/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q,
integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt,
doublereal *work, integer *iwork, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
DLAED1 computes the updated eigensystem of a diagonal
matrix after modification by a rank-one symmetric matrix. This
routine is used only for the eigenproblem which requires all
eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles
the case in which eigenvalues only or eigenvalues and eigenvectors
of a full symmetric matrix (which was reduced to tridiagonal form)
are desired.
T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
where Z = Q'u, u is a vector of length N with ones in the
CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
The eigenvectors of the original matrix are stored in Q, and the
eigenvalues are in D. The algorithm consists of three stages:
The first stage consists of deflating the size of the problem
when there are multiple eigenvalues or if there is a zero in
the Z vector. For each such occurence the dimension of the
secular equation problem is reduced by one. This stage is
performed by the routine DLAED2.
The second stage consists of calculating the updated
eigenvalues. This is done by finding the roots of the secular
equation via the routine DLAED4 (as called by DLAED3).
This routine also calculates the eigenvectors of the current
problem.
The final stage consists of computing the updated eigenvectors
directly using the updated eigenvalues. The eigenvectors for
the current problem are multiplied with the eigenvectors from
the overall problem.
Arguments
=========
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the eigenvalues of the rank-1-perturbed matrix.
On exit, the eigenvalues of the repaired matrix.
Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
On entry, the eigenvectors of the rank-1-perturbed matrix.
On exit, the eigenvectors of the repaired tridiagonal matrix.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
INDXQ (input/output) INTEGER array, dimension (N)
On entry, the permutation which separately sorts the two
subproblems in D into ascending order.
On exit, the permutation which will reintegrate the
subproblems back into sorted order,
i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
RHO (input) DOUBLE PRECISION
The subdiagonal entry used to create the rank-1 modification.
CUTPNT (input) INTEGER
The location of the last eigenvalue in the leading sub-matrix.
min(1,N) <= CUTPNT <= N/2.
WORK (workspace) DOUBLE PRECISION array, dimension (4*N + N**2)
IWORK (workspace) INTEGER array, dimension (4*N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
/* System generated locals */
integer q_dim1, q_offset, i__1, i__2;
/* Local variables */
static integer indx, i__, k, indxc;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer indxp;
extern /* Subroutine */ int dlaed2_(integer *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *,
integer *, integer *, integer *, integer *), dlaed3_(integer *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, integer *, integer *,
doublereal *, doublereal *, integer *);
static integer n1, n2, idlmda, is, iw, iz;
extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
integer *, integer *, integer *), xerbla_(char *, integer *);
static integer coltyp, iq2, zpp1;
#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
--d__;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
--indxq;
--work;
--iwork;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*ldq < max(1,*n)) {
*info = -4;
} else /* if(complicated condition) */ {
/* Computing MIN */
i__1 = 1, i__2 = *n / 2;
if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DLAED1", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* The following values are integer pointers which indicate
the portion of the workspace
used by a particular array in DLAED2 and DLAED3. */
iz = 1;
idlmda = iz + *n;
iw = idlmda + *n;
iq2 = iw + *n;
indx = 1;
indxc = indx + *n;
coltyp = indxc + *n;
indxp = coltyp + *n;
/* Form the z-vector which consists of the last row of Q_1 and the
first row of Q_2. */
dcopy_(cutpnt, &q_ref(*cutpnt, 1), ldq, &work[iz], &c__1);
zpp1 = *cutpnt + 1;
i__1 = *n - *cutpnt;
dcopy_(&i__1, &q_ref(zpp1, zpp1), ldq, &work[iz + *cutpnt], &c__1);
/* Deflate eigenvalues. */
dlaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[
iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[
indxc], &iwork[indxp], &iwork[coltyp], info);
if (*info != 0) {
goto L20;
}
/* Solve Secular Equation. */
if (k != 0) {
is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp +
1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2;
dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda],
&work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[
is], info);
if (*info != 0) {
goto L20;
}
