int32_t invert_matrix_checked(__CLPK_integer dim, double* matrix, MATRIX_INVERT_BUF1_TYPE* int_1d_buf, double* dbl_2d_buf) {
// This used to fall back on PLINK 1.07's SVD-based implementation when the
// rcond estimate was too small, but in practice that just slowed things down
// without meaningfully improving inversion of nonsingular matrices. So now
// this just exits a bit earlier, while leaving the old "binary search for
// the first row/column causing multicollinearity" logic to the caller.
__CLPK_integer lwork = dim * dim;
char cc = '1';
double norm = dlange_(&cc, &dim, &dim, matrix, &dim, dbl_2d_buf);
__CLPK_integer info;
double rcond;
dgetrf_(&dim, &dim, matrix, &dim, int_1d_buf, &info);
if (info > 0) {
return 1;
}
dgecon_(&cc, &dim, matrix, &dim, &norm, &rcond, dbl_2d_buf, &(int_1d_buf[dim]), &info);
if (rcond < MATRIX_SINGULAR_RCOND) {
return 1;
}
dgetri_(&dim, matrix, &dim, int_1d_buf, dbl_2d_buf, &lwork, &info);
return 0;
}
/* Subroutine */ int dlatdf_(integer *ijob, integer *n, doublereal *z__,
integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal,
integer *ipiv, integer *jpiv)
{
/* -- LAPACK auxiliary 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
=======
DLATDF uses the LU factorization of the n-by-n matrix Z computed by
DGETC2 and computes a contribution to the reciprocal Dif-estimate
by solving Z * x = b for x, and choosing the r.h.s. b such that
the norm of x is as large as possible. On entry RHS = b holds the
contribution from earlier solved sub-systems, and on return RHS = x.
The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q,
where P and Q are permutation matrices. L is lower triangular with
unit diagonal elements and U is upper triangular.
Arguments
=========
IJOB (input) INTEGER
IJOB = 2: First compute an approximative null-vector e
of Z using DGECON, e is normalized and solve for
Zx = +-e - f with the sign giving the greater value
of 2-norm(x). About 5 times as expensive as Default.
IJOB .ne. 2: Local look ahead strategy where all entries of
the r.h.s. b is choosen as either +1 or -1 (Default).
N (input) INTEGER
The number of columns of the matrix Z.
Z (input) DOUBLE PRECISION array, dimension (LDZ, N)
On entry, the LU part of the factorization of the n-by-n
matrix Z computed by DGETC2: Z = P * L * U * Q
LDZ (input) INTEGER
The leading dimension of the array Z. LDA >= max(1, N).
RHS (input/output) DOUBLE PRECISION array, dimension N.
On entry, RHS contains contributions from other subsystems.
On exit, RHS contains the solution of the subsystem with
entries acoording to the value of IJOB (see above).
RDSUM (input/output) DOUBLE PRECISION
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by DTGSYL, where the
scaling factor RDSCAL (see below) has been factored out.
On exit, the corresponding sum of squares updated with the
contributions from the current sub-system.
If TRANS = 'T' RDSUM is not touched.
NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL.
RDSCAL (input/output) DOUBLE PRECISION
On entry, scaling factor used to prevent overflow in RDSUM.
On exit, RDSCAL is updated w.r.t. the current contributions
in RDSUM.
If TRANS = 'T', RDSCAL is not touched.
NOTE: RDSCAL only makes sense when DTGSY2 is called by
DTGSYL.
IPIV (input) INTEGER array, dimension (N).
The pivot indices; for 1 <= i <= N, row i of the
matrix has been interchanged with row IPIV(i).
JPIV (input) INTEGER array, dimension (N).
The pivot indices; for 1 <= j <= N, column j of the
matrix has been interchanged with column JPIV(j).
Further Details
===============
Based on contributions by
Bo Kagstrom and Peter Poromaa, Department of Computing Science,
Umea University, S-901 87 Umea, Sweden.
This routine is a further developed implementation of algorithm
BSOLVE in [1] using complete pivoting in the LU factorization.
[1] Bo Kagstrom and Lars Westin,
Generalized Schur Methods with Condition Estimators for
Solving the Generalized Sylvester Equation, IEEE Transactions
on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.
