/* Subroutine */ int stimtd_(char *line, integer *nm, integer *mval, integer *
nn, integer *nval, integer *nnb, integer *nbval, integer *nxval,
integer *nlda, integer *ldaval, real *timmin, real *a, real *b, real *
d__, real *tau, real *work, real *reslts, integer *ldr1, integer *
ldr2, integer *ldr3, integer *nout, ftnlen line_len)
{
/* Initialized data */
static char subnam[6*4] = "SSYTRD" "TRED1 " "SORGTR" "SORMTR";
static char sides[1*2] = "L" "R";
static char transs[1*2] = "N" "T";
static char uplos[1*2] = "U" "L";
static integer iseed[4] = { 0,0,0,1 };
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
"*** \002)";
static char fmt_9997[] = "(5x,\002line \002,i2,\002 with LDA = \002,i5)";
static char fmt_9996[] = "(/5x,a6,\002 with UPLO = '\002,a1,\002'\002,/)";
static char fmt_9995[] = "(/5x,a6,\002 with SIDE = '\002,a1,\002', UPLO "
"= '\002,a1,\002', TRANS = '\002,a1,\002', \002,a1,\002 =\002,i6,"
"/)";
/* System generated locals */
integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2,
i__3, i__4, i__5, i__6;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
s_wsle(cilist *), e_wsle(void);
/* Local variables */
static integer ilda;
static char side[1];
static integer info;
static char path[3];
static real time;
static integer isub;
static char uplo[1];
extern /* Subroutine */ int tred1_(integer *, integer *, real *, real *,
real *, real *);
static integer i__, m, n;
static char cname[6];
static integer iside, itoff, itran;
extern doublereal sopla_(char *, integer *, integer *, integer *, integer
*, integer *);
extern /* Subroutine */ int icopy_(integer *, integer *, integer *,
integer *, integer *);
static char trans[1];
static integer iuplo, i3, i4, m1, n1;
static real s1, s2;
static integer ic;
extern /* Subroutine */ int sprtb3_(char *, char *, integer *, integer *,
integer *, integer *, integer *, integer *, real *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer nb, im, in, lw, nx, reseed[4];
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen);
extern doublereal second_(void);
extern /* Subroutine */ int atimin_(char *, char *, integer *, char *,
logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), slacpy_(
char *, integer *, integer *, real *, integer *, real *, integer *
), xlaenv_(integer *, integer *);
extern doublereal smflop_(real *, real *, integer *);
static real untime;
extern /* Subroutine */ int stimmg_(integer *, integer *, integer *, real
*, integer *, integer *, integer *);
static logical timsub[4];
extern /* Subroutine */ int slatms_(integer *, integer *, char *, integer
*, char *, real *, integer *, real *, real *, integer *, integer *
, char *, real *, integer *, real *, integer *), sprtbl_(char *, char *, integer *, integer *, integer *,
integer *, integer *, real *, integer *, integer *, integer *,
ftnlen, ftnlen), sorgtr_(char *, integer *, real *, integer *,
real *, real *, integer *, integer *), sormtr_(char *,
char *, char *, integer *, integer *, real *, integer *, real *,
real *, integer *, real *, integer *, integer *), ssytrd_(char *, integer *, real *, integer *, real *,
real *, real *, real *, integer *, integer *);
static integer lda, icl, inb;
static real ops;
static char lab1[1], lab2[1];
/* Fortran I/O blocks */
static cilist io___10 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___11 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___45 = { 0, 0, 0, 0, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9995, 0 };
#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]
/* -- LAPACK timing routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
STIMTD times the LAPACK routines SSYTRD, SORGTR, and SORMTR and the
EISPACK routine TRED1.
Arguments
=========
LINE (input) CHARACTER*80
The input line that requested this routine. The first six
characters contain either the name of a subroutine or a
generic path name. The remaining characters may be used to
specify the individual routines to be timed. See ATIMIN for
a full description of the format of the input line.
NM (input) INTEGER
The number of values of M contained in the vector MVAL.
MVAL (input) INTEGER array, dimension (NM)
The values of the matrix size M.
NN (input) INTEGER
The number of values of N contained in the vector NVAL.
NVAL (input) INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNB (input) INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL (input) INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL (input) INTEGER array, dimension (NNB)
The values of the crossover point NX.
