/* Subroutine */ int dtrt01_(char *uplo, char *diag, integer *n, doublereal *
a, integer *lda, doublereal *ainv, integer *ldainv, doublereal *rcond,
doublereal *work, doublereal *resid)
{
/* System generated locals */
integer a_dim1, a_offset, ainv_dim1, ainv_offset, i__1, i__2;
/* Local variables */
integer j;
doublereal eps;
doublereal anorm;
doublereal ainvnm;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTRT01 computes the residual for a triangular matrix A times its */
/* inverse: */
/* RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ), */
/* where EPS is the machine epsilon. */
/* Arguments */
/* ========== */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* The triangular matrix A. If UPLO = 'U', the leading n by n */
/* upper triangular part of the array A contains the upper */
/* triangular matrix, and the strictly lower triangular part of */
/* A is not referenced. If UPLO = 'L', the leading n by n lower */
/* triangular part of the array A contains the lower triangular */
/* matrix, and the strictly upper triangular part of A is not */
/* referenced. If DIAG = 'U', the diagonal elements of A are */
/* also not referenced and are assumed to be 1. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AINV (input/output) DOUBLE PRECISION array, dimension (LDAINV,N) */
/* On entry, the (triangular) inverse of the matrix A, in the */
/* same storage format as A. */
/* On exit, the contents of AINV are destroyed. */
/* LDAINV (input) INTEGER */
/* The leading dimension of the array AINV. LDAINV >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* The reciprocal condition number of A, computed as */
/* 1/(norm(A) * norm(AINV)). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* RESID (output) DOUBLE PRECISION */
/* norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0 */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
ainv_dim1 = *ldainv;
ainv_offset = 1 + ainv_dim1;
ainv -= ainv_offset;
--work;
/* Function Body */
if (*n <= 0) {
*rcond = 1.;
*resid = 0.;
return 0;
}
/* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. */
eps = dlamch_("Epsilon");
anorm = dlantr_("1", uplo, diag, n, n, &a[a_offset], lda, &work[1]);
ainvnm = dlantr_("1", uplo, diag, n, n, &ainv[ainv_offset], ldainv, &work[
1]);
if (anorm <= 0. || ainvnm <= 0.) {
*rcond = 0.;
*resid = 1. / eps;
return 0;
}
*rcond = 1. / anorm / ainvnm;
/* Set the diagonal of AINV to 1 if AINV has unit diagonal. */
if (lsame_(diag, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
ainv[j + j * ainv_dim1] = 1.;
/* L10: */
}
}
/* Compute A * AINV, overwriting AINV. */
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
dtrmv_("Upper", "No transpose", diag, &j, &a[a_offset], lda, &
ainv[j * ainv_dim1 + 1], &c__1);
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j + 1;
dtrmv_("Lower", "No transpose", diag, &i__2, &a[j + j * a_dim1],
lda, &ainv[j + j * ainv_dim1], &c__1);
/* L30: */
}
}
/* Subtract 1 from each diagonal element to form A*AINV - I. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
ainv[j + j * ainv_dim1] += -1.;
/* L40: */
}
/* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) */
*resid = dlantr_("1", uplo, "Non-unit", n, n, &ainv[ainv_offset], ldainv,
&work[1]);
*resid = *resid * *rcond / (doublereal) (*n) / eps;
return 0;
/* End of DTRT01 */
} /* dtrt01_ */
/* Subroutine */ int dtrcon_(char *norm, char *uplo, char *diag, integer *n,
doublereal *a, integer *lda, doublereal *rcond, doublereal *work,
integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
doublereal d__1;
/* Local variables */
integer ix, kase, kase1;
doublereal scale;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *,
integer *);
doublereal anorm;
logical upper;
doublereal xnorm;
extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal dlantr_(char *, char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *);
doublereal ainvnm;
extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *);
logical onenrm;
char normin[1];
doublereal smlnum;
logical nounit;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTRCON estimates the reciprocal of the condition number of a */
/* triangular matrix A, in either the 1-norm or the infinity-norm. */
/* The norm of A is computed and an estimate is obtained for */
/* norm(inv(A)), then the reciprocal of the condition number is */
/* computed as */
/* RCOND = 1 / ( norm(A) * norm(inv(A)) ). */
/* Arguments */
/* ========= */
/* NORM (input) CHARACTER*1 */
/* Specifies whether the 1-norm condition number or the */
/* infinity-norm condition number is required: */
/* = '1' or 'O': 1-norm; */
/* = 'I': Infinity-norm. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': A is upper triangular; */
/* = 'L': A is lower triangular. */
/* DIAG (input) CHARACTER*1 */
/* = 'N': A is non-unit triangular; */
/* = 'U': A is unit triangular. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* The triangular matrix A. If UPLO = 'U', the leading N-by-N */
/* upper triangular part of the array A contains the upper */
/* triangular matrix, and the strictly lower triangular part of */
/* A is not referenced. If UPLO = 'L', the leading N-by-N lower */
/* triangular part of the array A contains the lower triangular */
/* matrix, and the strictly upper triangular part of A is not */
/* referenced. If DIAG = 'U', the diagonal elements of A are */
/* also not referenced and are assumed to be 1. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* The reciprocal of the condition number of the matrix A, */
/* computed as RCOND = 1/(norm(A) * norm(inv(A))). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (3*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
nounit = lsame_(diag, "N");
if (! onenrm && ! lsame_(norm, "I")) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTRCON", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*rcond = 1.;
return 0;
}
*rcond = 0.;
smlnum = dlamch_("Safe minimum") * (doublereal) max(1,*n);
/* Compute the norm of the triangular matrix A. */
anorm = dlantr_(norm, uplo, diag, n, n, &a[a_offset], lda, &work[1]);
/* Continue only if ANORM > 0. */
if (anorm > 0.) {
/* Estimate the norm of the inverse of A. */
ainvnm = 0.;
*(unsigned char *)normin = 'N';
if (onenrm) {
kase1 = 1;
} else {
kase1 = 2;
}
kase = 0;
L10:
dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == kase1) {
/* Multiply by inv(A). */
