/* Subroutine */ int slatdf_(integer *ijob, integer *n, real *z__, integer *
ldz, real *rhs, real *rdsum, real *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
=======
SLATDF uses the LU factorization of the n-by-n matrix Z computed by
SGETC2 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 SGETC2 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 SGECON, 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) REAL array, dimension (LDZ, N)
On entry, the LU part of the factorization of the n-by-n
matrix Z computed by SGETC2: Z = P * L * U * Q
LDZ (input) INTEGER
The leading dimension of the array Z. LDA >= max(1, N).
RHS (input/output) REAL 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) REAL
On entry, the sum of squares of computed contributions to
the Dif-estimate under computation by STGSYL, 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 STGSY2 is called by STGSYL.
RDSCAL (input/output) REAL
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 STGSY2 is called by
STGSYL.
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 real c_b23 = 1.f;
static real c_b37 = -1.f;
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer info;
static real temp;
extern doublereal sdot_(integer *, real *, integer *, real *, integer *);
static real work[32];
static integer i__, j, k;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
static real pmone;
extern doublereal sasum_(integer *, real *, integer *);
static real sminu;
static integer iwork[8];
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), saxpy_(integer *, real *, real *, integer *, real *,
integer *);
static real splus;
extern /* Subroutine */ int sgesc2_(integer *, real *, integer *, real *,
integer *, integer *, real *);
static real bm, bp, xm[8], xp[8];
extern /* Subroutine */ int sgecon_(char *, integer *, real *, integer *,
real *, real *, real *, integer *, integer *), slassq_(
integer *, real *, integer *, real *, real *), slaswp_(integer *,
real *, 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;
slaswp_(&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.f;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
bp = rhs[j] + 1.f;
bm = rhs[j] - 1.f;
splus = 1.f;
/* 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 += sdot_(&i__2, &z___ref(j + 1, j), &c__1, &z___ref(j + 1,
j), &c__1);
i__2 = *n - j;
sminu = sdot_(&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.f;
}
/* Compute the remaining r.h.s. */
temp = -rhs[j];
i__2 = *n - j;
saxpy_(&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;
scopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
xp[*n - 1] = rhs[*n] + 1.f;
rhs[*n] += -1.f;
splus = 0.f;
sminu = 0.f;
for (i__ = *n; i__ >= 1; --i__) {
temp = 1.f / 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 += (r__1 = xp[i__ - 1], dabs(r__1));
sminu += (r__1 = rhs[i__], dabs(r__1));
/* L30: */
}
if (splus > sminu) {
scopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Apply the permutations JPIV to the computed solution (RHS) */
i__1 = *n - 1;
slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
/* Compute the sum of squares */
slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
} else {
/* IJOB = 2, Compute approximate nullvector XM of Z */
sgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, &
info);
scopy_(n, &work[*n], &c__1, xm, &c__1);
/* Compute RHS */
i__1 = *n - 1;
slaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
temp = 1.f / sqrt(sdot_(n, xm, &c__1, xm, &c__1));
sscal_(n, &temp, xm, &c__1);
scopy_(n, xm, &c__1, xp, &c__1);
saxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
saxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
sgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
sgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
if (sasum_(n, xp, &c__1) > sasum_(n, &rhs[1], &c__1)) {
scopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Compute the sum of squares */
slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
}
return 0;
/* End of SLATDF */
} /* slatdf_ */
int sgesvx_(char *fact, char *trans, int *n, int *
nrhs, float *a, int *lda, float *af, int *ldaf, int *ipiv,
char *equed, float *r__, float *c__, float *b, int *ldb, float *x,
int *ldx, float *rcond, float *ferr, float *berr, float *work,
int *iwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2;
float r__1, r__2;
/* Local variables */
int i__, j;
float amax;
char norm[1];
extern int lsame_(char *, char *);
float rcmin, rcmax, anorm;
int equil;
float colcnd;
extern double slamch_(char *), slange_(char *, int *,
int *, float *, int *, float *);
int nofact;
extern int slaqge_(int *, int *, float *, int
*, float *, float *, float *, float *, float *, char *),
xerbla_(char *, int *), sgecon_(char *, int *,
float *, int *, float *, float *, float *, int *, int *);
float bignum;
int infequ;
int colequ;
extern int sgeequ_(int *, int *, float *, int
*, float *, float *, float *, float *, float *, int *), sgerfs_(
char *, int *, int *, float *, int *, float *, int *
, int *, float *, int *, float *, int *, float *, float *,
float *, int *, int *), sgetrf_(int *,
int *, float *, int *, int *, int *);
float rowcnd;
extern int slacpy_(char *, int *, int *, float *,
int *, float *, int *);
int notran;
extern double slantr_(char *, char *, char *, int *, int *,
float *, int *, float *);
extern int sgetrs_(char *, int *, int *, float *,
int *, int *, float *, int *, int *);
float smlnum;
int rowequ;
float rpvgrw;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGESVX uses the LU factorization to compute the solution to a float */
/* 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', float 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) REAL 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) REAL 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 SGETRF. 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 SGETRF; 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL */
