/* Subroutine */ int sgbsvx_(char *fact, char *trans, integer *n, integer *kl,
integer *ku, integer *nrhs, real *ab, integer *ldab, real *afb,
integer *ldafb, 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)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3;
/* Local variables */
integer i__, j, j1, j2;
real amax;
char norm[1];
real rcmin, rcmax, anorm;
logical equil;
real colcnd;
logical nofact;
real bignum;
integer infequ;
logical colequ;
real rowcnd;
logical notran;
real smlnum;
logical rowequ;
real rpvgrw;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SGBSVX uses the LU factorization to compute the solution to a real */
/* system of linear equations A * X = B, A**T * X = B, or A**H * X = B, */
/* where A is a band matrix of order N with KL subdiagonals and KU */
/* superdiagonals, 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 by this subroutine: */
/* 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 = L * U, */
/* where L is a product of permutation and unit lower triangular */
/* matrices with KL subdiagonals, and U is upper triangular with */
/* KL+KU superdiagonals. */
/* 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, AFB 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. */
/* AB, AFB, and IPIV are not modified. */
/* = 'N': The matrix A will be copied to AFB and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AFB 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. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AB (input/output) REAL array, dimension (LDAB,N) */
/* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */
/* If FACT = 'F' and EQUED is not 'N', then A must have been */
/* equilibrated by the scaling factors in R and/or C. AB 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). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* AFB (input or output) REAL array, dimension (LDAFB,N) */
/* If FACT = 'F', then AFB is an input argument and on entry */
/* contains details of the LU factorization of the band matrix */
/* A, as computed by SGBTRF. U is stored as an upper triangular */
/* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */
/* and the multipliers used during the factorization are stored */
/* in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is */
/* the factored form of the equilibrated matrix A. */
/* If FACT = 'N', then AFB is an output argument and on exit */
/* returns details of the LU factorization of A. */
/* If FACT = 'E', then AFB is an output argument and on exit */
/* returns details of the LU factorization of the equilibrated */
/* matrix A (see the description of AB for the form of the */
/* equilibrated matrix). */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */
/* 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 = L*U */
/* as computed by SGBTRF; 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 = 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 = 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 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 (3*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. */
/* ===================================================================== */
/* Moved setting of INFO = N+1 so INFO does not subsequently get */
/* overwritten. Sven, 17 Mar 05. */
/* ===================================================================== */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_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 (*kl < 0) {
*info = -4;
} else if (*ku < 0) {
*info = -5;
} else if (*nrhs < 0) {
*info = -6;
} else if (*ldab < *kl + *ku + 1) {
*info = -8;
} else if (*ldafb < (*kl << 1) + *ku + 1) {
*info = -10;
} else if (lsame_(fact, "F") && ! (rowequ || colequ
|| lsame_(equed, "N"))) {
*info = -12;
} 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);
}
if (rcmin <= 0.f) {
*info = -13;
} 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);
}
if (rcmin <= 0.f) {
*info = -14;
} else if (*n > 0) {
colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
} else {
colcnd = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -16;
} else if (*ldx < max(1,*n)) {
*info = -18;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGBSVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
sgbequ_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &rowcnd,
&colcnd, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
slaqgb_(n, n, kl, ku, &ab[ab_offset], ldab, &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];
}
}
}
} 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];
}
}
}
if (nofact || equil) {
/* Compute the LU factorization of the band matrix A. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j - *ku;
j1 = max(i__2,1);
/* Computing MIN */
i__2 = j + *kl;
j2 = min(i__2,*n);
i__2 = j2 - j1 + 1;
scopy_(&i__2, &ab[*ku + 1 - j + j1 + j * ab_dim1], &c__1, &afb[*
kl + *ku + 1 - j + j1 + j * afb_dim1], &c__1);
}
sgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &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. */
anorm = 0.f;
i__1 = *info;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = *ku + 2 - j;
/* Computing MIN */
i__4 = *n + *ku + 1 - j, i__5 = *kl + *ku + 1;
i__3 = min(i__4,i__5);
for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
r__2 = anorm, r__3 = (r__1 = ab[i__ + j * ab_dim1], dabs(
r__1));
anorm = dmax(r__2,r__3);
}
}
/* Computing MIN */
i__3 = *info - 1, i__2 = *kl + *ku;
i__1 = min(i__3,i__2);
/* Computing MAX */
i__4 = 1, i__5 = *kl + *ku + 2 - *info;
rpvgrw = slantb_("M", "U", "N", info, &i__1, &afb[max(i__4, i__5)
+ afb_dim1], ldafb, &work[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = anorm / 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 = slangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &work[1]);
i__1 = *kl + *ku;
rpvgrw = slantb_("M", "U", "N", n, &i__1, &afb[afb_offset], ldafb, &work[
1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = slangb_("M", n, kl, ku, &ab[ab_offset], ldab, &work[1]) / rpvgrw;
}
/* Compute the reciprocal of the condition number of A. */
sgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond,
&work[1], &iwork[1], info);
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
sgbtrs_(trans, n, kl, ku, nrhs, &afb[afb_offset], ldafb, &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. */
sgbrfs_(trans, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset],
ldafb, &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__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
x[i__ + j * x_dim1] = c__[i__] * x[i__ + j * x_dim1];
}
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= colcnd;
}
}
} else if (rowequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
x[i__ + j * x_dim1] = r__[i__] * x[i__ + j * x_dim1];
}
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= rowcnd;
}
}
/* 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 SGBSVX */
} /* sgbsvx_ */
/* Subroutine */ int serrge_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
real a[16] /* was [4][4] */, b[4], c__[4];
integer i__, j;
real r__[4], w[12], x[4];
char c2[2];
real r1[4], r2[4], af[16] /* was [4][4] */;
char eq[1];
integer ip[4], iw[4];
real err_bnds_c__[12] /* was [4][3] */;
integer n_err_bnds__;
real err_bnds_n__[12] /* was [4][3] */, berr;
integer info;
real anrm, ccond, rcond;
extern /* Subroutine */ int sgbtf2_(integer *, integer *, integer *,
integer *, real *, integer *, integer *, integer *), sgetf2_(
integer *, integer *, real *, integer *, integer *, integer *),
alaesm_(char *, logical *, integer *), sgbcon_(char *,
integer *, integer *, integer *, real *, integer *, integer *,
real *, real *, real *, integer *, integer *), sgecon_(
char *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *);
extern logical lsamen_(integer *, char *, char *);
real params[1];
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), sgbequ_(integer *, integer *, integer *,
integer *, real *, integer *, real *, real *, real *, real *,
real *, integer *), sgbrfs_(char *, integer *, integer *, integer
*, integer *, real *, integer *, real *, integer *, integer *,
real *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *), sgbtrf_(integer *, integer *,
integer *, integer *, real *, integer *, integer *, integer *),
sgeequ_(integer *, integer *, real *, integer *, real *, real *,
real *, real *, real *, integer *), sgerfs_(char *, integer *,
integer *, real *, integer *, real *, integer *, integer *, real *
, integer *, real *, integer *, real *, real *, real *, integer *,
integer *), sgetrf_(integer *, integer *, real *,
integer *, integer *, integer *), sgetri_(integer *, real *,
integer *, integer *, real *, integer *, integer *), sgbtrs_(char
*, integer *, integer *, integer *, integer *, real *, integer *,
integer *, real *, integer *, integer *), sgetrs_(char *,
integer *, integer *, real *, integer *, integer *, real *,
integer *, integer *), sgbequb_(integer *, integer *,
integer *, integer *, real *, integer *, real *, real *, real *,
real *, real *, integer *), sgeequb_(integer *, integer *, real *,
integer *, real *, real *, real *, real *, real *, integer *);
integer nparams;
extern /* Subroutine */ int sgbrfsx_(char *, char *, integer *, integer *,
integer *, integer *, real *, integer *, real *, integer *,
integer *, real *, real *, real *, integer *, real *, integer *,
real *, real *, integer *, real *, real *, integer *, real *,
real *, integer *, integer *), sgerfsx_(char *,
char *, integer *, integer *, real *, integer *, real *, integer *
, integer *, real *, real *, real *, integer *, real *, integer *,
real *, real *, integer *, real *, real *, integer *, real *,
real *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SERRGE tests the error exits for the REAL routines */
/* for general matrices. */
/* Note that this file is used only when the XBLAS are available, */
/* otherwise serrge.f defines this subroutine. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a[i__ + (j << 2) - 5] = 1.f / (real) (i__ + j);
af[i__ + (j << 2) - 5] = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
c__[j - 1] = 0.f;
r__[j - 1] = 0.f;
ip[j - 1] = j;