[2] Peter Poromaa,
On Efficient and Robust Estimators for the Separation
between two Regular Matrix Pairs with Applications in
Condition Estimation. Report IMINF-95.05, Departement of
Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.
=====================================================================
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b23 = 1.;
static doublereal c_b37 = -1.;
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
static integer info;
static doublereal temp, work[32];
static integer i__, j, k;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern doublereal dasum_(integer *, doublereal *, integer *);
static doublereal pmone;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
static doublereal sminu;
static integer iwork[8];
static doublereal splus;
extern /* Subroutine */ int dgesc2_(integer *, doublereal *, integer *,
doublereal *, integer *, integer *, doublereal *);
static doublereal bm, bp;
extern /* Subroutine */ int dgecon_(char *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
integer *);
static doublereal xm[8], xp[8];
extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *), dlaswp_(integer *, doublereal *,
integer *, integer *, integer *, integer *, integer *);
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
z_dim1 = *ldz;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
--rhs;
--ipiv;
--jpiv;
/* Function Body */
if (*ijob != 2) {
/* Apply permutations IPIV to RHS */
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
/* Solve for L-part choosing RHS either to +1 or -1. */
pmone = -1.;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
bp = rhs[j] + 1.;
bm = rhs[j] - 1.;
splus = 1.;
/* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and
SMIN computed more efficiently than in BSOLVE [1]. */
i__2 = *n - j;
splus += ddot_(&i__2, &z___ref(j + 1, j), &c__1, &z___ref(j + 1,
j), &c__1);
i__2 = *n - j;
sminu = ddot_(&i__2, &z___ref(j + 1, j), &c__1, &rhs[j + 1], &
c__1);
splus *= rhs[j];
if (splus > sminu) {
rhs[j] = bp;
} else if (sminu > splus) {
rhs[j] = bm;
} else {
/* In this case the updating sums are equal and we can
choose RHS(J) +1 or -1. The first time this happens
we choose -1, thereafter +1. This is a simple way to
get good estimates of matrices like Byers well-known
example (see [1]). (Not done in BSOLVE.) */
rhs[j] += pmone;
pmone = 1.;
}
/* Compute the remaining r.h.s. */
temp = -rhs[j];
i__2 = *n - j;
daxpy_(&i__2, &temp, &z___ref(j + 1, j), &c__1, &rhs[j + 1], &
c__1);
/* L10: */
}
/* Solve for U-part, look-ahead for RHS(N) = +-1. This is not done
in BSOLVE and will hopefully give us a better estimate because
any ill-conditioning of the original matrix is transfered to U
and not to L. U(N, N) is an approximation to sigma_min(LU). */
i__1 = *n - 1;
dcopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
xp[*n - 1] = rhs[*n] + 1.;
rhs[*n] += -1.;
splus = 0.;
sminu = 0.;
for (i__ = *n; i__ >= 1; --i__) {
temp = 1. / z___ref(i__, i__);
xp[i__ - 1] *= temp;
rhs[i__] *= temp;
i__1 = *n;
for (k = i__ + 1; k <= i__1; ++k) {
xp[i__ - 1] -= xp[k - 1] * (z___ref(i__, k) * temp);
rhs[i__] -= rhs[k] * (z___ref(i__, k) * temp);
/* L20: */
}
splus += (d__1 = xp[i__ - 1], abs(d__1));
sminu += (d__1 = rhs[i__], abs(d__1));
/* L30: */
}
if (splus > sminu) {
dcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Apply the permutations JPIV to the computed solution (RHS) */
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
/* Compute the sum of squares */