NLDA (input) INTEGER
The number of values of LDA contained in the vector LDAVAL.
LDAVAL (input) INTEGER array, dimension (NLDA)
The values of the leading dimension of the array A.
TIMMIN (input) REAL
The minimum time a subroutine will be timed.
A (workspace) REAL array, dimension (LDAMAX*NMAX)
where LDAMAX and NMAX are the maximum values of LDA and N.
B (workspace) REAL array, dimension (LDAMAX*NMAX)
D (workspace) REAL array, dimension (2*NMAX-1)
TAU (workspace) REAL array, dimension (NMAX)
WORK (workspace) REAL array, dimension (NMAX*NBMAX)
where NBMAX is the maximum value of NB.
RESLTS (workspace) REAL array, dimension
(LDR1,LDR2,LDR3,4*NN+3)
The timing results for each subroutine over the relevant
values of M, (NB,NX), LDA, and N.
LDR1 (input) INTEGER
The first dimension of RESLTS. LDR1 >= max(1,NNB).
LDR2 (input) INTEGER
The second dimension of RESLTS. LDR2 >= max(1,NM).
LDR3 (input) INTEGER
The third dimension of RESLTS. LDR3 >= max(1,2*NLDA).
NOUT (input) INTEGER
The unit number for output.
Internal Parameters
===================
MODE INTEGER
The matrix type. MODE = 3 is a geometric distribution of
eigenvalues. See SLATMS for further details.
COND REAL
The condition number of the matrix. The singular values are
set to values from DMAX to DMAX/COND.
DMAX REAL
The magnitude of the largest singular value.
=====================================================================
Parameter adjustments */
--mval;
--nval;
--nbval;
--nxval;
--ldaval;
--a;
--b;
--d__;
--tau;
--work;
reslts_dim1 = *ldr1;
reslts_dim2 = *ldr2;
reslts_dim3 = *ldr3;
reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
);
reslts -= reslts_offset;
/* Function Body
Extract the timing request from the input line. */
s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "TD", (ftnlen)2, (ftnlen)2);
atimin_(path, line, &c__4, subnam, timsub, nout, &info, (ftnlen)3, (
ftnlen)80, (ftnlen)6);
if (info != 0) {
goto L240;
}
/* Check that M <= LDA for the input values. */
s_copy(cname, line, (ftnlen)6, (ftnlen)6);
atimck_(&c__2, cname, nm, &mval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___10.ciunit = *nout;
s_wsfe(&io___10);
do_fio(&c__1, cname, (ftnlen)6);
e_wsfe();
goto L240;
}
/* Check that K <= LDA for SORMTR */
if (timsub[3]) {
atimck_(&c__3, cname, nn, &nval[1], nlda, &ldaval[1], nout, &info, (
ftnlen)6);
if (info > 0) {
io___11.ciunit = *nout;
s_wsfe(&io___11);
do_fio(&c__1, subnam_ref(0, 4), (ftnlen)6);
e_wsfe();
timsub[3] = FALSE_;
}
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Do for each value of M: */
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
icopy_(&c__4, iseed, &c__1, reseed, &c__1);
/* Do for each value of LDA: */
i__2 = *nlda;
for (ilda = 1; ilda <= i__2; ++ilda) {
lda = ldaval[ilda];
i3 = (iuplo - 1) * *nlda + ilda;
/* Do for each pair of values (NB, NX) in NBVAL and NXVAL. */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Computing MAX */
i__4 = 1, i__5 = m * max(1,nb);
lw = max(i__4,i__5);
/* Generate a test matrix of order M. */
icopy_(&c__4, reseed, &c__1, iseed, &c__1);
slatms_(&m, &m, "Uniform", iseed, "Symmetric", &tau[1], &
c__3, &c_b27, &c_b28, &m, &m, "No packing", &b[1],
&lda, &work[1], &info);
if (timsub[1] && inb == 1 && iuplo == 2) {
/* TRED1: Eispack reduction using orthogonal
transformations. */
slacpy_(uplo, &m, &m, &b[1], &lda, &a[1], &lda);
ic = 0;
s1 = second_();
L10:
