/* Subroutine */ int dchkge_(logical *dotype, integer *nm, integer *mval,
integer *nn, integer *nval, integer *nnb, integer *nbval, integer *
nns, integer *nsval, doublereal *thresh, logical *tsterr, integer *
nmax, doublereal *a, doublereal *afac, doublereal *ainv, doublereal *
b, doublereal *x, doublereal *xact, doublereal *work, doublereal *
rwork, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(\002 M = \002,i5,\002, N =\002,i5,\002, NB "
"=\002,i4,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)"
;
static char fmt_9998[] = "(\002 TRANS='\002,a1,\002', N =\002,i5,\002, N"
"RHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g1"
"2.5)";
static char fmt_9997[] = "(\002 NORM ='\002,a1,\002', N =\002,i5,\002"
",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)"
;
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, k, m, n, nb, im, in, kl, ku, nt, lda, inb, ioff, mode, imat,
info;
char path[3], dist[1];
integer irhs, nrhs;
char norm[1], type__[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *), dget01_(
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *), dget02_(char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *), dget03_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *), dget04_(integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *);
integer nfail, iseed[4];
extern doublereal dget06_(doublereal *, doublereal *);
extern /* Subroutine */ int dget07_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, logical *,
doublereal *, doublereal *);
doublereal rcond;
integer nimat;
doublereal anorm;
integer itran;
char trans[1];
integer izero, nerrs;
doublereal dummy;
integer lwork;
logical zerot;
char xtype[1];
extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, char *);
extern doublereal dlange_(char *, integer *, integer *, doublereal *,
integer *, doublereal *);
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *), dgecon_(char *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, integer *, integer *);
doublereal rcondc;
extern /* Subroutine */ int derrge_(char *, integer *), dgerfs_(
char *, integer *, integer *, doublereal *, integer *, doublereal
*, integer *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
integer *), dgetrf_(integer *, integer *, doublereal *,
integer *, integer *, integer *), dlacpy_(char *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *), dlarhs_(char *, char *, char *, char *, integer *,
integer *, integer *, integer *, integer *, doublereal *, integer
*, doublereal *, integer *, doublereal *, integer *, integer *,
integer *);
doublereal rcondi;
extern /* Subroutine */ int dgetri_(integer *, doublereal *, integer *,
integer *, doublereal *, integer *, integer *), dlaset_(char *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
integer *), alasum_(char *, integer *, integer *, integer
*, integer *);
doublereal cndnum, anormi, rcondo;
extern /* Subroutine */ int dlatms_(integer *, integer *, char *, integer
*, char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublereal *, integer *, doublereal
*, integer *);
doublereal ainvnm;
extern /* Subroutine */ int dgetrs_(char *, integer *, integer *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *);
logical trfcon;
doublereal anormo;
extern /* Subroutine */ int xlaenv_(integer *, integer *);
doublereal result[8];
/* Fortran I/O blocks */
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9997, 0 };
/* -- LAPACK test routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* January 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DCHKGE tests DGETRF, -TRI, -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. */
/* 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 row dimension 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 contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NBVAL) */
/* The values of the blocksize NB. */
/* 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. */
/* NMAX (input) INTEGER */
/* The maximum value permitted for M or N, used in dimensioning */
/* the work arrays. */
/* A (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */
/* AFAC (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */
/* AINV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */
/* 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(2*NMAX,2*NSMAX+NWORK)) */
/* IWORK (workspace) INTEGER array, dimension (2*NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--afac;
--a;
--nsval;
--nbval;
--nval;
--mval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "GE", (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 */
xlaenv_(&c__1, &c__1);
if (*tsterr) {
derrge_(path, nout);
}
infoc_1.infot = 0;
xlaenv_(&c__2, &c__2);
/* Do for each value of M in MVAL */
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
lda = max(1,m);
/* Do for each value of N in NVAL */
i__2 = *nn;
for (in = 1; in <= i__2; ++in) {
n = nval[in];
*(unsigned char *)xtype = 'N';
nimat = 11;
if (m <= 0 || n <= 0) {
nimat = 1;
}
i__3 = nimat;
for (imat = 1; imat <= i__3; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L100;
}
/* Skip types 5, 6, or 7 if the matrix size is too small. */
zerot = imat >= 5 && imat <= 7;
if (zerot && n < imat - 4) {
goto L100;
}
/* Set up parameters with DLATB4 and generate a test matrix */
/* with DLATMS. */
dlatb4_(path, &imat, &m, &n, type__, &kl, &ku, &anorm, &mode,
&cndnum, dist);
s_copy(srnamc_1.srnamt, "DLATMS", (ftnlen)32, (ftnlen)6);
dlatms_(&m, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, "No packing", &a[1], &lda, &
work[1], &info);
/* Check error code from DLATMS. */
if (info != 0) {
alaerh_(path, "DLATMS", &info, &c__0, " ", &m, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L100;
}
/* For types 5-7, zero one or more columns of the matrix to */
/* test that INFO is returned correctly. */
if (zerot) {
if (imat == 5) {
izero = 1;
} else if (imat == 6) {
izero = min(m,n);
} else {
izero = min(m,n) / 2 + 1;
}
ioff = (izero - 1) * lda;
if (imat < 7) {
i__4 = m;
for (i__ = 1; i__ <= i__4; ++i__) {
a[ioff + i__] = 0.;
/* L20: */
}
} else {
i__4 = n - izero + 1;
dlaset_("Full", &m, &i__4, &c_b23, &c_b23, &a[ioff +
1], &lda);
}
} else {
izero = 0;
}
/* These lines, if used in place of the calls in the DO 60 */
/* loop, cause the code to bomb on a Sun SPARCstation. */
/* ANORMO = DLANGE( 'O', M, N, A, LDA, RWORK ) */
/* ANORMI = DLANGE( 'I', M, N, A, LDA, RWORK ) */
/* Do for each blocksize in NBVAL */
i__4 = *nnb;
for (inb = 1; inb <= i__4; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Compute the LU factorization of the matrix. */
dlacpy_("Full", &m, &n, &a[1], &lda, &afac[1], &lda);
s_copy(srnamc_1.srnamt, "DGETRF", (ftnlen)32, (ftnlen)6);
dgetrf_(&m, &n, &afac[1], &lda, &iwork[1], &info);
/* Check error code from DGETRF. */
if (info != izero) {
alaerh_(path, "DGETRF", &info, &izero, " ", &m, &n, &
c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
}
trfcon = FALSE_;
/* + TEST 1 */
/* Reconstruct matrix from factors and compute residual. */
dlacpy_("Full", &m, &n, &afac[1], &lda, &ainv[1], &lda);
dget01_(&m, &n, &a[1], &lda, &ainv[1], &lda, &iwork[1], &
rwork[1], result);
nt = 1;
/* + TEST 2 */
/* Form the inverse if the factorization was successful */
/* and compute the residual. */
if (m == n && info == 0) {
dlacpy_("Full", &n, &n, &afac[1], &lda, &ainv[1], &
lda);
s_copy(srnamc_1.srnamt, "DGETRI", (ftnlen)32, (ftnlen)
6);
nrhs = nsval[1];
lwork = *nmax * max(3,nrhs);
dgetri_(&n, &ainv[1], &lda, &iwork[1], &work[1], &
lwork, &info);
/* Check error code from DGETRI. */
if (info != 0) {
alaerh_(path, "DGETRI", &info, &c__0, " ", &n, &n,
&c_n1, &c_n1, &nb, &imat, &nfail, &nerrs,
nout);
}
/* Compute the residual for the matrix times its */
/* inverse. Also compute the 1-norm condition number */
/* of A. */
dget03_(&n, &a[1], &lda, &ainv[1], &lda, &work[1], &
lda, &rwork[1], &rcondo, &result[1]);
anormo = dlange_("O", &m, &n, &a[1], &lda, &rwork[1]);
/* Compute the infinity-norm condition number of A. */
anormi = dlange_("I", &m, &n, &a[1], &lda, &rwork[1]);
ainvnm = dlange_("I", &n, &n, &ainv[1], &lda, &rwork[
1]);
if (anormi <= 0. || ainvnm <= 0.) {
rcondi = 1.;
} else {
rcondi = 1. / anormi / ainvnm;
}
nt = 2;
} else {
/* Do only the condition estimate if INFO > 0. */
trfcon = TRUE_;
anormo = dlange_("O", &m, &n, &a[1], &lda, &rwork[1]);
anormi = dlange_("I", &m, &n, &a[1], &lda, &rwork[1]);
rcondo = 0.;
rcondi = 0.;
}
/* Print information about the tests so far that did not */
/* pass the threshold. */
i__5 = nt;