iw[j - 1] = j;
/* L20: */
}
infoc_1.ok = TRUE_;
if (lsamen_(&c__2, c2, "GE")) {
/* Test error exits of the routines that use the LU decomposition */
/* of a general matrix. */
/* SGETRF */
s_copy(srnamc_1.srnamt, "SGETRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetrf_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetrf_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgetrf_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("SGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETF2 */
s_copy(srnamc_1.srnamt, "SGETF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetf2_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetf2_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgetf2_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("SGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETRI */
s_copy(srnamc_1.srnamt, "SGETRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetri_(&c_n1, a, &c__1, ip, w, &c__12, &info);
chkxer_("SGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgetri_(&c__2, a, &c__1, ip, w, &c__12, &info);
chkxer_("SGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGETRS */
s_copy(srnamc_1.srnamt, "SGETRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("SGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGERFS */
s_copy(srnamc_1.srnamt, "SGERFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGERFSX */
n_err_bnds__ = 3;
nparams = 0;
s_copy(srnamc_1.srnamt, "SGERFSX", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgerfsx_("/", eq, &c__0, &c__0, a, &c__1, af, &c__1, ip, r__, c__, b,
&c__1, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
*(unsigned char *)eq = '/';
sgerfsx_("N", eq, &c__2, &c__1, a, &c__1, af, &c__2, ip, r__, c__, b,
&c__2, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
*(unsigned char *)eq = 'R';
sgerfsx_("N", eq, &c_n1, &c__0, a, &c__1, af, &c__1, ip, r__, c__, b,
&c__1, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgerfsx_("N", eq, &c__0, &c_n1, a, &c__1, af, &c__1, ip, r__, c__, b,
&c__1, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgerfsx_("N", eq, &c__2, &c__1, a, &c__1, af, &c__2, ip, r__, c__, b,
&c__2, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgerfsx_("N", eq, &c__2, &c__1, a, &c__2, af, &c__1, ip, r__, c__, b,
&c__2, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
*(unsigned char *)eq = 'C';
sgerfsx_("N", eq, &c__2, &c__1, a, &c__2, af, &c__2, ip, r__, c__, b,
&c__1, x, &c__2, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
sgerfsx_("N", eq, &c__2, &c__1, a, &c__2, af, &c__2, ip, r__, c__, b,
&c__2, x, &c__1, &rcond, &berr, &n_err_bnds__, err_bnds_n__,
err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGERFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGECON */
s_copy(srnamc_1.srnamt, "SGECON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEEQU */
s_copy(srnamc_1.srnamt, "SGEEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("SGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGEEQUB */
s_copy(srnamc_1.srnamt, "SGEEQUB", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgeequb_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info)
;
chkxer_("SGEEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgeequb_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info)
;
chkxer_("SGEEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgeequb_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info)
;
chkxer_("SGEEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "GB")) {
/* Test error exits of the routines that use the LU decomposition */
/* of a general band matrix. */
/* SGBTRF */
s_copy(srnamc_1.srnamt, "SGBTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("SGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBTF2 */
s_copy(srnamc_1.srnamt, "SGBTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("SGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBTRS */
s_copy(srnamc_1.srnamt, "SGBTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("SGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBRFS */
s_copy(srnamc_1.srnamt, "SGBRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbrfs_("N", &c_n1, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbrfs_("N", &c__1, &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbrfs_("N", &c__1, &c__0, &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sgbrfs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__2, af, &c__4, ip, b, &
c__2, x, &c__2, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
sgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip, b, &
c__2, x, &c__2, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
sgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__2, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
sgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__2, x, &c__1, r1, r2, w, iw, &info);
chkxer_("SGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBRFSX */
n_err_bnds__ = 3;
nparams = 0;
s_copy(srnamc_1.srnamt, "SGBRFSX", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgbrfsx_("/", eq, &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
*(unsigned char *)eq = '/';
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__1, af, &c__2, ip,
r__, c__, b, &c__2, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
*(unsigned char *)eq = 'R';
sgbrfsx_("N", eq, &c_n1, &c__1, &c__1, &c__0, a, &c__1, af, &c__1, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
*(unsigned char *)eq = 'R';
sgbrfsx_("N", eq, &c__2, &c_n1, &c__1, &c__1, a, &c__3, af, &c__4, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
*(unsigned char *)eq = 'R';
sgbrfsx_("N", eq, &c__2, &c__1, &c_n1, &c__1, a, &c__3, af, &c__4, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbrfsx_("N", eq, &c__0, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip,
r__, c__, b, &c__1, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__1, af, &c__2, ip,
r__, c__, b, &c__2, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip,
r__, c__, b, &c__2, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
*(unsigned char *)eq = 'C';
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__5, ip,
r__, c__, b, &c__1, x, &c__2, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
sgbrfsx_("N", eq, &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__5, ip,
r__, c__, b, &c__2, x, &c__1, &rcond, &berr, &n_err_bnds__,
err_bnds_n__, err_bnds_c__, &nparams, params, w, iw, &info);
chkxer_("SGBRFSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBCON */
s_copy(srnamc_1.srnamt, "SGBCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, iw,
&info);
chkxer_("SGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBEQU */
s_copy(srnamc_1.srnamt, "SGBEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SGBEQUB */
s_copy(srnamc_1.srnamt, "SGBEQUB", (ftnlen)32, (ftnlen)7);
infoc_1.infot = 1;
sgbequb_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sgbequb_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sgbequb_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
sgbequb_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
sgbequb_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("SGBEQUB", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of SERRGE */
} /* serrge_ */
/* Subroutine */ int 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_ */
doublereal sla_gbrcond__(char *trans, integer *n, integer *kl, integer *ku,
real *ab, integer *ldab, real *afb, integer *ldafb, integer *ipiv,
integer *cmode, real *c__, integer *info, real *work, integer *iwork,
ftnlen trans_len)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, i__1, i__2, i__3, i__4;
real ret_val, r__1;
/* Local variables */
integer i__, j, kd, ke;
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 sgbtrs_(char *, integer *, integer *, integer
*, integer *, real *, integer *, integer *, real *, integer *,
integer *);
logical notrans;
/* -- LAPACK routine (version 3.2.1) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- April 2009 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLA_GERCOND Estimates the Skeel condition number of op(A) * op2(C) */
/* where op2 is determined by CMODE as follows */
/* CMODE = 1 op2(C) = C */
/* CMODE = 0 op2(C) = I */
/* CMODE = -1 op2(C) = inv(C) */
/* The Skeel condition number cond(A) = norminf( |inv(A)||A| ) */
/* is computed by computing scaling factors R such that */
/* diag(R)*A*op2(C) is row equilibrated and computing the standard */
/* infinity-norm condition number. */
/* 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 number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* AB (input) REAL array, dimension (LDAB,N) */
/* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* AFB (input) REAL array, dimension (LDAFB,N) */
/* Details of the LU factorization of the band matrix A, as */
/* computed by SGBTRF. U is stored as an upper triangular */
/* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */
/* and the multipliers used during the factorization are stored */
/* in rows KL+KU+2 to 2*KL+KU+1. */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from the factorization A = P*L*U */
/* as computed by SGBTRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* CMODE (input) INTEGER */
/* Determines op2(C) in the formula op(A) * op2(C) as follows: */
/* CMODE = 1 op2(C) = C */
/* CMODE = 0 op2(C) = I */
/* CMODE = -1 op2(C) = inv(C) */
/* C (input) REAL array, dimension (N) */
/* The vector C in the formula op(A) * op2(C). */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* i > 0: The ith argument is invalid. */
/* WORK (input) REAL array, dimension (5*N). */
/* Workspace. */
/* IWORK (input) INTEGER array, dimension (N). */
/* Workspace. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_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 (*kl < 0 || *kl > *n - 1) {
*info = -3;
} else if (*ku < 0 || *ku > *n - 1) {
*info = -4;
} else if (*ldab < *kl + *ku + 1) {
*info = -6;
} else if (*ldafb < (*kl << 1) + *ku + 1) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLA_GBRCOND", &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. */
kd = *ku + 1;