tred1_(&lda, &m, &a[1], &d__[1], &d__[m + 1], &d__[m
+ 1]);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
slacpy_(uplo, &m, &m, &b[1], &lda, &a[1], &lda);
goto L10;
}
/* Subtract the time used in SLACPY. */
icl = 1;
s1 = second_();
L20:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
slacpy_(uplo, &m, &m, &b[1], &lda, &a[1], &lda);
goto L20;
}
time = (time - untime) / (real) ic;
ops = sopla_("SSYTRD", &m, &m, &c_n1, &c_n1, &nb);
reslts_ref(inb, im, ilda, 2) = smflop_(&ops, &time, &
info);
}
if (timsub[0]) {
/* SSYTRD: Reduction to tridiagonal form */
slacpy_(uplo, &m, &m, &b[1], &lda, &a[1], &lda);
ic = 0;
s1 = second_();
L30:
ssytrd_(uplo, &m, &a[1], &lda, &d__[1], &d__[m + 1], &
tau[1], &work[1], &lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
slacpy_(uplo, &m, &m, &b[1], &lda, &a[1], &lda);
goto L30;
}
/* Subtract the time used in SLACPY. */
icl = 1;
s1 = second_();
L40:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
slacpy_(uplo, &m, &m, &a[1], &lda, &b[1], &lda);
goto L40;
}
time = (time - untime) / (real) ic;
ops = sopla_("SSYTRD", &m, &m, &c_n1, &c_n1, &nb);
reslts_ref(inb, im, i3, 1) = smflop_(&ops, &time, &
info);
} else {
/* If SSYTRD was not timed, generate a matrix and
factor it using SSYTRD anyway so that the factored
form of the matrix can be used in timing the other
routines. */
slacpy_(uplo, &m, &m, &b[1], &lda, &a[1], &lda);
ssytrd_(uplo, &m, &a[1], &lda, &d__[1], &d__[m + 1], &
tau[1], &work[1], &lw, &info);
}
if (timsub[2]) {
/* SORGTR: Generate the orthogonal matrix Q from the
reduction to Hessenberg form A = Q*H*Q' */
slacpy_(uplo, &m, &m, &a[1], &lda, &b[1], &lda);
ic = 0;
s1 = second_();
L50:
sorgtr_(uplo, &m, &b[1], &lda, &tau[1], &work[1], &lw,
&info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
slacpy_(uplo, &m, &m, &a[1], &lda, &b[1], &lda);
goto L50;
}
/* Subtract the time used in SLACPY. */
icl = 1;
s1 = second_();
L60:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
slacpy_(uplo, &m, &m, &a[1], &lda, &b[1], &lda);
goto L60;
}
time = (time - untime) / (real) ic;
/* Op count for SORGTR: same as
SORGQR( N-1, N-1, N-1, ... ) */
i__4 = m - 1;
i__5 = m - 1;
i__6 = m - 1;
ops = sopla_("SORGQR", &i__4, &i__5, &i__6, &c_n1, &
nb);
reslts_ref(inb, im, i3, 3) = smflop_(&ops, &time, &
info);
}
if (timsub[3]) {
/* SORMTR: Multiply by Q stored as a product of
elementary transformations */
i4 = 3;
for (iside = 1; iside <= 2; ++iside) {
*(unsigned char *)side = *(unsigned char *)&sides[
iside - 1];
i__4 = *nn;
for (in = 1; in <= i__4; ++in) {
n = nval[in];
/* Computing MAX */
i__5 = 1, i__6 = max(1,nb) * n;
lw = max(i__5,i__6);
if (iside == 1) {
m1 = m;
n1 = n;
} else {
m1 = n;
n1 = m;
}
itoff = 0;
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char
*)&transs[itran - 1];
stimmg_(&c__0, &m1, &n1, &b[1], &lda, &
c__0, &c__0);
ic = 0;
s1 = second_();
L70:
sormtr_(side, uplo, trans, &m1, &n1, &a[1]
, &lda, &tau[1], &b[1], &lda, &
work[1], &lw, &info);
s2 = second_();
time = s2 - s1;
++ic;
if (time < *timmin) {
stimmg_(&c__0, &m1, &n1, &b[1], &lda,
&c__0, &c__0);
goto L70;
}
/* Subtract the time used in STIMMG. */
icl = 1;
s1 = second_();
L80:
s2 = second_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
stimmg_(&c__0, &m1, &n1, &b[1], &lda,
&c__0, &c__0);
goto L80;
}
time = (time - untime) / (real) ic;
/* Op count for SORMTR, SIDE='L': same as
SORMQR( 'L', TRANS, M-1, N, M-1, ...)
