void THLapack_(getrs)(char trans, int n, int nrhs, real *a, int lda, int *ipiv, real *b, int ldb, int *info)
{
#ifdef USE_LAPACK
#if defined(TH_REAL_IS_DOUBLE)
dgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
#else
sgetrs_(&trans, &n, &nrhs, a, &lda, ipiv, b, &ldb, info);
#endif
#else
THError("getrs : Lapack library not found in compile time\n");
#endif
}
DLLEXPORT MKL_INT s_lu_solve_factored(MKL_INT n, MKL_INT nrhs, float a[], MKL_INT ipiv[], float b[])
{
MKL_INT info = 0;
MKL_INT i;
for(i = 0; i < n; ++i ){
ipiv[i] += 1;
}
char trans ='N';
sgetrs_(&trans, &n, &nrhs, a, &n, ipiv, b, &n, &info);
for(i = 0; i < n; ++i ){
ipiv[i] -= 1;
}
return info;
}
DLLEXPORT int s_lu_solve_factored(int n, int nrhs, float a[], int ipiv[], float b[])
{
int info = 0;
int i;
for(i = 0; i < n; ++i ){
ipiv[i] += 1;
}
char trans ='N';
sgetrs_(&trans, &n, &nrhs, a, &n, ipiv, b, &n, &info);
for(i = 0; i < n; ++i ){
ipiv[i] -= 1;
}
return info;
}
DLLEXPORT MKL_INT s_lu_solve(MKL_INT n, MKL_INT nrhs, float a[], float b[])
{
float* clone = new float[n*n];
std::memcpy(clone, a, n*n*sizeof(float));
MKL_INT* ipiv = new MKL_INT[n];
MKL_INT info = 0;
sgetrf_(&n, &n, clone, &n, ipiv, &info);
if (info != 0){
delete[] ipiv;
delete[] clone;
return info;
}
char trans ='N';
sgetrs_(&trans, &n, &nrhs, clone, &n, ipiv, b, &n, &info);
delete[] ipiv;
delete[] clone;
return info;
}
DLLEXPORT int s_lu_solve(int n, int nrhs, float a[], float b[])
{
float* clone = new float[n*n];
memcpy(clone, a, n*n*sizeof(float));
int* ipiv = new int[n];
int info = 0;
sgetrf_(&n, &n, clone, &n, ipiv, &info);
if (info != 0){
delete[] ipiv;
delete[] clone;
return info;
}
char trans ='N';
sgetrs_(&trans, &n, &nrhs, clone, &n, ipiv, b, &n, &info);
delete[] ipiv;
delete[] clone;
return info;
}
/* ===================================================================== */
real sla_gercond_(char *trans, integer *n, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, integer *cmode, real *c__, integer * info, real *work, integer *iwork)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2;
real ret_val, r__1;
/* Local variables */
integer i__, j;
real tmp;
integer kase;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */
int slacn2_(integer *, real *, real *, integer *, real *, integer *, integer *), xerbla_(char *, integer *);
real ainvnm;
extern /* Subroutine */
int sgetrs_(char *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *);
logical notrans;
/* -- LAPACK computational 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 .. */
/* .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. 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;
--c__;
--work;
--iwork;
/* Function Body */
ret_val = 0.f;
*info = 0;
notrans = lsame_(trans, "N");
if (! notrans && ! lsame_(trans, "T") && ! lsame_( trans, "C"))
{
*info = -1;
}
else if (*n < 0)
{
*info = -2;
}
else if (*lda < max(1,*n))
{
*info = -4;
}
else if (*ldaf < max(1,*n))
{
*info = -6;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SLA_GERCOND", &i__1);
return ret_val;
}
if (*n == 0)
{
ret_val = 1.f;
return ret_val;
}
/* Compute the equilibration matrix R such that */
/* inv(R)*A*C has unit 1-norm. */
if (notrans)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
tmp = 0.f;
if (*cmode == 1)
{
i__2 = *n;
for (j = 1;
j <= i__2;
++j)
{
tmp += (r__1 = a[i__ + j * a_dim1] * c__[j], f2c_abs(r__1));
}
}
else if (*cmode == 0)
{
i__2 = *n;
for (j = 1;
j <= i__2;
++j)
{
tmp += (r__1 = a[i__ + j * a_dim1], f2c_abs(r__1));
}
}
else
{
i__2 = *n;
for (j = 1;
j <= i__2;
++j)
{
tmp += (r__1 = a[i__ + j * a_dim1] / c__[j], f2c_abs(r__1));
}
}
work[(*n << 1) + i__] = tmp;
}
}
else
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
tmp = 0.f;
if (*cmode == 1)
{
i__2 = *n;
for (j = 1;
j <= i__2;
++j)
{
tmp += (r__1 = a[j + i__ * a_dim1] * c__[j], f2c_abs(r__1));
}
}
else if (*cmode == 0)
{
i__2 = *n;
for (j = 1;
j <= i__2;
++j)
{
tmp += (r__1 = a[j + i__ * a_dim1], f2c_abs(r__1));
}
}
else
{
i__2 = *n;
for (j = 1;
j <= i__2;
++j)
{
tmp += (r__1 = a[j + i__ * a_dim1] / c__[j], f2c_abs(r__1));