ke = *kl + 1;
if (notrans) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.f;
if (*cmode == 1) {
/* Computing MAX */
i__2 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__3 = min(i__4,*n);
for (j = max(i__2,1); j <= i__3; ++j) {
tmp += (r__1 = ab[kd + i__ - j + j * ab_dim1] * c__[j],
dabs(r__1));
}
} else if (*cmode == 0) {
/* Computing MAX */
i__3 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__2 = min(i__4,*n);
for (j = max(i__3,1); j <= i__2; ++j) {
tmp += (r__1 = ab[kd + i__ - j + j * ab_dim1], dabs(r__1))
;
}
} else {
/* Computing MAX */
i__2 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__3 = min(i__4,*n);
for (j = max(i__2,1); j <= i__3; ++j) {
tmp += (r__1 = ab[kd + i__ - j + j * ab_dim1] / c__[j],
dabs(r__1));
}
}
work[(*n << 1) + i__] = tmp;
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.f;
if (*cmode == 1) {
/* Computing MAX */
i__3 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__2 = min(i__4,*n);
for (j = max(i__3,1); j <= i__2; ++j) {
tmp += (r__1 = ab[ke - i__ + j + i__ * ab_dim1] * c__[j],
dabs(r__1));
}
} else if (*cmode == 0) {
/* Computing MAX */
i__2 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__3 = min(i__4,*n);
for (j = max(i__2,1); j <= i__3; ++j) {
tmp += (r__1 = ab[ke - i__ + j + i__ * ab_dim1], dabs(
r__1));
}
} else {
/* Computing MAX */
i__3 = i__ - *kl;
/* Computing MIN */
i__4 = i__ + *ku;
i__2 = min(i__4,*n);
for (j = max(i__3,1); j <= i__2; ++j) {
tmp += (r__1 = ab[ke - i__ + j + i__ * ab_dim1] / c__[j],
dabs(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) {
sgbtrs_("No transpose", n, kl, ku, &c__1, &afb[afb_offset],
ldafb, &ipiv[1], &work[1], n, info);
} else {
sgbtrs_("Transpose", n, kl, ku, &c__1, &afb[afb_offset],
ldafb, &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'). */
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) {
sgbtrs_("Transpose", n, kl, ku, &c__1, &afb[afb_offset],
ldafb, &ipiv[1], &work[1], n, info);
} else {
sgbtrs_("No transpose", n, kl, ku, &c__1, &afb[afb_offset],
ldafb, &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;
} /* sla_gbrcond__ */
/* Subroutine */ int schkgb_(logical *dotype, integer *nm, integer *mval,
integer *nn, integer *nval, integer *nnb, integer *nbval, integer *
nns, integer *nsval, real *thresh, logical *tsterr, real *a, integer *
la, real *afac, integer *lafac, real *b, real *x, real *xact, real *
work, real *rwork, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(\002 *** In SCHKGB, LA=\002,i5,\002 is too sm"
"all for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU=\002"
",i4,/\002 ==> Increase LA to at least \002,i5)";
static char fmt_9998[] = "(\002 *** In SCHKGB, LAFAC=\002,i5,\002 is too"
" small for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU"
"=\002,i4,/\002 ==> Increase LAFAC to at least \002,i5)";
static char fmt_9997[] = "(\002 M =\002,i5,\002, N =\002,i5,\002, KL="
"\002,i5,\002, KU=\002,i5,\002, NB =\002,i4,\002, type \002,i1"
",\002, test(\002,i1,\002)=\002,g12.5)";
static char fmt_9996[] = "(\002 TRANS='\002,a1,\002', N=\002,i5,\002, "
"KL=\002,i5,\002, KU=\002,i5,\002, NRHS=\002,i3,\002, type \002,i"
"1,\002, test(\002,i1,\002)=\002,g12.5)";
static char fmt_9995[] = "(\002 NORM ='\002,a1,\002', N=\002,i5,\002, "
"KL=\002,i5,\002, KU=\002,i5,\002,\002,10x,\002 type \002,i1,\002"
", test(\002,i1,\002)=\002,g12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10,
i__11;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, m, n, i1, i2, nb, im, in, kl, ku, lda, ldb, inb, ikl,
nkl, iku, nku, ioff, mode, koff, imat, info;
char path[3], dist[1];
integer irhs, nrhs;
char norm[1], type__[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer nfail, iseed[4];
extern /* Subroutine */ int sgbt01_(integer *, integer *, integer *,
integer *, real *, integer *, real *, integer *, integer *, real *
, real *), sgbt02_(char *, integer *, integer *, integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *), sgbt05_(char *, integer *, integer *
, integer *, integer *, real *, integer *, real *, integer *,
real *, integer *, real *, integer *, real *, real *, real *);
real rcond;
extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer
*, real *, integer *, real *, real *);
integer nimat, klval[4];
extern doublereal sget06_(real *, real *);
real anorm;
integer itran, kuval[4];
char trans[1];
integer izero, nerrs;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
logical zerot;
char xtype[1];
extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, real *, integer *, real *, char *
);
integer ldafac;
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *);
extern doublereal slangb_(char *, integer *, integer *, integer *, real *,
integer *, real *);
real rcondc;
extern doublereal slange_(char *, integer *, integer *, real *, integer *,
real *);
extern /* Subroutine */ int sgbcon_(char *, integer *, integer *, integer
*, real *, integer *, integer *, real *, real *, real *, integer *
, integer *);
real rcondi;
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *);
real cndnum, anormi, rcondo;
extern /* Subroutine */ int serrge_(char *, integer *);
real ainvnm;
extern /* Subroutine */ int 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 *);
logical trfcon;
real anormo;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slarhs_(char *, char *,
char *, char *, integer *, integer *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, integer *, integer *), slaset_(
char *, integer *, integer *, real *, real *, real *, integer *), xlaenv_(integer *, integer *), slatms_(integer *,
integer *, char *, integer *, char *, real *, integer *, real *,
real *, integer *, integer *, char *, real *, integer *, real *,
integer *), sgbtrs_(char *, integer *,
integer *, integer *, integer *, real *, integer *, integer *,
real *, integer *, integer *);
real result[7];
/* Fortran I/O blocks */
static cilist io___25 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___26 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___59 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___61 = { 0, 0, 0, fmt_9995, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SCHKGB tests SGBTRF, -TRS, -RFS, and -CON */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NM (input) INTEGER */
/* The number of values of M contained in the vector MVAL. */
/* MVAL (input) INTEGER array, dimension (NM) */
/* The values of the matrix row dimension M. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NNB) */
/* The values of the blocksize NB. */
/* NNS (input) INTEGER */
/* The number of values of NRHS contained in the vector NSVAL. */
/* NSVAL (input) INTEGER array, dimension (NNS) */
/* The values of the number of right hand sides NRHS. */
/* THRESH (input) REAL */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* A (workspace) REAL array, dimension (LA) */
/* LA (input) INTEGER */
/* The length of the array A. LA >= (KLMAX+KUMAX+1)*NMAX */
/* where KLMAX is the largest entry in the local array KLVAL, */
/* KUMAX is the largest entry in the local array KUVAL and */
/* NMAX is the largest entry in the input array NVAL. */
/* AFAC (workspace) REAL array, dimension (LAFAC) */
/* LAFAC (input) INTEGER */
/* The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX */
/* where KLMAX is the largest entry in the local array KLVAL, */
/* KUMAX is the largest entry in the local array KUVAL and */
/* NMAX is the largest entry in the input array NVAL. */
/* B (workspace) REAL array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* X (workspace) REAL array, dimension (NMAX*NSMAX) */
/* XACT (workspace) REAL array, dimension (NMAX*NSMAX) */
/* WORK (workspace) REAL array, dimension */
/* (NMAX*max(3,NSMAX,NMAX)) */
/* RWORK (workspace) REAL array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* IWORK (workspace) INTEGER array, dimension (2*NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--afac;
--a;
--nsval;
--nbval;
--nval;
--mval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "GB", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Test the error exits */
if (*tsterr) {
serrge_(path, nout);
}
infoc_1.infot = 0;
xlaenv_(&c__2, &c__2);
/* Initialize the first value for the lower and upper bandwidths. */
klval[0] = 0;
kuval[0] = 0;
/* Do for each value of M in MVAL */
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
/* Set values to use for the lower bandwidth. */
klval[1] = m + (m + 1) / 4;
/* KLVAL( 2 ) = MAX( M-1, 0 ) */
klval[2] = (m * 3 - 1) / 4;
klval[3] = (m + 1) / 4;
/* Do for each value of N in NVAL */
i__2 = *nn;
for (in = 1; in <= i__2; ++in) {
n = nval[in];
*(unsigned char *)xtype = 'N';
/* Set values to use for the upper bandwidth. */
kuval[1] = n + (n + 1) / 4;
/* KUVAL( 2 ) = MAX( N-1, 0 ) */
kuval[2] = (n * 3 - 1) / 4;
kuval[3] = (n + 1) / 4;
/* Set limits on the number of loop iterations. */
/* Computing MIN */
i__3 = m + 1;
nkl = min(i__3,4);
if (n == 0) {
nkl = 2;
}
/* Computing MIN */
i__3 = n + 1;
nku = min(i__3,4);
if (m == 0) {
nku = 2;
}
nimat = 8;
if (m <= 0 || n <= 0) {
nimat = 1;
}
i__3 = nkl;
for (ikl = 1; ikl <= i__3; ++ikl) {
/* Do for KL = 0, (5*M+1)/4, (3M-1)/4, and (M+1)/4. This */
/* order makes it easier to skip redundant values for small */
/* values of M. */
kl = klval[ikl - 1];
i__4 = nku;
for (iku = 1; iku <= i__4; ++iku) {
/* Do for KU = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This */
/* order makes it easier to skip redundant values for */
/* small values of N. */
ku = kuval[iku - 1];
/* Check that A and AFAC are big enough to generate this */
/* matrix. */
lda = kl + ku + 1;
ldafac = (kl << 1) + ku + 1;
if (lda * n > *la || ldafac * n > *lafac) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
if (n * (kl + ku + 1) > *la) {
io___25.ciunit = *nout;
s_wsfe(&io___25);
do_fio(&c__1, (char *)&(*la), (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer)
);
i__5 = n * (kl + ku + 1);
do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof(
integer));
e_wsfe();
++nerrs;
}
if (n * ((kl << 1) + ku + 1) > *lafac) {
io___26.ciunit = *nout;
s_wsfe(&io___26);
do_fio(&c__1, (char *)&(*lafac), (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer)