dlatrs_(uplo, "No transpose", diag, normin, n, &a[a_offset],
lda, &work[1], &scale, &work[(*n << 1) + 1], info);
} else {
/* Multiply by inv(A'). */
dlatrs_(uplo, "Transpose", diag, normin, n, &a[a_offset], lda,
&work[1], &scale, &work[(*n << 1) + 1], info);
}
*(unsigned char *)normin = 'Y';
/* Multiply by 1/SCALE if doing so will not cause overflow. */
if (scale != 1.) {
ix = idamax_(n, &work[1], &c__1);
xnorm = (d__1 = work[ix], abs(d__1));
if (scale < xnorm * smlnum || scale == 0.) {
goto L20;
}
drscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
*rcond = 1. / anorm / ainvnm;
}
}
L20:
return 0;
/* End of DTRCON */
} /* dtrcon_ */
/* Subroutine */ int dtrt02_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, doublereal *a, integer *lda, doublereal *x, integer *
ldx, doublereal *b, integer *ldb, doublereal *work, doublereal *resid)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
doublereal d__1, d__2;
/* Local variables */
integer j;
doublereal eps;
doublereal anorm, bnorm;
doublereal xnorm;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTRT02 computes the residual for the computed solution to a */
/* triangular system of linear equations A*x = b or A'*x = b. */
/* Here A is a triangular matrix, A' is the transpose of A, and x and b */
/* are N by NRHS matrices. The test ratio is the maximum over the */
/* number of right hand sides of */
/* norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), */
/* where op(A) denotes A or A' and EPS is the machine epsilon. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* TRANS (input) CHARACTER*1 */
/* Specifies the operation applied to A. */
/* = 'N': A *x = b (No transpose) */
/* = 'T': A'*x = b (Transpose) */
/* = 'C': A'*x = b (Conjugate transpose = Transpose) */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* N (input) INTEGER */
/* 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 X and B. NRHS >= 0. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* The triangular matrix A. If UPLO = 'U', the leading n by n */
/* upper triangular part of the array A contains the upper */
/* triangular matrix, and the strictly lower triangular part of */
/* A is not referenced. If UPLO = 'L', the leading n by n lower */
/* triangular part of the array A contains the lower triangular */
/* matrix, and the strictly upper triangular part of A is not */
/* referenced. If DIAG = 'U', the diagonal elements of A are */
/* also not referenced and are assumed to be 1. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* X (input) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* The computed solution vectors for the system of linear */
/* equations. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/* The right hand side vectors for the system of linear */
/* equations. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* RESID (output) DOUBLE PRECISION */
/* The maximum over the number of right hand sides of */
/* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0 or NRHS = 0 */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
*resid = 0.;
return 0;
}
/* Compute the 1-norm of A or A'. */
if (lsame_(trans, "N")) {
anorm = dlantr_("1", uplo, diag, n, n, &a[a_offset], lda, &work[1]);
} else {
anorm = dlantr_("I", uplo, diag, n, n, &a[a_offset], lda, &work[1]);
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = dlamch_("Epsilon");
if (anorm <= 0.) {
*resid = 1. / eps;
return 0;
}
/* Compute the maximum over the number of right hand sides of */
/* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ) */
*resid = 0.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
dcopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
dtrmv_(uplo, trans, diag, n, &a[a_offset], lda, &work[1], &c__1);
daxpy_(n, &c_b10, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
bnorm = dasum_(n, &work[1], &c__1);
xnorm = dasum_(n, &x[j * x_dim1 + 1], &c__1);
if (xnorm <= 0.) {
*resid = 1. / eps;
} else {
/* Computing MAX */
d__1 = *resid, d__2 = bnorm / anorm / xnorm / eps;
*resid = max(d__1,d__2);
}
/* L10: */
}
return 0;
/* End of DTRT02 */
} /* dtrt02_ */
/* Subroutine */ int ddrvge_(logical *dotype, integer *nn, integer *nval,
integer *nrhs, doublereal *thresh, logical *tsterr, integer *nmax,
doublereal *a, doublereal *afac, doublereal *asav, doublereal *b,
doublereal *bsav, doublereal *x, doublereal *xact, doublereal *s,
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";
static char facts[1*3] = "F" "N" "E";
static char equeds[1*4] = "N" "R" "C" "B";
/* Format strings */
static char fmt_9999[] = "(1x,a,\002, N =\002,i5,\002, type \002,i2,\002"
", test(\002,i2,\002) =\002,g12.5)";
static char fmt_9997[] = "(1x,a,\002, FACT='\002,a1,\002', TRANS='\002,a"
"1,\002', N=\002,i5,\002, EQUED='\002,a1,\002', type \002,i2,\002"
", test(\002,i1,\002)=\002,g12.5)";
static char fmt_9998[] = "(1x,a,\002, FACT='\002,a1,\002', TRANS='\002,a"
"1,\002', N=\002,i5,\002, type \002,i2,\002, test(\002,i1,\002)"
"=\002,g12.5)";
/* System generated locals */
address a__1[2];
integer i__1, i__2, i__3, i__4, i__5[2];
doublereal d__1;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
extern /* Subroutine */ int debchvxx_(doublereal *, char *);
integer i__, k, n;
doublereal *errbnds_c__, *errbnds_n__;
integer k1, nb, in, kl, ku, nt, n_err_bnds__;
extern doublereal dla_rpvgrw__(integer *, integer *, doublereal *,
integer *, doublereal *, integer *);
integer lda;
char fact[1];
integer ioff, mode;
doublereal amax;
char path[3];
integer imat, info;
doublereal *berr;
char dist[1];
doublereal rpvgrw_svxx__;
char type__[1];
integer nrun;
extern /* Subroutine */ int dget01_(integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, doublereal *,
doublereal *), dget02_(char *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *);
integer ifact;
extern /* Subroutine */ int dget04_(integer *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *);
integer nfail, iseed[4], nfact;
extern doublereal dget06_(doublereal *, doublereal *);
extern /* Subroutine */ int dget07_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, logical *,
doublereal *, doublereal *);
extern logical lsame_(char *, char *);
char equed[1];
integer nbmin;
doublereal rcond, roldc;
integer nimat;
doublereal roldi;
extern /* Subroutine */ int dgesv_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, integer *, integer *);
