// Lock the given inode.
void
ilock(struct inode *ip)
{
struct buf *bp;
struct dinode *dip;
if(ip == 0 || ip->ref < 1)
panic("ilock");
acquire(&icache.lock);
while(ip->flags & I_BUSY)
sleep(ip, &icache.lock);
ip->flags |= I_BUSY;
release(&icache.lock);
if(!(ip->flags & I_VALID)){
bp = bread(ip->dev, IBLOCK(ip->inum));
dip = (struct dinode*)bp->data + ip->inum%IPB;
ip->type = dip->type;
ip->major = dip->major;
ip->minor = dip->minor;
ip->nlink = dip->nlink;
ip->size = dip->size;
memmove(ip->addrs, dip->addrs, sizeof(ip->addrs));
brelse(bp);
ip->flags |= I_VALID;
if(ip->type == 0)
panic("ilock: no type");
}
}
// Lock the given inode.
// Reads the inode from disk if necessary.
void ilock(struct inode* ip)
{
struct buf* bp;
struct dinode* dip;
// cprintf("ilock \n");
if (ip == 0 || ip->ref < 1)
panic("ilock");
acquire(&icache.lock);
while (ip->flags & I_BUSY)
sleep(ip, &icache.lock);
ip->flags |= I_BUSY;
release(&icache.lock);
if (!(ip->flags & I_VALID)) {
struct superblock sb;
sb = sbs[ip->part->number];
// cprintf("inode inum %d , part Number %d \n",ip->inum,ip->part->number);
bp = bread(ip->dev, IBLOCK(ip->inum, sb));
dip = (struct dinode*)bp->data + ip->inum % IPB;
ip->type = dip->type;
ip->major = dip->major;
ip->minor = dip->minor;
ip->nlink = dip->nlink;
ip->size = dip->size;
memmove(ip->addrs, dip->addrs, sizeof(ip->addrs));
brelse(bp);
ip->flags |= I_VALID;
if (ip->type == 0)
panic("ilock: no type");
}
}
//PAGEBREAK!
// Allocate a new inode with the given type on device dev.
// A free inode has a type of zero.
struct inode*
ialloc(uint dev, short type)
{
int inum;
struct buf *bp;
struct dinode *dip;
struct superblock sb;
readsb(dev, &sb);
for(inum = 1; inum < sb.ninodes; inum++){
bp = bread(dev, IBLOCK(inum));
dip = (struct dinode*)bp->data + inum%IPB;
if(dip->type == 0){ // a free inode
memset(dip, 0, sizeof(*dip));
dip->type = type;
log_write(bp); // mark it allocated on the disk
brelse(bp);
return iget(dev, inum);
}
brelse(bp);
}
panic("ialloc: no inodes");
return 0;
}
// Lock the given inode.
// Reads the inode from disk if necessary.
static void
sfs_ilock(struct inode *ip)
{
struct sfs_inode *sin = vop_info(ip, sfs_inode);
struct buf *bp;
struct sfs_dinode *dip;
if(sin == 0 || sin->ref < 1)
panic("ilock");
acquire(&icache.lock);
while(sin->flags & I_BUSY)
sleep(ip, &icache.lock);
sin->flags |= I_BUSY;
release(&icache.lock);
if(!(sin->flags & I_VALID)){
// cprintf("dev=%d, inum=%d\n", sin->dev, sin->inum);
bp = bread(sin->dev, IBLOCK(sin->inum));
dip = (struct sfs_dinode*)bp->data + sin->inum%IPB;
sin->type = dip->type;
sin->major = dip->major;
sin->minor = dip->minor;
sin->nlink = dip->nlink;
sin->size = dip->size;
memmove(sin->addrs, dip->addrs, sizeof(sin->addrs));
brelse(bp);
sin->flags |= I_VALID;
if(sin->type == 0)
panic("ilock: no type");
}
}
void
rinode(uint inum, struct dinode *ip)
{
char buf[BSIZE];
uint bn;
struct dinode *dip;
bn = IBLOCK(inum, sb);
rsect(bn, buf);
dip = ((struct dinode*)buf) + (inum % IPB);
*ip = *dip;
}
void
winode(uint inum, struct dinode *ip)
{
char buf[BSIZE];
uint bn;
struct dinode *dip;
bn = IBLOCK(inum);
printf("winode %d\n", bn);
rsect(bn, buf);
dip = ((struct dinode*)buf) + (inum % IPB);
*dip = *ip;
wsect(bn, buf);
}
void
log_iupdate(struct inode *ip)
{
struct dinode *dip;
bp[b_index] = bread(ip->dev, IBLOCK(ip->inum));
dip = (struct dinode*)bp[b_index]->data + ip->inum%IPB;
dip->type = ip->type;
dip->major = ip->major;
dip->minor = ip->minor;
dip->nlink = ip->nlink;
dip->size = ip->size;
memmove(dip->addrs, ip->addrs, sizeof(ip->addrs));
b_index++;
}
/* Copy a modified in-memory inode to disk. */
void iupdate(struct inode *ip)
{
struct buf *bp;
struct dinode *dip;
bp = bread(ip->dev, IBLOCK(ip->inum));
dip = (struct dinode *)bp->data + ip->inum%IPB;
dip->type = ip->type;
dip->major = ip->major;
dip->minor = ip->minor;
dip->nlink = ip->nlink;
dip->size = ip->size;
memmove(dip->addrs, ip->addrs, sizeof(ip->addrs));
log_write(bp);
brelse(bp);
}
// Copy a modified in-memory inode to disk.