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
} else {
/* IJOB = 2, Compute approximate nullvector XM of Z */
dgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
info);
dcopy_(n, &work[*n], &c__1, xm, &c__1);
/* Compute RHS */
i__1 = *n - 1;
dlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
temp = 1. / sqrt(ddot_(n, xm, &c__1, xm, &c__1));
dscal_(n, &temp, xm, &c__1);
dcopy_(n, xm, &c__1, xp, &c__1);
daxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
daxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
dgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
dgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
if (dasum_(n, xp, &c__1) > dasum_(n, &rhs[1], &c__1)) {
dcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Compute the sum of squares */
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
}
return 0;
/* End of DLATDF */
} /* dlatdf_ */
/* 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_ */
void u8rdivma ( uint8 * in1, int lines1, int columns1,
uint8 * in2, int lines2, int columns2,
uint8 * out){
char cNorm = 0;
int iExit = 0;
/*temporary variables*/
int iWork = 0;
int iInfo = 0;
int iMax = 0;
uint8 dblRcond = 0;
uint8 dblEps = 0;
uint8 dblAnorm = 0;
uint8 *pAf = NULL;
uint8 *pAt = NULL;
uint8 *pBt = NULL;
uint8 *pDwork = NULL;
int *pRank = NULL;
int *pIpiv = NULL;
int *pJpvt = NULL;
int *pIwork = NULL;
iWork = max(4 * columns2, max(min(lines2, columns2) + 3 * lines2 + 1, 2 * min(lines2, columns2) + lines1));
/* Array allocations*/
pAf = (uint8*)malloc(sizeof(uint8) * (unsigned int)columns2 * (unsigned int)lines2);
pAt = (uint8*)malloc(sizeof(uint8) * (unsigned int)columns2 *(unsigned int) lines2);
pBt = (uint8*)malloc(sizeof(uint8) * (unsigned int)max(lines2,columns2) * (unsigned int)lines1);
pRank = (int*)malloc(sizeof(int));
pIpiv = (int*)malloc(sizeof(int) * (unsigned int)columns2);
pJpvt = (int*)malloc(sizeof(int) * (unsigned int)lines2);
pIwork = (int*)malloc(sizeof(int) * (unsigned int)columns2);
cNorm = '1';
pDwork = (uint8*)malloc(sizeof(uint8) * (unsigned int)iWork);
dblEps = getRelativeMachinePrecision() ;
dblAnorm = dlange_(&cNorm, &lines2, &columns1, in2, &lines2, pDwork);
/*tranpose A and B*/
dtransposea(in2, lines2, columns2, pAt);
dtransposea(in1, lines1, columns2, pBt);
if(lines2 == columns2)
{
cNorm = 'F';
dlacpy_(&cNorm, &columns2, &columns2, pAt, &columns2, pAf, &columns2);
dgetrf_(&columns2, &columns2, pAf, &columns2, pIpiv, &iInfo);
if(iInfo == 0)
{
cNorm = '1';
dgecon_(&cNorm, &columns2, pAf, &columns2, &dblAnorm, &dblRcond, pDwork, pIwork, &iInfo);
if(dblRcond > sqrt(dblEps))
{
cNorm = 'N';
dgetrs_(&cNorm, &columns2, &lines1, pAf, &columns2, pIpiv, pBt, &columns2, &iInfo);
dtransposea(pBt, columns2, lines1, out);
iExit = 1;
}
}
}
if(iExit == 0)
{
dblRcond = sqrt(dblEps);
cNorm = 'F';
iMax = max(lines2, columns2);
memset(pJpvt, 0x00, (unsigned int)sizeof(int) * (unsigned int)lines2);
dgelsy_(&columns2, &lines2, &lines1, pAt, &columns2, pBt, &iMax,
pJpvt, &dblRcond, &pRank[0], pDwork, &iWork, &iInfo);
if(iInfo == 0)
{
/* TransposeRealMatrix(pBt, lines1, lines2, out, Max(lines1,columns1), lines2);*/
/*Mega caca de la mort qui tue des ours a mains nues
mais je ne sais pas comment le rendre "beau" :(*/
{
int i,j,ij,ji;
for(j = 0 ; j < lines2 ; j++)
{
for(i = 0 ; i < lines1 ; i++)
{
ij = i + j * lines1;
ji = j + i * max(lines2, columns2);
out[ij] = pBt[ji];
}
}
}
}
}
free(pAf);
free(pAt);
free(pBt);
free(pRank);
free(pIpiv);
free(pJpvt);
free(pIwork);
free(pDwork);
}