doublereal anorm;
integer itran;
logical equil;
doublereal roldo;
char trans[1];
integer izero, nerrs, lwork;
logical zerot;
char xtype[1];
extern /* Subroutine */ int dlatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, char *), aladhd_(integer *,
char *);
extern doublereal dlamch_(char *), 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 *), dlaqge_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, char *);
logical prefac;
doublereal colcnd, rcondc;
logical nofact;
integer iequed;
extern /* Subroutine */ int dgeequ_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *);
doublereal rcondi;
extern /* Subroutine */ int dgetrf_(integer *, integer *, doublereal *,
integer *, integer *, integer *), dgetri_(integer *, doublereal *,
integer *, integer *, doublereal *, integer *, integer *),
dlacpy_(char *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *), alasvm_(char *, integer *,
integer *, integer *, integer *);
doublereal cndnum, anormi, rcondo, ainvnm;
extern doublereal dlantr_(char *, char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dlarhs_(char *, char *, char *, char *,
integer *, integer *, integer *, integer *, integer *, doublereal
*, integer *, doublereal *, integer *, doublereal *, integer *,
integer *, integer *);
logical trfcon;
doublereal anormo, rowcnd;
extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *),
dgesvx_(char *, char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, char *, doublereal
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *
, integer *), dlatms_(integer *, integer *
, char *, integer *, char *, doublereal *, integer *, doublereal *
, doublereal *, integer *, integer *, char *, doublereal *,
integer *, doublereal *, integer *),
xlaenv_(integer *, integer *), derrvx_(char *, integer *);
doublereal result[7], rpvgrw;
extern /* Subroutine */ int dgesvxx_(char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *,
char *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___55 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___61 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___62 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___63 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___64 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___65 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___66 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___67 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___68 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___74 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___75 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___76 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___77 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___78 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___79 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___80 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___81 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DDRVGE tests the driver routines DGESV, -SVX, and -SVXX. */
/* Note that this file is used only when the XBLAS are available, */
/* otherwise ddrvge.f defines this subroutine. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* NRHS (input) INTEGER */
/* The number of right hand side vectors to be generated for */
/* each linear system. */
/* 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 N, used in dimensioning the */
/* work arrays. */
/* A (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */
/* AFAC (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */
/* ASAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) */
/* B (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */
/* BSAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */
/* X (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */
/* XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) */
/* S (workspace) DOUBLE PRECISION array, dimension (2*NMAX) */
/* WORK (workspace) DOUBLE PRECISION array, dimension */
/* (NMAX*max(3,NRHS)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*NRHS+NMAX) */
/* 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;
--s;
--xact;
--x;
--bsav;
--b;
--asav;
--afac;
--a;
--nval;
--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 */
if (*tsterr) {
derrvx_(path, nout);
}
infoc_1.infot = 0;
/* Set the block size and minimum block size for testing. */
nb = 1;
nbmin = 2;
xlaenv_(&c__1, &nb);
xlaenv_(&c__2, &nbmin);
/* Do for each value of N in NVAL */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
lda = max(n,1);
*(unsigned char *)xtype = 'N';
nimat = 11;
if (n <= 0) {
nimat = 1;
}
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L80;
}
/* Skip types 5, 6, or 7 if the matrix size is too small. */
zerot = imat >= 5 && imat <= 7;
if (zerot && n < imat - 4) {
goto L80;
}
/* Set up parameters with DLATB4 and generate a test matrix */
/* with DLATMS. */
dlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &
cndnum, dist);
rcondc = 1. / cndnum;
s_copy(srnamc_1.srnamt, "DLATMS", (ftnlen)32, (ftnlen)6);
dlatms_(&n, &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, " ", &n, &n, &c_n1, &
c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L80;
}
/* 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 = n;
} else {
izero = n / 2 + 1;
}
ioff = (izero - 1) * lda;
if (imat < 7) {
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
a[ioff + i__] = 0.;
/* L20: */
}
} else {
i__3 = n - izero + 1;
dlaset_("Full", &n, &i__3, &c_b20, &c_b20, &a[ioff + 1], &
lda);
}
} else {
izero = 0;
}
/* Save a copy of the matrix A in ASAV. */
dlacpy_("Full", &n, &n, &a[1], &lda, &asav[1], &lda);
for (iequed = 1; iequed <= 4; ++iequed) {
*(unsigned char *)equed = *(unsigned char *)&equeds[iequed -
1];
if (iequed == 1) {
nfact = 3;
} else {
nfact = 1;
}
i__3 = nfact;
for (ifact = 1; ifact <= i__3; ++ifact) {
*(unsigned char *)fact = *(unsigned char *)&facts[ifact -
1];
prefac = lsame_(fact, "F");
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
if (zerot) {
if (prefac) {
goto L60;
}
rcondo = 0.;
rcondi = 0.;
} else if (! nofact) {
/* Compute the condition number for comparison with */
/* the value returned by DGESVX (FACT = 'N' reuses */
/* the condition number from the previous iteration */
/* with FACT = 'F'). */
dlacpy_("Full", &n, &n, &asav[1], &lda, &afac[1], &
lda);
if (equil || iequed > 1) {
