#include "blaswrap.h"
/* -- translated by f2c (version 19990503).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
#include "f2c.h"
/* Common Block Declarations */
struct {
integer infot, nunit;
logical ok, lerr;
} infoc_;
#define infoc_1 infoc_
struct {
char srnamt[6];
} srnamc_;
#define srnamc_1 srnamc_
/* Table of constant values */
static integer c__2 = 2;
static integer c__0 = 0;
static integer c_n1 = -1;
static integer c__1 = 1;
static doublereal c_b46 = 1.;
static doublereal c_b47 = 0.;
static integer c__7 = 7;
/* Subroutine */ int dchkpt_(logical *dotype, integer *nn, integer *nval,
integer *nns, integer *nsval, doublereal *thresh, logical *tsterr,
doublereal *a, doublereal *d__, doublereal *e, doublereal *b,
doublereal *x, doublereal *xact, doublereal *work, doublereal *rwork,
integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 0,0,0,1 };
/* Format strings */
static char fmt_9999[] = "(\002 N =\002,i5,\002, type \002,i2,\002, te"
"st \002,i2,\002, ratio = \002,g12.5)";
static char fmt_9998[] = "(\002 N =\002,i5,\002, NRHS=\002,i3,\002, ty"
"pe \002,i2,\002, test(\002,i2,\002) = \002,g12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static doublereal cond;
static integer mode;
static doublereal dmax__;
static integer imat, info;
static char path[3], dist[1];
static integer irhs, nrhs;
static char type__[1];
static integer nrun, i__, j, k;
extern /* Subroutine */ int alahd_(integer *, char *);
static integer n;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dget04_(integer *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
static integer nfail, iseed[4];
static doublereal z__[3];
extern doublereal dget06_(doublereal *, doublereal *);
static doublereal rcond;
static integer nimat;
extern doublereal dasum_(integer *, doublereal *, integer *);
static doublereal anorm;
extern /* Subroutine */ int dptt01_(integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *), dcopy_(
integer *, doublereal *, integer *, doublereal *, integer *),
dptt02_(integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *),
dptt05_(integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *);
static integer izero, nerrs;
static logical zerot;
extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, char *);
static integer ia, in, kl;
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *);
static integer ku, ix;
extern integer idamax_(integer *, doublereal *, integer *);
static doublereal rcondc;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaptm_(integer *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *), alasum_(char *, integer *, integer *, integer *,
integer *), dlatms_(integer *, integer *, char *, integer
*, char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublereal *, integer *, doublereal
*, integer *);
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
extern /* Subroutine */ int dlarnv_(integer *, integer *, integer *,
doublereal *), derrgt_(char *, integer *);
static doublereal ainvnm;
extern /* Subroutine */ int dptcon_(integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *), dptrfs_(
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, integer *), dpttrf_(
integer *, doublereal *, doublereal *, integer *);
static doublereal result[7];
extern /* Subroutine */ int dpttrs_(integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *, integer *);
static integer lda;
/* Fortran I/O blocks */
static cilist io___29 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___35 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___37 = { 0, 0, 0, fmt_9999, 0 };
/* -- LAPACK test 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
=======
DCHKPT tests DPTTRF, -TRS, -RFS, and -CON
Arguments
=========
DOTYPE (input) LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
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 dimension N.
NNS (input) INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL (input) INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
THRESH (input) DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR (input) LOGICAL
Flag that indicates whether error exits are to be tested.
A (workspace) DOUBLE PRECISION array, dimension (NMAX*2)
D (workspace) DOUBLE PRECISION array, dimension (NMAX*2)
E (workspace) DOUBLE PRECISION array, dimension (NMAX*2)
B (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
where NSMAX is the largest entry in NSVAL.
X (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NSMAX)
WORK (workspace) DOUBLE PRECISION array, dimension
(NMAX*max(3,NSMAX))
RWORK (workspace) DOUBLE PRECISION array, dimension
(max(NMAX,2*NSMAX))
NOUT (input) INTEGER
The unit number for output.