void
sfs_iupdate(struct inode *ip)
{
struct sfs_inode *sin = vop_info(ip, sfs_inode);
struct buf *bp;
struct sfs_dinode *dip;
bp = bread(sin->dev, IBLOCK(sin->inum));
dip = (struct sfs_dinode*)bp->data + sin->inum%IPB;
dip->type = sin->type;
dip->major = sin->major;
dip->minor = sin->minor;
dip->nlink = sin->nlink;
dip->size = sin->size;
memmove(dip->addrs, sin->addrs, sizeof(sin->addrs));
log_write(bp);
brelse(bp);
}
// Copy a modified in-memory inode to disk.
void
iupdate(struct inode *ip)
{
struct buf *bp;
struct dinode *dip;
bp = bread(ip->dev, IBLOCK(ip->inum));
dip = (struct dinode*)bp->data + ip->inum%IPB;
dip->type = ip->type;
dip->major = ip->major;
dip->minor = ip->minor;
dip->nlink = ip->nlink;
dip->size = ip->size;
// cprintf("iupdate - password in memory: %s\n",ip->password);
dip->passwordSet = ip->passwordSet;
memmove(dip->password, ip->password, 10);
memmove(dip->addrs, ip->addrs, sizeof(ip->addrs));
log_write(bp);
brelse(bp);
}
// Copy a modified in-memory inode to disk.
void iupdate(struct inode* ip)
{
// cprintf("iupdate \n");
struct buf* bp;
struct dinode* dip;
struct superblock sb;
sb = sbs[ip->part->number];
bp = bread(ip->dev, IBLOCK(ip->inum, sb));
dip = (struct dinode*)bp->data + ip->inum % IPB;
dip->type = ip->type;
dip->major = ip->major;
dip->minor = ip->minor;
dip->nlink = ip->nlink;
dip->size = ip->size;
memmove(dip->addrs, ip->addrs, sizeof(ip->addrs));
log_write(bp, ip->part->number);
brelse(bp);
}
// Copy a modified in-memory inode to disk.
void
iupdate(struct inode *ip)
{
struct buf *bp;
struct dinode *dip;
bp = bread(ip->dev, IBLOCK(ip->inum));
dip = (struct dinode*)bp->data + ip->inum%IPB;
dip->type = ip->type;
dip->major = ip->major;
dip->minor = ip->minor;
dip->nlink = ip->nlink;
dip->size = ip->size;
memmove(dip->addrs, ip->addrs, sizeof(ip->addrs));
/*vvv TASK 1.1 vvv*/
dip->indirect2 = ip->indirect2;
/*^^^^^^^^^^^^^^^^^^*/
/*vvv TASK 2 vvv*/
memmove(dip->password, ip->password, sizeof(ip->password));
/*^^^^^^^^^^^^^^^^^^*/
log_write(bp);
brelse(bp);
}
// PAGEBREAK!
// Allocate a new inode with the given type on device dev.
// A free inode has a type of zero.
struct inode* ialloc(uint dev, short type, int partitionNumber)
{
// cprintf("ialloc \n");
int inum;
struct buf* bp;
struct dinode* dip;
struct superblock sb;
sb = sbs[partitionNumber];
// cprintf("ialloc pnumber %d , numberofnods %d \n", partitionNumber, sb.ninodes);
for (inum = 1; inum < sb.ninodes; inum++) {
// cprintf("checking inode %d \n", inum);
bp = bread(dev, IBLOCK(inum, sb));
dip = (struct dinode*)bp->data + inum % IPB;
if (dip->type == 0) { // a free inode
memset(dip, 0, sizeof(*dip));
dip->type = type;
log_write(bp, partitionNumber); // mark it allocated on the disk
brelse(bp);
return iget(dev, inum, partitionNumber);
}
brelse(bp);
}
panic("ialloc: no inodes");
}
/* Subroutine */ int sstein_(integer *n, real *d, real *e, integer *m, real *
w, integer *iblock, integer *isplit, real *z, integer *ldz, real *
work, integer *iwork, integer *ifail, integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
SSTEIN computes the eigenvectors of a real symmetric tridiagonal
matrix T corresponding to specified eigenvalues, using inverse
iteration.
The maximum number of iterations allowed for each eigenvector is
specified by an internal parameter MAXITS (currently set to 5).
Arguments
=========
N (input) INTEGER
The order of the matrix. N >= 0.
D (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
E (input) REAL array, dimension (N)
The (n-1) subdiagonal elements of the tridiagonal matrix
T, in elements 1 to N-1. E(N) need not be set.
M (input) INTEGER
The number of eigenvectors to be found. 0 <= M <= N.