for (k = 1; k <= i__5; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___41.ciunit = *nout;
s_wsfe(&io___41);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&nb, (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;
}
/* L30: */
}
nrun += nt;
/* Skip the remaining tests if this is not the first */
/* block size or if M .ne. N. Skip the solve tests if */
/* the matrix is singular. */
if (inb > 1 || m != n) {
goto L90;
}
if (trfcon) {
goto L70;
}
i__5 = *nns;
for (irhs = 1; irhs <= i__5; ++irhs) {
nrhs = nsval[irhs];
*(unsigned char *)xtype = 'N';
for (itran = 1; itran <= 3; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
if (itran == 1) {
rcondc = rcondo;
} else {
rcondc = rcondi;
}
/* + TEST 3 */
/* Solve and compute residual for A * X = B. */
s_copy(srnamc_1.srnamt, "DLARHS", (ftnlen)32, (
ftnlen)6);
dlarhs_(path, xtype, " ", trans, &n, &n, &kl, &ku,
&nrhs, &a[1], &lda, &xact[1], &lda, &b[1]
, &lda, iseed, &info);
*(unsigned char *)xtype = 'C';
dlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &
lda);
s_copy(srnamc_1.srnamt, "DGETRS", (ftnlen)32, (
ftnlen)6);
dgetrs_(trans, &n, &nrhs, &afac[1], &lda, &iwork[
1], &x[1], &lda, &info);
/* Check error code from DGETRS. */
if (info != 0) {
alaerh_(path, "DGETRS", &info, &c__0, trans, &
n, &n, &c_n1, &c_n1, &nrhs, &imat, &
nfail, &nerrs, nout);
}
dlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1],
&lda);
dget02_(trans, &n, &n, &nrhs, &a[1], &lda, &x[1],
&lda, &work[1], &lda, &rwork[1], &result[
2]);
/* + TEST 4 */
/* Check solution from generated exact solution. */
dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[3]);
/* + TESTS 5, 6, and 7 */
/* Use iterative refinement to improve the */
/* solution. */
s_copy(srnamc_1.srnamt, "DGERFS", (ftnlen)32, (
ftnlen)6);
dgerfs_(trans, &n, &nrhs, &a[1], &lda, &afac[1], &
lda, &iwork[1], &b[1], &lda, &x[1], &lda,
&rwork[1], &rwork[nrhs + 1], &work[1], &
iwork[n + 1], &info);
/* Check error code from DGERFS. */
if (info != 0) {
alaerh_(path, "DGERFS", &info, &c__0, trans, &
n, &n, &c_n1, &c_n1, &nrhs, &imat, &
nfail, &nerrs, nout);
}
dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[4]);
dget07_(trans, &n, &nrhs, &a[1], &lda, &b[1], &
lda, &x[1], &lda, &xact[1], &lda, &rwork[
1], &c_true, &rwork[nrhs + 1], &result[5]);
/* Print information about the tests that did not */
/* pass the threshold. */
for (k = 3; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___46.ciunit = *nout;
s_wsfe(&io___46);
do_fio(&c__1, trans, (ftnlen)1);
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;
}
/* L40: */
}
nrun += 5;
/* L50: */
}
/* L60: */
}
/* + TEST 8 */
/* Get an estimate of RCOND = 1/CNDNUM. */
L70:
for (itran = 1; itran <= 2; ++itran) {
if (itran == 1) {
anorm = anormo;
rcondc = rcondo;
*(unsigned char *)norm = 'O';
} else {
anorm = anormi;
rcondc = rcondi;
*(unsigned char *)norm = 'I';
}
s_copy(srnamc_1.srnamt, "DGECON", (ftnlen)32, (ftnlen)
6);
dgecon_(norm, &n, &afac[1], &lda, &anorm, &rcond, &
work[1], &iwork[n + 1], &info);
/* Check error code from DGECON. */
if (info != 0) {
alaerh_(path, "DGECON", &info, &c__0, norm, &n, &
n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &
nerrs, nout);
}
/* This line is needed on a Sun SPARCstation. */
dummy = rcond;
result[7] = dget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass */
/* the threshold. */
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, norm, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* L80: */
}
L90:
;
}
L100:
;
}
/* L110: */
}
/* L120: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of DCHKGE */
} /* dchkge_ */
/* Subroutine */ int derrge_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublereal a[16] /* was [4][4] */, b[4];
integer i__, j;
doublereal w[12], x[4];
char c2[2];
doublereal r1[4], r2[4], af[16] /* was [4][4] */;
integer ip[4], iw[4], info;
doublereal anrm, ccond, rcond;
extern /* Subroutine */ int dgbtf2_(integer *, integer *, integer *,
integer *, doublereal *, integer *, integer *, integer *),
dgetf2_(integer *, integer *, doublereal *, integer *, integer *,
integer *), dgbcon_(char *, integer *, integer *, integer *,
doublereal *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *), dgecon_(char *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *), alaesm_(char *,