/* 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) REAL 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) REAL 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) REAL 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 = slamch_("Safe minimum");
bignum = 1.f / 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.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = r__[j];
rcmin = MIN(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = r__[j];
rcmax = MAX(r__1,r__2);
/* L10: */
}
if (rcmin <= 0.f) {
*info = -11;
} else if (*n > 0) {
rowcnd = MAX(rcmin,smlnum) / MIN(rcmax,bignum);
} else {
rowcnd = 1.f;
}
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = c__[j];
rcmin = MIN(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = c__[j];
rcmax = MAX(r__1,r__2);
/* L20: */
}
if (rcmin <= 0.f) {
*info = -12;
} else if (*n > 0) {
colcnd = MAX(rcmin,smlnum) / MIN(rcmax,bignum);
} else {
colcnd = 1.f;
}
}
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_("SGESVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
sgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, &
amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
slaqge_(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. */
slacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
sgetrf_(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 = slantr_("M", "U", "N", info, info, &af[af_offset], ldaf,
&work[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = slange_("M", n, info, &a[a_offset], lda, &work[1]) / rpvgrw;
}
work[1] = rpvgrw;
*rcond = 0.f;
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 = slange_(norm, n, n, &a[a_offset], lda, &work[1]);
rpvgrw = slantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &work[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = slange_("M", n, n, &a[a_offset], lda, &work[1]) /
rpvgrw;
}
/* Compute the reciprocal of the condition number of A. */
sgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
info);
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
sgetrs_(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. */
sgerfs_(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: */
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
work[1] = rpvgrw;
return 0;
/* End of SGESVX */
} /* sgesvx_ */
/* Subroutine */ int serrge_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static real anrm, a[16] /* was [4][4] */, b[4];
static integer i__, j;
static real ccond, w[12], x[4], rcond;
static char c2[2];
static real r1[4], r2[4];
extern /* Subroutine */ int sgbtf2_(integer *, integer *, integer *,
integer *, real *, integer *, integer *, integer *), sgetf2_(
integer *, integer *, real *, integer *, integer *, integer *);
static real af[16] /* was [4][4] */;
static integer ip[4], iw[4];
extern /* Subroutine */ int alaesm_(char *, logical *, integer *),
sgbcon_(char *, integer *, integer *, integer *, real *, integer
*, integer *, real *, real *, real *, integer *, integer *), sgecon_(char *, integer *, real *, integer *, real *,
real *, real *, integer *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), sgbequ_(integer *, integer *, integer *,
integer *, real *, integer *, real *, real *, real *, real *,
real *, integer *), sgbrfs_(char *, integer *, integer *, integer
*, integer *, real *, integer *, real *, integer *, integer *,
real *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *), sgbtrf_(integer *, integer *,
integer *, integer *, real *, integer *, integer *, integer *),
sgeequ_(integer *, integer *, real *, integer *, real *, real *,
real *, real *, real *, integer *), sgerfs_(char *, integer *,
integer *, real *, integer *, real *, integer *, integer *, real *
, integer *, real *, integer *, real *, real *, real *, integer *,
integer *), sgetrf_(integer *, integer *, real *,
integer *, integer *, integer *), sgetri_(integer *, real *,
integer *, integer *, real *, integer *, integer *), sgbtrs_(char
*, integer *, integer *, integer *, integer *, real *, integer *,
integer *, real *, integer *, integer *), sgetrs_(char *,
integer *, integer *, real *, integer *, integer *, real *,
integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_ref(a_1,a_2) a[(a_2)*4 + a_1 - 5]
#define af_ref(a_1,a_2) af[(a_2)*4 + a_1 - 5]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
SERRGE tests the error exits for the REAL 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.
===================================================================== */
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_ref(i__, j) = 1.f / (real) (i__ + j);
af_ref(i__, j) = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
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.
SGETRF */
s_copy(srnamc_1.srnamt, "SGETRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgetrf_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetrf_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgetrf_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETF2 */
s_copy(srnamc_1.srnamt, "SGETF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgetf2_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetf2_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgetf2_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETRI */
s_copy(srnamc_1.srnamt, "SGETRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgetri_(&c_n1, a, &c__1, ip, w, &c__12, &info);
chkxer_("SGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgetri_(&c__2, a, &c__1, ip, w, &c__12, &info);
chkxer_("SGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETRS */
s_copy(srnamc_1.srnamt, "SGETRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGERFS */
s_copy(srnamc_1.srnamt, "SGERFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGECON */
s_copy(srnamc_1.srnamt, "SGECON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEEQU */
s_copy(srnamc_1.srnamt, "SGEEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &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.