/* Prepare the INDXQ sorting permutation. */
n1 = k;
n2 = *n - k;
dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]);
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
indxq[i__] = i__;
/* L10: */
}
}
L20:
return 0;
/* End of DLAED1 */
} /* dlaed1_ */
int main(int argc, char *argv[]){
if (argc != 3){
printf("Please enter a matrix size and a method: 0 for LAPACK, 1 for C\n");
return EXIT_SUCCESS;
}
int n = atoi(argv[1]); /* matrix size */
int m = n/2; /* subproblem size */
int method = atoi(argv[2]);
/* Initial matrix */
double *T_D;
double *T_L;
T_D = malloc(n*sizeof(double));
T_L = malloc((n-1)*sizeof(double));
init_tridiagonal(n, T_D, T_L);
int i, j;
/* Subproblems */
double *T1_D;
double *T1_L;
double *T2_D;
double *T2_L;
T1_D = malloc(m*sizeof(double));
T1_L = malloc((m-1)*sizeof(double));
T2_D = malloc((n-m)*sizeof(double));
T2_L = malloc((n-m-1)*sizeof(double));
double beta = T_L[m-1];
split(n, m, T_D, T_L, T1_D, T1_L, T2_D, T2_L, beta);
/* Solve differents problems */
double *Q_ini = malloc(n*n*sizeof(double));
memset(Q_ini, 0, n*n*sizeof(double));
int info = LAPACKE_dstedc(LAPACK_COL_MAJOR, 'I', n, T_D, T_L, Q_ini, n);
assert(!info);
double *Q1 = malloc(m*m*sizeof(double));
memset(Q1, 0, m*m*sizeof(double));
info = LAPACKE_dstedc(LAPACK_COL_MAJOR, 'I', m, T1_D, T1_L, Q1, m);
assert(!info);
double *Q2 = malloc((n-m)*(n-m)*sizeof(double));
memset(Q2, 0, (n-m)*(n-m)*sizeof(double));
info = LAPACKE_dstedc(LAPACK_COL_MAJOR, 'I', n-m, T2_D, T2_L, Q2, n-m);
assert(!info);
/* Eigenvalues of the rank-1 perturbed matrix */
double *D;
D = malloc(n*sizeof(double));
for (i=0; i<m; i++){
D[i] = T1_D[i];
}
for (i=0; i<n-m; i++){
D[m+i] = T2_D[i];
}
/* Eigenvectors of the rank-1 perturbed matrix */
double *Q = malloc(n*n*sizeof(double));
memset(Q, 0, n*n*sizeof(double));
for (i=0; i<m; i++){
for (j=0; j<m; j++){
Q[n*i+j] = Q1[m*i+j];
}
}
for (i=0; i<n-m; i++){
for (j=0; j<n-m; j++){
Q[n*(m+i)+m+j] = Q2[(n-m)*i+j];
}
}
/* Saved eigenvalues with rank-1 pertubation */
double *saved = malloc(n*sizeof(double));
for (i=0; i<n; i++){
saved[i] = D[i];
}
/* Eigenvalues permutation: no permutation here */
int *perm;
perm = malloc(n*sizeof(int));
/* For C */
if (method == 1){
for (i=0; i<m; i++){
perm[i] = i;
}
for (i=m; i<n; i++){
perm[i] = i-m;
}
}
/* For Fortran */
else{
for (i=0; i<m; i++){
perm[i] = i+1;
}
for (i=m; i<n; i++){
perm[i] = i-m+1;
}
}
int K;
double *Z = malloc((n*n+4*n)*sizeof(double));
for (i=0; i<m; i++){
Z[i] = Q1[m*i+m-1];
}
for (i=m; i<n; i++){
Z[i] = Q2[(i-m)*(n-m)];
}
double *DLAMBDA;
double *W_3;
double *W5;
double *Q2_3;
DLAMBDA = Z + n;
W_3 = DLAMBDA + n;
Q2_3 = W_3 + n;
memset(Q2_3, 0, n*n*sizeof(double));
int *INDX;
int *INDXC;
int *INDXP;
int *COLTYP;
INDX = malloc(4*n*sizeof(int));
INDXC = INDX + n;
COLTYP = INDXC + n;
INDXP = COLTYP + n;
/* C version */
if (method == 1){
dlaed2(&K, &n, &m, D, Q, &n, perm, &beta, Z,
DLAMBDA, W_3, Q2_3,
INDX, INDXC, INDXP,
COLTYP, &info);
}
/* LAPACK version */
else{
dlaed2_(&K, &n, &m, D, Q, &n, perm, &beta, Z,
DLAMBDA, W_3, Q2_3,
INDX, INDXC, INDXP,
COLTYP, &info);
assert(!info);
}
/* Comparison C/LAPACK */
/* printf("N %d K %d\n", n, K); */
/* for (i=0; i<K; i++){ */
/* printf("PERM %10d DLAMBDA %10f W %10f\n", perm[i], DLAMBDA[i], W_3[i]); */
/* printf("INDX %10d INDXC %10d INDXP %10d COLTYP %10d\n", INDX[i], INDXC[i], INDXP[i], COLTYP[i]); */
/* } */
/* For Fortran change C exit: for dlaed2 in C and dlaed3 in f77 */
/* if (method == 1){ */
/* for (i=0; i<n; i++){ */
/* INDXC[i]++; */
/* } */
/* } */
/* printf("\nEigenvectors comparison\n"); */
/* for (i=0; i<n; i++){ */
/* for (j=0; j<n; j++){ */
/* printf("%10f", Q[n*i+j]); */
/* } */
/* printf("\n"); */
/* } */
W5 = Q2_3 + (COLTYP[0]+COLTYP[1]) * m + (COLTYP[1]+COLTYP[2]) * (n-m);
/* C Version */
if (method == 1){
dlaed3(&K, &n, &m, D, Q, &n, &beta, DLAMBDA,
Q2_3, INDXC, COLTYP,
W_3, W5, &info);
}
/* LAPACK Version */
else{
dlaed3_(&K, &n, &m, D, Q, &n, &beta, DLAMBDA,
Q2_3, INDXC, COLTYP,
W_3, W5, &info);
assert(!info);
}
/* Sort eigenvalues */
int n2 = n - K;
int id1 = 1;
int id2 = -1;
dlamrg_(&K, &n2, D, &id1, &id2, perm);
double *saved_D = malloc(n*sizeof(double));
memcpy(saved_D, D, n*sizeof(double));
/* WARNING: same operation for eigenvectors */
for (i=0; i<n; i++){
D[i] = saved_D[perm[i]-1];
}
free(saved_D);
/* printf("\nEigenvalues with beta %f\n", beta); */
/* for (i=0; i<n; i++){ */
/* printf("Saved %10f Found %10f Expected %10f\n", saved[i], D[i], T_D[i]); */
/* } */
/* printf("\nEigenvectors comparison\n"); */
/* for (i=0; i<n; i++){ */
/* for (j=0; j<n; j++){ */
/* printf("%10f", Q[n*i+j]); */
/* } */
/* printf("\n"); */
/* } */
free(Z);
free(INDX);
free(perm);
free(T_D);
free(T_L);
free(T1_D);
free(T1_L);
free(T2_D);
free(T2_L);
free(Q_ini);
free(Q1);
free(Q2);
free(D);
free(saved);
free(Q);
return EXIT_SUCCESS;
}