=====================================================================
Parameter adjustments */
--rwork;
--work;
--xact;
--x;
--b;
--e;
--d__;
--a;
--nsval;
--nval;
--dotype;
/* Function Body */
s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "PT", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Test the error exits */
if (*tsterr) {
derrgt_(path, nout);
}
infoc_1.infot = 0;
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
/* Do for each value of N in NVAL. */
n = nval[in];
lda = max(1,n);
nimat = 12;
if (n <= 0) {
nimat = 1;
}
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (n > 0 && ! dotype[imat]) {
goto L100;
}
/* Set up parameters with DLATB4. */
dlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &
cond, dist);
zerot = imat >= 8 && imat <= 10;
if (imat <= 6) {
/* Type 1-6: generate a symmetric tridiagonal matrix of
known condition number in lower triangular band storage. */
s_copy(srnamc_1.srnamt, "DLATMS", (ftnlen)6, (ftnlen)6);
dlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond,
&anorm, &kl, &ku, "B", &a[1], &c__2, &work[1], &info);
/* Check the error code from DLATMS. */
if (info != 0) {
alaerh_(path, "DLATMS", &info, &c__0, " ", &n, &n, &kl, &
ku, &c_n1, &imat, &nfail, &nerrs, nout);
goto L100;
}
izero = 0;
/* Copy the matrix to D and E. */
ia = 1;
i__3 = n - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
d__[i__] = a[ia];
e[i__] = a[ia + 1];
ia += 2;
/* L20: */
}
if (n > 0) {
d__[n] = a[ia];
}
} else {
/* Type 7-12: generate a diagonally dominant matrix with
unknown condition number in the vectors D and E. */
if (! zerot || ! dotype[7]) {
/* Let D and E have values from [-1,1]. */
dlarnv_(&c__2, iseed, &n, &d__[1]);
i__3 = n - 1;
dlarnv_(&c__2, iseed, &i__3, &e[1]);
/* Make the tridiagonal matrix diagonally dominant. */
if (n == 1) {
d__[1] = abs(d__[1]);
} else {
d__[1] = abs(d__[1]) + abs(e[1]);
d__[n] = (d__1 = d__[n], abs(d__1)) + (d__2 = e[n - 1]
, abs(d__2));
i__3 = n - 1;
for (i__ = 2; i__ <= i__3; ++i__) {
d__[i__] = (d__1 = d__[i__], abs(d__1)) + (d__2 =
e[i__], abs(d__2)) + (d__3 = e[i__ - 1],
abs(d__3));
/* L30: */
}
}
/* Scale D and E so the maximum element is ANORM. */
ix = idamax_(&n, &d__[1], &c__1);
dmax__ = d__[ix];
d__1 = anorm / dmax__;
dscal_(&n, &d__1, &d__[1], &c__1);
i__3 = n - 1;
d__1 = anorm / dmax__;
dscal_(&i__3, &d__1, &e[1], &c__1);
} else if (izero > 0) {
/* Reuse the last matrix by copying back the zeroed out
elements. */
if (izero == 1) {
d__[1] = z__[1];
if (n > 1) {
e[1] = z__[2];
}
} else if (izero == n) {
e[n - 1] = z__[0];
d__[n] = z__[1];
} else {
e[izero - 1] = z__[0];
d__[izero] = z__[1];
e[izero] = z__[2];
}
}
/* For types 8-10, set one row and column of the matrix to
zero. */
izero = 0;
if (imat == 8) {
izero = 1;
z__[1] = d__[1];
d__[1] = 0.;
if (n > 1) {
z__[2] = e[1];
e[1] = 0.;
}
} else if (imat == 9) {
izero = n;
if (n > 1) {
z__[0] = e[n - 1];
e[n - 1] = 0.;
}
z__[1] = d__[n];
d__[n] = 0.;
} else if (imat == 10) {
izero = (n + 1) / 2;
if (izero > 1) {
z__[0] = e[izero - 1];
e[izero - 1] = 0.;
z__[2] = e[izero];
e[izero] = 0.;
}
z__[1] = d__[izero];
d__[izero] = 0.;
}
}
dcopy_(&n, &d__[1], &c__1, &d__[n + 1], &c__1);
if (n > 1) {
i__3 = n - 1;
dcopy_(&i__3, &e[1], &c__1, &e[n + 1], &c__1);
}
/* + TEST 1
Factor A as L*D*L' and compute the ratio
norm(L*D*L' - A) / (n * norm(A) * EPS ) */
dpttrf_(&n, &d__[n + 1], &e[n + 1], &info);
/* Check error code from DPTTRF. */
if (info != izero) {
alaerh_(path, "DPTTRF", &info, &izero, " ", &n, &n, &c_n1, &