/* 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 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_ */
/*< >*/
/* Subroutine */ int dlatdf_(integer *ijob, integer *n, doublereal *z__,
integer *ldz, doublereal *rhs, doublereal *rdsum, doublereal *rdscal,
integer *ipiv, integer *jpiv)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
doublereal bm, bp, xm[8], xp[8];
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
integer info;
doublereal temp, work[32];
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern doublereal dasum_(integer *, doublereal *, integer *);
doublereal pmone;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), daxpy_(integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *);
doublereal sminu;
integer iwork[8];
doublereal splus;
extern /* Subroutine */ int dgesc2_(integer *, doublereal *, integer *,
doublereal *, integer *, integer *, doublereal *), dgecon_(char *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *, ftnlen), dlassq_(integer *,
doublereal *, integer *, doublereal *, doublereal *), dlaswp_(
integer *, doublereal *, integer *, integer *, integer *, integer
*, integer *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< INTEGER IJOB, LDZ, N >*/
/*< DOUBLE PRECISION RDSCAL, RDSUM >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IPIV( * ), JPIV( * ) >*/
/*< DOUBLE PRECISION RHS( * ), Z( LDZ, * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* DLATDF uses the LU factorization of the n-by-n matrix Z computed by */
/* DGETC2 and computes a contribution to the reciprocal Dif-estimate */
/* by solving Z * x = b for x, and choosing the r.h.s. b such that */
/* the norm of x is as large as possible. On entry RHS = b holds the */
/* contribution from earlier solved sub-systems, and on return RHS = x. */
/* The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q, */
/* where P and Q are permutation matrices. L is lower triangular with */
/* unit diagonal elements and U is upper triangular. */
/* Arguments */
/* ========= */
/* IJOB (input) INTEGER */
/* IJOB = 2: First compute an approximative null-vector e */
/* of Z using DGECON, e is normalized and solve for */
/* Zx = +-e - f with the sign giving the greater value */
/* of 2-norm(x). About 5 times as expensive as Default. */
/* IJOB .ne. 2: Local look ahead strategy where all entries of */
/* the r.h.s. b is choosen as either +1 or -1 (Default). */
/* N (input) INTEGER */
/* The number of columns of the matrix Z. */
/* Z (input) DOUBLE PRECISION array, dimension (LDZ, N) */
/* On entry, the LU part of the factorization of the n-by-n */
/* matrix Z computed by DGETC2: Z = P * L * U * Q */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDA >= max(1, N). */
/* RHS (input/output) DOUBLE PRECISION array, dimension N. */
/* On entry, RHS contains contributions from other subsystems. */
/* On exit, RHS contains the solution of the subsystem with */
/* entries acoording to the value of IJOB (see above). */
/* RDSUM (input/output) DOUBLE PRECISION */
/* On entry, the sum of squares of computed contributions to */
/* the Dif-estimate under computation by DTGSYL, where the */
/* scaling factor RDSCAL (see below) has been factored out. */
/* On exit, the corresponding sum of squares updated with the */
/* contributions from the current sub-system. */
/* If TRANS = 'T' RDSUM is not touched. */
/* NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL. */
/* RDSCAL (input/output) DOUBLE PRECISION */
/* On entry, scaling factor used to prevent overflow in RDSUM. */