);
i__5 = n * ((kl << 1) + ku + 1);
do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof(
integer));
e_wsfe();
++nerrs;
}
goto L130;
}
i__5 = nimat;
for (imat = 1; imat <= i__5; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L120;
}
/* Skip types 2, 3, or 4 if the matrix size is too */
/* small. */
zerot = imat >= 2 && imat <= 4;
if (zerot && n < imat - 1) {
goto L120;
}
if (! zerot || ! dotype[1]) {
/* Set up parameters with SLATB4 and generate a */
/* test matrix with SLATMS. */
slatb4_(path, &imat, &m, &n, type__, &kl, &ku, &
anorm, &mode, &cndnum, dist);
/* Computing MAX */
i__6 = 1, i__7 = ku + 2 - n;
koff = max(i__6,i__7);
i__6 = koff - 1;
for (i__ = 1; i__ <= i__6; ++i__) {
a[i__] = 0.f;
/* L20: */
}
s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)6, (
ftnlen)6);
slatms_(&m, &n, dist, iseed, type__, &rwork[1], &
mode, &cndnum, &anorm, &kl, &ku, "Z", &a[
koff], &lda, &work[1], &info);
/* Check the error code from SLATMS. */
if (info != 0) {
alaerh_(path, "SLATMS", &info, &c__0, " ", &m,
&n, &kl, &ku, &c_n1, &imat, &nfail, &
nerrs, nout);
goto L120;
}
} else if (izero > 0) {
/* Use the same matrix for types 3 and 4 as for */
/* type 2 by copying back the zeroed out column. */
i__6 = i2 - i1 + 1;
scopy_(&i__6, &b[1], &c__1, &a[ioff + i1], &c__1);
}
/* For types 2, 3, and 4, zero one or more columns of */
/* the matrix to test that INFO is returned correctly. */
izero = 0;
if (zerot) {
if (imat == 2) {
izero = 1;
} else if (imat == 3) {
izero = min(m,n);
} else {
izero = min(m,n) / 2 + 1;
}
ioff = (izero - 1) * lda;
if (imat < 4) {
/* Store the column to be zeroed out in B. */
/* Computing MAX */
i__6 = 1, i__7 = ku + 2 - izero;
i1 = max(i__6,i__7);
/* Computing MIN */
i__6 = kl + ku + 1, i__7 = ku + 1 + (m -
izero);
i2 = min(i__6,i__7);
i__6 = i2 - i1 + 1;
scopy_(&i__6, &a[ioff + i1], &c__1, &b[1], &
c__1);
i__6 = i2;
for (i__ = i1; i__ <= i__6; ++i__) {
a[ioff + i__] = 0.f;
/* L30: */
}
} else {
i__6 = n;
for (j = izero; j <= i__6; ++j) {
/* Computing MAX */
i__7 = 1, i__8 = ku + 2 - j;
/* Computing MIN */
i__10 = kl + ku + 1, i__11 = ku + 1 + (m
- j);
i__9 = min(i__10,i__11);
for (i__ = max(i__7,i__8); i__ <= i__9;
++i__) {
a[ioff + i__] = 0.f;
/* L40: */
}
ioff += lda;
/* L50: */
}
}
}
/* These lines, if used in place of the calls in the */
/* loop over INB, cause the code to bomb on a Sun */
/* SPARCstation. */
/* ANORMO = SLANGB( 'O', N, KL, KU, A, LDA, RWORK ) */
/* ANORMI = SLANGB( 'I', N, KL, KU, A, LDA, RWORK ) */
/* Do for each blocksize in NBVAL */
i__6 = *nnb;
for (inb = 1; inb <= i__6; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Compute the LU factorization of the band matrix. */
if (m > 0 && n > 0) {
i__9 = kl + ku + 1;
slacpy_("Full", &i__9, &n, &a[1], &lda, &afac[
kl + 1], &ldafac);
}
s_copy(srnamc_1.srnamt, "SGBTRF", (ftnlen)6, (
ftnlen)6);
sgbtrf_(&m, &n, &kl, &ku, &afac[1], &ldafac, &
iwork[1], &info);
/* Check error code from SGBTRF. */
if (info != izero) {
alaerh_(path, "SGBTRF", &info, &izero, " ", &
m, &n, &kl, &ku, &nb, &imat, &nfail, &
nerrs, nout);
}
trfcon = FALSE_;
/* + TEST 1 */
/* Reconstruct matrix from factors and compute */
/* residual. */
sgbt01_(&m, &n, &kl, &ku, &a[1], &lda, &afac[1], &
ldafac, &iwork[1], &work[1], result);
/* Print information about the tests so far that */
/* did not pass the threshold. */
if (result[0] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___45.ciunit = *nout;
s_wsfe(&io___45);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)
sizeof(real));
e_wsfe();
++nfail;
}
++nrun;
/* Skip the remaining tests if this is not the */
/* first block size or if M .ne. N. */
if (inb > 1 || m != n) {
goto L110;
}
anormo = slangb_("O", &n, &kl, &ku, &a[1], &lda, &
rwork[1]);
anormi = slangb_("I", &n, &kl, &ku, &a[1], &lda, &
rwork[1]);
if (info == 0) {
/* Form the inverse of A so we can get a good */
/* estimate of CNDNUM = norm(A) * norm(inv(A)). */
ldb = max(1,n);
slaset_("Full", &n, &n, &c_b63, &c_b64, &work[
1], &ldb);
s_copy(srnamc_1.srnamt, "SGBTRS", (ftnlen)6, (
ftnlen)6);
sgbtrs_("No transpose", &n, &kl, &ku, &n, &
afac[1], &ldafac, &iwork[1], &work[1],
&ldb, &info);
/* Compute the 1-norm condition number of A. */
ainvnm = slange_("O", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormo <= 0.f || ainvnm <= 0.f) {
rcondo = 1.f;
} else {
rcondo = 1.f / anormo / ainvnm;
}
/* Compute the infinity-norm condition number of */
/* A. */
ainvnm = slange_("I", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormi <= 0.f || ainvnm <= 0.f) {
rcondi = 1.f;
} else {
rcondi = 1.f / anormi / ainvnm;
}
} else {
/* Do only the condition estimate if INFO.NE.0. */
trfcon = TRUE_;
rcondo = 0.f;
rcondi = 0.f;
}
/* Skip the solve tests if the matrix is singular. */
if (trfcon) {
goto L90;
}
i__9 = *nns;
for (irhs = 1; irhs <= i__9; ++irhs) {
nrhs = nsval[irhs];
*(unsigned char *)xtype = 'N';
for (itran = 1; itran <= 3; ++itran) {
*(unsigned char *)trans = *(unsigned char
*)&transs[itran - 1];
if (itran == 1) {
rcondc = rcondo;
*(unsigned char *)norm = 'O';
} else {
rcondc = rcondi;
*(unsigned char *)norm = 'I';
}
/* + TEST 2: */
/* Solve and compute residual for A * X = B. */
s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)
6, (ftnlen)6);
slarhs_(path, xtype, " ", trans, &n, &n, &
kl, &ku, &nrhs, &a[1], &lda, &
xact[1], &ldb, &b[1], &ldb, iseed,
&info);
*(unsigned char *)xtype = 'C';
slacpy_("Full", &n, &nrhs, &b[1], &ldb, &
x[1], &ldb);
s_copy(srnamc_1.srnamt, "SGBTRS", (ftnlen)
6, (ftnlen)6);
sgbtrs_(trans, &n, &kl, &ku, &nrhs, &afac[
1], &ldafac, &iwork[1], &x[1], &
ldb, &info);
/* Check error code from SGBTRS. */
if (info != 0) {
alaerh_(path, "SGBTRS", &info, &c__0,
trans, &n, &n, &kl, &ku, &
c_n1, &imat, &nfail, &nerrs,
nout);
}
slacpy_("Full", &n, &nrhs, &b[1], &ldb, &
work[1], &ldb);
sgbt02_(trans, &m, &n, &kl, &ku, &nrhs, &
a[1], &lda, &x[1], &ldb, &work[1],
&ldb, &result[1]);
/* + TEST 3: */
/* Check solution from generated exact */
/* solution. */
sget04_(&n, &nrhs, &x[1], &ldb, &xact[1],
&ldb, &rcondc, &result[2]);
/* + TESTS 4, 5, 6: */
/* Use iterative refinement to improve the */
/* solution. */
s_copy(srnamc_1.srnamt, "SGBRFS", (ftnlen)
6, (ftnlen)6);
sgbrfs_(trans, &n, &kl, &ku, &nrhs, &a[1],
&lda, &afac[1], &ldafac, &iwork[
1], &b[1], &ldb, &x[1], &ldb, &
rwork[1], &rwork[nrhs + 1], &work[
1], &iwork[n + 1], &info);
/* Check error code from SGBRFS. */
if (info != 0) {
alaerh_(path, "SGBRFS", &info, &c__0,
trans, &n, &n, &kl, &ku, &
nrhs, &imat, &nfail, &nerrs,
nout);
}
sget04_(&n, &nrhs, &x[1], &ldb, &xact[1],
&ldb, &rcondc, &result[3]);
sgbt05_(trans, &n, &kl, &ku, &nrhs, &a[1],
&lda, &b[1], &ldb, &x[1], &ldb, &
xact[1], &ldb, &rwork[1], &rwork[
nrhs + 1], &result[4]);
for (k = 2; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___59.ciunit = *nout;
s_wsfe(&io___59);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nrhs, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[k -
1], (ftnlen)sizeof(real));
e_wsfe();
++nfail;
}
/* L60: */
}
nrun += 5;
/* L70: */
}
/* L80: */
}
/* + TEST 7: */
/* Get an estimate of RCOND = 1/CNDNUM. */
L90:
for (itran = 1; itran <= 2; ++itran) {
if (itran == 1) {
anorm = anormo;
rcondc = rcondo;
*(unsigned char *)norm = 'O';
} else {
anorm = anormi;
rcondc = rcondi;
*(unsigned char *)norm = 'I';
}
s_copy(srnamc_1.srnamt, "SGBCON", (ftnlen)6, (
ftnlen)6);
sgbcon_(norm, &n, &kl, &ku, &afac[1], &ldafac,
&iwork[1], &anorm, &rcond, &work[1],
&iwork[n + 1], &info);
/* Check error code from SGBCON. */
if (info != 0) {
alaerh_(path, "SGBCON", &info, &c__0,
norm, &n, &n, &kl, &ku, &c_n1, &
imat, &nfail, &nerrs, nout);
}
result[6] = sget06_(&rcond, &rcondc);
/* Print information about the tests that did */
/* not pass the threshold. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___61.ciunit = *nout;
s_wsfe(&io___61);
do_fio(&c__1, norm, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&c__7, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)
sizeof(real));
e_wsfe();
++nfail;
}
++nrun;
/* L100: */
}
L110:
;
}
L120:
;
}
L130:
;
}
/* L140: */
}
/* L150: */
}
/* L160: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of SCHKGB */
} /* schkgb_ */
/* Subroutine */ int sgbsv_(integer *n, integer *kl, integer *ku, integer *
nrhs, real *ab, integer *ldab, integer *ipiv, real *b, integer *ldb,
integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern /* Subroutine */ int xerbla_(char *, integer *), sgbtrf_(
integer *, integer *, integer *, integer *, real *, integer *,
integer *, integer *), sgbtrs_(char *, integer *, integer *,
integer *, integer *, real *, integer *, integer *, real *,
integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGBSV computes the solution to a real system of linear equations */
/* A * X = B, where A is a band matrix of order N with KL subdiagonals */
/* and KU superdiagonals, 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 = L * U, where L is a product of permutation */
/* and unit lower triangular matrices with KL subdiagonals, and U is */
/* upper triangular with KL+KU superdiagonals. 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. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* AB (input/output) REAL array, dimension (LDAB,N) */
/* On entry, the matrix A in band storage, in rows KL+1 to */
/* 2*KL+KU+1; rows 1 to KL of the array need not be set. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) */
/* On exit, details of the factorization: U is stored as an */
/* upper triangular band matrix with KL+KU superdiagonals in */
/* rows 1 to KL+KU+1, and the multipliers used during the */
/* factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */
/* See below for further details. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */
/* 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 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, and the solution has not been computed. */
/* Further Details */
/* =============== */
/* The band storage scheme is illustrated by the following example, when */
/* M = N = 6, KL = 2, KU = 1: */
/* On entry: On exit: */
/* * * * + + + * * * u14 u25 u36 */