/* Compute row and column scale factors to */
/* equilibrate the matrix A. */
dgeequ_(&n, &n, &afac[1], &lda, &s[1], &s[n + 1],
&rowcnd, &colcnd, &amax, &info);
if (info == 0 && n > 0) {
if (lsame_(equed, "R"))
{
rowcnd = 0.;
colcnd = 1.;
} else if (lsame_(equed, "C")) {
rowcnd = 1.;
colcnd = 0.;
} else if (lsame_(equed, "B")) {
rowcnd = 0.;
colcnd = 0.;
}
/* Equilibrate the matrix. */
dlaqge_(&n, &n, &afac[1], &lda, &s[1], &s[n +
1], &rowcnd, &colcnd, &amax, equed);
}
}
/* Save the condition number of the non-equilibrated */
/* system for use in DGET04. */
if (equil) {
roldo = rcondo;
roldi = rcondi;
}
/* Compute the 1-norm and infinity-norm of A. */
anormo = dlange_("1", &n, &n, &afac[1], &lda, &rwork[
1]);
anormi = dlange_("I", &n, &n, &afac[1], &lda, &rwork[
1]);
/* Factor the matrix A. */
dgetrf_(&n, &n, &afac[1], &lda, &iwork[1], &info);
/* Form the inverse of A. */
dlacpy_("Full", &n, &n, &afac[1], &lda, &a[1], &lda);
lwork = *nmax * max(3,*nrhs);
dgetri_(&n, &a[1], &lda, &iwork[1], &work[1], &lwork,
&info);
/* Compute the 1-norm condition number of A. */
ainvnm = dlange_("1", &n, &n, &a[1], &lda, &rwork[1]);
if (anormo <= 0. || ainvnm <= 0.) {
rcondo = 1.;
} else {
rcondo = 1. / anormo / ainvnm;
}
/* Compute the infinity-norm condition number of A. */
ainvnm = dlange_("I", &n, &n, &a[1], &lda, &rwork[1]);
if (anormi <= 0. || ainvnm <= 0.) {
rcondi = 1.;
} else {
rcondi = 1. / anormi / ainvnm;
}
}
for (itran = 1; itran <= 3; ++itran) {
for (i__ = 1; i__ <= 7; ++i__) {
result[i__ - 1] = 0.;
}
/* Do for each value of TRANS. */
*(unsigned char *)trans = *(unsigned char *)&transs[
itran - 1];
if (itran == 1) {
rcondc = rcondo;
} else {
rcondc = rcondi;
}
/* Restore the matrix A. */
dlacpy_("Full", &n, &n, &asav[1], &lda, &a[1], &lda);
/* Form an exact solution and set the right hand side. */
s_copy(srnamc_1.srnamt, "DLARHS", (ftnlen)32, (ftnlen)
6);
dlarhs_(path, xtype, "Full", 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, &bsav[1], &lda);
if (nofact && itran == 1) {
/* --- Test DGESV --- */
/* Compute the LU factorization of the matrix and */
/* solve the system. */
dlacpy_("Full", &n, &n, &a[1], &lda, &afac[1], &
lda);
dlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &
lda);
s_copy(srnamc_1.srnamt, "DGESV ", (ftnlen)32, (
ftnlen)6);
dgesv_(&n, nrhs, &afac[1], &lda, &iwork[1], &x[1],
&lda, &info);
/* Check error code from DGESV . */
if (info != izero) {
alaerh_(path, "DGESV ", &info, &izero, " ", &
n, &n, &c_n1, &c_n1, nrhs, &imat, &
nfail, &nerrs, nout);
goto L50;
}
/* Reconstruct matrix from factors and compute */
/* residual. */
dget01_(&n, &n, &a[1], &lda, &afac[1], &lda, &
iwork[1], &rwork[1], result);
nt = 1;
if (izero == 0) {
/* Compute residual of the computed solution. */
dlacpy_("Full", &n, nrhs, &b[1], &lda, &work[
1], &lda);
dget02_("No transpose", &n, &n, nrhs, &a[1], &
lda, &x[1], &lda, &work[1], &lda, &
rwork[1], &result[1]);
/* Check solution from generated exact solution. */
dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&rcondc, &result[2]);
nt = 3;
}
/* Print information about the tests that did not */
/* pass the threshold. */
i__4 = nt;
for (k = 1; k <= i__4; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___55.ciunit = *nout;
s_wsfe(&io___55);
do_fio(&c__1, "DGESV ", (ftnlen)6);
do_fio(&c__1, (char *)&n, (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;
}
/* --- Test DGESVX --- */
if (! prefac) {
dlaset_("Full", &n, &n, &c_b20, &c_b20, &afac[1],
&lda);
}
dlaset_("Full", &n, nrhs, &c_b20, &c_b20, &x[1], &lda);
if (iequed > 1 && n > 0) {
/* Equilibrate the matrix if FACT = 'F' and */
/* EQUED = 'R', 'C', or 'B'. */
dlaqge_(&n, &n, &a[1], &lda, &s[1], &s[n + 1], &
rowcnd, &colcnd, &amax, equed);
}
/* Solve the system and compute the condition number */
/* and error bounds using DGESVX. */
s_copy(srnamc_1.srnamt, "DGESVX", (ftnlen)32, (ftnlen)
6);
dgesvx_(fact, trans, &n, nrhs, &a[1], &lda, &afac[1],
&lda, &iwork[1], equed, &s[1], &s[n + 1], &b[
1], &lda, &x[1], &lda, &rcond, &rwork[1], &
rwork[*nrhs + 1], &work[1], &iwork[n + 1], &
info);
/* Check the error code from DGESVX. */
if (info == n + 1) {
goto L50;
}
if (info != izero) {
/* Writing concatenation */
i__5[0] = 1, a__1[0] = fact;
i__5[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2);
alaerh_(path, "DGESVX", &info, &izero, ch__1, &n,
&n, &c_n1, &c_n1, nrhs, &imat, &nfail, &
nerrs, nout);
goto L50;
}
/* Compare WORK(1) from DGESVX with the computed */
/* reciprocal pivot growth factor RPVGRW */
if (info != 0) {
rpvgrw = dlantr_("M", "U", "N", &info, &info, &
afac[1], &lda, &work[1]);
if (rpvgrw == 0.) {
rpvgrw = 1.;
} else {
rpvgrw = dlange_("M", &n, &info, &a[1], &lda,
&work[1]) / rpvgrw;
}
} else {
rpvgrw = dlantr_("M", "U", "N", &n, &n, &afac[1],
&lda, &work[1]);
if (rpvgrw == 0.) {
rpvgrw = 1.;
} else {
rpvgrw = dlange_("M", &n, &n, &a[1], &lda, &
work[1]) / rpvgrw;
}
}
result[6] = (d__1 = rpvgrw - work[1], abs(d__1)) /
max(work[1],rpvgrw) / dlamch_("E");
if (! prefac) {
/* Reconstruct matrix from factors and compute */
/* residual. */
dget01_(&n, &n, &a[1], &lda, &afac[1], &lda, &
iwork[1], &rwork[(*nrhs << 1) + 1],
result);
k1 = 1;
} else {
k1 = 2;
}
if (info == 0) {
trfcon = FALSE_;
/* Compute residual of the computed solution. */
dlacpy_("Full", &n, nrhs, &bsav[1], &lda, &work[1]
, &lda);
dget02_(trans, &n, &n, nrhs, &asav[1], &lda, &x[1]
, &lda, &work[1], &lda, &rwork[(*nrhs <<
1) + 1], &result[1]);
/* Check solution from generated exact solution. */
if (nofact || prefac && lsame_(equed, "N")) {
dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&rcondc, &result[2]);
} else {
if (itran == 1) {
roldc = roldo;
} else {
roldc = roldi;
}
dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&roldc, &result[2]);
}
/* Check the error bounds from iterative */
/* refinement. */
dget07_(trans, &n, nrhs, &asav[1], &lda, &b[1], &
lda, &x[1], &lda, &xact[1], &lda, &rwork[
1], &c_true, &rwork[*nrhs + 1], &result[3]
);
} else {
trfcon = TRUE_;
}
/* Compare RCOND from DGESVX with the computed value */
/* in RCONDC. */
result[5] = dget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass */
/* the threshold. */
if (! trfcon) {
for (k = k1; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___61.ciunit = *nout;
s_wsfe(&io___61);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, equed, (ftnlen)1);
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();