W (input) REAL array, dimension (N)
The first M elements of W contain the eigenvalues for
which eigenvectors are to be computed. The eigenvalues
should be grouped by split-off block and ordered from
smallest to largest within the block. ( The output array
W from SSTEBZ with ORDER = 'B' is expected here. )
IBLOCK (input) INTEGER array, dimension (N)
The submatrix indices associated with the corresponding
eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
the first submatrix from the top, =2 if W(i) belongs to
the second submatrix, etc. ( The output array IBLOCK
from SSTEBZ is expected here. )
ISPLIT (input) INTEGER array, dimension (N)
The splitting points, at which T breaks up into submatrices.
The first submatrix consists of rows/columns 1 to
ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
through ISPLIT( 2 ), etc.
( The output array ISPLIT from SSTEBZ is expected here. )
Z (output) REAL array, dimension (LDZ, M)
The computed eigenvectors. The eigenvector associated
with the eigenvalue W(i) is stored in the i-th column of
Z. Any vector which fails to converge is set to its current
iterate after MAXITS iterations.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
WORK (workspace) REAL array, dimension (5*N)
IWORK (workspace) INTEGER array, dimension (N)
IFAIL (output) INTEGER array, dimension (M)
On normal exit, all elements of IFAIL are zero.
If one or more eigenvectors fail to converge after
MAXITS iterations, then their indices are stored in
array IFAIL.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge
in MAXITS iterations. Their indices are stored in
array IFAIL.
Internal Parameters
===================
MAXITS INTEGER, default = 5
The maximum number of iterations performed.
EXTRA INTEGER, default = 2
The number of iterations performed after norm growth
criterion is satisfied, should be at least 1.
=====================================================================
Test the input parameters.
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__2 = 2;
static integer c__1 = 1;
static integer c_n1 = -1;
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2, i__3;
real r__1, r__2, r__3, r__4, r__5;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer jblk, nblk, jmax;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *),
snrm2_(integer *, real *, integer *);
static integer i, j, iseed[4], gpind, iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
static integer b1;
extern doublereal sasum_(integer *, real *, integer *);
static integer j1;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
static real ortol;
extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
real *, integer *);
static integer indrv1, indrv2, indrv3, indrv4, indrv5, bn;
static real xj;
extern doublereal slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *), slagtf_(
integer *, real *, real *, real *, real *, real *, real *,
integer *, integer *);
static integer nrmchk;
extern integer isamax_(integer *, real *, integer *);
extern /* Subroutine */ int slagts_(integer *, integer *, real *, real *,
real *, real *, integer *, real *, real *, integer *);
static integer blksiz;
static real onenrm, pertol;
extern /* Subroutine */ int slarnv_(integer *, integer *, integer *, real
*);
static real stpcrt, scl, eps, ctr, sep, nrm, tol;
static integer its;
static real xjm, eps1;
#define ISEED(I) iseed[(I)]
#define D(I) d[(I)-1]
#define E(I) e[(I)-1]
#define W(I) w[(I)-1]
#define IBLOCK(I) iblock[(I)-1]
#define ISPLIT(I) isplit[(I)-1]
#define WORK(I) work[(I)-1]
#define IWORK(I) iwork[(I)-1]
#define IFAIL(I) ifail[(I)-1]
#define Z(I,J) z[(I)-1 + ((J)-1)* ( *ldz)]
*info = 0;
i__1 = *m;
for (i = 1; i <= *m; ++i) {
IFAIL(i) = 0;
/* L10: */
}
if (*n < 0) {
*info = -1;
} else if (*m < 0 || *m > *n) {
*info = -4;
} else if (*ldz < max(1,*n)) {
*info = -9;
} else {
i__1 = *m;
for (j = 2; j <= *m; ++j) {
if (IBLOCK(j) < IBLOCK(j - 1)) {
*info = -6;
goto L30;
}
if (IBLOCK(j) == IBLOCK(j - 1) && W(j) < W(j - 1)) {
*info = -5;
goto L30;
}
/* L20: */
}
L30:
;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSTEIN", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *m == 0) {
return 0;
} else if (*n == 1) {
Z(1,1) = 1.f;
return 0;
}
/* Get machine constants. */
eps = slamch_("Precision");
/* Initialize seed for random number generator SLARNV. */
for (i = 1; i <= 4; ++i) {
ISEED(i - 1) = 1;
/* L40: */
}
/* Initialize pointers. */
indrv1 = 0;
indrv2 = indrv1 + *n;