Op count for SORMTR, SIDE='R': same as
SORMQR( 'R', TRANS, M, N-1, N-1, ...) */
if (iside == 1) {
i__5 = m1 - 1;
i__6 = m1 - 1;
ops = sopla_("SORMQR", &i__5, &n1, &
i__6, &c_n1, &nb);
} else {
i__5 = n1 - 1;
i__6 = n1 - 1;
ops = sopla_("SORMQR", &m1, &i__5, &
i__6, &c__1, &nb);
}
reslts_ref(inb, im, i3, i4 + itoff + in) =
smflop_(&ops, &time, &info);
itoff = *nn;
/* L90: */
}
/* L100: */
}
i4 += *nn << 1;
/* L110: */
}
}
/* L120: */
}
/* L130: */
}
/* L140: */
}
/* L150: */
}
/* Print tables of results for SSYTRD, TRED1, and SORGTR */
for (isub = 1; isub <= 3; ++isub) {
if (! timsub[isub - 1]) {
goto L180;
}
io___42.ciunit = *nout;
s_wsfe(&io___42);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
if (*nlda > 1) {
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___44.ciunit = *nout;
s_wsfe(&io___44);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(integer));
e_wsfe();
/* L160: */
}
}
if (isub == 2) {
io___45.ciunit = *nout;
s_wsle(&io___45);
e_wsle();
sprtb3_(" ", "N", &c__1, &nbval[1], &nxval[1], nm, &mval[1], nlda,
&reslts_ref(1, 1, 1, isub), ldr1, ldr2, nout, (ftnlen)1,
(ftnlen)1);
} else {
i3 = 1;
for (iuplo = 1; iuplo <= 2; ++iuplo) {
io___46.ciunit = *nout;
s_wsfe(&io___46);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, uplos + (iuplo - 1), (ftnlen)1);
e_wsfe();
sprtb3_("( NB, NX)", "N", nnb, &nbval[1], &nxval[1], nm, &
mval[1], nlda, &reslts_ref(1, 1, i3, isub), ldr1,
ldr2, nout, (ftnlen)11, (ftnlen)1);
i3 += *nlda;
/* L170: */
}
}
L180:
;
}
/* Print tables of results for SORMTR */
isub = 4;
if (timsub[isub - 1]) {
i4 = 3;
for (iside = 1; iside <= 2; ++iside) {
if (iside == 1) {
*(unsigned char *)lab1 = 'M';
*(unsigned char *)lab2 = 'N';
if (*nlda > 1) {
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
i__1 = *nlda;
for (i__ = 1; i__ <= i__1; ++i__) {
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&i__, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ldaval[i__], (ftnlen)sizeof(
integer));
e_wsfe();
/* L190: */
}
}
} else {
*(unsigned char *)lab1 = 'N';
*(unsigned char *)lab2 = 'M';
}
for (itran = 1; itran <= 2; ++itran) {
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
i3 = 1;
for (iuplo = 1; iuplo <= 2; ++iuplo) {
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, sides + (iside - 1), (ftnlen)1);
do_fio(&c__1, uplos + (iuplo - 1), (ftnlen)1);
do_fio(&c__1, transs + (itran - 1), (ftnlen)1);
do_fio(&c__1, lab2, (ftnlen)1);
do_fio(&c__1, (char *)&nval[in], (ftnlen)sizeof(
integer));
e_wsfe();
sprtbl_("NB", lab1, nnb, &nbval[1], nm, &mval[1],
nlda, &reslts_ref(1, 1, i3, i4 + in), ldr1,
ldr2, nout, (ftnlen)2, (ftnlen)1);
i3 += *nlda;
/* L200: */
}
/* L210: */
}
i4 += *nn;
/* L220: */
}
/* L230: */
}
}
L240:
/* Print a table of results for each timed routine. */
return 0;
/* End of STIMTD */
} /* stimtd_ */
/* Subroutine */ int rsgba_(integer *nm, integer *n, doublereal *a,
doublereal *b, doublereal *w, integer *matz, doublereal *z__,
doublereal *fv1, doublereal *fv2, integer *ierr)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset;
/* Local variables */
extern /* Subroutine */ int tred1_(integer *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *), tred2_(integer *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *)
, reduc2_(integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *), rebakb_(integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *), tqlrat_(
integer *, doublereal *, doublereal *, integer *), tql2_(integer *
, integer *, doublereal *, doublereal *, doublereal *, integer *);
/* THIS SUBROUTINE CALLS THE RECOMMENDED SEQUENCE OF */
/* SUBROUTINES FROM THE EIGENSYSTEM SUBROUTINE PACKAGE (EISPACK) */
/* TO FIND THE EIGENVALUES AND EIGENVECTORS (IF DESIRED) */
/* FOR THE REAL SYMMETRIC GENERALIZED EIGENPROBLEM BAX = (LAMBDA)X.