SGBTRF */
s_copy(srnamc_1.srnamt, "SGBTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBTF2 */
s_copy(srnamc_1.srnamt, "SGBTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBTRS */
s_copy(srnamc_1.srnamt, "SGBTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBRFS */
s_copy(srnamc_1.srnamt, "SGBRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgbrfs_("/", &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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBCON */
s_copy(srnamc_1.srnamt, "SGBCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBEQU */
s_copy(srnamc_1.srnamt, "SGBEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &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 SERRGE */
} /* serrge_ */
/* Subroutine */ int serrge_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
real a[16] /* was [4][4] */, b[4], c__[4];
integer i__, j;
real r__[4], w[12], x[4];
char c2[2];
real r1[4], r2[4], af[16] /* was [4][4] */;
char eq[1];
integer ip[4], iw[4];
real err_bnds_c__[12] /* was [4][3] */;
integer n_err_bnds__;
real err_bnds_n__[12] /* was [4][3] */, berr;
integer info;
real anrm, ccond, rcond;
extern /* Subroutine */ int sgbtf2_(integer *, integer *, integer *,
integer *, real *, integer *, integer *, integer *), sgetf2_(
integer *, integer *, real *, integer *, integer *, integer *),
alaesm_(char *, logical *, integer *), sgbcon_(char *,
integer *, integer *, integer *, real *, integer *, integer *,
real *, real *, real *, integer *, integer *), sgecon_(
char *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *);
extern logical lsamen_(integer *, char *, char *);
real params[1];
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), sgbequ_(integer *, integer *, integer *,
integer *, real *, integer *, real *, real *, real *, real *,
real *, integer *), sgbrfs_(char *, integer *, integer *, integer
*, integer *, real *, integer *, real *, integer *, integer *,
real *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *), sgbtrf_(integer *, integer *,
integer *, integer *, real *, integer *, integer *, integer *),
sgeequ_(integer *, integer *, real *, integer *, real *, real *,
real *, real *, real *, integer *), sgerfs_(char *, integer *,
integer *, real *, integer *, real *, integer *, integer *, real *
, integer *, real *, integer *, real *, real *, real *, integer *,
integer *), sgetrf_(integer *, integer *, real *,
integer *, integer *, integer *), sgetri_(integer *, real *,
integer *, integer *, real *, integer *, integer *), sgbtrs_(char
*, integer *, integer *, integer *, integer *, real *, integer *,
integer *, real *, integer *, integer *), sgetrs_(char *,
integer *, integer *, real *, integer *, integer *, real *,
integer *, integer *), sgbequb_(integer *, integer *,
integer *, integer *, real *, integer *, real *, real *, real *,
real *, real *, integer *), sgeequb_(integer *, integer *, real *,
integer *, real *, real *, real *, real *, real *, integer *);
integer nparams;
extern /* Subroutine */ int sgbrfsx_(char *, char *, integer *, integer *,
integer *, integer *, real *, integer *, real *, integer *,
integer *, real *, real *, real *, integer *, real *, integer *,
real *, real *, integer *, real *, real *, integer *, real *,
real *, integer *, integer *), sgerfsx_(char *,
char *, integer *, integer *, real *, integer *, real *, integer *
, integer *, real *, real *, real *, integer *, real *, integer *,
real *, real *, integer *, real *, real *, integer *, real *,
real *, 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 */
/* ======= */
/* SERRGE tests the error exits for the REAL routines */
/* for general matrices. */
/* Note that this file is used only when the XBLAS are available, */
/* otherwise serrge.f defines this subroutine. */
/* 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.f / (real) (i__ + j);
af[i__ + (j << 2) - 5] = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
c__[j - 1] = 0.f;
r__[j - 1] = 0.f;
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. */
/* SGETRF */
s_copy(srnamc_1.srnamt, "SGETRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetrf_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetrf_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgetrf_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETF2 */
s_copy(srnamc_1.srnamt, "SGETF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetf2_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetf2_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgetf2_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETRI */
s_copy(srnamc_1.srnamt, "SGETRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetri_(&c_n1, a, &c__1, ip, w, &c__12, &info);
chkxer_("SGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgetri_(&c__2, a, &c__1, ip, w, &c__12, &info);
chkxer_("SGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETRS */
s_copy(srnamc_1.srnamt, "SGETRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGERFS */
s_copy(srnamc_1.srnamt, "SGERFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGERFSX */
n_err_bnds__ = 3;
nparams = 0;
s_copy(srnamc_1.srnamt, "SGERFSX", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgerfsx_("/", eq, &c__0, &c__0, a, &c__1, af, &c__1, ip, r__, c__, b,
&c__1, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
*(unsigned char *)eq = '/';
sgerfsx_("N", eq, &c__2, &c__1, a, &c__1, af, &c__2, ip, r__, c__, b,
&c__2, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
*(unsigned char *)eq = 'R';
sgerfsx_("N", eq, &c_n1, &c__0, a, &c__1, af, &c__1, ip, r__, c__, b,