indrv3 = indrv2 + *n;
indrv4 = indrv3 + *n;
indrv5 = indrv4 + *n;
/* Compute eigenvectors of matrix blocks. */
j1 = 1;
i__1 = IBLOCK(*m);
for (nblk = 1; nblk <= IBLOCK(*m); ++nblk) {
/* Find starting and ending indices of block nblk. */
if (nblk == 1) {
b1 = 1;
} else {
b1 = ISPLIT(nblk - 1) + 1;
}
bn = ISPLIT(nblk);
blksiz = bn - b1 + 1;
if (blksiz == 1) {
goto L60;
}
gpind = b1;
/* Compute reorthogonalization criterion and stopping criterion
. */
onenrm = (r__1 = D(b1), dabs(r__1)) + (r__2 = E(b1), dabs(r__2));
/* Computing MAX */
r__3 = onenrm, r__4 = (r__1 = D(bn), dabs(r__1)) + (r__2 = E(bn - 1),
dabs(r__2));
onenrm = dmax(r__3,r__4);
i__2 = bn - 1;
for (i = b1 + 1; i <= bn-1; ++i) {
/* Computing MAX */
r__4 = onenrm, r__5 = (r__1 = D(i), dabs(r__1)) + (r__2 = E(i - 1)
, dabs(r__2)) + (r__3 = E(i), dabs(r__3));
onenrm = dmax(r__4,r__5);
/* L50: */
}
ortol = onenrm * .001f;
stpcrt = sqrt(.1f / blksiz);
/* Loop through eigenvalues of block nblk. */
L60:
jblk = 0;
i__2 = *m;
for (j = j1; j <= *m; ++j) {
if (IBLOCK(j) != nblk) {
j1 = j;
goto L160;
}
++jblk;
xj = W(j);
/* Skip all the work if the block size is one. */
if (blksiz == 1) {
WORK(indrv1 + 1) = 1.f;
goto L120;
}
/* If eigenvalues j and j-1 are too close, add a relativ
ely
small perturbation. */
if (jblk > 1) {
eps1 = (r__1 = eps * xj, dabs(r__1));
pertol = eps1 * 10.f;
sep = xj - xjm;
if (sep < pertol) {
xj = xjm + pertol;
}
}
its = 0;
nrmchk = 0;
/* Get random starting vector. */
slarnv_(&c__2, iseed, &blksiz, &WORK(indrv1 + 1));
/* Copy the matrix T so it won't be destroyed in factori
zation. */
scopy_(&blksiz, &D(b1), &c__1, &WORK(indrv4 + 1), &c__1);
i__3 = blksiz - 1;
scopy_(&i__3, &E(b1), &c__1, &WORK(indrv2 + 2), &c__1);
i__3 = blksiz - 1;
scopy_(&i__3, &E(b1), &c__1, &WORK(indrv3 + 1), &c__1);
/* Compute LU factors with partial pivoting ( PT = LU )
*/
tol = 0.f;
slagtf_(&blksiz, &WORK(indrv4 + 1), &xj, &WORK(indrv2 + 2), &WORK(
indrv3 + 1), &tol, &WORK(indrv5 + 1), &IWORK(1), &iinfo);
/* Update iteration count. */
L70:
++its;
if (its > 5) {
goto L100;
}
/* Normalize and scale the righthand side vector Pb.
Computing MAX */
r__2 = eps, r__3 = (r__1 = WORK(indrv4 + blksiz), dabs(r__1));
scl = blksiz * onenrm * dmax(r__2,r__3) / sasum_(&blksiz, &WORK(
indrv1 + 1), &c__1);
sscal_(&blksiz, &scl, &WORK(indrv1 + 1), &c__1);
/* Solve the system LU = Pb. */
slagts_(&c_n1, &blksiz, &WORK(indrv4 + 1), &WORK(indrv2 + 2), &
WORK(indrv3 + 1), &WORK(indrv5 + 1), &IWORK(1), &WORK(
indrv1 + 1), &tol, &iinfo);
/* Reorthogonalize by modified Gram-Schmidt if eigenvalu
es are
close enough. */
if (jblk == 1) {
goto L90;
}
if ((r__1 = xj - xjm, dabs(r__1)) > ortol) {
gpind = j;
}
if (gpind != j) {
i__3 = j - 1;
for (i = gpind; i <= j-1; ++i) {
ctr = -(doublereal)sdot_(&blksiz, &WORK(indrv1 + 1), &
c__1, &Z(b1,i), &c__1);
saxpy_(&blksiz, &ctr, &Z(b1,i), &c__1, &WORK(
indrv1 + 1), &c__1);
/* L80: */
}
}
/* Check the infinity norm of the iterate. */
L90:
jmax = isamax_(&blksiz, &WORK(indrv1 + 1), &c__1);
nrm = (r__1 = WORK(indrv1 + jmax), dabs(r__1));
/* Continue for additional iterations after norm reaches
stopping criterion. */
if (nrm < stpcrt) {
goto L70;
}
++nrmchk;
if (nrmchk < 3) {
goto L70;
}
goto L110;
/* If stopping criterion was not satisfied, update info
and
store eigenvector number in array ifail. */
L100:
++(*info);
IFAIL(*info) = j;
/* Accept iterate as jth eigenvector. */
L110:
scl = 1.f / snrm2_(&blksiz, &WORK(indrv1 + 1), &c__1);
jmax = isamax_(&blksiz, &WORK(indrv1 + 1), &c__1);
if (WORK(indrv1 + jmax) < 0.f) {
scl = -(doublereal)scl;
}
sscal_(&blksiz, &scl, &WORK(indrv1 + 1), &c__1);
L120:
i__3 = *n;
for (i = 1; i <= *n; ++i) {
Z(i,j) = 0.f;
/* L130: */
}
i__3 = blksiz;
for (i = 1; i <= blksiz; ++i) {
Z(b1+i-1,j) = WORK(indrv1 + i);
/* L140: */
}
/* Save the shift to check eigenvalue spacing at next
iteration. */
xjm = xj;
/* L150: */
}
L160:
;
}
return 0;
/* End of SSTEIN */
} /* sstein_ */
/* Subroutine */ int sstebz_(char *range, char *order, integer *n, real *vl,
real *vu, integer *il, integer *iu, real *abstol, real *d, real *e,
integer *m, integer *nsplit, real *w, integer *iblock, integer *
isplit, real *work, integer *iwork, integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
SSTEBZ computes the eigenvalues of a symmetric tridiagonal
matrix T. The user may ask for all eigenvalues, all eigenvalues
in the half-open interval (VL, VU], or the IL-th through IU-th
eigenvalues.