}
}
work[(*n << 1) + i__] = tmp;
}
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.f;
kase = 0;
L10:
slacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
if (kase != 0)
{
if (kase == 2)
{
/* Multiply by R. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
work[i__] *= work[(*n << 1) + i__];
}
if (notrans)
{
sgetrs_("No transpose", n, &c__1, &af[af_offset], ldaf, &ipiv[ 1], &work[1], n, info);
}
else
{
sgetrs_("Transpose", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1], n, info);
}
/* Multiply by inv(C). */
if (*cmode == 1)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
work[i__] /= c__[i__];
}
}
else if (*cmode == -1)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
work[i__] *= c__[i__];
}
}
}
else
{
/* Multiply by inv(C**T). */
if (*cmode == 1)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
work[i__] /= c__[i__];
}
}
else if (*cmode == -1)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
work[i__] *= c__[i__];
}
}
if (notrans)
{
sgetrs_("Transpose", n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1], n, info);
}
else
{
sgetrs_("No transpose", n, &c__1, &af[af_offset], ldaf, &ipiv[ 1], &work[1], n, info);
}
/* Multiply by R. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
work[i__] *= work[(*n << 1) + i__];
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f)
{
ret_val = 1.f / ainvnm;
}
return ret_val;
}
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 dsgesv_(integer *n, integer *nrhs, doublereal *a,
integer *lda, integer *ipiv, doublereal *b, integer *ldb, doublereal *
x, integer *ldx, doublereal *work, real *swork, integer *iter,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, work_dim1, work_offset,
x_dim1, x_offset, i__1;
doublereal d__1;
/* Local variables */
integer i__;
doublereal cte, eps, anrm;
integer ptsa;
doublereal rnrm, xnrm;
integer ptsx;
integer iiter;
/* -- LAPACK PROTOTYPE driver routine (version 3.2) -- */
/* February 2007 */
/* Purpose */
/* ======= */
/* DSGESV computes 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. */
/* DSGESV first attempts to factorize the matrix in SINGLE PRECISION */
/* and use this factorization within an iterative refinement procedure */
/* to produce a solution with DOUBLE PRECISION normwise backward error */
/* quality (see below). If the approach fails the method switches to a */
/* DOUBLE PRECISION factorization and solve. */
/* The iterative refinement is not going to be a winning strategy if */
/* the ratio SINGLE PRECISION performance over DOUBLE PRECISION */
/* performance is too small. A reasonable strategy should take the */
/* number of right-hand sides and the size of the matrix into account. */
/* This might be done with a call to ILAENV in the future. Up to now, we */
/* always try iterative refinement. */
/* The iterative refinement process is stopped if */
/* ITER > ITERMAX */
/* or for all the RHS we have: */
/* RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX */
/* where */
/* o ITER is the number of the current iteration in the iterative */
/* refinement process */
/* o RNRM is the infinity-norm of the residual */
/* o XNRM is the infinity-norm of the solution */
/* o ANRM is the infinity-operator-norm of the matrix A */
/* o EPS is the machine epsilon returned by DLAMCH('Epsilon') */
/* The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 */
/* respectively. */
/* Arguments */
/* ========= */
/* 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 matrix B. NRHS >= 0. */
/* A (input or input/ouptut) DOUBLE PRECISION array, */
/* dimension (LDA,N) */
/* On entry, the N-by-N coefficient matrix A. */
/* On exit, if iterative refinement has been successfully used */
/* (INFO.EQ.0 and ITER.GE.0, see description below), then A is */
/* unchanged, if double precision factorization has been used */
/* (INFO.EQ.0 and ITER.LT.0, see description below), then the */
/* array A contains the factors L and U from the factorization */
/* A = P*L*U; the unit diagonal elements of L are not stored. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (output) INTEGER array, dimension (N) */