&c__1, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgerfsx_("N", eq, &c__0, &c_n1, a, &c__1, af, &c__1, ip, r__, c__, b,
&c__1, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgerfsx_("N", eq, &c__2, &c__1, a, &c__1, af, &c__2, ip, r__, c__, b,
&c__2, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgerfsx_("N", eq, &c__2, &c__1, a, &c__2, af, &c__1, ip, r__, c__, b,
&c__2, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
*(unsigned char *)eq = 'C';
sgerfsx_("N", eq, &c__2, &c__1, a, &c__2, af, &c__2, ip, r__, c__, b,
&c__1, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
sgerfsx_("N", eq, &c__2, &c__1, a, &c__2, af, &c__2, ip, r__, c__, b,
&c__2, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGECON */
s_copy(srnamc_1.srnamt, "SGECON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEEQU */
s_copy(srnamc_1.srnamt, "SGEEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEEQUB */
s_copy(srnamc_1.srnamt, "SGEEQUB", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgeequb_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info)
;
chkxer_("SGEEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeequb_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info)
;
chkxer_("SGEEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeequb_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info)
;
chkxer_("SGEEQUB", &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. */
/* SGBTRF */
s_copy(srnamc_1.srnamt, "SGBTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBTF2 */
s_copy(srnamc_1.srnamt, "SGBTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBTRS */
s_copy(srnamc_1.srnamt, "SGBTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBRFS */
s_copy(srnamc_1.srnamt, "SGBRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbrfs_("/", &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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
sgbrfs_("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_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBRFSX */
n_err_bnds__ = 3;
nparams = 0;
s_copy(srnamc_1.srnamt, "SGBRFSX", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgbrfsx_("/", eq, &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
*(unsigned char *)eq = '/';
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__1, af, &c__2, ip,
r__, c__, b, &c__2, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
*(unsigned char *)eq = 'R';
sgbrfsx_("N", eq, &c_n1, &c__1, &c__1, &c__0, a, &c__1, af, &c__1, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
*(unsigned char *)eq = 'R';
sgbrfsx_("N", eq, &c__2, &c_n1, &c__1, &c__1, a, &c__3, af, &c__4, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
*(unsigned char *)eq = 'R';
sgbrfsx_("N", eq, &c__2, &c__1, &c_n1, &c__1, a, &c__3, af, &c__4, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbrfsx_("N", eq, &c__0, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__1, af, &c__2, ip,
r__, c__, b, &c__2, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip,
r__, c__, b, &c__2, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
*(unsigned char *)eq = 'C';
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__5, ip,
r__, c__, b, &c__1, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__5, ip,
r__, c__, b, &c__2, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBCON */
s_copy(srnamc_1.srnamt, "SGBCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBEQU */
s_copy(srnamc_1.srnamt, "SGBEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBEQUB */
s_copy(srnamc_1.srnamt, "SGBEQUB", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgbequb_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbequb_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbequb_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbequb_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbequb_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &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 SERRGE */
} /* serrge_ */
/* Subroutine */ int sgerfsx_(char *trans, char *equed, integer *n, integer *
nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv,
real *r__, real *c__, real *b, integer *ldb, real *x, integer *ldx,
real *rcond, real *berr, integer *n_err_bnds__, real *err_bnds_norm__,
real *err_bnds_comp__, integer *nparams, real *params, real *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, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real illrcond_thresh__, unstable_thresh__, err_lbnd__;
integer ref_type__;
extern integer ilatrans_(char *);
integer j;
real rcond_tmp__;
integer prec_type__, trans_type__;
extern doublereal sla_gercond__(char *, integer *, real *, integer *,
real *, integer *, integer *, integer *, real *, integer *, real *
, integer *, ftnlen);
real cwise_wrong__;
extern /* Subroutine */ int sla_gerfsx_extended__(integer *, integer *,
integer *, integer *, real *, integer *, real *, integer *,
integer *, logical *, real *, real *, integer *, real *, integer *
, real *, integer *, real *, real *, real *, real *, real *, real
*, real *, integer *, real *, real *, logical *, integer *);
char norm[1];
logical ignore_cwise__;
extern logical lsame_(char *, char *);
real anorm;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *), sgecon_(
char *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *);
logical colequ, notran, rowequ;
extern integer ilaprec_(char *);
integer ithresh, n_norms__;
real rthresh;
/* -- LAPACK routine (version 3.2.1) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- April 2009 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGERFSX improves the computed solution to a system of linear */