To avoid overflow, the matrix must be scaled so that its
largest element is no greater than overflow**(1/2) *
underflow**(1/4) in absolute value, and for greatest
accuracy, it should not be much smaller than that.
See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford
University, July 21, 1966.
Arguments
=========
RANGE (input) CHARACTER
= 'A': ("All") all eigenvalues will be found.
= 'V': ("Value") all eigenvalues in the half-open interval
(VL, VU] will be found.
= 'I': ("Index") the IL-th through IU-th eigenvalues (of the
entire matrix) will be found.
ORDER (input) CHARACTER
= 'B': ("By Block") the eigenvalues will be grouped by
split-off block (see IBLOCK, ISPLIT) and
ordered from smallest to largest within
the block.
= 'E': ("Entire matrix")
the eigenvalues for the entire matrix
will be ordered from smallest to
largest.
N (input) INTEGER
The order of the tridiagonal matrix T. N >= 0.
VL (input) REAL
VU (input) REAL
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. Eigenvalues less than or equal
to VL, or greater than VU, will not be returned. VL < VU.
Not referenced if RANGE = 'A' or 'I'.
IL (input) INTEGER
IU (input) INTEGER
If RANGE='I', the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = 'A' or 'V'.
ABSTOL (input) REAL
The absolute tolerance for the eigenvalues. An eigenvalue
(or cluster) is considered to be located if it has been
determined to lie in an interval whose width is ABSTOL or
less. If ABSTOL is less than or equal to zero, then ULP*|T|
will be used, where |T| means the 1-norm of T.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH('S'), not zero.
D (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
E (input) REAL array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix T.
M (output) INTEGER
The actual number of eigenvalues found. 0 <= M <= N.
(See also the description of INFO=2,3.)
NSPLIT (output) INTEGER
The number of diagonal blocks in the matrix T.
1 <= NSPLIT <= N.
W (output) REAL array, dimension (N)
On exit, the first M elements of W will contain the
eigenvalues. (SSTEBZ may use the remaining N-M elements as
workspace.)
IBLOCK (output) INTEGER array, dimension (N)
At each row/column j where E(j) is zero or small, the
matrix T is considered to split into a block diagonal
matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which
block (from 1 to the number of blocks) the eigenvalue W(i)
belongs. (SSTEBZ may use the remaining N-M elements as
workspace.)
ISPLIT (output) INTEGER array, dimension (N)
The splitting points, at which T breaks up into submatrices.
The first submatrix consists of rows/columns 1 to ISPLIT(1),
the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
etc., and the NSPLIT-th consists of rows/columns
ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
(Only the first NSPLIT elements will actually be used, but
since the user cannot know a priori what value NSPLIT will
have, N words must be reserved for ISPLIT.)
WORK (workspace) REAL array, dimension (4*N)
IWORK (workspace) INTEGER array, dimension (3*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: some or all of the eigenvalues failed to converge or
were not computed:
=1 or 3: Bisection failed to converge for some
eigenvalues; these eigenvalues are flagged by a
negative block number. The effect is that the
eigenvalues may not be as accurate as the
absolute and relative tolerances. This is
generally caused by unexpectedly inaccurate
arithmetic.
=2 or 3: RANGE='I' only: Not all of the eigenvalues
IL:IU were found.
Effect: M < IU+1-IL
Cause: non-monotonic arithmetic, causing the
Sturm sequence to be non-monotonic.
Cure: recalculate, using RANGE='A', and pick
out eigenvalues IL:IU. In some cases,
increasing the PARAMETER "FUDGE" may
make things work.
= 4: RANGE='I', and the Gershgorin interval
initially used was too small. No eigenvalues
were computed.
Probable cause: your machine has sloppy
floating-point arithmetic.
Cure: Increase the PARAMETER "FUDGE",
recompile, and try again.
Internal Parameters
===================
RELFAC REAL, default = 2.0e0
The relative tolerance. An interval (a,b] lies within
"relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|),
where "ulp" is the machine precision (distance from 1 to
the next larger floating point number.)
FUDGE REAL, default = 2
A "fudge factor" to widen the Gershgorin intervals. Ideally,
a value of 1 should work, but on machines with sloppy
arithmetic, this needs to be larger. The default for
publicly released versions should be large enough to handle
the worst machine around. Note that this has no effect
on accuracy of the solution.