*/
/* ON INPUT */
/* NM MUST BE SET TO THE ROW DIMENSION OF THE TWO-DIMENSIONAL */
/* ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM */
/* DIMENSION STATEMENT. */
/* N IS THE ORDER OF THE MATRICES A AND B. */
/* A CONTAINS A REAL SYMMETRIC MATRIX. */
/* B CONTAINS A POSITIVE DEFINITE REAL SYMMETRIC MATRIX. */
/* MATZ IS AN INTEGER VARIABLE SET EQUAL TO ZERO IF */
/* ONLY EIGENVALUES ARE DESIRED. OTHERWISE IT IS SET TO */
/* ANY NON-ZERO INTEGER FOR BOTH EIGENVALUES AND EIGENVECTORS. */
/* ON OUTPUT */
/* W CONTAINS THE EIGENVALUES IN ASCENDING ORDER. */
/* Z CONTAINS THE EIGENVECTORS IF MATZ IS NOT ZERO. */
/* IERR IS AN INTEGER OUTPUT VARIABLE SET EQUAL TO AN ERROR */
/* COMPLETION CODE DESCRIBED IN THE DOCUMENTATION FOR TQLRAT */
/* AND TQL2. THE NORMAL COMPLETION CODE IS ZERO. */
/* FV1 AND FV2 ARE TEMPORARY STORAGE ARRAYS. */
/* QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW, */
/* MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
*/
/* THIS VERSION DATED AUGUST 1983. */
/* ------------------------------------------------------------------
*/
/* Parameter adjustments */
--fv2;
--fv1;
z_dim1 = *nm;
z_offset = z_dim1 + 1;
z__ -= z_offset;
--w;
b_dim1 = *nm;
b_offset = b_dim1 + 1;
b -= b_offset;
a_dim1 = *nm;
a_offset = a_dim1 + 1;
a -= a_offset;
/* Function Body */
if (*n <= *nm) {
goto L10;
}
*ierr = *n * 10;
goto L50;
L10:
reduc2_(nm, n, &a[a_offset], &b[b_offset], &fv2[1], ierr);
if (*ierr != 0) {
goto L50;
}
if (*matz != 0) {
goto L20;
}
/* .......... FIND EIGENVALUES ONLY .......... */
tred1_(nm, n, &a[a_offset], &w[1], &fv1[1], &fv2[1]);
tqlrat_(n, &w[1], &fv2[1], ierr);
goto L50;
/* .......... FIND BOTH EIGENVALUES AND EIGENVECTORS .......... */
L20:
tred2_(nm, n, &a[a_offset], &w[1], &fv1[1], &z__[z_offset]);
tql2_(nm, n, &w[1], &fv1[1], &z__[z_offset], ierr);
if (*ierr != 0) {
goto L50;
}
rebakb_(nm, n, &b[b_offset], &fv2[1], n, &z__[z_offset]);
L50:
return 0;
} /* rsgba_ */
/*< subroutine rsg(nm,n,a,b,w,matz,z,fv1,fv2,ierr) >*/
/* Subroutine */ int rsg_(integer *nm, integer *n, doublereal *a, doublereal *
b, doublereal *w, integer *matz, doublereal *z__, doublereal *fv1,
doublereal *fv2, integer *ierr)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset;
/* Local variables */
extern /* Subroutine */ int tql2_(integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *), tred1_(integer *, integer
*, doublereal *, doublereal *, doublereal *, doublereal *),
tred2_(integer *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *), rebak_(integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *), reduc_(
integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *), tqlrat_(integer *, doublereal *, doublereal *,
integer *);
/*< integer n,nm,ierr,matz >*/
/*< double precision a(nm,n),b(nm,n),w(n),z(nm,n),fv1(n),fv2(n) >*/
/* this subroutine calls the recommended sequence of */
/* subroutines from the eigensystem subroutine package (eispack) */
/* to find the eigenvalues and eigenvectors (if desired) */
