/* cgttrf.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 cgttrf_(integer *n, complex *dl, complex *d__, complex *
du, complex *du2, integer *ipiv, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4;
complex q__1, q__2;
/* Builtin functions */
double r_imag(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
integer i__;
complex fact, temp;
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 */
/* ======= */
/* CGTTRF computes an LU factorization of a complex tridiagonal matrix A */
/* using elimination with partial pivoting and row interchanges. */
/* The factorization has the form */
/* A = L * U */
/* where L is a product of permutation and unit lower bidiagonal */
/* matrices and U is upper triangular with nonzeros in only the main */
/* diagonal and first two superdiagonals. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. */
/* DL (input/output) COMPLEX array, dimension (N-1) */
/* On entry, DL must contain the (n-1) sub-diagonal elements of */
/* A. */
/* On exit, DL is overwritten by the (n-1) multipliers that */
/* define the matrix L from the LU factorization of A. */
/* D (input/output) COMPLEX array, dimension (N) */
/* On entry, D must contain the diagonal elements of A. */
/* On exit, D is overwritten by the n diagonal elements of the */
/* upper triangular matrix U from the LU factorization of A. */
/* DU (input/output) COMPLEX array, dimension (N-1) */
/* On entry, DU must contain the (n-1) super-diagonal elements */
/* of A. */
/* On exit, DU is overwritten by the (n-1) elements of the first */
/* super-diagonal of U. */
/* DU2 (output) COMPLEX array, dimension (N-2) */
/* On exit, DU2 is overwritten by the (n-2) elements of the */
/* second super-diagonal of U. */
/* IPIV (output) INTEGER array, dimension (N) */
/* The pivot indices; for 1 <= i <= n, row i of the matrix was */
/* interchanged with row IPIV(i). IPIV(i) will always be either */
/* i or i+1; IPIV(i) = i indicates a row interchange was not */
/* required. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -k, the k-th argument had an illegal value */
/* > 0: if INFO = k, U(k,k) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly */
/* singular, and division by zero will occur if it is used */
/* to solve a system of equations. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--ipiv;
--du2;
--du;
--d__;
--dl;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
i__1 = -(*info);
xerbla_("CGTTRF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Initialize IPIV(i) = i and DU2(i) = 0 */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
ipiv[i__] = i__;
/* L10: */
}
i__1 = *n - 2;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
du2[i__2].r = 0.f, du2[i__2].i = 0.f;
/* L20: */
}
i__1 = *n - 2;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if ((r__1 = d__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) >= (r__3 = dl[i__3].r, dabs(r__3)) + (r__4 =
r_imag(&dl[i__]), dabs(r__4))) {
/* No row interchange required, eliminate DL(I) */
i__2 = i__;
if ((r__1 = d__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) != 0.f) {
c_div(&q__1, &dl[i__], &d__[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__2 = i__;
dl[i__2].r = fact.r, dl[i__2].i = fact.i;
i__2 = i__ + 1;
i__3 = i__ + 1;
i__4 = i__;
q__2.r = fact.r * du[i__4].r - fact.i * du[i__4].i, q__2.i =
fact.r * du[i__4].i + fact.i * du[i__4].r;
q__1.r = d__[i__3].r - q__2.r, q__1.i = d__[i__3].i - q__2.i;
d__[i__2].r = q__1.r, d__[i__2].i = q__1.i;
}
} else {
/* Interchange rows I and I+1, eliminate DL(I) */
c_div(&q__1, &d__[i__], &dl[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__2 = i__;
i__3 = i__;
d__[i__2].r = dl[i__3].r, d__[i__2].i = dl[i__3].i;
i__2 = i__;
dl[i__2].r = fact.r, dl[i__2].i = fact.i;
i__2 = i__;
temp.r = du[i__2].r, temp.i = du[i__2].i;
i__2 = i__;
i__3 = i__ + 1;
du[i__2].r = d__[i__3].r, du[i__2].i = d__[i__3].i;
i__2 = i__ + 1;
i__3 = i__ + 1;
q__2.r = fact.r * d__[i__3].r - fact.i * d__[i__3].i, q__2.i =
fact.r * d__[i__3].i + fact.i * d__[i__3].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i;
d__[i__2].r = q__1.r, d__[i__2].i = q__1.i;
i__2 = i__;
i__3 = i__ + 1;
du2[i__2].r = du[i__3].r, du2[i__2].i = du[i__3].i;
i__2 = i__ + 1;
q__2.r = -fact.r, q__2.i = -fact.i;
i__3 = i__ + 1;
q__1.r = q__2.r * du[i__3].r - q__2.i * du[i__3].i, q__1.i =
q__2.r * du[i__3].i + q__2.i * du[i__3].r;
du[i__2].r = q__1.r, du[i__2].i = q__1.i;
ipiv[i__] = i__ + 1;
}
/* L30: */
}
if (*n > 1) {
i__ = *n - 1;
i__1 = i__;
i__2 = i__;
if ((r__1 = d__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) >= (r__3 = dl[i__2].r, dabs(r__3)) + (r__4 =
r_imag(&dl[i__]), dabs(r__4))) {
i__1 = i__;
if ((r__1 = d__[i__1].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) != 0.f) {
c_div(&q__1, &dl[i__], &d__[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__1 = i__;
dl[i__1].r = fact.r, dl[i__1].i = fact.i;
i__1 = i__ + 1;
i__2 = i__ + 1;
i__3 = i__;
q__2.r = fact.r * du[i__3].r - fact.i * du[i__3].i, q__2.i =
fact.r * du[i__3].i + fact.i * du[i__3].r;
q__1.r = d__[i__2].r - q__2.r, q__1.i = d__[i__2].i - q__2.i;
d__[i__1].r = q__1.r, d__[i__1].i = q__1.i;
}
} else {
c_div(&q__1, &d__[i__], &dl[i__]);
fact.r = q__1.r, fact.i = q__1.i;
i__1 = i__;
i__2 = i__;
d__[i__1].r = dl[i__2].r, d__[i__1].i = dl[i__2].i;
i__1 = i__;
dl[i__1].r = fact.r, dl[i__1].i = fact.i;
i__1 = i__;
temp.r = du[i__1].r, temp.i = du[i__1].i;
i__1 = i__;
i__2 = i__ + 1;
du[i__1].r = d__[i__2].r, du[i__1].i = d__[i__2].i;
i__1 = i__ + 1;
i__2 = i__ + 1;
q__2.r = fact.r * d__[i__2].r - fact.i * d__[i__2].i, q__2.i =
fact.r * d__[i__2].i + fact.i * d__[i__2].r;
q__1.r = temp.r - q__2.r, q__1.i = temp.i - q__2.i;
d__[i__1].r = q__1.r, d__[i__1].i = q__1.i;
ipiv[i__] = i__ + 1;
}
}
/* Check for a zero on the diagonal of U. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
if ((r__1 = d__[i__2].r, dabs(r__1)) + (r__2 = r_imag(&d__[i__]),
dabs(r__2)) == 0.f) {
*info = i__;
goto L50;
}
/* L40: */
}
L50:
return 0;
/* End of CGTTRF */
} /* cgttrf_ */
