/* Subroutine */ int claed0_(integer *qsiz, integer *n, real *d__, real *e,
complex *q, integer *ldq, complex *qstore, integer *ldqs, real *rwork,
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
September 30, 1994
Purpose
=======
Using the divide and conquer method, CLAED0 computes all eigenvalues
of a symmetric tridiagonal matrix which is one diagonal block of
those from reducing a dense or band Hermitian matrix and
corresponding eigenvectors of the dense or band matrix.
Arguments
=========
QSIZ (input) INTEGER
The dimension of the unitary matrix used to reduce
the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix.
On exit, the eigenvalues in ascending order.
E (input/output) REAL array, dimension (N-1)
On entry, the off-diagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Q (input/output) COMPLEX array, dimension (LDQ,N)
On entry, Q must contain an QSIZ x N matrix whose columns
unitarily orthonormal. It is a part of the unitary matrix
that reduces the full dense Hermitian matrix to a
(reducible) symmetric tridiagonal matrix.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
IWORK (workspace) INTEGER array,
the dimension of IWORK must be at least
6 + 6*N + 5*N*lg N
( lg( N ) = smallest integer k
such that 2^k >= N )
RWORK (workspace) REAL array,
dimension (1 + 3*N + 2*N*lg N + 3*N**2)
( lg( N ) = smallest integer k
such that 2^k >= N )
QSTORE (workspace) COMPLEX array, dimension (LDQS, N)
Used to store parts of
the eigenvector matrix when the updating matrix multiplies
take place.
LDQS (input) INTEGER
The leading dimension of the array QSTORE.
LDQS >= max(1,N).
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute an eigenvalue while
working on the submatrix lying in rows and columns
INFO/(N+1) through mod(INFO,N+1).
=====================================================================
Warning: N could be as big as QSIZ!
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__9 = 9;
static integer c__0 = 0;
static integer c__2 = 2;
static integer c__1 = 1;
/* System generated locals */
integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double log(doublereal);
integer pow_ii(integer *, integer *);
/* Local variables */
static real temp;
static integer curr, i__, j, k, iperm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
static integer indxq, iwrem;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
static integer iqptr;
extern /* Subroutine */ int claed7_(integer *, integer *, integer *,
integer *, integer *, integer *, real *, complex *, integer *,
real *, integer *, real *, integer *, integer *, integer *,
integer *, integer *, real *, complex *, real *, integer *,
integer *);
static integer tlvls, ll, iq;
extern /* Subroutine */ int clacrm_(integer *, integer *, complex *,
integer *, real *, integer *, complex *, integer *, real *);
static integer igivcl;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer igivnm, submat, curprb, subpbs, igivpt, curlvl, matsiz,
iprmpt, smlsiz;
extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *,
real *, integer *, real *, integer *);
static integer lgn, msd2, smm1, spm1, spm2;
#define q_subscr(a_1,a_2) (a_2)*q_dim1 + a_1
#define q_ref(a_1,a_2) q[q_subscr(a_1,a_2)]
#define qstore_subscr(a_1,a_2) (a_2)*qstore_dim1 + a_1
#define qstore_ref(a_1,a_2) qstore[qstore_subscr(a_1,a_2)]
--d__;
--e;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
qstore_dim1 = *ldqs;
qstore_offset = 1 + qstore_dim1 * 1;
qstore -= qstore_offset;
--rwork;
--iwork;
/* Function Body */
*info = 0;
/* IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN
INFO = -1
ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) )
$ THEN */
if (*qsiz < max(0,*n)) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldq < max(1,*n)) {
*info = -6;
} else if (*ldqs < max(1,*n)) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLAED0", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
smlsiz = ilaenv_(&c__9, "CLAED0", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/* Determine the size and placement of the submatrices, and save in
the leading elements of IWORK. */
iwork[1] = *n;
subpbs = 1;
tlvls = 0;
L10:
if (iwork[subpbs] > smlsiz) {
for (j = subpbs; j >= 1; --j) {
iwork[j * 2] = (iwork[j] + 1) / 2;
iwork[(j << 1) - 1] = iwork[j] / 2;
/* L20: */
}
++tlvls;
subpbs <<= 1;
goto L10;
}
i__1 = subpbs;
for (j = 2; j <= i__1; ++j) {
iwork[j] += iwork[j - 1];
/* L30: */
}
/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
using rank-1 modifications (cuts). */
spm1 = subpbs - 1;
i__1 = spm1;
for (i__ = 1; i__ <= i__1; ++i__) {
submat = iwork[i__] + 1;
smm1 = submat - 1;
d__[smm1] -= (r__1 = e[smm1], dabs(r__1));
d__[submat] -= (r__1 = e[smm1], dabs(r__1));
/* L40: */
}
indxq = (*n << 2) + 3;