} else {
io___62.ciunit = *nout;
s_wsfe(&io___62);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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 *)&k, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[k - 1],
(ftnlen)sizeof(doublereal));
e_wsfe();
}
++nfail;
}
/* L40: */
}
nrun = nrun + 7 - k1;
} else {
if (result[0] >= *thresh && ! prefac) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___63.ciunit = *nout;
s_wsfe(&io___63);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__1, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)
sizeof(doublereal));
e_wsfe();
} else {
io___64.ciunit = *nout;
s_wsfe(&io___64);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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__1, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)
sizeof(doublereal));
e_wsfe();
}
++nfail;
++nrun;
}
if (result[5] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___65.ciunit = *nout;
s_wsfe(&io___65);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__6, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[5], (ftnlen)
sizeof(doublereal));
e_wsfe();
} else {
io___66.ciunit = *nout;
s_wsfe(&io___66);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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__6, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[5], (ftnlen)
sizeof(doublereal));
e_wsfe();
}
++nfail;
++nrun;
}
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___67.ciunit = *nout;
s_wsfe(&io___67);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__7, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)
sizeof(doublereal));
e_wsfe();
} else {
io___68.ciunit = *nout;
s_wsfe(&io___68);
do_fio(&c__1, "DGESVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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__7, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)
sizeof(doublereal));
e_wsfe();
}
++nfail;
++nrun;
}
}
/* --- Test DGESVXX --- */
/* Restore the matrices A and B. */
dlacpy_("Full", &n, &n, &asav[1], &lda, &a[1], &lda);
dlacpy_("Full", &n, nrhs, &bsav[1], &lda, &b[1], &lda);
if (! prefac) {
dlaset_("Full", &n, &n, &c_b20, &c_b20, &afac[1],
&lda);
}
dlaset_("Full", &n, nrhs, &c_b20, &c_b20, &x[1], &lda);
if (iequed > 1 && n > 0) {
/* Equilibrate the matrix if FACT = 'F' and */
/* EQUED = 'R', 'C', or 'B'. */
dlaqge_(&n, &n, &a[1], &lda, &s[1], &s[n + 1], &
rowcnd, &colcnd, &amax, equed);
}
/* Solve the system and compute the condition number */
/* and error bounds using DGESVXX. */
s_copy(srnamc_1.srnamt, "DGESVXX", (ftnlen)32, (
ftnlen)7);
n_err_bnds__ = 3;
dalloc3();
dgesvxx_(fact, trans, &n, nrhs, &a[1], &lda, &afac[1],
&lda, &iwork[1], equed, &s[1], &s[n + 1], &b[
1], &lda, &x[1], &lda, &rcond, &rpvgrw_svxx__,
berr, &n_err_bnds__, errbnds_n__,
errbnds_c__, &c__0, &c_b20, &work[1], &iwork[
n + 1], &info);
free3();
/* Check the error code from DGESVXX. */
if (info == n + 1) {
goto L50;
}
if (info != izero) {
/* Writing concatenation */
i__5[0] = 1, a__1[0] = fact;
i__5[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2);
alaerh_(path, "DGESVXX", &info, &izero, ch__1, &n,
&n, &c_n1, &c_n1, nrhs, &imat, &nfail, &
nerrs, nout);
goto L50;
}
/* Compare rpvgrw_svxx from DGESVXX with the computed */
/* reciprocal pivot growth factor RPVGRW */
if (info > 0 && info < n + 1) {
rpvgrw = dla_rpvgrw__(&n, &info, &a[1], &lda, &
afac[1], &lda);
} else {
rpvgrw = dla_rpvgrw__(&n, &n, &a[1], &lda, &afac[
1], &lda);
}
result[6] = (d__1 = rpvgrw - rpvgrw_svxx__, abs(d__1))
/ max(rpvgrw_svxx__,rpvgrw) / dlamch_("E");
if (! prefac) {
/* Reconstruct matrix from factors and compute */
/* residual. */
dget01_(&n, &n, &a[1], &lda, &afac[1], &lda, &
iwork[1], &rwork[(*nrhs << 1) + 1],
result);
k1 = 1;
} else {
k1 = 2;
}
if (info == 0) {
trfcon = FALSE_;
/* Compute residual of the computed solution. */
dlacpy_("Full", &n, nrhs, &bsav[1], &lda, &work[1]
, &lda);
dget02_(trans, &n, &n, nrhs, &asav[1], &lda, &x[1]
, &lda, &work[1], &lda, &rwork[(*nrhs <<
1) + 1], &result[1]);
/* Check solution from generated exact solution. */
if (nofact || prefac && lsame_(equed, "N")) {
dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&rcondc, &result[2]);
} else {
if (itran == 1) {
roldc = roldo;
} else {
roldc = roldi;
}
dget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&roldc, &result[2]);
}
} else {
trfcon = TRUE_;
}
/* Compare RCOND from DGESVXX with the computed value */
/* in RCONDC. */
result[5] = dget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass */
/* the threshold. */
if (! trfcon) {
for (k = k1; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___74.ciunit = *nout;
s_wsfe(&io___74);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, equed, (ftnlen)1);
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();
} else {
io___75.ciunit = *nout;
s_wsfe(&io___75);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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 *)&k, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[k - 1],
(ftnlen)sizeof(doublereal));
e_wsfe();
}
++nfail;
}
/* L45: */
}
nrun = nrun + 7 - k1;
} else {
if (result[0] >= *thresh && ! prefac) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___76.ciunit = *nout;
s_wsfe(&io___76);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__1, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)
sizeof(doublereal));
e_wsfe();
} else {
io___77.ciunit = *nout;
s_wsfe(&io___77);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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__1, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)
sizeof(doublereal));
e_wsfe();
}
++nfail;
++nrun;
}
if (result[5] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___78.ciunit = *nout;
s_wsfe(&io___78);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__6, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[5], (ftnlen)
sizeof(doublereal));
e_wsfe();
} else {
io___79.ciunit = *nout;
s_wsfe(&io___79);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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__6, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[5], (ftnlen)
sizeof(doublereal));
e_wsfe();
}
++nfail;
++nrun;
}
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___80.ciunit = *nout;
s_wsfe(&io___80);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__7, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)