logical *, integer *), dgbequ_(integer *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *)
, dgbrfs_(char *, integer *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, integer *),
dgbtrf_(integer *, integer *, integer *, integer *, doublereal *,
integer *, integer *, integer *), dgeequ_(integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *), dgerfs_(char *, integer *
, integer *, doublereal *, integer *, doublereal *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, integer *, integer *), dgetrf_(integer *, integer *, doublereal *, integer *,
integer *, integer *), dgetri_(integer *, doublereal *, integer *,
integer *, doublereal *, integer *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), dgbtrs_(char *, integer *, integer *,
integer *, integer *, doublereal *, integer *, integer *,
doublereal *, integer *, integer *), dgetrs_(char *,
integer *, integer *, doublereal *, integer *, integer *,
doublereal *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DERRGE tests the error exits for the DOUBLE PRECISION routines */
/* for general matrices. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a[i__ + (j << 2) - 5] = 1. / (doublereal) (i__ + j);
af[i__ + (j << 2) - 5] = 1. / (doublereal) (i__ + j);
/* L10: */
}
b[j - 1] = 0.;
r1[j - 1] = 0.;
r2[j - 1] = 0.;
w[j - 1] = 0.;
x[j - 1] = 0.;
ip[j - 1] = j;
iw[j - 1] = j;
/* L20: */
}
infoc_1.ok = TRUE_;
if (lsamen_(&c__2, c2, "GE")) {
/* Test error exits of the routines that use the LU decomposition */
/* of a general matrix. */
/* DGETRF */
s_copy(srnamc_1.srnamt, "DGETRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgetrf_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgetrf_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgetrf_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGETF2 */
s_copy(srnamc_1.srnamt, "DGETF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgetf2_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgetf2_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgetf2_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGETRI */
s_copy(srnamc_1.srnamt, "DGETRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgetri_(&c_n1, a, &c__1, ip, w, &c__12, &info);
chkxer_("DGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgetri_(&c__2, a, &c__1, ip, w, &c__12, &info);
chkxer_("DGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGETRS */
s_copy(srnamc_1.srnamt, "DGETRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGERFS */
s_copy(srnamc_1.srnamt, "DGERFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGECON */
s_copy(srnamc_1.srnamt, "DGECON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGEEQU */
s_copy(srnamc_1.srnamt, "DGEEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "GB")) {
/* Test error exits of the routines that use the LU decomposition */
/* of a general band matrix. */
/* DGBTRF */
s_copy(srnamc_1.srnamt, "DGBTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGBTF2 */
s_copy(srnamc_1.srnamt, "DGBTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGBTRS */
s_copy(srnamc_1.srnamt, "DGBTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, &
info);
chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGBRFS */
s_copy(srnamc_1.srnamt, "DGBRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgbrfs_("N", &c_n1, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgbrfs_("N", &c__1, &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgbrfs_("N", &c__1, &c__0, &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgbrfs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__2, af, &c__4, ip, b, &
c__2, x, &c__2, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
dgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip, b, &
c__2, x, &c__2, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__2, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
dgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__2, x, &c__1, r1, r2, w, iw, &info);
chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGBCON */
s_copy(srnamc_1.srnamt, "DGBCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGBEQU */
s_copy(srnamc_1.srnamt, "DGBEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of DERRGE */