/* The pivot indices that define the permutation matrix P; */
/* row i of the matrix was interchanged with row IPIV(i). */
/* Corresponds either to the single precision factorization */
/* (if INFO.EQ.0 and ITER.GE.0) or the double precision */
/* factorization (if INFO.EQ.0 and ITER.LT.0). */
/* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/* The N-by-NRHS right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* If INFO = 0, the N-by-NRHS solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N*NRHS) */
/* This array is used to hold the residual vectors. */
/* SWORK (workspace) REAL array, dimension (N*(N+NRHS)) */
/* This array is used to use the single precision matrix and the */
/* right-hand sides or solutions in single precision. */
/* ITER (output) INTEGER */
/* < 0: iterative refinement has failed, double precision */
/* factorization has been performed */
/* -1 : the routine fell back to full precision for */
/* implementation- or machine-specific reasons */
/* -2 : narrowing the precision induced an overflow, */
/* the routine fell back to full precision */
/* -3 : failure of SGETRF */
/* -31: stop the iterative refinement after the 30th */
/* iterations */
/* > 0: iterative refinement has been sucessfully used. */
/* Returns the number of iterations */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is */
/* exactly zero. The factorization has been completed, */
/* but the factor U is exactly singular, so the solution */
/* could not be computed. */
/* ========= */
/* Parameter adjustments */
work_dim1 = *n;
work_offset = 1 + work_dim1;
work -= work_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--swork;
/* Function Body */
*info = 0;
*iter = 0;
/* Test the input parameters. */
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldx < max(1,*n)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSGESV", &i__1);
return 0;
}
/* Quick return if (N.EQ.0). */
if (*n == 0) {
return 0;
}
/* Skip single precision iterative refinement if a priori slower */
/* than double precision factorization. */
if (FALSE_) {
*iter = -1;
goto L40;
}
/* Compute some constants. */
anrm = dlange_("I", n, n, &a[a_offset], lda, &work[work_offset]);
eps = dlamch_("Epsilon");
cte = anrm * eps * sqrt((doublereal) (*n)) * 1.;
/* Set the indices PTSA, PTSX for referencing SA and SX in SWORK. */
ptsa = 1;
ptsx = ptsa + *n * *n;
/* Convert B from double precision to single precision and store the */
/* result in SX. */
dlag2s_(n, nrhs, &b[b_offset], ldb, &swork[ptsx], n, info);
if (*info != 0) {
*iter = -2;
goto L40;
}
/* Convert A from double precision to single precision and store the */
/* result in SA. */
dlag2s_(n, n, &a[a_offset], lda, &swork[ptsa], n, info);
if (*info != 0) {
*iter = -2;
goto L40;
}
/* Compute the LU factorization of SA. */
sgetrf_(n, n, &swork[ptsa], n, &ipiv[1], info);
if (*info != 0) {
*iter = -3;
goto L40;
}
/* Solve the system SA*SX = SB. */
sgetrs_("No transpose", n, nrhs, &swork[ptsa], n, &ipiv[1], &swork[ptsx],
n, info);
/* Convert SX back to double precision */
slag2d_(n, nrhs, &swork[ptsx], n, &x[x_offset], ldx, info);
/* Compute R = B - AX (R is WORK). */
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
dgemm_("No Transpose", "No Transpose", n, nrhs, n, &c_b10, &a[a_offset],
lda, &x[x_offset], ldx, &c_b11, &work[work_offset], n);
/* Check whether the NRHS normwise backward errors satisfy the */
/* stopping criterion. If yes, set ITER=0 and return. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ *
x_dim1], abs(d__1));
rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1) +
i__ * work_dim1], abs(d__1));
if (rnrm > xnrm * cte) {
goto L10;
}
}
/* If we are here, the NRHS normwise backward errors satisfy the */
/* stopping criterion. We are good to exit. */
*iter = 0;
return 0;
L10:
for (iiter = 1; iiter <= 30; ++iiter) {
/* Convert R (in WORK) from double precision to single precision */
/* and store the result in SX. */
dlag2s_(n, nrhs, &work[work_offset], n, &swork[ptsx], n, info);