sizeof(doublereal));
e_wsfe();
} else {
io___81.ciunit = *nout;
s_wsfe(&io___81);
do_fio(&c__1, "DGESVXX", (ftnlen)7);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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__7, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)
sizeof(doublereal));
e_wsfe();
}
++nfail;
++nrun;
}
}
L50:
;
}
L60:
;
}
/* L70: */
}
L80:
;
}
/* L90: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
/* Test Error Bounds from DGESVXX */
debchvxx_(thresh, path);
return 0;
/* End of DDRVGE */
} /* ddrvge_ */
/* Subroutine */ int dchktr_(logical *dotype, integer *nn, integer *nval,
integer *nnb, integer *nbval, integer *nns, integer *nsval,
doublereal *thresh, logical *tsterr, integer *nmax, doublereal *a,
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 uplos[1*2] = "U" "L";
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', DIAG='\002,a1,\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 UPLO='\002,a1,\002', TRANS='\002,a1,\002"
"', DIAG='\002,a1,\002', N=\002,i5,\002, NB=\002,i4,\002, type"
" \002,i2,\002, test(\002,i2,\002)= \002,g12"
".5)";
static char fmt_9997[] = "(\002 NORM='\002,a1,\002', UPLO ='\002,a1,\002"
"', N=\002,i5,\002,\002,11x,\002 type \002,i2,\002, test(\002,i2"
",\002)=\002,g12.5)";
static char fmt_9996[] = "(1x,a6,\002( '\002,a1,\002', '\002,a1,\002', "
"'\002,a1,\002', '\002,a1,\002',\002,i5,\002, ... ), type \002,i2,"
"\002, test(\002,i2,\002)=\002,g12.5)";
/* System generated locals */
address a__1[2], a__2[3], a__3[4];
integer i__1, i__2, i__3[2], i__4, i__5[3], i__6[4];
char ch__1[2], ch__2[3], ch__3[4];
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen), s_cat(char *,
char **, integer *, integer *, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, k, n, nb, in, lda, inb;
char diag[1];
integer imat, info;
char path[3];
integer irhs, nrhs;
char norm[1], uplo[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer idiag;
doublereal scale;
extern /* Subroutine */ int dget04_(integer *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *);
integer nfail, iseed[4];
extern logical lsame_(char *, char *);
doublereal rcond, anorm;
integer itran;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), dtrt01_(char *, char *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *), dtrt02_(char *, char
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *), dtrt03_(char *, char *,
char *, integer *, integer *, doublereal *, integer *, doublereal
*, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *), dtrt05_(char *, char *, char *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *), dtrt06_(
doublereal *, doublereal *, char *, char *, integer *, doublereal
*, integer *, doublereal *, doublereal *);
char trans[1];
integer iuplo, nerrs;
doublereal dummy;
char xtype[1];
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *);
doublereal rcondc;
extern /* Subroutine */ int 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 alasum_(char *, integer *, integer *, integer
*, integer *);
doublereal rcondo;
extern doublereal dlantr_(char *, char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *);
doublereal ainvnm;
extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *), dlattr_(
integer *, char *, char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *), dtrcon_(char *, char *, char *, integer *
, doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), xlaenv_(integer *, integer *),
derrtr_(char *, integer *), dtrrfs_(char *, char *, char
*, integer *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *),
dtrtri_(char *, char *, integer *, doublereal *, integer *,
integer *);
doublereal result[9];
extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *);
/* Fortran I/O blocks */
static cilist io___27 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___36 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___38 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9996, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NNB) */
/* 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 leading dimension of the work arrays. */
/* NMAX >= the maximum value of N in NVAL. */
/* A (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(NMAX,2*NSMAX)) */
/* IWORK (workspace) INTEGER array, dimension (NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--a;
--nsval;
--nbval;
--nval;
--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, "TR", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Test the error exits */
if (*tsterr) {
derrtr_(path, nout);
}
infoc_1.infot = 0;
xlaenv_(&c__2, &c__2);
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
/* Do for each value of N in NVAL */
n = nval[in];
lda = max(1,n);
*(unsigned char *)xtype = 'N';
for (imat = 1; imat <= 10; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L80;
}
for (iuplo = 1; iuplo <= 2; ++iuplo) {
/* Do first for UPLO = 'U', then for UPLO = 'L' */
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Call DLATTR to generate a triangular test matrix. */
s_copy(srnamc_1.srnamt, "DLATTR", (ftnlen)6, (ftnlen)6);
dlattr_(&imat, uplo, "No transpose", diag, iseed, &n, &a[1], &
lda, &x[1], &work[1], &info);
/* Set IDIAG = 1 for non-unit matrices, 2 for unit. */
if (lsame_(diag, "N")) {
idiag = 1;
} else {
idiag = 2;
}
i__2 = *nnb;
for (inb = 1; inb <= i__2; ++inb) {
/* Do for each blocksize in NBVAL */
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* + TEST 1 */
/* Form the inverse of A. */
dlacpy_(uplo, &n, &n, &a[1], &lda, &ainv[1], &lda);
s_copy(srnamc_1.srnamt, "DTRTRI", (ftnlen)6, (ftnlen)6);
dtrtri_(uplo, diag, &n, &ainv[1], &lda, &info);
/* Check error code from DTRTRI. */
if (info != 0) {
/* Writing concatenation */
i__3[0] = 1, a__1[0] = uplo;
i__3[1] = 1, a__1[1] = diag;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
alaerh_(path, "DTRTRI", &info, &c__0, ch__1, &n, &n, &
c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
}
/* Compute the infinity-norm condition number of A. */
anorm = dlantr_("I", uplo, diag, &n, &n, &a[1], &lda, &
rwork[1]);
ainvnm = dlantr_("I", uplo, diag, &n, &n, &ainv[1], &lda,
&rwork[1]);
if (anorm <= 0. || ainvnm <= 0.) {
rcondi = 1.;
} else {
rcondi = 1. / anorm / ainvnm;
}
/* Compute the residual for the triangular matrix times */
/* its inverse. Also compute the 1-norm condition number */