c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L100;
}
if (info > 0) {
rcondc = 0.;
goto L90;
}
dptt01_(&n, &d__[1], &e[1], &d__[n + 1], &e[n + 1], &work[1],
result);
/* Print the test ratio if greater than or equal to THRESH. */
if (result[0] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* Compute RCONDC = 1 / (norm(A) * norm(inv(A))
Compute norm(A). */
anorm = dlanst_("1", &n, &d__[1], &e[1]);
/* Use DPTTRS to solve for one column at a time of inv(A),
computing the maximum column sum as we go. */
ainvnm = 0.;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = n;
for (j = 1; j <= i__4; ++j) {
x[j] = 0.;
/* L40: */
}
x[i__] = 1.;
dpttrs_(&n, &c__1, &d__[n + 1], &e[n + 1], &x[1], &lda, &info)
;
/* Computing MAX */
d__1 = ainvnm, d__2 = dasum_(&n, &x[1], &c__1);
ainvnm = max(d__1,d__2);
/* L50: */
}
/* Computing MAX */
d__1 = 1., d__2 = anorm * ainvnm;
rcondc = 1. / max(d__1,d__2);
i__3 = *nns;
for (irhs = 1; irhs <= i__3; ++irhs) {
nrhs = nsval[irhs];
/* Generate NRHS random solution vectors. */
ix = 1;
i__4 = nrhs;
for (j = 1; j <= i__4; ++j) {
dlarnv_(&c__2, iseed, &n, &xact[ix]);
ix += lda;
/* L60: */
}
/* Set the right hand side. */
dlaptm_(&n, &nrhs, &c_b46, &d__[1], &e[1], &xact[1], &lda, &
c_b47, &b[1], &lda);
/* + TEST 2
Solve A*x = b and compute the residual. */
dlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
dpttrs_(&n, &nrhs, &d__[n + 1], &e[n + 1], &x[1], &lda, &info)
;
/* Check error code from DPTTRS. */
if (info != 0) {
alaerh_(path, "DPTTRS", &info, &c__0, " ", &n, &n, &c_n1,
&c_n1, &nrhs, &imat, &nfail, &nerrs, nout);
}
dlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda);
dptt02_(&n, &nrhs, &d__[1], &e[1], &x[1], &lda, &work[1], &
lda, &result[1]);
/* + TEST 3
Check solution from generated exact solution. */
dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
result[2]);
/* + TESTS 4, 5, and 6
Use iterative refinement to improve the solution. */
s_copy(srnamc_1.srnamt, "DPTRFS", (ftnlen)6, (ftnlen)6);
dptrfs_(&n, &nrhs, &d__[1], &e[1], &d__[n + 1], &e[n + 1], &b[
1], &lda, &x[1], &lda, &rwork[1], &rwork[nrhs + 1], &
work[1], &info);
/* Check error code from DPTRFS. */
if (info != 0) {
alaerh_(path, "DPTRFS", &info, &c__0, " ", &n, &n, &c_n1,
&c_n1, &nrhs, &imat, &nfail, &nerrs, nout);
}
dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
result[3]);
dptt05_(&n, &nrhs, &d__[1], &e[1], &b[1], &lda, &x[1], &lda, &
xact[1], &lda, &rwork[1], &rwork[nrhs + 1], &result[4]
);
/* Print information about the tests that did not pass the
threshold. */
for (k = 2; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___35.ciunit = *nout;
s_wsfe(&io___35);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
/* L70: */
}
nrun += 5;
/* L80: */
}
/* + TEST 7
Estimate the reciprocal of the condition number of the
matrix. */
L90:
s_copy(srnamc_1.srnamt, "DPTCON", (ftnlen)6, (ftnlen)6);
dptcon_(&n, &d__[n + 1], &e[n + 1], &anorm, &rcond, &rwork[1], &
info);
/* Check error code from DPTCON. */
if (info != 0) {
alaerh_(path, "DPTCON", &info, &c__0, " ", &n, &n, &c_n1, &
c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
}
result[6] = dget06_(&rcond, &rcondc);
/* Print the test ratio if greater than or equal to THRESH. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___37.ciunit = *nout;
s_wsfe(&io___37);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__7, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof(doublereal));
e_wsfe();
++nfail;
}
++nrun;
L100:
;
}
/* L110: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of DCHKPT */
} /* dchkpt_ */