if (*info != 0) {
*iter = -2;
goto L40;
}
/* Solve the system SA*SX = SR. */
sgetrs_("No transpose", n, nrhs, &swork[ptsa], n, &ipiv[1], &swork[
ptsx], n, info);
/* Convert SX back to double precision and update the current */
/* iterate. */
slag2d_(n, nrhs, &swork[ptsx], n, &work[work_offset], n, info);
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
daxpy_(n, &c_b11, &work[i__ * work_dim1 + 1], &c__1, &x[i__ *
x_dim1 + 1], &c__1);
}
/* Compute R = B - AX (R is WORK). */
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
dgemm_("No Transpose", "No Transpose", n, nrhs, n, &c_b10, &a[
a_offset], lda, &x[x_offset], ldx, &c_b11, &work[work_offset],
n);
/* Check whether the NRHS normwise backward errors satisfy the */
/* stopping criterion. If yes, set ITER=IITER>0 and return. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ *
x_dim1], abs(d__1));
rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1)
+ i__ * work_dim1], abs(d__1));
if (rnrm > xnrm * cte) {
goto L20;
}
}
/* If we are here, the NRHS normwise backward errors satisfy the */
/* stopping criterion, we are good to exit. */
*iter = iiter;
return 0;
L20:
;
}
/* If we are at this place of the code, this is because we have */
/* performed ITER=ITERMAX iterations and never satisified the */
/* stopping criterion, set up the ITER flag accordingly and follow up */
/* on double precision routine. */
*iter = -31;
L40:
/* Single-precision iterative refinement failed to converge to a */
/* satisfactory solution, so we resort to double precision. */
dgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
if (*info != 0) {
return 0;
}
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
dgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &x[x_offset]
, ldx, info);
return 0;
/* End of DSGESV. */
} /* dsgesv_ */
/* Subroutine */ int sgerfs_(char *trans, integer *n, integer *nrhs, real *a,
integer *lda, real *af, integer *ldaf, integer *ipiv, real *b,
integer *ldb, real *x, integer *ldx, real *ferr, real *berr, real *
work, integer *iwork, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
SGERFS improves the computed solution to a system of linear
equations and provides error bounds and backward error estimates for
the solution.
Arguments
=========
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)
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).
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).
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) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Internal Parameters
===================
ITMAX is the maximum number of steps of iterative refinement.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static real c_b15 = -1.f;
static real c_b17 = 1.f;
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3;
real r__1, r__2, r__3;
/* Local variables */
static integer kase;
static real safe1, safe2;
static integer i__, j, k;
static real s;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
static integer count;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), saxpy_(integer *, real *, real *, integer *, real *,
integer *);
static real xk;
extern doublereal slamch_(char *);
static integer nz;
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), slacon_(
integer *, real *, real *, integer *, real *, integer *);
static logical notran;
extern /* Subroutine */ int sgetrs_(char *, integer *, integer *, real *,
integer *, integer *, real *, integer *, integer *);
static char transt[1];
static real lstres, eps;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#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;
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;
notran = lsame_(trans, "N");
if (! notran && ! lsame_(trans, "T") && ! lsame_(
trans, "C")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldaf < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGERFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)transt = 'T';
} else {
*(unsigned char *)transt = 'N';
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied.
Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
scopy_(n, &b_ref(1, j), &c__1, &work[*n + 1], &c__1);
sgemv_(trans, n, n, &c_b15, &a[a_offset], lda, &x_ref(1, j), &c__1, &
c_b17, &work[*n + 1], &c__1);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th components of the
numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] = (r__1 = b_ref(i__, j), dabs(r__1));
/* L30: */
}
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
xk = (r__1 = x_ref(k, j), dabs(r__1));
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
work[i__] += (r__1 = a_ref(i__, k), dabs(r__1)) * xk;
/* L40: */
}
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
s += (r__1 = a_ref(i__, k), dabs(r__1)) * (r__2 = x_ref(
i__, j), dabs(r__2));
/* L60: */
}
work[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (work[i__] > safe2) {
/* Computing MAX */
r__2 = s, r__3 = (r__1 = work[*n + i__], dabs(r__1)) / work[
i__];
s = dmax(r__2,r__3);
} else {
/* Computing MAX */
r__2 = s, r__3 = ((r__1 = work[*n + i__], dabs(r__1)) + safe1)
/ (work[i__] + safe1);
s = dmax(r__2,r__3);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
sgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[*n
+ 1], n, info);
saxpy_(n, &c_b17, &work[*n + 1], &c__1, &x_ref(1, j), &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula
norm(X - XTRUE) / norm(X) .le. FERR =
norm( abs(inv(op(A)))*
( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(op(A)) is the inverse of op(A)
abs(Z) is the componentwise absolute value of the matrix or
vector Z
NZ is the maximum number of nonzeros in any row of A, plus 1
EPS is machine epsilon
The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(op(A))*abs(X) + abs(B) is less than SAFE2.
Use SLACON to estimate the infinity-norm of the matrix
inv(op(A)) * diag(W),
where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (work[i__] > safe2) {
work[i__] = (r__1 = work[*n + i__], dabs(r__1)) + nz * eps *
work[i__];
} else {
work[i__] = (r__1 = work[*n + i__], dabs(r__1)) + nz * eps *
work[i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
slacon_(n, &work[(*n << 1) + 1], &work[*n + 1], &iwork[1], &ferr[j], &
kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**T). */
sgetrs_(transt, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
work[*n + 1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
/* L110: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] = work[i__] * work[*n + i__];
/* L120: */
}
sgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
work[*n + 1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
r__2 = lstres, r__3 = (r__1 = x_ref(i__, j), dabs(r__1));
lstres = dmax(r__2,r__3);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of SGERFS */
} /* sgerfs_ */
/* 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_ */
inline void getrs( const char& transa, const int& n, const int& nrhs, const float da[], const int& lda, int ipivot[], float db[], const int& ldb, int& info)
{
sgetrs_(transa,n,nrhs,da,lda,ipivot,db,ldb,info);
}
/* Subroutine */ int sla_gerfsx_extended__(integer *prec_type__, integer *
trans_type__, integer *n, integer *nrhs, real *a, integer *lda, real *
af, integer *ldaf, integer *ipiv, logical *colequ, real *c__, real *b,
integer *ldb, real *y, integer *ldy, real *berr_out__, integer *
n_norms__, real *err_bnds_norm__, real *err_bnds_comp__, real *res,
real *ayb, real *dy, real *y_tail__, real *rcond, integer *ithresh,
real *rthresh, real *dz_ub__, logical *ignore_cwise__, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1,
y_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3;
real r__1, r__2;
char ch__1[1];
/* Local variables */
real dxratmax, dzratmax;
integer i__, j;
logical incr_prec__;
real prev_dz_z__, yk, final_dx_x__, final_dz_z__;
real prevnormdx;
integer cnt;
real dyk, eps, incr_thresh__, dx_x__, dz_z__, ymin;
integer y_prec_state__;
real dxrat, dzrat;
char trans[1];
real normx, normy;
real normdx;
real hugeval;
integer x_state__, z_state__;