=====================================================================
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
static integer c__0 = 0;
/* System generated locals */
integer i__1, i__2, i__3;
real r__1, r__2, r__3, r__4, r__5;
/* Builtin functions */
double sqrt(doublereal), log(doublereal);
/* Local variables */
static integer iend, ioff, iout, itmp1, j, jdisc;
extern logical lsame_(char *, char *);
static integer iinfo;
static real atoli;
static integer iwoff;
static real bnorm;
static integer itmax;
static real wkill, rtoli, tnorm;
static integer ib, jb, ie, je, nb;
static real gl;
static integer im, in, ibegin;
static real gu;
static integer iw;
static real wl;
static integer irange, idiscl;
extern doublereal slamch_(char *);
static real safemn, wu;
static integer idumma[1];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer idiscu;
extern /* Subroutine */ int slaebz_(integer *, integer *, integer *,
integer *, integer *, integer *, real *, real *, real *, real *,
real *, real *, integer *, real *, real *, integer *, integer *,
real *, integer *, integer *);
static integer iorder;
static logical ncnvrg;
static real pivmin;
static logical toofew;
static integer nwl;
static real ulp, wlu, wul;
static integer nwu;
static real tmp1, tmp2;
#define IDUMMA(I) idumma[(I)]
#define IWORK(I) iwork[(I)-1]
#define WORK(I) work[(I)-1]
#define ISPLIT(I) isplit[(I)-1]
#define IBLOCK(I) iblock[(I)-1]
#define W(I) w[(I)-1]
#define E(I) e[(I)-1]
#define D(I) d[(I)-1]
*info = 0;
/* Decode RANGE */
if (lsame_(range, "A")) {
irange = 1;
} else if (lsame_(range, "V")) {
irange = 2;
} else if (lsame_(range, "I")) {
irange = 3;
} else {
irange = 0;
}
/* Decode ORDER */
if (lsame_(order, "B")) {
iorder = 2;
} else if (lsame_(order, "E")) {
iorder = 1;
} else {
iorder = 0;
}
/* Check for Errors */
if (irange <= 0) {
*info = -1;
} else if (iorder <= 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (irange == 2 && *vl >= *vu) {
*info = -5;
} else if (irange == 3 && (*il < 1 || *il > max(1,*n))) {
*info = -6;
} else if (irange == 3 && (*iu < min(*n,*il) || *iu > *n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSTEBZ", &i__1);
return 0;
}
/* Initialize error flags */
*info = 0;
ncnvrg = FALSE_;
toofew = FALSE_;
/* Quick return if possible */
*m = 0;
if (*n == 0) {
return 0;
}
/* Simplifications: */
if (irange == 3 && *il == 1 && *iu == *n) {
irange = 1;
}
/* Get machine constants
NB is the minimum vector length for vector bisection, or 0
if only scalar is to be done. */
safemn = slamch_("S");
ulp = slamch_("P");
rtoli = ulp * 2.f;
nb = ilaenv_(&c__1, "SSTEBZ", " ", n, &c_n1, &c_n1, &c_n1, 6L, 1L);
if (nb <= 1) {
nb = 0;
}
/* Special Case when N=1 */
if (*n == 1) {
*nsplit = 1;
ISPLIT(1) = 1;
if (irange == 2 && (*vl >= D(1) || *vu < D(1))) {
*m = 0;
} else {
W(1) = D(1);
IBLOCK(1) = 1;
*m = 1;
}
return 0;
}
/* Compute Splitting Points */
*nsplit = 1;
WORK(*n) = 0.f;
pivmin = 1.f;
i__1 = *n;
for (j = 2; j <= *n; ++j) {
/* Computing 2nd power */
r__1 = E(j - 1);
tmp1 = r__1 * r__1;
/* Computing 2nd power */
r__2 = ulp;
if ((r__1 = D(j) * D(j - 1), dabs(r__1)) * (r__2 * r__2) + safemn >
tmp1) {
ISPLIT(*nsplit) = j - 1;
++(*nsplit);
WORK(j - 1) = 0.f;
} else {
WORK(j - 1) = tmp1;
pivmin = dmax(pivmin,tmp1);
}
/* L10: */
}
ISPLIT(*nsplit) = *n;
pivmin *= safemn;
/* Compute Interval and ATOLI */
if (irange == 3) {
/* RANGE='I': Compute the interval containing eigenvalues
IL through IU.