/* Set up workspaces for eigenvalues only/accumulate new vectors
routine */
temp = log((real) (*n)) / log(2.f);
lgn = (integer) temp;
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
iprmpt = indxq + *n + 1;
iperm = iprmpt + *n * lgn;
iqptr = iperm + *n * lgn;
igivpt = iqptr + *n + 2;
igivcl = igivpt + *n * lgn;
igivnm = 1;
iq = igivnm + (*n << 1) * lgn;
/* Computing 2nd power */
i__1 = *n;
iwrem = iq + i__1 * i__1 + 1;
/* Initialize pointers */
i__1 = subpbs;
for (i__ = 0; i__ <= i__1; ++i__) {
iwork[iprmpt + i__] = 1;
iwork[igivpt + i__] = 1;
/* L50: */
}
iwork[iqptr] = 1;
/* Solve each submatrix eigenproblem at the bottom of the divide and
conquer tree. */
curr = 0;
i__1 = spm1;
for (i__ = 0; i__ <= i__1; ++i__) {
if (i__ == 0) {
submat = 1;
matsiz = iwork[1];
} else {
submat = iwork[i__] + 1;
matsiz = iwork[i__ + 1] - iwork[i__];
}
ll = iq - 1 + iwork[iqptr + curr];
ssteqr_("I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, &
rwork[1], info);
clacrm_(qsiz, &matsiz, &q_ref(1, submat), ldq, &rwork[ll], &matsiz, &
qstore_ref(1, submat), ldqs, &rwork[iwrem]);
/* Computing 2nd power */
i__2 = matsiz;
iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
++curr;
if (*info > 0) {
*info = submat * (*n + 1) + submat + matsiz - 1;
return 0;
}
k = 1;
i__2 = iwork[i__ + 1];
for (j = submat; j <= i__2; ++j) {
iwork[indxq + j] = k;
++k;
/* L60: */
}
/* L70: */
}
/* Successively merge eigensystems of adjacent submatrices
into eigensystem for the corresponding larger matrix.
while ( SUBPBS > 1 ) */
curlvl = 1;
L80:
if (subpbs > 1) {
spm2 = subpbs - 2;
i__1 = spm2;
for (i__ = 0; i__ <= i__1; i__ += 2) {
if (i__ == 0) {
submat = 1;
matsiz = iwork[2];
msd2 = iwork[1];
curprb = 0;
} else {
submat = iwork[i__] + 1;
matsiz = iwork[i__ + 2] - iwork[i__];
msd2 = matsiz / 2;
++curprb;
}
/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
into an eigensystem of size MATSIZ. CLAED7 handles the case
when the eigenvectors of a full or band Hermitian matrix (which
was reduced to tridiagonal form) are desired.
I am free to use Q as a valuable working space until Loop 150. */
claed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[
submat], &qstore_ref(1, submat), ldqs, &e[submat + msd2 -
1], &iwork[indxq + submat], &rwork[iq], &iwork[iqptr], &
iwork[iprmpt], &iwork[iperm], &iwork[igivpt], &iwork[
igivcl], &rwork[igivnm], &q_ref(1, submat), &rwork[iwrem],
&iwork[subpbs + 1], info);
if (*info > 0) {
*info = submat * (*n + 1) + submat + matsiz - 1;
return 0;
}
iwork[i__ / 2 + 1] = iwork[i__ + 2];
/* L90: */
}
subpbs /= 2;
++curlvl;
goto L80;
}
/* end while
Re-merge the eigenvalues/vectors which were deflated at the final
merge step. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
j = iwork[indxq + i__];
rwork[i__] = d__[j];
ccopy_(qsiz, &qstore_ref(1, j), &c__1, &q_ref(1, i__), &c__1);
/* L100: */
}
scopy_(n, &rwork[1], &c__1, &d__[1], &c__1);
return 0;
/* End of CLAED0 */
} /* claed0_ */
/* Subroutine */ int slaed0_(integer *icompq, integer *qsiz, integer *n, real
*d__, real *e, real *q, integer *ldq, real *qstore, integer *ldqs,
real *work, integer *iwork, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double log(doublereal);
integer pow_ii(integer *, integer *);
/* Local variables */
static real temp;
static integer curr, i__, j, k;
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
static integer iperm, indxq, iwrem;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
static integer iqptr, tlvls;
extern /* Subroutine */ int slaed1_(integer *, real *, real *, integer *,
integer *, real *, integer *, real *, integer *, integer *),
slaed7_(integer *, integer *, integer *, integer *, integer *,
integer *, real *, real *, integer *, integer *, real *, integer *
, real *, integer *, integer *, integer *, integer *, integer *,
real *, real *, integer *, integer *);
static integer iq, igivcl;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer igivnm, submat;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *);
static integer curprb, subpbs, igivpt, curlvl, matsiz, iprmpt, smlsiz;
extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *,
real *, integer *, real *, integer *);
static integer lgn, msd2, smm1, spm1, spm2;
#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
#define qstore_ref(a_1,a_2) qstore[(a_2)*qstore_dim1 + a_1]
/* -- LAPACK routine (instrumented to count operations, version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Common block to return operation count and iteration count
ITCNT is unchanged, OPS is only incremented
Purpose
=======
SLAED0 computes all eigenvalues and corresponding eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
Arguments
=========
ICOMPQ (input) INTEGER
= 0: Compute eigenvalues only.
