/* dsptrd.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;
static doublereal c_b8 = 0.;
static doublereal c_b14 = -1.;
/* Subroutine */ int dsptrd_(char *uplo, integer *n, doublereal *ap,
doublereal *d__, doublereal *e, doublereal *tau, integer *info)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
integer i__, i1, ii, i1i1;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal taui;
extern /* Subroutine */ int dspr2_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *);
doublereal alpha;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *), dspmv_(char *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, integer *);
logical upper;
extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *), 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 */
/* ======= */
/* DSPTRD reduces a real symmetric matrix A stored in packed form to */
/* symmetric tridiagonal form T by an orthogonal similarity */
/* transformation: Q**T * A * Q = T. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the symmetric matrix */
/* A, packed columnwise in a linear array. The j-th column of A */
/* is stored in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */
/* On exit, if UPLO = 'U', the diagonal and first superdiagonal */
/* of A are overwritten by the corresponding elements of the */
/* tridiagonal matrix T, and the elements above the first */
/* superdiagonal, with the array TAU, represent the orthogonal */
/* matrix Q as a product of elementary reflectors; if UPLO */
/* = 'L', the diagonal and first subdiagonal of A are over- */
/* written by the corresponding elements of the tridiagonal */
/* matrix T, and the elements below the first subdiagonal, with */
/* the array TAU, represent the orthogonal matrix Q as a product */
/* of elementary reflectors. See Further Details. */
/* D (output) DOUBLE PRECISION array, dimension (N) */
/* The diagonal elements of the tridiagonal matrix T: */
/* D(i) = A(i,i). */
/* E (output) DOUBLE PRECISION array, dimension (N-1) */
/* The off-diagonal elements of the tridiagonal matrix T: */
/* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */
/* TAU (output) DOUBLE PRECISION array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* If UPLO = 'U', the matrix Q is represented as a product of elementary */
/* reflectors */
/* Q = H(n-1) . . . H(2) H(1). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a real scalar, and v is a real vector with */
/* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP, */
/* overwriting A(1:i-1,i+1), and tau is stored in TAU(i). */
/* If UPLO = 'L', the matrix Q is represented as a product of elementary */
/* reflectors */
/* Q = H(1) H(2) . . . H(n-1). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a real scalar, and v is a real vector with */
/* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP, */
/* overwriting A(i+2:n,i), and tau is stored in TAU(i). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
--tau;
--e;
--d__;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPTRD", &i__1);
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
return 0;
}
if (upper) {
/* Reduce the upper triangle of A. */
/* I1 is the index in AP of A(1,I+1). */
i1 = *n * (*n - 1) / 2 + 1;
for (i__ = *n - 1; i__ >= 1; --i__) {
/* Generate elementary reflector H(i) = I - tau * v * v' */
/* to annihilate A(1:i-1,i+1) */
dlarfg_(&i__, &ap[i1 + i__ - 1], &ap[i1], &c__1, &taui);
e[i__] = ap[i1 + i__ - 1];
if (taui != 0.) {
/* Apply H(i) from both sides to A(1:i,1:i) */
ap[i1 + i__ - 1] = 1.;
/* Compute y := tau * A * v storing y in TAU(1:i) */
dspmv_(uplo, &i__, &taui, &ap[1], &ap[i1], &c__1, &c_b8, &tau[
1], &c__1);
/* Compute w := y - 1/2 * tau * (y'*v) * v */
alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &ap[i1], &
c__1);
daxpy_(&i__, &alpha, &ap[i1], &c__1, &tau[1], &c__1);
/* Apply the transformation as a rank-2 update: */
/* A := A - v * w' - w * v' */
dspr2_(uplo, &i__, &c_b14, &ap[i1], &c__1, &tau[1], &c__1, &
ap[1]);
ap[i1 + i__ - 1] = e[i__];
}
d__[i__ + 1] = ap[i1 + i__];
tau[i__] = taui;
i1 -= i__;
/* L10: */
}
d__[1] = ap[1];
} else {
/* Reduce the lower triangle of A. II is the index in AP of */
/* A(i,i) and I1I1 is the index of A(i+1,i+1). */
ii = 1;
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i1i1 = ii + *n - i__ + 1;
/* Generate elementary reflector H(i) = I - tau * v * v' */
/* to annihilate A(i+2:n,i) */
i__2 = *n - i__;
dlarfg_(&i__2, &ap[ii + 1], &ap[ii + 2], &c__1, &taui);
e[i__] = ap[ii + 1];
if (taui != 0.) {
/* Apply H(i) from both sides to A(i+1:n,i+1:n) */
ap[ii + 1] = 1.;
/* Compute y := tau * A * v storing y in TAU(i:n-1) */
i__2 = *n - i__;
dspmv_(uplo, &i__2, &taui, &ap[i1i1], &ap[ii + 1], &c__1, &
c_b8, &tau[i__], &c__1);
/* Compute w := y - 1/2 * tau * (y'*v) * v */
i__2 = *n - i__;
alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &ap[ii +
1], &c__1);
i__2 = *n - i__;
daxpy_(&i__2, &alpha, &ap[ii + 1], &c__1, &tau[i__], &c__1);
/* Apply the transformation as a rank-2 update: */
/* A := A - v * w' - w * v' */
i__2 = *n - i__;
dspr2_(uplo, &i__2, &c_b14, &ap[ii + 1], &c__1, &tau[i__], &
c__1, &ap[i1i1]);
ap[ii + 1] = e[i__];
}
d__[i__] = ap[ii];
tau[i__] = taui;
ii = i1i1;
/* L20: */
}
d__[*n] = ap[ii];
}
return 0;
/* End of DSPTRD */
} /* dsptrd_ */