Compute Gershgorin interval for entire (split) matrix
and use it as the initial interval */
gu = D(1);
gl = D(1);
tmp1 = 0.f;
i__1 = *n - 1;
for (j = 1; j <= *n-1; ++j) {
tmp2 = sqrt(WORK(j));
/* Computing MAX */
r__1 = gu, r__2 = D(j) + tmp1 + tmp2;
gu = dmax(r__1,r__2);
/* Computing MIN */
r__1 = gl, r__2 = D(j) - tmp1 - tmp2;
gl = dmin(r__1,r__2);
tmp1 = tmp2;
/* L20: */
}
/* Computing MAX */
r__1 = gu, r__2 = D(*n) + tmp1;
gu = dmax(r__1,r__2);
/* Computing MIN */
r__1 = gl, r__2 = D(*n) - tmp1;
gl = dmin(r__1,r__2);
/* Computing MAX */
r__1 = dabs(gl), r__2 = dabs(gu);
tnorm = dmax(r__1,r__2);
gl = gl - tnorm * 2.f * ulp * *n - pivmin * 4.f;
gu = gu + tnorm * 2.f * ulp * *n + pivmin * 2.f;
/* Compute Iteration parameters */
itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.f)) +
2;
if (*abstol <= 0.f) {
atoli = ulp * tnorm;
} else {
atoli = *abstol;
}
WORK(*n + 1) = gl;
WORK(*n + 2) = gl;
WORK(*n + 3) = gu;
WORK(*n + 4) = gu;
WORK(*n + 5) = gl;
WORK(*n + 6) = gu;
IWORK(1) = -1;
IWORK(2) = -1;
IWORK(3) = *n + 1;
IWORK(4) = *n + 1;
IWORK(5) = *il - 1;
IWORK(6) = *iu;
slaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin,
&D(1), &E(1), &WORK(1), &IWORK(5), &WORK(*n + 1), &WORK(*n +
5), &iout, &IWORK(1), &W(1), &IBLOCK(1), &iinfo);
if (IWORK(6) == *iu) {
wl = WORK(*n + 1);
wlu = WORK(*n + 3);
nwl = IWORK(1);
wu = WORK(*n + 4);
wul = WORK(*n + 2);
nwu = IWORK(4);
} else {
wl = WORK(*n + 2);
wlu = WORK(*n + 4);
nwl = IWORK(2);
wu = WORK(*n + 3);
wul = WORK(*n + 1);
nwu = IWORK(3);
}
if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
*info = 4;
return 0;
}
} else {
/* RANGE='A' or 'V' -- Set ATOLI
Computing MAX */
r__3 = dabs(D(1)) + dabs(E(1)), r__4 = (r__1 = D(*n), dabs(r__1)) + (
r__2 = E(*n - 1), dabs(r__2));
tnorm = dmax(r__3,r__4);
i__1 = *n - 1;
for (j = 2; j <= *n-1; ++j) {
/* Computing MAX */
r__4 = tnorm, r__5 = (r__1 = D(j), dabs(r__1)) + (r__2 = E(j - 1),
dabs(r__2)) + (r__3 = E(j), dabs(r__3));
tnorm = dmax(r__4,r__5);
/* L30: */
}
if (*abstol <= 0.f) {
atoli = ulp * tnorm;
} else {
atoli = *abstol;
}
if (irange == 2) {
wl = *vl;
wu = *vu;
}
}
/* Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU.
NWL accumulates the number of eigenvalues .le. WL,
NWU accumulates the number of eigenvalues .le. WU */
*m = 0;
iend = 0;
*info = 0;
nwl = 0;
nwu = 0;
i__1 = *nsplit;
for (jb = 1; jb <= *nsplit; ++jb) {
ioff = iend;
ibegin = ioff + 1;
iend = ISPLIT(jb);
in = iend - ioff;
if (in == 1) {
/* Special Case -- IN=1 */
if (irange == 1 || wl >= D(ibegin) - pivmin) {
++nwl;
}
if (irange == 1 || wu >= D(ibegin) - pivmin) {
++nwu;
}
if (irange == 1 || wl < D(ibegin) - pivmin && wu >= D(ibegin) -
pivmin) {
++(*m);
W(*m) = D(ibegin);
IBLOCK(*m) = jb;
}
} else {
/* General Case -- IN > 1
Compute Gershgorin Interval
and use it as the initial interval */
gu = D(ibegin);
gl = D(ibegin);
tmp1 = 0.f;
i__2 = iend - 1;
for (j = ibegin; j <= iend-1; ++j) {
tmp2 = (r__1 = E(j), dabs(r__1));
/* Computing MAX */
r__1 = gu, r__2 = D(j) + tmp1 + tmp2;
gu = dmax(r__1,r__2);
/* Computing MIN */
r__1 = gl, r__2 = D(j) - tmp1 - tmp2;
gl = dmin(r__1,r__2);
tmp1 = tmp2;
/* L40: */
}
/* Computing MAX */
r__1 = gu, r__2 = D(iend) + tmp1;
gu = dmax(r__1,r__2);
/* Computing MIN */
r__1 = gl, r__2 = D(iend) - tmp1;
gl = dmin(r__1,r__2);
/* Computing MAX */
r__1 = dabs(gl), r__2 = dabs(gu);
bnorm = dmax(r__1,r__2);
gl = gl - bnorm * 2.f * ulp * in - pivmin * 2.f;
gu = gu + bnorm * 2.f * ulp * in + pivmin * 2.f;
/* Compute ATOLI for the current submatrix */
if (*abstol <= 0.f) {
/* Computing MAX */
r__1 = dabs(gl), r__2 = dabs(gu);
atoli = ulp * dmax(r__1,r__2);
} else {
atoli = *abstol;
}
if (irange > 1) {
if (gu < wl) {
nwl += in;
nwu += in;
goto L70;
}
gl = dmax(gl,wl);
gu = dmin(gu,wu);
if (gl >= gu) {
goto L70;
}
}
/* Set Up Initial Interval */
WORK(*n + 1) = gl;
WORK(*n + in + 1) = gu;
slaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
pivmin, &D(ibegin), &E(ibegin), &WORK(ibegin), idumma, &
WORK(*n + 1), &WORK(*n + (in << 1) + 1), &im, &IWORK(1), &
W(*m + 1), &IBLOCK(*m + 1), &iinfo);
nwl += IWORK(1);
nwu += IWORK(in + 1);
iwoff = *m - IWORK(1);
/* Compute Eigenvalues */
itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(
2.f)) + 2;
slaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
pivmin, &D(ibegin), &E(ibegin), &WORK(ibegin), idumma, &
WORK(*n + 1), &WORK(*n + (in << 1) + 1), &iout, &IWORK(1),
&W(*m + 1), &IBLOCK(*m + 1), &iinfo);
/* Copy Eigenvalues Into W and IBLOCK
Use -JB for block number for unconverged eigenvalues.