/* * * + + + + * * u13 u24 u35 u46 */
/* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */
/* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */
/* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * */
/* a31 a42 a53 a64 * * m31 m42 m53 m64 * * */
/* Array elements marked * are not used by the routine; elements marked */
/* + need not be set on entry, but are required by the routine to store */
/* elements of U because of fill-in resulting from the row interchanges. */
/* ===================================================================== */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*kl < 0) {
*info = -2;
} else if (*ku < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < (*kl << 1) + *ku + 1) {
*info = -6;
} else if (*ldb < max(*n,1)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGBSV ", &i__1);
return 0;
}
/* Compute the LU factorization of the band matrix A. */
sgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
sgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[
1], &b[b_offset], ldb, info);
}
return 0;
/* End of SGBSV */
} /* sgbsv_ */
/* Subroutine */ int sgbsvxx_(char *fact, char *trans, integer *n, integer *
kl, integer *ku, integer *nrhs, real *ab, integer *ldab, real *afb,
integer *ldafb, integer *ipiv, char *equed, real *r__, real *c__,
real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *
rpvgrw, real *berr, integer *n_err_bnds__, real *err_bnds_norm__,
real *err_bnds_comp__, integer *nparams, real *params, real *work,
integer *iwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2;
real r__1, r__2;
/* Local variables */
integer i__, j;
real amax;
extern doublereal sla_gbrpvgrw__(integer *, integer *, integer *, integer
*, real *, integer *, real *, integer *);
extern logical lsame_(char *, char *);
real rcmin, rcmax;
logical equil;
real colcnd;
extern doublereal slamch_(char *);
extern /* Subroutine */ int slaqgb_(integer *, integer *, integer *,
integer *, real *, integer *, real *, real *, real *, real *,
real *, char *);
logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
integer infequ;
logical colequ;
extern /* Subroutine */ int sgbtrf_(integer *, integer *, integer *,
integer *, real *, integer *, integer *, integer *), slacpy_(char
*, integer *, integer *, real *, integer *, real *, integer *);
real rowcnd;
logical notran;
extern /* Subroutine */ int sgbtrs_(char *, integer *, integer *, integer
*, integer *, real *, integer *, integer *, real *, integer *,
integer *);
real smlnum;
logical rowequ;
extern /* Subroutine */ int slascl2_(integer *, integer *, real *, real *,
integer *), sgbequb_(integer *, integer *, integer *, integer *,
real *, integer *, real *, real *, real *, real *, real *,
integer *), 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 *);
/* -- LAPACK driver routine (version 3.2) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SGBSVXX 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. */
/* If requested, both normwise and maximum componentwise error bounds */
/* are returned. SGBSVXX will return a solution with a tiny */
/* guaranteed error (O(eps) where eps is the working machine */
/* precision) unless the matrix is very ill-conditioned, in which */
/* case a warning is returned. Relevant condition numbers also are */
/* calculated and returned. */
/* SGBSVXX accepts user-provided factorizations and equilibration */
/* factors; see the definitions of the FACT and EQUED options. */
/* Solving with refinement and using a factorization from a previous */
/* SGBSVXX call will also produce a solution with either O(eps) */
/* errors or warnings, but we cannot make that claim for general */
/* user-provided factorizations and equilibration factors if they */
/* differ from what SGBSVXX would itself produce. */
/* 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 (see */
/* argument RCOND). If the reciprocal of the condition number is less */
/* than machine precision, 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. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */
/* the routine will use iterative refinement to try to get a small */
/* error and error bounds. Refinement calculates the residual to at */
/* least twice the working precision. */
/* 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 */
/* ========= */
/* Some optional parameters are bundled in the PARAMS array. These */
/* settings determine how refinement is performed, but often the */
/* defaults are acceptable. If the defaults are acceptable, users */
/* can pass NPARAMS = 0 which prevents the source code from accessing */
/* the PARAMS argument. */
/* 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 (Conjugate Transpose = Transpose) */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AB (input/output) REAL array, dimension (LDAB,N) */
/* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */
/* If FACT = 'F' and EQUED is not 'N', then AB must have been */
/* equilibrated by the scaling factors in R and/or C. AB 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). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* AFB (input or output) REAL array, dimension (LDAFB,N) */
/* If FACT = 'F', then AFB is an input argument and on entry */
/* contains details of the LU factorization of the band matrix */
/* A, as computed by SGBTRF. U is stored as an upper triangular */
/* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */
/* and the multipliers used during the factorization are stored */
/* in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB 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). */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */
/* 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. */
/* If R is output, each element of R is a power of the radix. */
/* If R is input, each element of R should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* C (input or output) REAL array, dimension (N) */
/* The column scale factors for A. If EQUED = 'C' or 'B', A is */
/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
/* is not accessed. C is an input argument if FACT = 'F'; */
/* otherwise, C is an output argument. If FACT = 'F' and */
/* EQUED = 'C' or 'B', each element of C must be positive. */
/* If C is output, each element of C is a power of the radix. */
/* If C is input, each element of C should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* B (input/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, 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 */
/* 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. */
/* RPVGRW (output) REAL */
/* Reciprocal pivot growth. On exit, this contains the reciprocal */
/* pivot growth factor norm(A)/norm(U). The "max absolute element" */
/* norm is used. If this 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, estimated condition numbers, */
/* and error bounds could be unreliable. If factorization fails with */
/* 0<INFO<=N, then this contains the reciprocal pivot growth factor */
/* for the leading INFO columns of A. In SGESVX, this quantity is */
/* returned in WORK(1). */
/* BERR (output) REAL array, dimension (NRHS) */
/* Componentwise relative backward error. This is the */
/* componentwise relative backward error of each solution vector X(j) */
/* (i.e., the smallest relative change in any element of A or B that */
/* makes X(j) an exact solution). */
/* N_ERR_BNDS (input) INTEGER */
/* Number of error bounds to return for each right hand side */
/* and each type (normwise or componentwise). See ERR_BNDS_NORM and */
/* ERR_BNDS_COMP below. */
/* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* normwise relative error, which is defined as follows: */
/* Normwise relative error in the ith solution vector: */
/* max_j (abs(XTRUE(j,i) - X(j,i))) */
/* ------------------------------ */
/* max_j abs(X(j,i)) */
/* The array is indexed by the type of error information as described */
/* below. There currently are up to three pieces of information */
/* returned. */
/* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_NORM(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated normwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*A, where S scales each row by a power of the */
/* radix so all absolute row sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* componentwise relative error, which is defined as follows: */
/* Componentwise relative error in the ith solution vector: */
/* abs(XTRUE(j,i) - X(j,i)) */
/* max_j ---------------------- */
/* abs(X(j,i)) */
/* The array is indexed by the right-hand side i (on which the */
/* componentwise relative error depends), and the type of error */
/* information as described below. There currently are up to three */
/* pieces of information returned for each right-hand side. If */
/* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */
/* the first (:,N_ERR_BNDS) entries are returned. */
/* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_COMP(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated componentwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*(A*diag(x)), where x is the solution for the */
/* current right-hand side and S scales each row of */
/* A*diag(x) by a power of the radix so all absolute row */
/* sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* NPARAMS (input) INTEGER */
/* Specifies the number of parameters set in PARAMS. If .LE. 0, the */
/* PARAMS array is never referenced and default values are used. */
/* PARAMS (input / output) REAL array, dimension NPARAMS */
/* Specifies algorithm parameters. If an entry is .LT. 0.0, then */
/* that entry will be filled with default value used for that */
/* parameter. Only positions up to NPARAMS are accessed; defaults */
/* are used for higher-numbered parameters. */
/* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
/* refinement or not. */
/* Default: 1.0 */
/* = 0.0 : No refinement is performed, and no error bounds are */
/* computed. */
/* = 1.0 : Use the double-precision refinement algorithm, */
/* possibly with doubled-single computations if the */