/* equations and provides error bounds and backward error estimates */
/* for the solution. In addition to normwise error bound, the code */
/* provides maximum componentwise error bound if possible. See */
/* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */
/* error bounds. */
/* The original system of linear equations may have been equilibrated */
/* before calling this routine, as described by arguments EQUED, R */
/* and C below. In this case, the solution and error bounds returned */
/* are for the original unequilibrated system. */
/* Arguments */
/* ========= */
/* Some optional parameters are bundled in the PARAMS array. These */
/* settings determine how refinement is performed, but often the */
/* defaults are acceptable. If the defaults are acceptable, users */
/* can pass NPARAMS = 0 which prevents the source code from accessing */
/* the PARAMS argument. */
/* 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 (Conjugate transpose = Transpose) */
/* EQUED (input) CHARACTER*1 */
/* Specifies the form of equilibration that was done to A */
/* before calling this routine. This is needed to compute */
/* the solution and error bounds correctly. */
/* = 'N': No equilibration */
/* = '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). */
/* The right hand side B has been changed accordingly. */
/* 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 B and X. NRHS >= 0. */
/* A (input) REAL array, dimension (LDA,N) */
/* The original N-by-N matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) REAL array, dimension (LDAF,N) */
/* The factors L and U from the factorization A = P*L*U */
/* as computed by SGETRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from SGETRF; for 1<=i<=N, row i of the */
/* matrix was interchanged with row IPIV(i). */
/* R (input or output) REAL 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. */
/* If R is output, each element of R is a power of the radix. */
/* If R is input, each element of R should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* C (input or output) REAL 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. */
/* If C is output, each element of C is a power of the radix. */
/* If C is input, each element of C should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* B (input) REAL array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input/output) REAL array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by SGETRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) REAL */
/* Reciprocal scaled condition number. This is an estimate of the */
/* reciprocal Skeel condition number of the matrix A after */
/* equilibration (if done). If this is less than the machine */
/* precision (in particular, if it is zero), the matrix is singular */
/* to working precision. Note that the error may still be small even */
/* if this number is very small and the matrix appears ill- */
/* conditioned. */
/* BERR (output) REAL array, dimension (NRHS) */
/* Componentwise relative backward error. This is 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). */
/* N_ERR_BNDS (input) INTEGER */
/* Number of error bounds to return for each right hand side */
/* and each type (normwise or componentwise). See ERR_BNDS_NORM and */
/* ERR_BNDS_COMP below. */
/* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* normwise relative error, which is defined as follows: */
/* Normwise relative error in the ith solution vector: */
/* max_j (abs(XTRUE(j,i) - X(j,i))) */
/* ------------------------------ */
/* max_j abs(X(j,i)) */
/* The array is indexed by the type of error information as described */
/* below. There currently are up to three pieces of information */
/* returned. */
/* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_NORM(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated normwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*A, where S scales each row by a power of the */
/* radix so all absolute row sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* componentwise relative error, which is defined as follows: */
/* Componentwise relative error in the ith solution vector: */
/* abs(XTRUE(j,i) - X(j,i)) */
/* max_j ---------------------- */
/* abs(X(j,i)) */
/* The array is indexed by the right-hand side i (on which the */
/* componentwise relative error depends), and the type of error */
/* information as described below. There currently are up to three */
/* pieces of information returned for each right-hand side. If */
/* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */
/* the first (:,N_ERR_BNDS) entries are returned. */
/* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_COMP(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated componentwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*(A*diag(x)), where x is the solution for the */
/* current right-hand side and S scales each row of */
/* A*diag(x) by a power of the radix so all absolute row */
/* sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* NPARAMS (input) INTEGER */
/* Specifies the number of parameters set in PARAMS. If .LE. 0, the */
/* PARAMS array is never referenced and default values are used. */
/* PARAMS (input / output) REAL array, dimension NPARAMS */
/* Specifies algorithm parameters. If an entry is .LT. 0.0, then */
/* that entry will be filled with default value used for that */
/* parameter. Only positions up to NPARAMS are accessed; defaults */
/* are used for higher-numbered parameters. */
/* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
/* refinement or not. */
/* Default: 1.0 */
/* = 0.0 : No refinement is performed, and no error bounds are */
/* computed. */
/* = 1.0 : Use the double-precision refinement algorithm, */
/* possibly with doubled-single computations if the */
/* compilation environment does not support DOUBLE */
/* PRECISION. */
/* (other values are reserved for future use) */
/* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
/* computations allowed for refinement. */
/* Default: 10 */
/* Aggressive: Set to 100 to permit convergence using approximate */
/* factorizations or factorizations other than LU. If */
/* the factorization uses a technique other than */
/* Gaussian elimination, the guarantees in */
/* err_bnds_norm and err_bnds_comp may no longer be */
/* trustworthy. */
/* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
/* will attempt to find a solution with small componentwise */
/* relative error in the double-precision algorithm. Positive */
/* is true, 0.0 is false. */
/* Default: 1.0 (attempt componentwise convergence) */
/* WORK (workspace) REAL array, dimension (4*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: Successful exit. The solution to every right-hand side is */
/* guaranteed. */
/* < 0: If INFO = -i, the i-th argument had an illegal value */
/* > 0 and <= N: U(INFO,INFO) 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+J: The solution corresponding to the Jth right-hand side is */
/* not guaranteed. The solutions corresponding to other right- */
/* hand sides K with K > J may not be guaranteed as well, but */
/* only the first such right-hand side is reported. If a small */
/* componentwise error is not requested (PARAMS(3) = 0.0) then */
/* the Jth right-hand side is the first with a normwise error */
/* bound that is not guaranteed (the smallest J such */
/* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
/* the Jth right-hand side is the first with either a normwise or */
/* componentwise error bound that is not guaranteed (the smallest */
/* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
/* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
/* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
/* about all of the right-hand sides check ERR_BNDS_NORM or */
/* ERR_BNDS_COMP. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Check the input parameters. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
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;
--berr;
--params;
--work;
--iwork;
/* Function Body */
*info = 0;
trans_type__ = ilatrans_(trans);
ref_type__ = 1;
if (*nparams >= 1) {
if (params[1] < 0.f) {
params[1] = 1.f;
} else {
ref_type__ = params[1];
}
}
/* Set default parameters. */
illrcond_thresh__ = (real) (*n) * slamch_("Epsilon");
ithresh = 10;
rthresh = .5f;
unstable_thresh__ = .25f;
ignore_cwise__ = FALSE_;
if (*nparams >= 2) {
if (params[2] < 0.f) {
params[2] = (real) ithresh;
} else {
ithresh = (integer) params[2];
}
}
if (*nparams >= 3) {
if (params[3] < 0.f) {
if (ignore_cwise__) {
params[3] = 0.f;
} else {
params[3] = 1.f;
}
} else {
ignore_cwise__ = params[3] == 0.f;
}
}
if (ref_type__ == 0 || *n_err_bnds__ == 0) {
n_norms__ = 0;
} else if (ignore_cwise__) {
n_norms__ = 1;
} else {
n_norms__ = 2;
}
notran = lsame_(trans, "N");
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
/* Test input parameters. */
if (trans_type__ == -1) {
*info = -1;
} else if (! rowequ && ! colequ && ! lsame_(equed, "N")) {
*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 (*ldb < max(1,*n)) {
*info = -13;
} else if (*ldx < max(1,*n)) {
*info = -15;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGERFSX", &i__1);
return 0;
}
/* Quick return if possible. */
if (*n == 0 || *nrhs == 0) {
*rcond = 1.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 0.f;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
} else if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.f;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.f;
} else if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.f;
}
}
return 0;
}
/* Default to failure. */
*rcond = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
berr[j] = 1.f;
if (*n_err_bnds__ >= 1) {
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
} else if (*n_err_bnds__ >= 2) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
} else if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.f;
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.f;
}
}
/* Compute the norm of A and the reciprocal of the condition */
/* number of A. */
if (notran) {
*(unsigned char *)norm = 'I';
} else {
*(unsigned char *)norm = '1';
}
anorm = slange_(norm, n, n, &a[a_offset], lda, &work[1]);
sgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
info);
/* Perform refinement on each right-hand side */
if (ref_type__ != 0) {
prec_type__ = ilaprec_("D");
if (notran) {
sla_gerfsx_extended__(&prec_type__, &trans_type__, n, nrhs, &a[
a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &colequ, &
c__[1], &b[b_offset], ldb, &x[x_offset], ldx, &berr[1], &
n_norms__, &err_bnds_norm__[err_bnds_norm_offset], &
err_bnds_comp__[err_bnds_comp_offset], &work[*n + 1], &
work[1], &work[(*n << 1) + 1], &work[1], rcond, &ithresh,
&rthresh, &unstable_thresh__, &ignore_cwise__, info);
} else {
sla_gerfsx_extended__(&prec_type__, &trans_type__, n, nrhs, &a[
a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &rowequ, &
r__[1], &b[b_offset], ldb, &x[x_offset], ldx, &berr[1], &
n_norms__, &err_bnds_norm__[err_bnds_norm_offset], &
