from SLAGTF. */
/* C (input) REAL array, dimension (N-1) */
/* On entry, C must contain the sub-diagonal elements of L as */
/* returned from SLAGTF. */
/* D (input) REAL array, dimension (N-2) */
/* On entry, D must contain the second super-diagonal elements */
/* of U as returned from SLAGTF. */
/* IN (input) INTEGER array, dimension (N) */
/* On entry, IN must contain details of the matrix P as returned */
/* from SLAGTF. */
/* Y (input/output) REAL array, dimension (N) */
/* On entry, the right hand side vector y. */
/* On exit, Y is overwritten by the solution vector x. */
/* TOL (input/output) REAL */
/* On entry, with JOB .lt. 0, TOL should be the minimum */
/* perturbation to be made to very small diagonal elements of U. */
/* TOL should normally be chosen as about eps*norm(U), where eps */
/* is the relative machine precision, but if TOL is supplied as */
/* non-positive, then it is reset to eps*max( abs( u(i,j) ) ). */
/* If JOB .gt. 0 then TOL is not referenced. */
/* On exit, TOL is changed as described above, only if TOL is */
/* non-positive on entry. Otherwise TOL is unchanged. */
/* INFO (output) INTEGER */
/* = 0 : successful exit */
/* .lt. 0: if INFO = -i, the i-th argument had an illegal value */
/* .gt. 0: overflow would occur when computing the INFO(th) */
/* element of the solution vector x. This can only occur */
/* when JOB is supplied as positive and either means */
/* that a diagonal element of U is very small, or that */
/* the elements of the right-hand side vector y are very */
/* large. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--y;
--in;
--d__;
--c__;
--b;
--a;
/* Function Body */
*info = 0;
if (abs(*job) > 2 || *job == 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLAGTS", &i__1);
return 0;
}
if (*n == 0) {
return 0;
}
eps = slamch_("Epsilon");
sfmin = slamch_("Safe minimum");
bignum = 1.f / sfmin;
if (*job < 0) {
if (*tol <= 0.f) {
*tol = dabs(a[1]);
if (*n > 1) {
/* Computing MAX */
r__1 = *tol, r__2 = dabs(a[2]), r__1 = max(r__1,r__2), r__2 =
dabs(b[1]);
*tol = dmax(r__1,r__2);
}
i__1 = *n;
for (k = 3; k <= i__1; ++k) {
/* Computing MAX */
r__4 = *tol, r__5 = (r__1 = a[k], dabs(r__1)), r__4 = max(
r__4,r__5), r__5 = (r__2 = b[k - 1], dabs(r__2)),
r__4 = max(r__4,r__5), r__5 = (r__3 = d__[k - 2],
dabs(r__3));
*tol = dmax(r__4,r__5);
/* L10: */
}
*tol *= eps;
if (*tol == 0.f) {
*tol = eps;
}
}
}
if (abs(*job) == 1) {
i__1 = *n;
for (k = 2; k <= i__1; ++k) {
if (in[k - 1] == 0) {
y[k] -= c__[k - 1] * y[k - 1];
} else {
temp = y[k - 1];
y[k - 1] = y[k];
y[k] = temp - c__[k - 1] * y[k];
}
/* L20: */
}
if (*job == 1) {
for (k = *n; k >= 1; --k) {
if (k <= *n - 2) {
temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
} else if (k == *n - 1) {
temp = y[k] - b[k] * y[k + 1];
} else {
temp = y[k];
}
ak = a[k];
absak = dabs(ak);
if (absak < 1.f) {
if (absak < sfmin) {
if (absak == 0.f || dabs(temp) * sfmin > absak) {
*info = k;
return 0;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (dabs(temp) > absak * bignum) {
*info = k;
return 0;
}
}
y[k] = temp / ak;
/* L30: */
}
} else {
for (k = *n; k >= 1; --k) {
if (k <= *n - 2) {
temp = y[k] - b[k] * y[k + 1] - d__[k] * y[k + 2];
} else if (k == *n - 1) {
temp = y[k] - b[k] * y[k + 1];
} else {
temp = y[k];
}
ak = a[k];
pert = r_sign(tol, &ak);
L40:
absak = dabs(ak);
if (absak < 1.f) {
if (absak < sfmin) {
if (absak == 0.f || dabs(temp) * sfmin > absak) {
ak += pert;
pert *= 2;
goto L40;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (dabs(temp) > absak * bignum) {
ak += pert;
pert *= 2;
goto L40;
}
}
y[k] = temp / ak;
/* L50: */
}
}
} else {
/* Come to here if JOB = 2 or -2 */
if (*job == 2) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (k >= 3) {
temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
} else if (k == 2) {
temp = y[k] - b[k - 1] * y[k - 1];
} else {
temp = y[k];
}
ak = a[k];
absak = dabs(ak);
if (absak < 1.f) {
if (absak < sfmin) {
if (absak == 0.f || dabs(temp) * sfmin > absak) {
*info = k;
return 0;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (dabs(temp) > absak * bignum) {
*info = k;
return 0;
}
}
y[k] = temp / ak;
/* L60: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (k >= 3) {
temp = y[k] - b[k - 1] * y[k - 1] - d__[k - 2] * y[k - 2];
} else if (k == 2) {
temp = y[k] - b[k - 1] * y[k - 1];
} else {
temp = y[k];
}
ak = a[k];
pert = r_sign(tol, &ak);
L70:
absak = dabs(ak);
if (absak < 1.f) {
if (absak < sfmin) {
if (absak == 0.f || dabs(temp) * sfmin > absak) {
ak += pert;
pert *= 2;
goto L70;
} else {
temp *= bignum;
ak *= bignum;
}
} else if (dabs(temp) > absak * bignum) {
ak += pert;
pert *= 2;
goto L70;
}
}
y[k] = temp / ak;
/* L80: */
}
}
for (k = *n; k >= 2; --k) {
if (in[k - 1] == 0) {
y[k - 1] -= c__[k - 1] * y[k];
} else {
temp = y[k - 1];
y[k - 1] = y[k];
y[k] = temp - c__[k - 1] * y[k];
}
/* L90: */
}
}
/* End of SLAGTS */
return 0;
} /* slagts_ */
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