/* On exit, RDSCAL is updated w.r.t. the current contributions */
/* in RDSUM. */
/* If TRANS = 'T', RDSCAL is not touched. */
/* NOTE: RDSCAL only makes sense when DTGSY2 is called by */
/* DTGSYL. */
/* IPIV (input) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= i <= N, row i of the */
/* matrix has been interchanged with row IPIV(i). */
/* JPIV (input) INTEGER array, dimension (N). */
/* The pivot indices; for 1 <= j <= N, column j of the */
/* matrix has been interchanged with column JPIV(j). */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* This routine is a further developed implementation of algorithm */
/* BSOLVE in [1] using complete pivoting in the LU factorization. */
/* [1] Bo Kagstrom and Lars Westin, */
/* Generalized Schur Methods with Condition Estimators for */
/* Solving the Generalized Sylvester Equation, IEEE Transactions */
/* on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751. */
/* [2] Peter Poromaa, */
/* On Efficient and Robust Estimators for the Separation */
/* between two Regular Matrix Pairs with Applications in */
/* Condition Estimation. Report IMINF-95.05, Departement of */
/* Computing Science, Umea University, S-901 87 Umea, Sweden, 1995. */
/* ===================================================================== */
/* .. Parameters .. */
/*< INTEGER MAXDIM >*/
/*< PARAMETER ( MAXDIM = 8 ) >*/
/*< DOUBLE PRECISION ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, INFO, J, K >*/
/*< DOUBLE PRECISION BM, BP, PMONE, SMINU, SPLUS, TEMP >*/
/* .. */
/* .. Local Arrays .. */
/*< INTEGER IWORK( MAXDIM ) >*/
/*< DOUBLE PRECISION WORK( 4*MAXDIM ), XM( MAXDIM ), XP( MAXDIM ) >*/
/* .. */
/* .. External Subroutines .. */
/*< >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DASUM, DDOT >*/
/*< EXTERNAL DASUM, DDOT >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, SQRT >*/
/* .. */
/* .. Executable Statements .. */
/*< IF( IJOB.NE.2 ) THEN >*/
/* Parameter adjustments */
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--rhs;
--ipiv;
--jpiv;
/* Function Body */
if (*ijob != 2) {
/* Apply permutations IPIV to RHS */
/*< CALL DLASWP( 1, RHS, LDZ, 1, N-1, IPIV, 1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &ipiv[1], &c__1);
/* Solve for L-part choosing RHS either to +1 or -1. */
/*< PMONE = -ONE >*/
pmone = -1.;
/*< DO 10 J = 1, N - 1 >*/
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
/*< BP = RHS( J ) + ONE >*/
bp = rhs[j] + 1.;
/*< BM = RHS( J ) - ONE >*/
bm = rhs[j] - 1.;
/*< SPLUS = ONE >*/
splus = 1.;
/* Look-ahead for L-part RHS(1:N-1) = + or -1, SPLUS and */
/* SMIN computed more efficiently than in BSOLVE [1]. */
/*< SPLUS = SPLUS + DDOT( N-J, Z( J+1, J ), 1, Z( J+1, J ), 1 ) >*/
i__2 = *n - j;
splus += ddot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1
+ j * z_dim1], &c__1);
/*< SMINU = DDOT( N-J, Z( J+1, J ), 1, RHS( J+1 ), 1 ) >*/
i__2 = *n - j;
sminu = ddot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
&c__1);
/*< SPLUS = SPLUS*RHS( J ) >*/
splus *= rhs[j];
/*< IF( SPLUS.GT.SMINU ) THEN >*/
if (splus > sminu) {
/*< RHS( J ) = BP >*/
rhs[j] = bp;
/*< ELSE IF( SMINU.GT.SPLUS ) THEN >*/
} else if (sminu > splus) {
/*< RHS( J ) = BM >*/
rhs[j] = bm;
/*< ELSE >*/
} else {
/* In this case the updating sums are equal and we can */
/* choose RHS(J) +1 or -1. The first time this happens */
/* we choose -1, thereafter +1. This is a simple way to */
/* get good estimates of matrices like Byers well-known */
/* example (see [1]). (Not done in BSOLVE.) */