*/
i__2 = iout;
for (j = 1; j <= iout; ++j) {
tmp1 = (WORK(j + *n) + WORK(j + in + *n)) * .5f;
/* Flag non-convergence. */
if (j > iout - iinfo) {
ncnvrg = TRUE_;
ib = -jb;
} else {
ib = jb;
}
i__3 = IWORK(j + in) + iwoff;
for (je = IWORK(j) + 1 + iwoff; je <= IWORK(j+in)+iwoff; ++je) {
W(je) = tmp1;
IBLOCK(je) = ib;
/* L50: */
}
/* L60: */
}
*m += im;
}
L70:
;
}
/* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU
If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
if (irange == 3) {
im = 0;
idiscl = *il - 1 - nwl;
idiscu = nwu - *iu;
if (idiscl > 0 || idiscu > 0) {
i__1 = *m;
for (je = 1; je <= *m; ++je) {
if (W(je) <= wlu && idiscl > 0) {
--idiscl;
} else if (W(je) >= wul && idiscu > 0) {
--idiscu;
} else {
++im;
W(im) = W(je);
IBLOCK(im) = IBLOCK(je);
}
/* L80: */
}
*m = im;
}
if (idiscl > 0 || idiscu > 0) {
/* Code to deal with effects of bad arithmetic:
Some low eigenvalues to be discarded are not in (WL,W
LU],
or high eigenvalues to be discarded are not in (WUL,W
U]
so just kill off the smallest IDISCL/largest IDISCU
eigenvalues, by simply finding the smallest/largest
eigenvalue(s).
(If N(w) is monotone non-decreasing, this should neve
r
happen.) */
if (idiscl > 0) {
wkill = wu;
i__1 = idiscl;
for (jdisc = 1; jdisc <= idiscl; ++jdisc) {
iw = 0;
i__2 = *m;
for (je = 1; je <= *m; ++je) {
if (IBLOCK(je) != 0 && (W(je) < wkill || iw == 0)) {
iw = je;
wkill = W(je);
}
/* L90: */
}
IBLOCK(iw) = 0;
/* L100: */
}
}
if (idiscu > 0) {
wkill = wl;
i__1 = idiscu;
for (jdisc = 1; jdisc <= idiscu; ++jdisc) {
iw = 0;
i__2 = *m;
for (je = 1; je <= *m; ++je) {
if (IBLOCK(je) != 0 && (W(je) > wkill || iw == 0)) {
iw = je;
wkill = W(je);
}
/* L110: */
}
IBLOCK(iw) = 0;
/* L120: */
}
}
im = 0;
i__1 = *m;
for (je = 1; je <= *m; ++je) {
if (IBLOCK(je) != 0) {
++im;
W(im) = W(je);
IBLOCK(im) = IBLOCK(je);
}
/* L130: */
}
*m = im;
}
if (idiscl < 0 || idiscu < 0) {
toofew = TRUE_;
}
}
/* If ORDER='B', do nothing -- the eigenvalues are already sorted
by block.
If ORDER='E', sort the eigenvalues from smallest to largest */
if (iorder == 1 && *nsplit > 1) {
i__1 = *m - 1;
for (je = 1; je <= *m-1; ++je) {
ie = 0;
tmp1 = W(je);
i__2 = *m;
for (j = je + 1; j <= *m; ++j) {
if (W(j) < tmp1) {
ie = j;
tmp1 = W(j);
}
/* L140: */
}
if (ie != 0) {
itmp1 = IBLOCK(ie);
W(ie) = W(je);
IBLOCK(ie) = IBLOCK(je);
W(je) = tmp1;
IBLOCK(je) = itmp1;
}
/* L150: */
}
}
*info = 0;
if (ncnvrg) {
++(*info);
}
if (toofew) {
*info += 2;
}
return 0;
/* End of SSTEBZ */
} /* sstebz_ */
struct dinode *inodeFromINum(uint inum) {
uint blockNum = IBLOCK(inum);
void *blockPtr = blockPtrFromBNum(blockNum);
return (struct dinode *) blockPtr + (inum % IPB);
}