/* of A. */
dtrt01_(uplo, diag, &n, &a[1], &lda, &ainv[1], &lda, &
rcondo, &rwork[1], result);
/* Print the test ratio if it is .GE. THRESH. */
if (result[0] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___27.ciunit = *nout;
s_wsfe(&io___27);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
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 *)&c__1, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* Skip remaining tests if not the first block size. */
if (inb != 1) {
goto L60;
}
i__4 = *nns;
for (irhs = 1; irhs <= i__4; ++irhs) {
nrhs = nsval[irhs];
*(unsigned char *)xtype = 'N';
for (itran = 1; itran <= 3; ++itran) {
/* Do for op(A) = A, A**T, or A**H. */
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
if (itran == 1) {
*(unsigned char *)norm = 'O';
rcondc = rcondo;
} else {
*(unsigned char *)norm = 'I';
rcondc = rcondi;
}
/* + TEST 2 */
/* Solve and compute residual for op(A)*x = b. */
s_copy(srnamc_1.srnamt, "DLARHS", (ftnlen)6, (
ftnlen)6);
dlarhs_(path, xtype, uplo, trans, &n, &n, &c__0, &
idiag, &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, "DTRTRS", (ftnlen)6, (
ftnlen)6);
dtrtrs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&x[1], &lda, &info);
/* Check error code from DTRTRS. */
if (info != 0) {
/* Writing concatenation */
i__5[0] = 1, a__2[0] = uplo;
i__5[1] = 1, a__2[1] = trans;
i__5[2] = 1, a__2[2] = diag;
s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3);
alaerh_(path, "DTRTRS", &info, &c__0, ch__2, &
n, &n, &c_n1, &c_n1, &nrhs, &imat, &
nfail, &nerrs, nout);
}
/* This line is needed on a Sun SPARCstation. */
if (n > 0) {
dummy = a[1];
}
dtrt02_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&x[1], &lda, &b[1], &lda, &work[1], &
result[1]);
/* + TEST 3 */
/* Check solution from generated exact solution. */
dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
/* + TESTS 4, 5, and 6 */
/* Use iterative refinement to improve the solution */
/* and compute error bounds. */
s_copy(srnamc_1.srnamt, "DTRRFS", (ftnlen)6, (
ftnlen)6);
dtrrfs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&b[1], &lda, &x[1], &lda, &rwork[1], &
rwork[nrhs + 1], &work[1], &iwork[1], &
info);
/* Check error code from DTRRFS. */
if (info != 0) {
/* Writing concatenation */
i__5[0] = 1, a__2[0] = uplo;
i__5[1] = 1, a__2[1] = trans;
i__5[2] = 1, a__2[2] = diag;
s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3);
alaerh_(path, "DTRRFS", &info, &c__0, ch__2, &
n, &n, &c_n1, &c_n1, &nrhs, &imat, &
nfail, &nerrs, nout);
}
dget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[3]);
dtrt05_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&b[1], &lda, &x[1], &lda, &xact[1], &lda,
&rwork[1], &rwork[nrhs + 1], &result[4]);
/* Print information about the tests that did not */
/* pass the threshold. */
for (k = 2; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___36.ciunit = *nout;
s_wsfe(&io___36);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (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;
}
/* L20: */
}
nrun += 5;
/* L30: */
}
/* L40: */
}
/* + TEST 7 */
/* Get an estimate of RCOND = 1/CNDNUM. */
for (itran = 1; itran <= 2; ++itran) {
if (itran == 1) {
*(unsigned char *)norm = 'O';
rcondc = rcondo;
} else {
*(unsigned char *)norm = 'I';
rcondc = rcondi;
}
s_copy(srnamc_1.srnamt, "DTRCON", (ftnlen)6, (ftnlen)
6);
dtrcon_(norm, uplo, diag, &n, &a[1], &lda, &rcond, &
work[1], &iwork[1], &info);
/* Check error code from DTRCON. */
if (info != 0) {
/* Writing concatenation */
i__5[0] = 1, a__2[0] = norm;
i__5[1] = 1, a__2[1] = uplo;
i__5[2] = 1, a__2[2] = diag;
s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3);
alaerh_(path, "DTRCON", &info, &c__0, ch__2, &n, &
n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &
nerrs, nout);
}
dtrt06_(&rcond, &rcondc, uplo, diag, &n, &a[1], &lda,
&rwork[1], &result[6]);
/* Print the test ratio if it is .GE. THRESH. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___38.ciunit = *nout;
s_wsfe(&io___38);
do_fio(&c__1, norm, (ftnlen)1);
do_fio(&c__1, uplo, (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__7, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* L50: */
}
L60:
;
}
/* L70: */
}
L80:
;
}
/* Use pathological test matrices to test DLATRS. */
for (imat = 11; imat <= 18; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L110;
}
for (iuplo = 1; iuplo <= 2; ++iuplo) {
/* Do first for UPLO = 'U', then for UPLO = 'L' */
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
for (itran = 1; itran <= 3; ++itran) {
/* Do for op(A) = A, A**T, and A**H. */
*(unsigned char *)trans = *(unsigned char *)&transs[itran
- 1];
/* Call DLATTR to generate a triangular test matrix. */
s_copy(srnamc_1.srnamt, "DLATTR", (ftnlen)6, (ftnlen)6);
dlattr_(&imat, uplo, trans, diag, iseed, &n, &a[1], &lda,
&x[1], &work[1], &info);
/* + TEST 8 */
/* Solve the system op(A)*x = b. */
s_copy(srnamc_1.srnamt, "DLATRS", (ftnlen)6, (ftnlen)6);
dcopy_(&n, &x[1], &c__1, &b[1], &c__1);
dlatrs_(uplo, trans, diag, "N", &n, &a[1], &lda, &b[1], &
scale, &rwork[1], &info);
/* Check error code from DLATRS. */
if (info != 0) {
/* Writing concatenation */
i__6[0] = 1, a__3[0] = uplo;
i__6[1] = 1, a__3[1] = trans;
i__6[2] = 1, a__3[2] = diag;
i__6[3] = 1, a__3[3] = "N";
s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4);
alaerh_(path, "DLATRS", &info, &c__0, ch__3, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
dtrt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale,
&rwork[1], &c_b101, &b[1], &lda, &x[1], &lda, &
work[1], &result[7]);
/* + TEST 9 */
/* Solve op(A)*X = b again with NORMIN = 'Y'. */
dcopy_(&n, &x[1], &c__1, &b[n + 1], &c__1);
dlatrs_(uplo, trans, diag, "Y", &n, &a[1], &lda, &b[n + 1]
, &scale, &rwork[1], &info);
/* Check error code from DLATRS. */
if (info != 0) {
/* Writing concatenation */
i__6[0] = 1, a__3[0] = uplo;
i__6[1] = 1, a__3[1] = trans;
i__6[2] = 1, a__3[2] = diag;
i__6[3] = 1, a__3[3] = "Y";
s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4);
alaerh_(path, "DLATRS", &info, &c__0, ch__3, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
dtrt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale,
&rwork[1], &c_b101, &b[n + 1], &lda, &x[1], &lda,
&work[1], &result[8]);
/* Print information about the tests that did not pass */
/* the threshold. */
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___40.ciunit = *nout;