/*< RHS( J ) = RHS( J ) + PMONE >*/
rhs[j] += pmone;
/*< PMONE = ONE >*/
pmone = 1.;
/*< END IF >*/
}
/* Compute the remaining r.h.s. */
/*< TEMP = -RHS( J ) >*/
temp = -rhs[j];
/*< CALL DAXPY( N-J, TEMP, Z( J+1, J ), 1, RHS( J+1 ), 1 ) >*/
i__2 = *n - j;
daxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &c__1, &rhs[j + 1],
&c__1);
/*< 10 CONTINUE >*/
/* L10: */
}
/* Solve for U-part, look-ahead for RHS(N) = +-1. This is not done */
/* in BSOLVE and will hopefully give us a better estimate because */
/* any ill-conditioning of the original matrix is transfered to U */
/* and not to L. U(N, N) is an approximation to sigma_min(LU). */
/*< CALL DCOPY( N-1, RHS, 1, XP, 1 ) >*/
i__1 = *n - 1;
dcopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
/*< XP( N ) = RHS( N ) + ONE >*/
xp[*n - 1] = rhs[*n] + 1.;
/*< RHS( N ) = RHS( N ) - ONE >*/
rhs[*n] += -1.;
/*< SPLUS = ZERO >*/
splus = 0.;
/*< SMINU = ZERO >*/
sminu = 0.;
/*< DO 30 I = N, 1, -1 >*/
for (i__ = *n; i__ >= 1; --i__) {
/*< TEMP = ONE / Z( I, I ) >*/
temp = 1. / z__[i__ + i__ * z_dim1];
/*< XP( I ) = XP( I )*TEMP >*/
xp[i__ - 1] *= temp;
/*< RHS( I ) = RHS( I )*TEMP >*/
rhs[i__] *= temp;
/*< DO 20 K = I + 1, N >*/
i__1 = *n;
for (k = i__ + 1; k <= i__1; ++k) {
/*< XP( I ) = XP( I ) - XP( K )*( Z( I, K )*TEMP ) >*/
xp[i__ - 1] -= xp[k - 1] * (z__[i__ + k * z_dim1] * temp);
/*< RHS( I ) = RHS( I ) - RHS( K )*( Z( I, K )*TEMP ) >*/
rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp);
/*< 20 CONTINUE >*/
/* L20: */
}
/*< SPLUS = SPLUS + ABS( XP( I ) ) >*/
splus += (d__1 = xp[i__ - 1], abs(d__1));
/*< SMINU = SMINU + ABS( RHS( I ) ) >*/
sminu += (d__1 = rhs[i__], abs(d__1));
/*< 30 CONTINUE >*/
/* L30: */
}
/*< >*/
if (splus > sminu) {
dcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Apply the permutations JPIV to the computed solution (RHS) */
/*< CALL DLASWP( 1, RHS, LDZ, 1, N-1, JPIV, -1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
/* Compute the sum of squares */
/*< CALL DLASSQ( N, RHS, 1, RDSCAL, RDSUM ) >*/
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
/*< ELSE >*/
} else {
/* IJOB = 2, Compute approximate nullvector XM of Z */
/*< CALL DGECON( 'I', N, Z, LDZ, ONE, TEMP, WORK, IWORK, INFO ) >*/
dgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
info, (ftnlen)1);
/*< CALL DCOPY( N, WORK( N+1 ), 1, XM, 1 ) >*/
dcopy_(n, &work[*n], &c__1, xm, &c__1);
/* Compute RHS */
/*< CALL DLASWP( 1, XM, LDZ, 1, N-1, IPIV, -1 ) >*/
i__1 = *n - 1;
dlaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
/*< TEMP = ONE / SQRT( DDOT( N, XM, 1, XM, 1 ) ) >*/
temp = 1. / sqrt(ddot_(n, xm, &c__1, xm, &c__1));
/*< CALL DSCAL( N, TEMP, XM, 1 ) >*/
dscal_(n, &temp, xm, &c__1);
/*< CALL DCOPY( N, XM, 1, XP, 1 ) >*/
dcopy_(n, xm, &c__1, xp, &c__1);
/*< CALL DAXPY( N, ONE, RHS, 1, XP, 1 ) >*/
daxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
/*< CALL DAXPY( N, -ONE, XM, 1, RHS, 1 ) >*/
daxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
/*< CALL DGESC2( N, Z, LDZ, RHS, IPIV, JPIV, TEMP ) >*/
dgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
/*< CALL DGESC2( N, Z, LDZ, XP, IPIV, JPIV, TEMP ) >*/
dgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
/*< >*/
if (dasum_(n, xp, &c__1) > dasum_(n, &rhs[1], &c__1)) {
dcopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Compute the sum of squares */
/*< CALL DLASSQ( N, RHS, 1, RDSCAL, RDSUM ) >*/
dlassq_(n, &rhs[1], &c__1, rdscal, rdsum);
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of DLATDF */
/*< END >*/
} /* dlatdf_ */