/* compilation environment does not support DOUBLE */
/* PRECISION. */
/* (other values are reserved for future use) */
/* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
/* computations allowed for refinement. */
/* Default: 10 */
/* Aggressive: Set to 100 to permit convergence using approximate */
/* factorizations or factorizations other than LU. If */
/* the factorization uses a technique other than */
/* Gaussian elimination, the guarantees in */
/* err_bnds_norm and err_bnds_comp may no longer be */
/* trustworthy. */
/* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
/* will attempt to find a solution with small componentwise */
/* relative error in the double-precision algorithm. Positive */
/* is true, 0.0 is false. */
/* Default: 1.0 (attempt componentwise convergence) */
/* WORK (workspace) REAL array, dimension (4*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: Successful exit. The solution to every right-hand side is */
/* guaranteed. */
/* < 0: If INFO = -i, the i-th argument had an illegal value */
/* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly singular, so */
/* the solution and error bounds could not be computed. RCOND = 0 */
/* is returned. */
/* = N+J: The solution corresponding to the Jth right-hand side is */
/* not guaranteed. The solutions corresponding to other right- */
/* hand sides K with K > J may not be guaranteed as well, but */
/* only the first such right-hand side is reported. If a small */
/* componentwise error is not requested (PARAMS(3) = 0.0) then */
/* the Jth right-hand side is the first with a normwise error */
/* bound that is not guaranteed (the smallest J such */
/* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
/* the Jth right-hand side is the first with either a normwise or */
/* componentwise error bound that is not guaranteed (the smallest */
/* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
/* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
/* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
/* about all of the right-hand sides check ERR_BNDS_NORM or */
/* ERR_BNDS_COMP. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
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");
}
/* Default is failure. If an input parameter is wrong or */
/* factorization fails, make everything look horrible. Only the */
/* pivot growth is set here, the rest is initialized in SGBRFSX. */
*rpvgrw = 0.f;
/* Test the input parameters. PARAMS is not tested until SGBRFSX. */
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 (*kl < 0) {
*info = -4;
} else if (*ku < 0) {
*info = -5;
} else if (*nrhs < 0) {
*info = -6;
} else if (*ldab < *kl + *ku + 1) {
*info = -8;
} else if (*ldafb < (*kl << 1) + *ku + 1) {
*info = -10;
} else if (lsame_(fact, "F") && ! (rowequ || colequ
|| lsame_(equed, "N"))) {
*info = -12;
} 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 = -13;
} 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 = -14;
} else if (*n > 0) {
colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
} else {
colcnd = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -15;
} else if (*ldx < max(1,*n)) {
*info = -16;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGBSVXX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
sgbequb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &
rowcnd, &colcnd, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
slaqgb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &
rowcnd, &colcnd, &amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed,
"B");
colequ = lsame_(equed, "C") || lsame_(equed,
"B");
}
/* If the scaling factors are not applied, set them to 1.0. */
if (! rowequ) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
r__[j] = 1.f;
}
}
if (! colequ) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
c__[j] = 1.f;
}
}
}
/* Scale the right hand side. */
if (notran) {
if (rowequ) {
slascl2_(n, nrhs, &r__[1], &b[b_offset], ldb);
}
} else {
if (colequ) {
slascl2_(n, nrhs, &c__[1], &b[b_offset], ldb);
}
}
if (nofact || equil) {
/* Compute the LU factorization of A. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = (*kl << 1) + *ku + 1;
for (i__ = *kl + 1; i__ <= i__2; ++i__) {
afb[i__ + j * afb_dim1] = ab[i__ - *kl + j * ab_dim1];
/* L30: */
}
/* L40: */
}
sgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
/* Pivot in column INFO is exactly 0 */
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
*rpvgrw = sla_gbrpvgrw__(n, kl, ku, info, &ab[ab_offset], ldab, &
afb[afb_offset], ldafb);
return 0;
}
}
/* Compute the reciprocal pivot growth factor RPVGRW. */
*rpvgrw = sla_gbrpvgrw__(n, kl, ku, n, &ab[ab_offset], ldab, &afb[
afb_offset], ldafb);
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
sgbtrs_(trans, n, kl, ku, nrhs, &afb[afb_offset], ldafb, &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. */
sgbrfsx_(trans, equed, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[
afb_offset], ldafb, &ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb,
&x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, &
err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[
err_bnds_comp_offset], nparams, ¶ms[1], &work[1], &iwork[1],
info);
/* Scale solutions. */
if (colequ && notran) {
slascl2_(n, nrhs, &c__[1], &x[x_offset], ldx);
} else if (rowequ && ! notran) {
slascl2_(n, nrhs, &r__[1], &x[x_offset], ldx);
}
return 0;
/* End of SGBSVXX */
} /* sgbsvxx_ */
/* Subroutine */ int sdrvgb_(logical *dotype, integer *nn, integer *nval,
integer *nrhs, real *thresh, logical *tsterr, real *a, integer *la,
real *afb, integer *lafb, real *asav, real *b, real *bsav, real *x,
real *xact, real *s, real *work, real *rwork, integer *iwork, integer
*nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char transs[1*3] = "N" "T" "C";
static char facts[1*3] = "F" "N" "E";
static char equeds[1*4] = "N" "R" "C" "B";
/* Format strings */
static char fmt_9999[] = "(\002 *** In SDRVGB, LA=\002,i5,\002 is too sm"
"all for N=\002,i5,\002, KU=\002,i5,\002, KL=\002,i5,/\002 ==> In"
"crease LA to at least \002,i5)";
static char fmt_9998[] = "(\002 *** In SDRVGB, LAFB=\002,i5,\002 is too "
"small for N=\002,i5,\002, KU=\002,i5,\002, KL=\002,i5,/\002 ==> "
"Increase LAFB to at least \002,i5)";
static char fmt_9997[] = "(1x,a,\002, N=\002,i5,\002, KL=\002,i5,\002, K"
"U=\002,i5,\002, type \002,i1,\002, test(\002,i1,\002)=\002,g12.5)"
;
static char fmt_9995[] = "(1x,a,\002( '\002,a1,\002','\002,a1,\002',\002"
",i5,\002,\002,i5,\002,\002,i5,\002,...), EQUED='\002,a1,\002', t"
"ype \002,i1,\002, test(\002,i1,\002)=\002,g12.5)";
static char fmt_9996[] = "(1x,a,\002( '\002,a1,\002','\002,a1,\002',\002"
",i5,\002,\002,i5,\002,\002,i5,\002,...), type \002,i1,\002, test("
"\002,i1,\002)=\002,g12.5)";
/* System generated locals */
address a__1[2];
integer i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10,
i__11[2];
real r__1, r__2, r__3;
char ch__1[2];
/* Local variables */
integer i__, j, k, n, i1, i2, k1, nb, in, kl, ku, nt, lda, ldb, ikl, nkl,
iku, nku;
char fact[1];
integer ioff, mode;
real amax;
char path[3];
integer imat, info;
char dist[1], type__[1];
integer nrun, ldafb, ifact, nfail, iseed[4], nfact;
char equed[1];
integer nbmin;
real rcond, roldc;
integer nimat;
real roldi;
real anorm;
integer itran;
logical equil;
real roldo;
char trans[1];
integer izero, nerrs;
logical zerot;
char xtype[1];
logical prefac;
real colcnd;
real rcondc;
logical nofact;
integer iequed;
real rcondi;
real cndnum, anormi, rcondo, ainvnm;
logical trfcon;
real anormo, rowcnd;
real anrmpv;
real result[7], rpvgrw;
/* Fortran I/O blocks */
static cilist io___26 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___27 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___65 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___72 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___73 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___74 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___75 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___76 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___77 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___78 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___79 = { 0, 0, 0, fmt_9996, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SDRVGB tests the driver routines SGBSV and -SVX. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* NRHS (input) INTEGER */
/* The number of right hand side vectors to be generated for */
/* each linear system. */
/* THRESH (input) REAL */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* A (workspace) REAL array, dimension (LA) */
/* LA (input) INTEGER */
/* The length of the array A. LA >= (2*NMAX-1)*NMAX */
/* where NMAX is the largest entry in NVAL. */
/* AFB (workspace) REAL array, dimension (LAFB) */
/* LAFB (input) INTEGER */
/* The length of the array AFB. LAFB >= (3*NMAX-2)*NMAX */
/* where NMAX is the largest entry in NVAL. */
/* ASAV (workspace) REAL array, dimension (LA) */
/* B (workspace) REAL array, dimension (NMAX*NRHS) */
/* BSAV (workspace) REAL array, dimension (NMAX*NRHS) */
/* X (workspace) REAL array, dimension (NMAX*NRHS) */
/* XACT (workspace) REAL array, dimension (NMAX*NRHS) */
/* S (workspace) REAL array, dimension (2*NMAX) */
/* WORK (workspace) REAL array, dimension */
/* (NMAX*max(3,NRHS,NMAX)) */
/* RWORK (workspace) REAL array, dimension */
/* (max(NMAX,2*NRHS)) */
/* IWORK (workspace) INTEGER array, dimension (2*NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--rwork;
--work;
--s;
--xact;
--x;
--bsav;
--b;
--asav;
--afb;
--a;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "GB", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Test the error exits */
if (*tsterr) {
serrvx_(path, nout);
}
infoc_1.infot = 0;
/* Set the block size and minimum block size for testing. */
nb = 1;
nbmin = 2;
xlaenv_(&c__1, &nb);
xlaenv_(&c__2, &nbmin);
/* Do for each value of N in NVAL */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
ldb = max(n,1);
*(unsigned char *)xtype = 'N';
/* Set limits on the number of loop iterations. */
/* Computing MAX */
i__2 = 1, i__3 = min(n,4);