} /* derrge_ */
/* Subroutine */ int dgesvx_(char *fact, char *trans, integer *n, integer *
nrhs, doublereal *a, integer *lda, doublereal *af, integer *ldaf,
integer *ipiv, char *equed, doublereal *r__, doublereal *c__,
doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *
rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *
iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2;
doublereal d__1, d__2;
/* Local variables */
integer i__, j;
doublereal amax;
char norm[1];
extern logical lsame_(char *, char *);
doublereal rcmin, rcmax, anorm;
logical equil;
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dlaqge_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, char *), dgecon_(char *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *);
doublereal colcnd;
logical nofact;
extern /* Subroutine */ int dgeequ_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *), dgerfs_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, integer *),
dgetrf_(integer *, integer *, doublereal *, integer *, integer *,
integer *), dlacpy_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *), xerbla_(char *,
integer *);
doublereal bignum;
extern doublereal dlantr_(char *, char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *);
integer infequ;
logical colequ;
extern /* Subroutine */ int dgetrs_(char *, integer *, integer *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *);
doublereal rowcnd;
logical notran;
doublereal smlnum;
logical rowequ;
doublereal rpvgrw;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGESVX uses the LU factorization to compute the solution to a real */
/* system of linear equations */
/* A * X = B, */
/* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
/* Error bounds on the solution and a condition estimate are also */
/* provided. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'E', real scaling factors are computed to equilibrate */
/* the system: */
/* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */
/* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
/* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */
/* Whether or not the system will be equilibrated depends on the */
/* scaling of the matrix A, but if equilibration is used, A is */
/* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
/* or diag(C)*B (if TRANS = 'T' or 'C'). */
/* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */
/* matrix A (after equilibration if FACT = 'E') as */
/* A = P * L * U, */
/* where P is a permutation matrix, L is a unit lower triangular */
/* matrix, and U is upper triangular. */
/* 3. If some U(i,i)=0, so that U is exactly singular, then the routine */
/* returns with INFO = i. Otherwise, the factored form of A is used */
/* to estimate the condition number of the matrix A. If the */
/* reciprocal of the condition number is less than machine precision, */
/* INFO = N+1 is returned as a warning, but the routine still goes on */
/* to solve for X and compute error bounds as described below. */
/* 4. The system of equations is solved for X using the factored form */
/* of A. */
/* 5. Iterative refinement is applied to improve the computed solution */
/* matrix and calculate error bounds and backward error estimates */
/* for it. */
/* 6. If equilibration was used, the matrix X is premultiplied by */
/* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
/* that it solves the original system before equilibration. */
/* Arguments */
/* ========= */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of the matrix A is */
/* supplied on entry, and if not, whether the matrix A should be */
/* equilibrated before it is factored. */
/* = 'F': On entry, AF and IPIV contain the factored form of A. */
/* If EQUED is not 'N', the matrix A has been */
/* equilibrated with scaling factors given by R and C. */
/* A, AF, and IPIV are not modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AF and factored. */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Transpose) */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */
/* not 'N', then A must have been equilibrated by the scaling */
/* factors in R and/or C. A is not modified if FACT = 'F' or */
/* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