/* for the real symmetric generalized eigenproblem ax = (lambda)bx. */
/* on input */
/* nm must be set to the row dimension of the two-dimensional */
/* array parameters as declared in the calling program */
/* dimension statement. */
/* n is the order of the matrices a and b. */
/* a contains a real symmetric matrix. */
/* b contains a positive definite real symmetric matrix. */
/* matz is an integer variable set equal to zero if */
/* only eigenvalues are desired. otherwise it is set to */
/* any non-zero integer for both eigenvalues and eigenvectors. */
/* on output */
/* w contains the eigenvalues in ascending order. */
/* z contains the eigenvectors if matz is not zero. */
/* ierr is an integer output variable set equal to an error */
/* completion code described in the documentation for tqlrat */
/* and tql2. the normal completion code is zero. */
/* fv1 and fv2 are temporary storage arrays. */
/* questions and comments should be directed to burton s. garbow, */
/* mathematics and computer science div, argonne national laboratory */
/* this version dated august 1983. */
/* ------------------------------------------------------------------ */
/*< if (n .le. nm) go to 10 >*/
/* Parameter adjustments */
--fv2;
--fv1;
z_dim1 = *nm;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--w;
b_dim1 = *nm;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *nm;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
if (*n <= *nm) {
goto L10;
}
/*< ierr = 10 * n >*/
*ierr = *n * 10;
/*< go to 50 >*/
goto L50;
/*< 10 call reduc(nm,n,a,b,fv2,ierr) >*/
L10:
reduc_(nm, n, &a[a_offset], &b[b_offset], &fv2[1], ierr);
/*< if (ierr .ne. 0) go to 50 >*/
if (*ierr != 0) {
goto L50;
}
/*< if (matz .ne. 0) go to 20 >*/
if (*matz != 0) {
goto L20;
}
/* .......... find eigenvalues only .......... */
/*< call tred1(nm,n,a,w,fv1,fv2) >*/
tred1_(nm, n, &a[a_offset], &w[1], &fv1[1], &fv2[1]);
/*< call tqlrat(n,w,fv2,ierr) >*/
tqlrat_(n, &w[1], &fv2[1], ierr);
/*< go to 50 >*/
goto L50;
/* .......... find both eigenvalues and eigenvectors .......... */
/*< 20 call tred2(nm,n,a,w,fv1,z) >*/
L20:
tred2_(nm, n, &a[a_offset], &w[1], &fv1[1], &z__[z_offset]);
/*< call tql2(nm,n,w,fv1,z,ierr) >*/
tql2_(nm, n, &w[1], &fv1[1], &z__[z_offset], ierr);
/*< if (ierr .ne. 0) go to 50 >*/
if (*ierr != 0) {
goto L50;
}
/*< call rebak(nm,n,b,fv2,n,z) >*/
rebak_(nm, n, &b[b_offset], &fv2[1], n, &z__[z_offset]);
/*< 50 return >*/
L50:
return 0;
/*< end >*/
} /* rsg_ */
int mri_svd_shrink( MRI_IMAGE *fim , float tau , float *sv )
{
int nn , n1 , mm , ii,jj,kk , kbot,mev ;
MRI_IMAGE *aim ;
double *asym,*sval,*eval, *fv1,*fv2,*fv3,*fv4,*fv5,*fv6,*fv7,*fv8,*vv ;
register double sum ; register float *xk ; float *xx ;
integer imm , imev , *iv1 , ierr ;
double tcut ;
if( fim == NULL || fim->kind != MRI_float || tau <= 0.0f ) return -1 ;
nn = fim->nx ; mm = fim->ny ; if( nn < mm || mm < 2 ) return -1 ;
xx = MRI_FLOAT_PTR(fim) ; if( xx == NULL ) return -1 ;
n1 = nn-1 ; tcut = (double)tau ;