nkl = max(i__2,i__3);
if (n == 0) {
nkl = 1;
}
nku = nkl;
nimat = 8;
if (n <= 0) {
nimat = 1;
}
i__2 = nkl;
for (ikl = 1; ikl <= i__2; ++ikl) {
/* Do for KL = 0, N-1, (3N-1)/4, and (N+1)/4. This order makes */
/* it easier to skip redundant values for small values of N. */
if (ikl == 1) {
kl = 0;
} else if (ikl == 2) {
/* Computing MAX */
i__3 = n - 1;
kl = max(i__3,0);
} else if (ikl == 3) {
kl = (n * 3 - 1) / 4;
} else if (ikl == 4) {
kl = (n + 1) / 4;
}
i__3 = nku;
for (iku = 1; iku <= i__3; ++iku) {
/* Do for KU = 0, N-1, (3N-1)/4, and (N+1)/4. This order */
/* makes it easier to skip redundant values for small */
/* values of N. */
if (iku == 1) {
ku = 0;
} else if (iku == 2) {
/* Computing MAX */
i__4 = n - 1;
ku = max(i__4,0);
} else if (iku == 3) {
ku = (n * 3 - 1) / 4;
} else if (iku == 4) {
ku = (n + 1) / 4;
}
/* Check that A and AFB are big enough to generate this */
/* matrix. */
lda = kl + ku + 1;
ldafb = (kl << 1) + ku + 1;
if (lda * n > *la || ldafb * n > *lafb) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (lda * n > *la) {
io___26.ciunit = *nout;
s_wsfe(&io___26);
do_fio(&c__1, (char *)&(*la), (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer));
i__4 = n * (kl + ku + 1);
do_fio(&c__1, (char *)&i__4, (ftnlen)sizeof(integer));
e_wsfe();
++nerrs;
}
if (ldafb * n > *lafb) {
io___27.ciunit = *nout;
s_wsfe(&io___27);
do_fio(&c__1, (char *)&(*lafb), (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer));
i__4 = n * ((kl << 1) + ku + 1);
do_fio(&c__1, (char *)&i__4, (ftnlen)sizeof(integer));
e_wsfe();
++nerrs;
}
goto L130;
}
i__4 = nimat;
for (imat = 1; imat <= i__4; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L120;
}
/* Skip types 2, 3, or 4 if the matrix is too small. */
zerot = imat >= 2 && imat <= 4;
if (zerot && n < imat - 1) {
goto L120;
}
/* Set up parameters with SLATB4 and generate a */
/* test matrix with SLATMS. */
slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &
mode, &cndnum, dist);
rcondc = 1.f / cndnum;
s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6);
slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, "Z", &a[1], &lda, &work[
1], &info);
/* Check the error code from SLATMS. */
if (info != 0) {
alaerh_(path, "SLATMS", &info, &c__0, " ", &n, &n, &
kl, &ku, &c_n1, &imat, &nfail, &nerrs, nout);
goto L120;
}
/* For types 2, 3, and 4, zero one or more columns of */
/* the matrix to test that INFO is returned correctly. */
izero = 0;
if (zerot) {
if (imat == 2) {
izero = 1;
} else if (imat == 3) {
izero = n;
} else {
izero = n / 2 + 1;
}
ioff = (izero - 1) * lda;
if (imat < 4) {
/* Computing MAX */
i__5 = 1, i__6 = ku + 2 - izero;
i1 = max(i__5,i__6);
/* Computing MIN */
i__5 = kl + ku + 1, i__6 = ku + 1 + (n - izero);
i2 = min(i__5,i__6);
i__5 = i2;
for (i__ = i1; i__ <= i__5; ++i__) {
a[ioff + i__] = 0.f;
/* L20: */
}
} else {
i__5 = n;
for (j = izero; j <= i__5; ++j) {
/* Computing MAX */
i__6 = 1, i__7 = ku + 2 - j;
/* Computing MIN */
i__9 = kl + ku + 1, i__10 = ku + 1 + (n - j);
i__8 = min(i__9,i__10);
for (i__ = max(i__6,i__7); i__ <= i__8; ++i__)
{
a[ioff + i__] = 0.f;
/* L30: */
}
ioff += lda;
/* L40: */
}
}
}
/* Save a copy of the matrix A in ASAV. */
i__5 = kl + ku + 1;
slacpy_("Full", &i__5, &n, &a[1], &lda, &asav[1], &lda);
for (iequed = 1; iequed <= 4; ++iequed) {
*(unsigned char *)equed = *(unsigned char *)&equeds[
iequed - 1];
if (iequed == 1) {
nfact = 3;
} else {
nfact = 1;
}
i__5 = nfact;
for (ifact = 1; ifact <= i__5; ++ifact) {
*(unsigned char *)fact = *(unsigned char *)&facts[
ifact - 1];
prefac = lsame_(fact, "F");
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
if (zerot) {
if (prefac) {
goto L100;
}
rcondo = 0.f;
rcondi = 0.f;
} else if (! nofact) {
/* Compute the condition number for comparison */
/* with the value returned by SGESVX (FACT = */
/* 'N' reuses the condition number from the */
/* previous iteration with FACT = 'F'). */
i__8 = kl + ku + 1;
slacpy_("Full", &i__8, &n, &asav[1], &lda, &
afb[kl + 1], &ldafb);
if (equil || iequed > 1) {
/* Compute row and column scale factors to */
/* equilibrate the matrix A. */
sgbequ_(&n, &n, &kl, &ku, &afb[kl + 1], &
ldafb, &s[1], &s[n + 1], &rowcnd,
&colcnd, &amax, &info);
if (info == 0 && n > 0) {
if (lsame_(equed, "R")) {
rowcnd = 0.f;
colcnd = 1.f;
} else if (lsame_(equed, "C")) {
rowcnd = 1.f;
colcnd = 0.f;
} else if (lsame_(equed, "B")) {
rowcnd = 0.f;
colcnd = 0.f;
}
/* Equilibrate the matrix. */
slaqgb_(&n, &n, &kl, &ku, &afb[kl + 1]
, &ldafb, &s[1], &s[n + 1], &
rowcnd, &colcnd, &amax, equed);
}
}
/* Save the condition number of the */
/* non-equilibrated system for use in SGET04. */
if (equil) {
roldo = rcondo;
roldi = rcondi;
}
/* Compute the 1-norm and infinity-norm of A. */
anormo = slangb_("1", &n, &kl, &ku, &afb[kl +
1], &ldafb, &rwork[1]);
anormi = slangb_("I", &n, &kl, &ku, &afb[kl +
1], &ldafb, &rwork[1]);
/* Factor the matrix A. */
sgbtrf_(&n, &n, &kl, &ku, &afb[1], &ldafb, &
iwork[1], &info);
/* Form the inverse of A. */
slaset_("Full", &n, &n, &c_b48, &c_b49, &work[
1], &ldb);
s_copy(srnamc_1.srnamt, "SGBTRS", (ftnlen)32,
(ftnlen)6);
sgbtrs_("No transpose", &n, &kl, &ku, &n, &
afb[1], &ldafb, &iwork[1], &work[1], &
ldb, &info);
/* Compute the 1-norm condition number of A. */
ainvnm = slange_("1", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormo <= 0.f || ainvnm <= 0.f) {
rcondo = 1.f;
} else {
rcondo = 1.f / anormo / ainvnm;
}
/* Compute the infinity-norm condition number */
/* of A. */
ainvnm = slange_("I", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormi <= 0.f || ainvnm <= 0.f) {
rcondi = 1.f;
} else {
rcondi = 1.f / anormi / ainvnm;
}
}
for (itran = 1; itran <= 3; ++itran) {
/* Do for each value of TRANS. */
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
if (itran == 1) {
rcondc = rcondo;
} else {
rcondc = rcondi;
}
/* Restore the matrix A. */
i__8 = kl + ku + 1;
slacpy_("Full", &i__8, &n, &asav[1], &lda, &a[
1], &lda);
/* Form an exact solution and set the right hand */
/* side. */
s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32,
(ftnlen)6);
slarhs_(path, xtype, "Full", trans, &n, &n, &
kl, &ku, nrhs, &a[1], &lda, &xact[1],
&ldb, &b[1], &ldb, iseed, &info);
*(unsigned char *)xtype = 'C';
slacpy_("Full", &n, nrhs, &b[1], &ldb, &bsav[
1], &ldb);
if (nofact && itran == 1) {
/* --- Test SGBSV --- */
/* Compute the LU factorization of the matrix */
/* and solve the system. */
i__8 = kl + ku + 1;
slacpy_("Full", &i__8, &n, &a[1], &lda, &
afb[kl + 1], &ldafb);
slacpy_("Full", &n, nrhs, &b[1], &ldb, &x[
1], &ldb);
s_copy(srnamc_1.srnamt, "SGBSV ", (ftnlen)
32, (ftnlen)6);
sgbsv_(&n, &kl, &ku, nrhs, &afb[1], &
ldafb, &iwork[1], &x[1], &ldb, &
info);
/* Check error code from SGBSV . */
if (info != izero) {
alaerh_(path, "SGBSV ", &info, &izero,
" ", &n, &n, &kl, &ku, nrhs,
&imat, &nfail, &nerrs, nout);
}
/* Reconstruct matrix from factors and */
/* compute residual. */
sgbt01_(&n, &n, &kl, &ku, &a[1], &lda, &
afb[1], &ldafb, &iwork[1], &work[
1], result);
nt = 1;
if (izero == 0) {
/* Compute residual of the computed */
/* solution. */
slacpy_("Full", &n, nrhs, &b[1], &ldb,
&work[1], &ldb);
sgbt02_("No transpose", &n, &n, &kl, &
ku, nrhs, &a[1], &lda, &x[1],
&ldb, &work[1], &ldb, &result[
1]);
/* Check solution from generated exact */
/* solution. */
sget04_(&n, nrhs, &x[1], &ldb, &xact[
1], &ldb, &rcondc, &result[2])
;
nt = 3;
}
/* Print information about the tests that did */
/* not pass the threshold. */
i__8 = nt;
for (k = 1; k <= i__8; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___65.ciunit = *nout;
s_wsfe(&io___65);
do_fio(&c__1, "SGBSV ", (ftnlen)6)
;
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[k -
1], (ftnlen)sizeof(real));
e_wsfe();
++nfail;
}
/* L50: */
}
nrun += nt;
}
/* --- Test SGBSVX --- */
if (! prefac) {
i__8 = (kl << 1) + ku + 1;
slaset_("Full", &i__8, &n, &c_b48, &c_b48,
&afb[1], &ldafb);
}
slaset_("Full", &n, nrhs, &c_b48, &c_b48, &x[
1], &ldb);
if (iequed > 1 && n > 0) {
/* Equilibrate the matrix if FACT = 'F' and */
/* EQUED = 'R', 'C', or 'B'. */
slaqgb_(&n, &n, &kl, &ku, &a[1], &lda, &s[
1], &s[n + 1], &rowcnd, &colcnd, &
amax, equed);
}
/* Solve the system and compute the condition */
/* number and error bounds using SGBSVX. */
s_copy(srnamc_1.srnamt, "SGBSVX", (ftnlen)32,
(ftnlen)6);
sgbsvx_(fact, trans, &n, &kl, &ku, nrhs, &a[1]
, &lda, &afb[1], &ldafb, &iwork[1],
equed, &s[1], &s[n + 1], &b[1], &ldb,
&x[1], &ldb, &rcond, &rwork[1], &
rwork[*nrhs + 1], &work[1], &iwork[n
+ 1], &info);
/* Check the error code from SGBSVX. */
if (info != izero) {
/* Writing concatenation */
i__11[0] = 1, a__1[0] = fact;
i__11[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__11, &c__2, (ftnlen)
2);
alaerh_(path, "SGBSVX", &info, &izero,
ch__1, &n, &n, &kl, &ku, nrhs, &
imat, &nfail, &nerrs, nout);
}
/* Compare WORK(1) from SGBSVX with the computed */
/* reciprocal pivot growth factor RPVGRW */
if (info != 0) {
anrmpv = 0.f;
i__8 = info;
for (j = 1; j <= i__8; ++j) {
/* Computing MAX */
i__6 = ku + 2 - j;
/* Computing MIN */
i__9 = n + ku + 1 - j, i__10 = kl +
ku + 1;
i__7 = min(i__9,i__10);
for (i__ = max(i__6,1); i__ <= i__7;
++i__) {
/* Computing MAX */
r__2 = anrmpv, r__3 = (r__1 = a[
i__ + (j - 1) * lda],
dabs(r__1));
anrmpv = dmax(r__2,r__3);
/* L60: */
}
/* L70: */
}
/* Computing MIN */
i__7 = info - 1, i__6 = kl + ku;
i__8 = min(i__7,i__6);
/* Computing MAX */
i__9 = 1, i__10 = kl + ku + 2 - info;
rpvgrw = slantb_("M", "U", "N", &info, &
i__8, &afb[max(i__9, i__10)], &
ldafb, &work[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = anrmpv / rpvgrw;
}
} else {
i__8 = kl + ku;
rpvgrw = slantb_("M", "U", "N", &n, &i__8,
&afb[1], &ldafb, &work[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = slangb_("M", &n, &kl, &ku, &
a[1], &lda, &work[1]) / rpvgrw;
}
}
result[6] = (r__1 = rpvgrw - work[1], dabs(
r__1)) / dmax(work[1],rpvgrw) /
slamch_("E");
if (! prefac) {
/* Reconstruct matrix from factors and */
/* compute residual. */
sgbt01_(&n, &n, &kl, &ku, &a[1], &lda, &
afb[1], &ldafb, &iwork[1], &work[
1], result);
k1 = 1;
} else {
k1 = 2;
}
if (info == 0) {
trfcon = FALSE_;
/* Compute residual of the computed solution. */