/* -- 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. -- */
/* Purpose */
/* ======= */
/* SLA_GERFSX_EXTENDED improves the computed solution to a system of */
/* linear equations by performing extra-precise iterative refinement */
/* and provides error bounds and backward error estimates for the solution. */
/* This subroutine is called by SGERFSX to perform iterative refinement. */
/* 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. Note that this */
/* subroutine is only resonsible for setting the second fields of */
/* ERR_BNDS_NORM and ERR_BNDS_COMP. */
/* Arguments */
/* ========= */
/* PREC_TYPE (input) INTEGER */
/* Specifies the intermediate precision to be used in refinement. */
/* The value is defined by ILAPREC(P) where P is a CHARACTER and */
/* P = 'S': Single */
/* = 'D': Double */
/* = 'I': Indigenous */
/* = 'X', 'E': Extra */
/* TRANS_TYPE (input) INTEGER */
/* Specifies the transposition operation on A. */
/* The value is defined by ILATRANS(T) where T is a CHARACTER and */
/* T = 'N': No transpose */
/* = 'T': Transpose */
/* = 'C': Conjugate 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 */
/* matrix B. */
/* A (input) REAL array, dimension (LDA,N) */
/* On entry, the 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 the factorization A = P*L*U */
/* as computed by SGETRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* COLEQU (input) LOGICAL */
/* If .TRUE. then column equilibration was done to A before calling */
/* this routine. This is needed to compute the solution and error */
/* bounds correctly. */
/* C (input) REAL array, dimension (N) */
/* The column scale factors for A. If COLEQU = .FALSE., C */
/* is not accessed. 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). */
/* Y (input/output) REAL array, dimension (LDY,NRHS) */
/* On entry, the solution matrix X, as computed by SGETRS. */
/* On exit, the improved solution matrix Y. */
/* LDY (input) INTEGER */
/* The leading dimension of the array Y. LDY >= max(1,N). */
/* BERR_OUT (output) REAL array, dimension (NRHS) */
/* On exit, BERR_OUT(j) contains the componentwise relative backward */
/* error for right-hand-side j from the formula */
/* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. This is computed by SLA_LIN_BERR. */
/* N_NORMS (input) INTEGER */
/* Determines which error bounds to return (see ERR_BNDS_NORM */
/* and ERR_BNDS_COMP). */
/* If N_NORMS >= 1 return normwise error bounds. */
/* If N_NORMS >= 2 return componentwise error bounds. */
/* ERR_BNDS_NORM (input/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. */
/* This subroutine is only responsible for setting the second field */
/* above. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (input/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. */
/* This subroutine is only responsible for setting the second field */
/* above. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* RES (input) REAL array, dimension (N) */
/* Workspace to hold the intermediate residual. */
/* AYB (input) REAL array, dimension (N) */
/* Workspace. This can be the same workspace passed for Y_TAIL. */
/* DY (input) REAL array, dimension (N) */
/* Workspace to hold the intermediate solution. */
/* Y_TAIL (input) REAL array, dimension (N) */
/* Workspace to hold the trailing bits of the intermediate solution. */
/* RCOND (input) 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. */
/* ITHRESH (input) INTEGER */
/* The maximum number of residual computations allowed for */
/* refinement. The default is 10. For '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. */
/* RTHRESH (input) REAL */
/* Determines when to stop refinement if the error estimate stops */
/* decreasing. Refinement will stop when the next solution no longer */
/* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */
/* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */
/* default value is 0.5. For 'aggressive' set to 0.9 to permit */
/* convergence on extremely ill-conditioned matrices. See LAWN 165 */