err_bnds_comp__[err_bnds_comp_offset], &work[*n + 1], &
work[1], &work[(*n << 1) + 1], &work[1], rcond, &ithresh,
&rthresh, &unstable_thresh__, &ignore_cwise__, info);
}
}
/* Computing MAX */
r__1 = 10.f, r__2 = sqrt((real) (*n));
err_lbnd__ = dmax(r__1,r__2) * slamch_("Epsilon");
if (*n_err_bnds__ >= 1 && n_norms__ >= 1) {
/* Compute scaled normwise condition number cond(A*C). */
if (colequ && notran) {
rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &c_n1, &c__[1], info, &work[1]
, &iwork[1], (ftnlen)1);
} else if (rowequ && ! notran) {
rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &c_n1, &r__[1], info, &work[1]
, &iwork[1], (ftnlen)1);
} else {
rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &c__0, &r__[1], info, &work[1]
, &iwork[1], (ftnlen)1);
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1
<< 1)] > 1.f) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.f;
err_bnds_norm__[j + err_bnds_norm_dim1] = 0.f;
if (*info <= *n) {
*info = *n + j;
}
} else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] <
err_lbnd__) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__;
err_bnds_norm__[j + err_bnds_norm_dim1] = 1.f;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__;
}
}
}
if (*n_err_bnds__ >= 1 && n_norms__ >= 2) {
/* Compute componentwise condition number cond(A*diag(Y(:,J))) for */
/* each right-hand side using the current solution as an estimate of */
/* the true solution. If the componentwise error estimate is too */
/* large, then the solution is a lousy estimate of truth and the */
/* estimated RCOND may be too optimistic. To avoid misleading users, */
/* the inverse condition number is set to 0.0 when the estimated */
/* cwise error is at least CWISE_WRONG. */
cwise_wrong__ = sqrt(slamch_("Epsilon"));
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
cwise_wrong__) {
rcond_tmp__ = sla_gercond__(trans, n, &a[a_offset], lda, &af[
af_offset], ldaf, &ipiv[1], &c__1, &x[j * x_dim1 + 1],
info, &work[1], &iwork[1], (ftnlen)1);
} else {
rcond_tmp__ = 0.f;
}
/* Cap the error at 1.0. */
if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1
<< 1)] > 1.f) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
}
/* Threshold the error (see LAWN). */
if (rcond_tmp__ < illrcond_thresh__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.f;
err_bnds_comp__[j + err_bnds_comp_dim1] = 0.f;
if (params[3] == 1.f && *info < *n + j) {
*info = *n + j;
}
} else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
err_lbnd__) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__;
err_bnds_comp__[j + err_bnds_comp_dim1] = 1.f;
}
/* Save the condition number. */
if (*n_err_bnds__ >= 3) {
err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__;
}
}
}
return 0;
/* End of SGERFSX */
} /* sgerfsx_ */
/* Subroutine */
int slatdf_(integer *ijob, integer *n, real *z__, integer * ldz, real *rhs, real *rdsum, real *rdscal, integer *ipiv, integer * jpiv)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
real bm, bp, xm[8], xp[8];
integer info;
real temp;
extern real sdot_(integer *, real *, integer *, real *, integer *);
real work[32];
extern /* Subroutine */
int sscal_(integer *, real *, real *, integer *);
real pmone;
extern real sasum_(integer *, real *, integer *);
real sminu;
integer iwork[8];
extern /* Subroutine */
int scopy_(integer *, real *, integer *, real *, integer *), saxpy_(integer *, real *, real *, integer *, real *, integer *);
real splus;
extern /* Subroutine */
int sgesc2_(integer *, real *, integer *, real *, integer *, integer *, real *), sgecon_(char *, integer *, real *, integer *, real *, real *, real *, integer *, integer *), slassq_(integer *, real *, integer *, real *, real *), slaswp_( integer *, real *, integer *, integer *, integer *, integer *, integer *);
/* -- LAPACK auxiliary routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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 */
i__1 = *n - 1;
slaswp_(&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.f;
i__1 = *n - 1;
for (j = 1;
j <= i__1;
++j)
{
bp = rhs[j] + 1.f;
bm = rhs[j] - 1.f;
splus = 1.f;
/* 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 += sdot_(&i__2, &z__[j + 1 + j * z_dim1], &c__1, &z__[j + 1 + j * z_dim1], &c__1);
i__2 = *n - j;
sminu = sdot_(&i__2, &z__[j + 1 + j * z_dim1], &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.f;
}
/* Compute the remaining r.h.s. */
temp = -rhs[j];
i__2 = *n - j;
saxpy_(&i__2, &temp, &z__[j + 1 + j * z_dim1], &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;
scopy_(&i__1, &rhs[1], &c__1, xp, &c__1);
xp[*n - 1] = rhs[*n] + 1.f;
rhs[*n] += -1.f;
splus = 0.f;
sminu = 0.f;
for (i__ = *n;
i__ >= 1;
--i__)
{
temp = 1.f / z__[i__ + i__ * z_dim1];
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__[i__ + k * z_dim1] * temp);
rhs[i__] -= rhs[k] * (z__[i__ + k * z_dim1] * temp);
/* L20: */
}
splus += (r__1 = xp[i__ - 1], abs(r__1));
sminu += (r__1 = rhs[i__], abs(r__1));
/* L30: */
}
if (splus > sminu)
{
scopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Apply the permutations JPIV to the computed solution (RHS) */
i__1 = *n - 1;
slaswp_(&c__1, &rhs[1], ldz, &c__1, &i__1, &jpiv[1], &c_n1);
/* Compute the sum of squares */
slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
}
else
{
/* IJOB = 2, Compute approximate nullvector XM of Z */
sgecon_("I", n, &z__[z_offset], ldz, &c_b23, &temp, work, iwork, & info);
scopy_(n, &work[*n], &c__1, xm, &c__1);
/* Compute RHS */
i__1 = *n - 1;
slaswp_(&c__1, xm, ldz, &c__1, &i__1, &ipiv[1], &c_n1);
temp = 1.f / sqrt(sdot_(n, xm, &c__1, xm, &c__1));