slacpy_("Full", &n, nrhs, &bsav[1], &ldb,
&work[1], &ldb);
sgbt02_(trans, &n, &n, &kl, &ku, nrhs, &
asav[1], &lda, &x[1], &ldb, &work[
1], &ldb, &result[1]);
/* Check solution from generated exact */
/* solution. */
if (nofact || prefac && lsame_(equed,
"N")) {
sget04_(&n, nrhs, &x[1], &ldb, &xact[
1], &ldb, &rcondc, &result[2])
;
} else {
if (itran == 1) {
roldc = roldo;
} else {
roldc = roldi;
}
sget04_(&n, nrhs, &x[1], &ldb, &xact[
1], &ldb, &roldc, &result[2]);
}
/* Check the error bounds from iterative */
/* refinement. */
sgbt05_(trans, &n, &kl, &ku, nrhs, &asav[
1], &lda, &b[1], &ldb, &x[1], &
ldb, &xact[1], &ldb, &rwork[1], &
rwork[*nrhs + 1], &result[3]);
} else {
trfcon = TRUE_;
}
/* Compare RCOND from SGBSVX with the computed */
/* value in RCONDC. */
result[5] = sget06_(&rcond, &rcondc);
/* Print information about the tests that did */
/* not pass the threshold. */
if (! trfcon) {
for (k = k1; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___72.ciunit = *nout;
s_wsfe(&io___72);
do_fio(&c__1, "SGBSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(real));
e_wsfe();
} else {
io___73.ciunit = *nout;
s_wsfe(&io___73);
do_fio(&c__1, "SGBSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(real));
e_wsfe();
}
++nfail;
}
/* L80: */
}
nrun = nrun + 7 - k1;
} else {
if (result[0] >= *thresh && ! prefac) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___74.ciunit = *nout;
s_wsfe(&io___74);
do_fio(&c__1, "SGBSVX", (ftnlen)6)
;
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__1, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[0],
(ftnlen)sizeof(real));
e_wsfe();
} else {
io___75.ciunit = *nout;
s_wsfe(&io___75);
do_fio(&c__1, "SGBSVX", (ftnlen)6)
;
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__1, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[0],
(ftnlen)sizeof(real));
e_wsfe();
}
++nfail;
++nrun;
}
if (result[5] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___76.ciunit = *nout;
s_wsfe(&io___76);
do_fio(&c__1, "SGBSVX", (ftnlen)6)
;
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__6, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[5],
(ftnlen)sizeof(real));
e_wsfe();
} else {
io___77.ciunit = *nout;
s_wsfe(&io___77);
do_fio(&c__1, "SGBSVX", (ftnlen)6)
;
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__6, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[5],
(ftnlen)sizeof(real));
e_wsfe();
}
++nfail;
++nrun;
}
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___78.ciunit = *nout;
s_wsfe(&io___78);
do_fio(&c__1, "SGBSVX", (ftnlen)6)
;
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__7, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[6],
(ftnlen)sizeof(real));
e_wsfe();
} else {
io___79.ciunit = *nout;
s_wsfe(&io___79);
do_fio(&c__1, "SGBSVX", (ftnlen)6)
;
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&kl, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ku, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__7, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[6],
(ftnlen)sizeof(real));
e_wsfe();
}
++nfail;
++nrun;
}
}
/* L90: */
}
L100:
;
}
/* L110: */
}
L120:
;
}
L130:
;
}
/* L140: */
}
/* L150: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of SDRVGB */
} /* sdrvgb_ */
/* Subroutine */ int sla_gbrfsx_extended__(integer *prec_type__, integer *
trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs,
real *ab, integer *ldab, real *afb, integer *ldafb, 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 ab_dim1, ab_offset, afb_dim1, afb_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, m;
extern /* Subroutine */ int sla_gbamv__(integer *, integer *, integer *,
integer *, integer *, real *, real *, integer *, real *, integer *
, real *, real *, integer *);
logical incr_prec__;
real prev_dz_z__, yk, final_dx_x__, final_dz_z__;
extern /* Subroutine */ int sla_wwaddw__(integer *, real *, real *, real *
);
real prevnormdx;
integer cnt;
real dyk, eps, incr_thresh__, dx_x__, dz_z__, ymin;
extern /* Subroutine */ int sla_lin_berr__(integer *, integer *, integer *
, real *, real *, real *), blas_sgbmv_x__(integer *, integer *,
integer *, integer *, integer *, real *, real *, integer *, real *
, integer *, real *, real *, integer *, integer *);
integer y_prec_state__;
extern /* Subroutine */ int blas_sgbmv2_x__(integer *, integer *, integer
*, integer *, integer *, real *, real *, integer *, real *, real *
, integer *, real *, real *, integer *, integer *), sgbmv_(char *,
integer *, integer *, integer *, integer *, real *, real *,
integer *, real *, integer *, real *, real *, integer *);
real dxrat, dzrat;
char trans[1];
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *);
real normx, normy;
extern /* Subroutine */ int saxpy_(integer *, real *, real *, integer *,
real *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int sgbtrs_(char *, integer *, integer *, integer
*, integer *, real *, integer *, integer *, real *, integer *,
integer *);
real normdx;
extern /* Character */ VOID chla_transtype__(char *, ftnlen, integer *);
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. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SLA_GBRFSX_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 SGBRFSX 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. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 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 SGBTRF. */
/* 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 SGBTRF; 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 SGBTRS. */
/* 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 */
/* is .FALSE.. */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* < 0: if INFO = -i, the ith argument to SGBTRS had an illegal */
/* value */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1;
afb -= afb_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;
m = *kl + *ku + 1;
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) {
sgbmv_(trans, &m, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[
j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1);
} else if (y_prec_state__ == 1) {
blas_sgbmv_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[
ab_offset], ldab, &y[j * y_dim1 + 1], &c__1, &c_b8, &
res[1], &c__1, prec_type__);
} else {
blas_sgbmv2_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[
ab_offset], ldab, &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);
sgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &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);
sgbmv_(trans, n, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &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_gbamv__(trans_type__, n, n, kl, ku, &c_b8, &ab[ab_offset], ldab, &
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_gbrfsx_extended__ */
/* Subroutine */ int sgbrfs_(char *trans, integer *n, integer *kl, integer *
ku, integer *nrhs, real *ab, integer *ldab, real *afb, integer *ldafb,
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
=======
SGBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is banded, 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.
KL (input) INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
AB (input) REAL array, dimension (LDAB,N)
The original band matrix A, stored in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB (input) REAL array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.
LDAFB (input) INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
IPIV (input) INTEGER array, dimension (N)
The pivot indices from SGBTRF; 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 SGBTRS.
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 ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
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 sgbmv_(char *, integer *, integer *, 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 integer kk;
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 sgbtrs_(char *, integer *, integer *, integer
*, integer *, real *, integer *, integer *, real *, integer *,
integer *);
static char transt[1];
static real lstres, eps;
#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]
#define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1]
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
afb_dim1 = *ldafb;
afb_offset = 1 + afb_dim1 * 1;
afb -= afb_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 (*kl < 0) {
*info = -3;
} else if (*ku < 0) {
*info = -4;
} else if (*nrhs < 0) {
*info = -5;
} else if (*ldab < *kl + *ku + 1) {
*info = -7;
} else if (*ldafb < (*kl << 1) + *ku + 1) {
*info = -9;
} else if (*ldb < max(1,*n)) {
*info = -12;
} else if (*ldx < max(1,*n)) {
*info = -14;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGBRFS", &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
Computing MIN */
i__1 = *kl + *ku + 2, i__2 = *n + 1;
nz = min(i__1,i__2);
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);
sgbmv_(trans, n, n, kl, ku, &c_b15, &ab[ab_offset], ldab, &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) {
kk = *ku + 1 - k;
xk = (r__1 = x_ref(k, j), dabs(r__1));
/* Computing MAX */
i__3 = 1, i__4 = k - *ku;
/* Computing MIN */
i__6 = *n, i__7 = k + *kl;
i__5 = min(i__6,i__7);
for (i__ = max(i__3,i__4); i__ <= i__5; ++i__) {
work[i__] += (r__1 = ab_ref(kk + i__, k), dabs(r__1)) *
xk;
/* L40: */
}
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
kk = *ku + 1 - k;
/* Computing MAX */
i__5 = 1, i__3 = k - *ku;
/* Computing MIN */
i__6 = *n, i__7 = k + *kl;
i__4 = min(i__6,i__7);
for (i__ = max(i__5,i__3); i__ <= i__4; ++i__) {
s += (r__1 = ab_ref(kk + 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. */
sgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &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). */
sgbtrs_(transt, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
ipiv[1], &work[*n + 1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[*n + i__] *= work[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__];
/* L120: */
}
sgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
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 SGBRFS */
} /* sgbrfs_ */