/* On exit, if EQUED .ne. 'N', A is scaled as follows: */
/* EQUED = 'R': A := diag(R) * A */
/* EQUED = 'C': A := A * diag(C) */
/* EQUED = 'B': A := diag(R) * A * diag(C). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input or output) DOUBLE PRECISION array, dimension (LDAF,N) */
/* If FACT = 'F', then AF is an input argument and on entry */
/* contains the factors L and U from the factorization */
/* A = P*L*U as computed by DGETRF. If EQUED .ne. 'N', then */
/* AF is the factored form of the equilibrated matrix A. */
/* If FACT = 'N', then AF is an output argument and on exit */
/* returns the factors L and U from the factorization A = P*L*U */
/* of the original matrix A. */
/* If FACT = 'E', then AF is an output argument and on exit */
/* returns the factors L and U from the factorization A = P*L*U */
/* of the equilibrated matrix A (see the description of A for */
/* the form of the equilibrated matrix). */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input or output) INTEGER array, dimension (N) */
/* If FACT = 'F', then IPIV is an input argument and on entry */
/* contains the pivot indices from the factorization A = P*L*U */
/* as computed by DGETRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the original matrix A. */
/* If FACT = 'E', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the equilibrated matrix A. */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'R': Row equilibration, i.e., A has been premultiplied by */
/* diag(R). */
/* = 'C': Column equilibration, i.e., A has been postmultiplied */
/* by diag(C). */
/* = 'B': Both row and column equilibration, i.e., A has been */
/* replaced by diag(R) * A * diag(C). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* R (input or output) DOUBLE PRECISION array, dimension (N) */
/* The row scale factors for A. If EQUED = 'R' or 'B', A is */
/* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
/* is not accessed. R is an input argument if FACT = 'F'; */
/* otherwise, R is an output argument. If FACT = 'F' and */
/* EQUED = 'R' or 'B', each element of R must be positive. */
/* C (input or output) DOUBLE PRECISION array, dimension (N) */
/* The column scale factors for A. If EQUED = 'C' or 'B', A is */
/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
/* is not accessed. C is an input argument if FACT = 'F'; */
/* otherwise, C is an output argument. If FACT = 'F' and */
/* EQUED = 'C' or 'B', each element of C must be positive. */
/* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, */
/* if EQUED = 'N', B is not modified; */
/* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
/* diag(R)*B; */
/* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
/* overwritten by diag(C)*B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */
/* to the original system of equations. Note that A and B are */
/* modified on exit if EQUED .ne. 'N', and the solution to the */
/* equilibrated system is inv(diag(C))*X if TRANS = 'N' and */
/* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */
/* and EQUED = 'R' or 'B'. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* The estimate of the reciprocal condition number of the matrix */
/* A after equilibration (if done). If RCOND is less than the */
/* machine precision (in particular, if RCOND = 0), the matrix */
/* is singular to working precision. This condition is */
/* indicated by a return code of INFO > 0. */
/* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (4*N) */
/* On exit, WORK(1) contains the reciprocal pivot growth */
/* factor norm(A)/norm(U). The "max absolute element" norm is */
/* used. If WORK(1) is much less than 1, then the stability */
/* of the LU factorization of the (equilibrated) matrix A */
/* could be poor. This also means that the solution X, condition */
/* estimator RCOND, and forward error bound FERR could be */
/* unreliable. If factorization fails with 0<INFO<=N, then */
/* WORK(1) contains the reciprocal pivot growth factor for the */
/* leading INFO columns of A. */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, and i is */
/* <= N: U(i,i) is exactly zero. The factorization has */
/* been completed, but the factor U is exactly */
/* singular, so the solution and error bounds */