= 1: Compute eigenvectors of original dense symmetric matrix
also. On entry, Q contains the orthogonal matrix used
to reduce the original matrix to tridiagonal form.
= 2: Compute eigenvalues and eigenvectors of tridiagonal
matrix.
QSIZ (input) INTEGER
The dimension of the orthogonal matrix used to reduce
the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the main diagonal of the tridiagonal matrix.
On exit, its eigenvalues.
E (input) REAL array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Q (input/output) REAL array, dimension (LDQ, N)
On entry, Q must contain an N-by-N orthogonal matrix.
If ICOMPQ = 0 Q is not referenced.
If ICOMPQ = 1 On entry, Q is a subset of the columns of the
orthogonal matrix used to reduce the full
matrix to tridiagonal form corresponding to
the subset of the full matrix which is being
decomposed at this time.
If ICOMPQ = 2 On entry, Q will be the identity matrix.
On exit, Q contains the eigenvectors of the
tridiagonal matrix.
LDQ (input) INTEGER
The leading dimension of the array Q. If eigenvectors are
desired, then LDQ >= max(1,N). In any case, LDQ >= 1.
QSTORE (workspace) REAL array, dimension (LDQS, N)
Referenced only when ICOMPQ = 1. Used to store parts of
the eigenvector matrix when the updating matrix multiplies
take place.
LDQS (input) INTEGER
The leading dimension of the array QSTORE. If ICOMPQ = 1,
then LDQS >= max(1,N). In any case, LDQS >= 1.
WORK (workspace) REAL array,
If ICOMPQ = 0 or 1, the dimension of WORK must be at least
1 + 3*N + 2*N*lg N + 2*N**2
( lg( N ) = smallest integer k
such that 2^k >= N )
If ICOMPQ = 2, the dimension of WORK must be at least
4*N + N**2.
IWORK (workspace) INTEGER array,
If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
6 + 6*N + 5*N*lg N.
( lg( N ) = smallest integer k
such that 2^k >= N )
If ICOMPQ = 2, the dimension of IWORK must be at least
3 + 5*N.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute an eigenvalue while
working on the submatrix lying in rows and columns
INFO/(N+1) through mod(INFO,N+1).
Further Details
===============
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
=====================================================================
Test the input parameters.
Parameter adjustments */
--d__;
--e;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
qstore_dim1 = *ldqs;
qstore_offset = 1 + qstore_dim1 * 1;
qstore -= qstore_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
if (*icompq < 0 || *icompq > 2) {
*info = -1;
} else if (*icompq == 1 && *qsiz < max(0,*n)) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ldq < max(1,*n)) {
*info = -7;
} else if (*ldqs < max(1,*n)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLAED0", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
smlsiz = ilaenv_(&c__9, "SLAED0", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/* Determine the size and placement of the submatrices, and save in
the leading elements of IWORK. */
iwork[1] = *n;
subpbs = 1;
tlvls = 0;
L10:
if (iwork[subpbs] > smlsiz) {
for (j = subpbs; j >= 1; --j) {
iwork[j * 2] = (iwork[j] + 1) / 2;
iwork[(j << 1) - 1] = iwork[j] / 2;
/* L20: */
}
++tlvls;
subpbs <<= 1;
goto L10;
}
i__1 = subpbs;
for (j = 2; j <= i__1; ++j) {
iwork[j] += iwork[j - 1];
/* L30: */
}
/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1
using rank-1 modifications (cuts). */
spm1 = subpbs - 1;
latime_1.ops += spm1 << 1;
i__1 = spm1;
for (i__ = 1; i__ <= i__1; ++i__) {
submat = iwork[i__] + 1;
smm1 = submat - 1;
d__[smm1] -= (r__1 = e[smm1], dabs(r__1));
d__[submat] -= (r__1 = e[smm1], dabs(r__1));
/* L40: */
}
indxq = (*n << 2) + 3;
if (*icompq != 2) {
/* Set up workspaces for eigenvalues only/accumulate new vectors
routine */
latime_1.ops += 3;
temp = log((real) (*n)) / log(2.f);