/* for more details. */
/* DZ_UB (input) REAL */
/* Determines when to start considering componentwise convergence. */
/* Componentwise convergence is only considered after each component */
/* of the solution Y is stable, which we definte as the relative */
/* change in each component being less than DZ_UB. The default value */
/* is 0.25, requiring the first bit to be stable. See LAWN 165 for */
/* more details. */
/* IGNORE_CWISE (input) LOGICAL */
/* If .TRUE. then ignore componentwise convergence. Default value */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* < 0: if INFO = -i, the ith argument to SGETRS had an illegal */
/* value */
/* ===================================================================== */
/* 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;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--berr_out__;
--res;
--ayb;
--dy;
--y_tail__;
/* Function Body */
if (*info != 0) {
return 0;
}
chla_transtype__(ch__1, (ftnlen)1, trans_type__);
*(unsigned char *)trans = *(unsigned char *)&ch__1[0];
eps = slamch_("Epsilon");
hugeval = slamch_("Overflow");
/* Force HUGEVAL to Inf */
hugeval *= hugeval;
/* Using HUGEVAL may lead to spurious underflows. */
incr_thresh__ = (real) (*n) * eps;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
y_prec_state__ = 1;
if (y_prec_state__ == 2) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
y_tail__[i__] = 0.f;
}
}
dxrat = 0.f;
dxratmax = 0.f;
dzrat = 0.f;
dzratmax = 0.f;
final_dx_x__ = hugeval;
final_dz_z__ = hugeval;
prevnormdx = hugeval;
prev_dz_z__ = hugeval;
dz_z__ = hugeval;
dx_x__ = hugeval;
x_state__ = 1;
z_state__ = 0;
incr_prec__ = FALSE_;
i__2 = *ithresh;
for (cnt = 1; cnt <= i__2; ++cnt) {
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
scopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
if (y_prec_state__ == 0) {
sgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 +
1], &c__1, &c_b8, &res[1], &c__1);
} else if (y_prec_state__ == 1) {
blas_sgemv_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, &
y[j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1,
prec_type__);
} else {
blas_sgemv2_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda,
&y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b8, &res[
1], &c__1, prec_type__);
}
/* XXX: RES is no longer needed. */
scopy_(n, &res[1], &c__1, &dy[1], &c__1);
sgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &dy[1],
n, info);
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
normx = 0.f;
normy = 0.f;
normdx = 0.f;
dz_z__ = 0.f;
ymin = hugeval;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
yk = (r__1 = y[i__ + j * y_dim1], dabs(r__1));
dyk = (r__1 = dy[i__], dabs(r__1));
if (yk != 0.f) {
/* Computing MAX */
r__1 = dz_z__, r__2 = dyk / yk;
dz_z__ = dmax(r__1,r__2);
} else if (dyk != 0.f) {
dz_z__ = hugeval;
}
ymin = dmin(ymin,yk);
normy = dmax(normy,yk);
if (*colequ) {
/* Computing MAX */
r__1 = normx, r__2 = yk * c__[i__];
normx = dmax(r__1,r__2);
/* Computing MAX */
r__1 = normdx, r__2 = dyk * c__[i__];
normdx = dmax(r__1,r__2);
} else {
normx = normy;
normdx = dmax(normdx,dyk);
}
}
if (normx != 0.f) {
dx_x__ = normdx / normx;
} else if (normdx == 0.f) {
dx_x__ = 0.f;
} else {
dx_x__ = hugeval;
}
dxrat = normdx / prevnormdx;
dzrat = dz_z__ / prev_dz_z__;
/* Check termination criteria */
if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy
&& y_prec_state__ < 2) {
incr_prec__ = TRUE_;
}
if (x_state__ == 3 && dxrat <= *rthresh) {
x_state__ = 1;
}
if (x_state__ == 1) {
if (dx_x__ <= eps) {
x_state__ = 2;
} else if (dxrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
x_state__ = 3;
}
} else {
if (dxrat > dxratmax) {
dxratmax = dxrat;
}
}
if (x_state__ > 1) {
final_dx_x__ = dx_x__;
}
}
if (z_state__ == 0 && dz_z__ <= *dz_ub__) {
z_state__ = 1;
}
if (z_state__ == 3 && dzrat <= *rthresh) {
z_state__ = 1;
}
if (z_state__ == 1) {
if (dz_z__ <= eps) {
z_state__ = 2;
} else if (dz_z__ > *dz_ub__) {
z_state__ = 0;
dzratmax = 0.f;