s_wsfe(&io___40);
do_fio(&c__1, "DLATRS", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, "N", (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;
}
if (result[8] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___41.ciunit = *nout;
s_wsfe(&io___41);
do_fio(&c__1, "DLATRS", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, "Y", (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__9, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[8], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
nrun += 2;
/* L90: */
}
/* L100: */
}
L110:
;
}
/* L120: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of DCHKTR */
} /* dchktr_ */
/* 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 dtrcon_(char *norm, char *uplo, char *diag, integer *n, doublereal *a, integer *lda, doublereal *rcond, doublereal *work, integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
doublereal d__1;
/* Local variables */
integer ix, kase, kase1;
doublereal scale;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */
int drscl_(integer *, doublereal *, doublereal *, integer *);
doublereal anorm;
logical upper;
doublereal xnorm;
extern /* Subroutine */
int dlacn2_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */
int xerbla_(char *, integer *);
extern doublereal dlantr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, doublereal *);
doublereal ainvnm;
extern /* Subroutine */
int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *);
logical onenrm;
char normin[1];
doublereal smlnum;
logical nounit;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
nounit = lsame_(diag, "N");
if (! onenrm && ! lsame_(norm, "I"))
{
*info = -1;
}
else if (! upper && ! lsame_(uplo, "L"))
{
*info = -2;
}
else if (! nounit && ! lsame_(diag, "U"))
{
*info = -3;
}
else if (*n < 0)
{
*info = -4;
}
else if (*lda < max(1,*n))
{
*info = -6;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("DTRCON", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
*rcond = 1.;
return 0;
}
*rcond = 0.;
smlnum = dlamch_("Safe minimum") * (doublereal) max(1,*n);
/* Compute the norm of the triangular matrix A. */
anorm = dlantr_(norm, uplo, diag, n, n, &a[a_offset], lda, &work[1]);
/* Continue only if ANORM > 0. */
if (anorm > 0.)
{
/* Estimate the norm of the inverse of A. */
ainvnm = 0.;
*(unsigned char *)normin = 'N';
if (onenrm)
{
kase1 = 1;
}
else
{
kase1 = 2;
}
kase = 0;
L10:
dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0)
{
if (kase == kase1)
{
/* Multiply by inv(A). */
dlatrs_(uplo, "No transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info);
}
else
{
/* Multiply by inv(A**T). */
dlatrs_(uplo, "Transpose", diag, normin, n, &a[a_offset], lda, &work[1], &scale, &work[(*n << 1) + 1], info);
}
*(unsigned char *)normin = 'Y';
/* Multiply by 1/SCALE if doing so will not cause overflow. */
if (scale != 1.)
{
ix = idamax_(n, &work[1], &c__1);
xnorm = (d__1 = work[ix], abs(d__1));
if (scale < xnorm * smlnum || scale == 0.)
{
goto L20;
}
drscl_(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.)
{
*rcond = 1. / anorm / ainvnm;
}
}
L20:
return 0;
/* End of DTRCON */
}
/* Subroutine */ int dtrt06_(doublereal *rcond, doublereal *rcondc, char *
uplo, char *diag, integer *n, doublereal *a, integer *lda, doublereal
*work, doublereal *rat)
{
/* System generated locals */
integer a_dim1, a_offset;
doublereal d__1, d__2;
/* Local variables */
doublereal eps, rmin, rmax, anorm;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
doublereal bignum;
extern doublereal dlantr_(char *, char *, char *, integer *, integer *,
doublereal *, integer *, doublereal *);
doublereal smlnum;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTRT06 computes a test ratio comparing RCOND (the reciprocal */
/* condition number of a triangular matrix A) and RCONDC, the estimate */
/* computed by DTRCON. Information about the triangular matrix A is */
/* used if one estimate is zero and the other is non-zero to decide if */
/* underflow in the estimate is justified. */
/* Arguments */
/* ========= */
/* RCOND (input) DOUBLE PRECISION */
/* The estimate of the reciprocal condition number obtained by */
/* forming the explicit inverse of the matrix A and computing */
/* RCOND = 1/( norm(A) * norm(inv(A)) ). */
/* RCONDC (input) DOUBLE PRECISION */
/* The estimate of the reciprocal condition number computed by */
/* DTRCON. */
/* UPLO (input) CHARACTER */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* DIAG (input) CHARACTER */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* The triangular matrix A. If UPLO = 'U', the leading n by n */
/* upper triangular part of the array A contains the upper */
/* triangular matrix, and the strictly lower triangular part of */
/* A is not referenced. If UPLO = 'L', the leading n by n lower */
/* triangular part of the array A contains the lower triangular */
/* matrix, and the strictly upper triangular part of A is not */
/* referenced. If DIAG = 'U', the diagonal elements of A are */
/* also not referenced and are assumed to be 1. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* RAT (output) DOUBLE PRECISION */
/* The test ratio. If both RCOND and RCONDC are nonzero, */
/* RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1. */
/* If RAT = 0, the two estimates are exactly the same. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
/* Function Body */
eps = dlamch_("Epsilon");
rmax = max(*rcond,*rcondc);
rmin = min(*rcond,*rcondc);
/* Do the easy cases first. */
if (rmin < 0.) {
/* Invalid value for RCOND or RCONDC, return 1/EPS. */
*rat = 1. / eps;
} else if (rmin > 0.) {
/* Both estimates are positive, return RMAX/RMIN - 1. */
*rat = rmax / rmin - 1.;
} else if (rmax == 0.) {
/* Both estimates zero. */
*rat = 0.;
} else {
/* One estimate is zero, the other is non-zero. If the matrix is */
/* ill-conditioned, return the nonzero estimate multiplied by */
/* 1/EPS; if the matrix is badly scaled, return the nonzero */
/* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum */
/* element in absolute value in A. */
smlnum = dlamch_("Safe minimum");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
anorm = dlantr_("M", uplo, diag, n, n, &a[a_offset], lda, &work[1]);
/* Computing MIN */
d__1 = bignum / max(1.,anorm), d__2 = 1. / eps;
*rat = rmax * min(d__1,d__2);
}
return 0;
/* End of DTRT06 */
} /* dtrt06_ */