aim = mri_make_xxt( fim ) ; if( aim == NULL ) return -1 ;
asym = MRI_DOUBLE_PTR(aim) ; /* symmetric matrix */
eval = (double *)calloc(sizeof(double),mm) ; /* its eigenvalues */
sval = (double *)malloc(sizeof(double)*mm) ; /* scaling values */
/** reduction to tridiagonal form (stored in fv1..3) **/
fv1 = (double *)malloc(sizeof(double)*(mm+9)) ; /* workspaces */
fv2 = (double *)malloc(sizeof(double)*(mm+9)) ;
fv3 = (double *)malloc(sizeof(double)*(mm+9)) ;
fv4 = (double *)malloc(sizeof(double)*(mm+9)) ;
fv5 = (double *)malloc(sizeof(double)*(mm+9)) ;
fv6 = (double *)malloc(sizeof(double)*(mm+9)) ;
fv7 = (double *)malloc(sizeof(double)*(mm+9)) ;
fv8 = (double *)malloc(sizeof(double)*(mm+9)) ;
iv1 = (integer *)malloc(sizeof(integer)*(mm+9)) ;
imm = (integer)mm ;
tred1_( &imm , &imm , asym , fv1,fv2,fv3 ) ;
/** find all the eigenvalues of the tridiagonal matrix **/
(void)imtqlv_( &imm , fv1,fv2,fv3 , eval , iv1 , &ierr , fv4 ) ;
/** convert to singular values [ascending order],
and then to scaling values for eigenvectors **/
kbot = -1 ; /* index of first nonzero scaling value */
for( ii=0 ; ii < mm ; ii++ ){
sval[ii] = (eval[ii] <= 0.0) ? 0.0 : sqrt(eval[ii]) ;
if( sv != NULL ) sv[ii] = (float)sval[ii] ; /* save singular values */
if( sval[ii] <= tcut ){ /* too small ==> scaling value is zero */
sval[ii] = 0.0 ;
} else { /* scale factor for ii-th eigenvector (< 1) */
sval[ii] = (sval[ii]-tcut) / sval[ii] ;
if( kbot < 0 ) kbot = ii ;
}
}
if( kbot < 0 ){ /*** all singular values are smaller than tau? ***/
free(iv1) ;
free(fv8) ; free(fv7) ; free(fv6) ; free(fv5) ;
free(fv4) ; free(fv3) ; free(fv2) ; free(fv1) ;
free(sval) ; mri_free(aim) ; return -1 ;
}
/** find eigenvectors, starting at the kbot-th one **/
mev = mm - kbot ; /* number of eigenvectors to compute */
vv = (double *)calloc(sizeof(double),mm*mev) ;
if( kbot > 0 ){ /* shift scaling values down to start at index=0 */
for( kk=0 ; kk < mev ; kk++ ) sval[kk] = sval[kk+kbot] ;
}
imev = (integer)mev ;
(void)tinvit_( &imm , &imm , fv1,fv2,fv3 , &imev , eval+kbot , iv1 ,
vv , &ierr , fv4,fv5,fv6,fv7,fv8 ) ;
/** back transform eigenvectors to original space **/
(void)trbak1_( &imm , &imm , asym , fv2 , &imev , vv ) ;
free(iv1) ;
free(fv8) ; free(fv7) ; free(fv6) ; free(fv5) ;
free(fv4) ; free(fv3) ; free(fv2) ; free(fv1) ; free(eval) ;
/** form m x m transformation matrix [V] diag[sval] [V]' into asym **/
for( ii=0 ; ii < mm ; ii++ ){
for( jj=0 ; jj <= ii ; jj++ ){
sum = 0.0 ;
for( kk=0 ; kk < mev ; kk++ )
sum += vv[ii+kk*mm]*vv[jj+kk*mm]*sval[kk] ;
A(ii,jj) = sum ; if( jj < ii ) A(jj,ii) = sum ;
}
}
free(vv) ; free(sval) ;
/** transform input matrix (in place) **/
xk = (float *)malloc(sizeof(float)*mm) ;
for( ii=0 ; ii < nn ; ii++ ){
for( jj=0 ; jj < mm ; jj++ ){
sum = 0.0 ;
for( kk=0 ; kk < mm ; kk++ ) sum += xx[ii+kk*nn]*A(kk,jj) ;
xk[jj] = (float)sum ;
}
for( kk=0 ; kk < mm ; kk++ ) xx[ii+kk*nn] = xk[kk] ;
}
/** vamoose the ranch **/
free(xk) ; mri_free(aim) ;
return mev ;
}