/* could not be computed. RCOND = 0 is returned. */
/* = N+1: U is nonsingular, but RCOND is less than machine */
/* precision, meaning that the matrix is singular */
/* to working precision. Nevertheless, the */
/* solution and error bounds are computed because */
/* there are a number of situations where the */
/* computed solution can be more accurate than the */
/* value of RCOND would suggest. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rowequ = FALSE_;
colequ = FALSE_;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed,
"B");
colequ = lsame_(equed, "C") || lsame_(equed,
"B");
smlnum = dlamch_("Safe minimum");
bignum = 1. / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldaf < max(1,*n)) {
*info = -8;
} else if (lsame_(fact, "F") && ! (rowequ || colequ
|| lsame_(equed, "N"))) {
*info = -10;
} else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = rcmin, d__2 = r__[j];
rcmin = min(d__1,d__2);
/* Computing MAX */
d__1 = rcmax, d__2 = r__[j];
rcmax = max(d__1,d__2);
/* L10: */
}
if (rcmin <= 0.) {
*info = -11;
} else if (*n > 0) {
rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
} else {
rowcnd = 1.;
}
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = rcmin, d__2 = c__[j];
rcmin = min(d__1,d__2);
/* Computing MAX */
d__1 = rcmax, d__2 = c__[j];
rcmax = max(d__1,d__2);
/* L20: */
}
if (rcmin <= 0.) {
*info = -12;
} else if (*n > 0) {
colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
} else {
colcnd = 1.;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -14;
} else if (*ldx < max(1,*n)) {
*info = -16;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGESVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
dgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, &
amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
dlaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &
colcnd, &amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed,
"B");
colequ = lsame_(equed, "C") || lsame_(equed,
"B");
}
}
/* Scale the right hand side. */
if (notran) {
if (rowequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = r__[i__] * b[i__ + j * b_dim1];
/* L30: */
}
/* L40: */
}
}
} else if (colequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = c__[i__] * b[i__ + j * b_dim1];
/* L50: */
}
/* L60: */
}
}
if (nofact || equil) {
/* Compute the LU factorization of A. */
dlacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
dgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
rpvgrw = dlantr_("M", "U", "N", info, info, &af[af_offset], ldaf,
&work[1]);
if (rpvgrw == 0.) {
rpvgrw = 1.;
} else {
rpvgrw = dlange_("M", n, info, &a[a_offset], lda, &work[1]) / rpvgrw;
}
work[1] = rpvgrw;
*rcond = 0.;
return 0;
}
}
/* Compute the norm of the matrix A and the */
/* reciprocal pivot growth factor RPVGRW. */
if (notran) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = dlange_(norm, n, n, &a[a_offset], lda, &work[1]);
rpvgrw = dlantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &work[1]);
if (rpvgrw == 0.) {
rpvgrw = 1.;
} else {
rpvgrw = dlange_("M", n, n, &a[a_offset], lda, &work[1]) /
rpvgrw;
}
/* Compute the reciprocal of the condition number of A. */
dgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
info);
/* Compute the solution matrix X. */
dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
dgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx,
info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
dgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1],
&b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[
1], &iwork[1], info);
/* Transform the solution matrix X to a solution of the original */
/* system. */
if (notran) {
if (colequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ + j * x_dim1] = c__[i__] * x[i__ + j * x_dim1];
/* L70: */
}
/* L80: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= colcnd;
/* L90: */
}
}
} else if (rowequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ + j * x_dim1] = r__[i__] * x[i__ + j * x_dim1];
/* L100: */
}
/* L110: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= rowcnd;
/* L120: */
}
}
work[1] = rpvgrw;
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon")) {
*info = *n + 1;
}
return 0;
/* End of DGESVX */
} /* dgesvx_ */