lgn = (integer) temp;
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
iprmpt = indxq + *n + 1;
iperm = iprmpt + *n * lgn;
iqptr = iperm + *n * lgn;
igivpt = iqptr + *n + 2;
igivcl = igivpt + *n * lgn;
igivnm = 1;
iq = igivnm + (*n << 1) * lgn;
/* Computing 2nd power */
i__1 = *n;
iwrem = iq + i__1 * i__1 + 1;
/* Initialize pointers */
i__1 = subpbs;
for (i__ = 0; i__ <= i__1; ++i__) {
iwork[iprmpt + i__] = 1;
iwork[igivpt + i__] = 1;
/* L50: */
}
iwork[iqptr] = 1;
}
/* Solve each submatrix eigenproblem at the bottom of the divide and
conquer tree. */
curr = 0;
i__1 = spm1;
for (i__ = 0; i__ <= i__1; ++i__) {
if (i__ == 0) {
submat = 1;
matsiz = iwork[1];
} else {
submat = iwork[i__] + 1;
matsiz = iwork[i__ + 1] - iwork[i__];
}
if (*icompq == 2) {
ssteqr_("I", &matsiz, &d__[submat], &e[submat], &q_ref(submat,
submat), ldq, &work[1], info);
if (*info != 0) {
goto L130;
}
} else {
ssteqr_("I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 +
iwork[iqptr + curr]], &matsiz, &work[1], info);
if (*info != 0) {
goto L130;
}
if (*icompq == 1) {
latime_1.ops += (real) (*qsiz) * 2 * matsiz * matsiz;
sgemm_("N", "N", qsiz, &matsiz, &matsiz, &c_b23, &q_ref(1,
submat), ldq, &work[iq - 1 + iwork[iqptr + curr]], &
matsiz, &c_b24, &qstore_ref(1, submat), ldqs);
}
/* Computing 2nd power */
i__2 = matsiz;
iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
++curr;
}
k = 1;
i__2 = iwork[i__ + 1];
for (j = submat; j <= i__2; ++j) {
iwork[indxq + j] = k;
++k;
/* L60: */
}
/* L70: */
}
/* Successively merge eigensystems of adjacent submatrices
into eigensystem for the corresponding larger matrix.
while ( SUBPBS > 1 ) */
curlvl = 1;
L80:
if (subpbs > 1) {
spm2 = subpbs - 2;
i__1 = spm2;
for (i__ = 0; i__ <= i__1; i__ += 2) {
if (i__ == 0) {
submat = 1;
matsiz = iwork[2];
msd2 = iwork[1];
curprb = 0;
} else {
submat = iwork[i__] + 1;
matsiz = iwork[i__ + 2] - iwork[i__];
msd2 = matsiz / 2;
++curprb;
}
/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2)
into an eigensystem of size MATSIZ.
SLAED1 is used only for the full eigensystem of a tridiagonal
matrix.
SLAED7 handles the cases in which eigenvalues only or eigenvalues
and eigenvectors of a full symmetric matrix (which was reduced to
tridiagonal form) are desired. */
if (*icompq == 2) {
slaed1_(&matsiz, &d__[submat], &q_ref(submat, submat), ldq, &
iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, &
work[1], &iwork[subpbs + 1], info);
} else {
slaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[
submat], &qstore_ref(1, submat), ldqs, &iwork[indxq +
submat], &e[submat + msd2 - 1], &msd2, &work[iq], &
iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[
igivpt], &iwork[igivcl], &work[igivnm], &work[iwrem],
&iwork[subpbs + 1], info);
}
if (*info != 0) {
goto L130;
}
iwork[i__ / 2 + 1] = iwork[i__ + 2];
/* L90: */
}
subpbs /= 2;
++curlvl;
goto L80;
}
/* end while
Re-merge the eigenvalues/vectors which were deflated at the final
merge step. */
if (*icompq == 1) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
j = iwork[indxq + i__];
work[i__] = d__[j];
scopy_(qsiz, &qstore_ref(1, j), &c__1, &q_ref(1, i__), &c__1);
/* L100: */
}
scopy_(n, &work[1], &c__1, &d__[1], &c__1);
} else if (*icompq == 2) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
j = iwork[indxq + i__];
work[i__] = d__[j];
scopy_(n, &q_ref(1, j), &c__1, &work[*n * i__ + 1], &c__1);
/* L110: */
}
scopy_(n, &work[1], &c__1, &d__[1], &c__1);
slacpy_("A", n, n, &work[*n + 1], n, &q[q_offset], ldq);
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
j = iwork[indxq + i__];
work[i__] = d__[j];
/* L120: */
}
scopy_(n, &work[1], &c__1, &d__[1], &c__1);
}
goto L140;
L130:
*info = submat * (*n + 1) + submat + matsiz - 1;
L140:
return 0;
/* End of SLAED0 */
} /* slaed0_ */