final_dz_z__ = hugeval;
} else if (dzrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
z_state__ = 3;
}
} else {
if (dzrat > dzratmax) {
dzratmax = dzrat;
}
}
if (z_state__ > 1) {
final_dz_z__ = dz_z__;
}
}
/* Exit if both normwise and componentwise stopped working, */
/* but if componentwise is unstable, let it go at least two */
/* iterations. */
if (x_state__ != 1) {
if (*ignore_cwise__) {
goto L666;
}
if (z_state__ == 3 || z_state__ == 2) {
goto L666;
}
if (z_state__ == 0 && cnt > 1) {
goto L666;
}
}
if (incr_prec__) {
incr_prec__ = FALSE_;
++y_prec_state__;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
y_tail__[i__] = 0.f;
}
}
prevnormdx = normdx;
prev_dz_z__ = dz_z__;
/* Update soluton. */
if (y_prec_state__ < 2) {
saxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
} else {
sla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
}
}
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */
L666:
/* Set final_* when cnt hits ithresh. */
if (x_state__ == 1) {
final_dx_x__ = dx_x__;
}
if (z_state__ == 1) {
final_dz_z__ = dz_z__;
}
/* Compute error bounds */
if (*n_norms__ >= 1) {
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / (
1 - dxratmax);
}
if (*n_norms__ >= 2) {
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / (
1 - dzratmax);
}
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. */
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
scopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
sgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 1], &
c__1, &c_b8, &res[1], &c__1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
ayb[i__] = (r__1 = b[i__ + j * b_dim1], dabs(r__1));
}
/* Compute abs(op(A_s))*abs(Y) + abs(B_s). */
sla_geamv__(trans_type__, n, n, &c_b8, &a[a_offset], lda, &y[j *
y_dim1 + 1], &c__1, &c_b8, &ayb[1], &c__1);
sla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
/* End of loop for each RHS. */
}
return 0;
} /* sla_gerfsx_extended__ */
/* Subroutine */ int sgesv_(integer *n, integer *nrhs, real *a, integer *lda,
integer *ipiv, real *b, integer *ldb, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern /* Subroutine */ int xerbla_(char *, integer *), sgetrf_(
integer *, integer *, real *, integer *, integer *, integer *),
sgetrs_(char *, integer *, integer *, real *, integer *, integer *
, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGESV computes 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. */
/* The LU decomposition with partial pivoting and row interchanges is */
/* used to factor A as */
/* A = P * L * U, */
/* where P is a permutation matrix, L is unit lower triangular, and U is */
/* upper triangular. The factored form of A is then used to solve the */
/* system of equations A * X = B. */
/* Arguments */
/* ========= */
/* 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 matrix B. NRHS >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the N-by-N coefficient matrix A. */
/* On exit, the factors L and U from the factorization */
/* A = P*L*U; the unit diagonal elements of L are not stored. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (output) INTEGER array, dimension (N) */
/* The pivot indices that define the permutation matrix P; */
/* row i of the matrix was interchanged with row IPIV(i). */
/* B (input/output) REAL array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS matrix of right hand side matrix B. */
/* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, U(i,i) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly */
/* singular, so the solution could not be computed. */
/* ===================================================================== */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGESV ", &i__1);
return 0;
}
/* Compute the LU factorization of A. */
sgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
sgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[
b_offset], ldb, info);
}
return 0;
/* End of SGESV */
} /* sgesv_ */
/* 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_ */