sscal_(n, &temp, xm, &c__1);
scopy_(n, xm, &c__1, xp, &c__1);
saxpy_(n, &c_b23, &rhs[1], &c__1, xp, &c__1);
saxpy_(n, &c_b37, xm, &c__1, &rhs[1], &c__1);
sgesc2_(n, &z__[z_offset], ldz, &rhs[1], &ipiv[1], &jpiv[1], &temp);
sgesc2_(n, &z__[z_offset], ldz, xp, &ipiv[1], &jpiv[1], &temp);
if (sasum_(n, xp, &c__1) > sasum_(n, &rhs[1], &c__1))
{
scopy_(n, xp, &c__1, &rhs[1], &c__1);
}
/* Compute the sum of squares */
slassq_(n, &rhs[1], &c__1, rdscal, rdsum);
}
return 0;
/* End of SLATDF */
}
/* Subroutine */ int sgesvx_(char *fact, char *trans, integer *n, integer *
nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv,
char *equed, real *r__, real *c__, real *b, integer *ldb, real *x,
integer *ldx, real *rcond, real *ferr, real *berr, real *work,
integer *iwork, integer *info)
{
/* -- LAPACK driver 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
=======
SGESVX 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) REAL 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) REAL 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 SGETRF. 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 SGETRF; 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL
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) REAL 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) REAL 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) REAL 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.
=====================================================================
Parameter adjustments */
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2;
real r__1, r__2;
/* Local variables */
static real amax;
static char norm[1];
static integer i__, j;
extern logical lsame_(char *, char *);
static real rcmin, rcmax, anorm;
static logical equil;
static real colcnd;
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
static logical nofact;
extern /* Subroutine */ int slaqge_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, real *, char *),
xerbla_(char *, integer *), sgecon_(char *, integer *,
real *, integer *, real *, real *, real *, integer *, integer *);
static real bignum;
static integer infequ;
static logical colequ;
extern /* Subroutine */ int sgeequ_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, real *, integer *), sgerfs_(
char *, integer *, integer *, real *, integer *, real *, integer *
, integer *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *), sgetrf_(integer *,
integer *, real *, integer *, integer *, integer *);
static real rowcnd;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *);
static logical notran;
extern doublereal slantr_(char *, char *, char *, integer *, integer *,
real *, integer *, real *);
extern /* Subroutine */ int sgetrs_(char *, integer *, integer *, real *,
integer *, integer *, real *, integer *, integer *);
static real smlnum;
static logical rowequ;
static real rpvgrw;
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1 * 1;
af -= af_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
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 = slamch_("Safe minimum");
bignum = 1.f / 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.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = r__[j];
rcmin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = r__[j];
rcmax = dmax(r__1,r__2);
/* L10: */
}
if (rcmin <= 0.f) {
*info = -11;
} else if (*n > 0) {
rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
} else {
rowcnd = 1.f;
}
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = c__[j];
rcmin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = c__[j];
rcmax = dmax(r__1,r__2);
/* L20: */
}
if (rcmin <= 0.f) {
*info = -12;
} else if (*n > 0) {
colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
} else {
colcnd = 1.f;
}
}
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_("SGESVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
sgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, &
amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
slaqge_(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_ref(i__, j) = r__[i__] * b_ref(i__, j);
/* 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_ref(i__, j) = c__[i__] * b_ref(i__, j);
/* L50: */
}
/* L60: */
}
}
if (nofact || equil) {
/* Compute the LU factorization of A. */
slacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
sgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info != 0) {
if (*info > 0) {
/* Compute the reciprocal pivot growth factor of the
leading rank-deficient INFO columns of A. */
rpvgrw = slantr_("M", "U", "N", info, info, &af[af_offset],
ldaf, &work[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = slange_("M", n, info, &a[a_offset], lda, &work[1]
) / rpvgrw;
}
work[1] = rpvgrw;
*rcond = 0.f;
}
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 = slange_(norm, n, n, &a[a_offset], lda, &work[1]);
rpvgrw = slantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &work[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = slange_("M", n, n, &a[a_offset], lda, &work[1]) /
rpvgrw;
}
/* Compute the reciprocal of the condition number of A. */
sgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
sgetrs_(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. */
sgerfs_(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_ref(i__, j) = c__[i__] * x_ref(i__, j);
/* 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_ref(i__, j) = r__[i__] * x_ref(i__, j);
/* L100: */
}
/* L110: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= rowcnd;
/* L120: */
}
}
work[1] = rpvgrw;
return 0;
/* End of SGESVX */
} /* sgesvx_ */
