//! see full matrix case.
inline void solvecomplex(fortranVectorF<n>& Zr,fortranVectorF<n>& Zi,
const MatrixReal& Jac)
{
#include "Ivdep.hpp"
for(int i=n;i>=1;i--)
{
Z2N(2*i-1)=Zr(i);
Z2N(2*i)=Zi(i);
}
int nn=n,knsub=nsub,knsup=nsup,lldab=ldab,un=1,ier; char notrans='n';
zgbtrs_(¬rans,&nn,&knsub,&knsup,&un,&E2R,&lldab,&(ipivc[0]),
&Z2N,&nn,&ier);
if(ier!=0)
throw OdesException("odes::Matrices::slvrad, zgetrs,ier=",ier);
#include "Ivdep.hpp"
for(int i=1;i<=n;i++)
{
Zi(i)=Z2N(2*i);
Zr(i)=Z2N(2*i-1);
}
}
int zgbsv_(int *n, int *kl, int *ku, int *
nrhs, doublecomplex *ab, int *ldab, int *ipiv, doublecomplex *
b, int *ldb, int *info)
{
/* System generated locals */
int ab_dim1, ab_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern int xerbla_(char *, int *), zgbtrf_(
int *, int *, int *, int *, doublecomplex *,
int *, int *, int *), zgbtrs_(char *, int *,
int *, int *, int *, doublecomplex *, int *,
int *, doublecomplex *, int *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGBSV computes the solution to a complex 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) COMPLEX*16 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) COMPLEX*16 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_("ZGBSV ", &i__1);
return 0;
}
/* Compute the LU factorization of the band matrix A. */
zgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
zgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[
1], &b[b_offset], ldb, info);
}
return 0;
/* End of ZGBSV */
} /* zgbsv_ */
/* Subroutine */ int zgbrfs_(char *trans, integer *n, integer *kl, integer *
ku, integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *
afb, integer *ldafb, integer *ipiv, doublecomplex *b, integer *ldb,
doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr,
doublecomplex *work, doublereal *rwork, 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, i__6, i__7;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
integer i__, j, k;
doublereal s;
integer kk;
doublereal xk;
integer nz;
doublereal eps;
integer kase;
doublereal safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int zgbmv_(char *, integer *, integer *, integer *
, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer count;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), zlacn2_(
integer *, doublecomplex *, doublecomplex *, doublereal *,
integer *, integer *);
extern doublereal dlamch_(char *);
doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical notran;
char transn[1], transt[1];
doublereal lstres;
extern /* Subroutine */ int zgbtrs_(char *, integer *, integer *, integer
*, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGBRFS 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) */
/* 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) COMPLEX*16 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) COMPLEX*16 array, dimension (LDAFB,N) */
/* Details of the LU factorization of the band matrix A, as */
/* computed by ZGBTRF. 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 ZGBTRF; for 1<=i<=N, row i of the */
/* matrix was interchanged with row IPIV(i). */
/* B (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by ZGBTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION 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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* 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;
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;
--rwork;
/* 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_("ZGBRFS", &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.;
berr[j] = 0.;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)transn = 'N';
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transn = 'C';
*(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 = dlamch_("Epsilon");
safmin = dlamch_("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.;
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. */
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
z__1.r = -1., z__1.i = -0.;
zgbmv_(trans, n, n, kl, ku, &z__1, &ab[ab_offset], ldab, &x[j *
x_dim1 + 1], &c__1, &c_b1, &work[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__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[
i__ + j * b_dim1]), abs(d__2));
/* 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;
i__3 = k + j * x_dim1;
xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[k + j *
x_dim1]), abs(d__2));
/* 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__) {
i__3 = kk + i__ + k * ab_dim1;
rwork[i__] += ((d__1 = ab[i__3].r, abs(d__1)) + (d__2 =
d_imag(&ab[kk + i__ + k * ab_dim1]), abs(d__2))) *
xk;
/* L40: */
}
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.;
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__) {
i__5 = kk + i__ + k * ab_dim1;
i__3 = i__ + j * x_dim1;
s += ((d__1 = ab[i__5].r, abs(d__1)) + (d__2 = d_imag(&ab[
kk + i__ + k * ab_dim1]), abs(d__2))) * ((d__3 =
x[i__3].r, abs(d__3)) + (d__4 = d_imag(&x[i__ + j
* x_dim1]), abs(d__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__4 = i__;
d__3 = s, d__4 = ((d__1 = work[i__4].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2))) / rwork[i__];
s = max(d__3,d__4);
} else {
/* Computing MAX */
i__4 = i__;
d__3 = s, d__4 = ((d__1 = work[i__4].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__]
+ safe1);
s = max(d__3,d__4);
}
/* 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. <= lstres && count <= 5) {
/* Update solution and try again. */
zgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1]
, &work[1], n, info);
zaxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &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 ZLACN2 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 (rwork[i__] > safe2) {
i__4 = i__;
rwork[i__] = (d__1 = work[i__4].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
;
} else {
i__4 = i__;
rwork[i__] = (d__1 = work[i__4].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
+ safe1;
}
/* L90: */
}
kase = 0;
L100:
zlacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**H). */
zgbtrs_(transt, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
ipiv[1], &work[1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__4 = i__;
i__5 = i__;
i__3 = i__;
z__1.r = rwork[i__5] * work[i__3].r, z__1.i = rwork[i__5]
* work[i__3].i;
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
/* L110: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__4 = i__;
i__5 = i__;
i__3 = i__;
z__1.r = rwork[i__5] * work[i__3].r, z__1.i = rwork[i__5]
* work[i__3].i;
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
/* L120: */
}
zgbtrs_(transn, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
ipiv[1], &work[1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__4 = i__ + j * x_dim1;
d__3 = lstres, d__4 = (d__1 = x[i__4].r, abs(d__1)) + (d__2 =
d_imag(&x[i__ + j * x_dim1]), abs(d__2));
lstres = max(d__3,d__4);
/* L130: */
}
if (lstres != 0.) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of ZGBRFS */
} /* zgbrfs_ */
doublereal zla_gbrcond_x__(char *trans, integer *n, integer *kl, integer *ku,
doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb,
integer *ipiv, doublecomplex *x, integer *info, doublecomplex *work,
doublereal *rwork, ftnlen trans_len)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, i__1, i__2, i__3, i__4;
doublereal ret_val, d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, kd, ke;
doublereal tmp;
integer kase;
extern logical lsame_(char *, char *);
integer isave[3];
doublereal anorm;
extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *,
doublecomplex *, doublereal *, integer *, integer *), xerbla_(
char *, integer *);
doublereal ainvnm;
extern /* Subroutine */ int zgbtrs_(char *, integer *, integer *, integer
*, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, 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 */
/* ======= */
/* ZLA_GBRCOND_X Computes the infinity norm condition number of */
/* op(A) * diag(X) where X is a COMPLEX*16 vector. */
/* 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) COMPLEX*16 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) COMPLEX*16 array, dimension (LDAFB,N) */
/* Details of the LU factorization of the band matrix A, as */
/* computed by ZGBTRF. 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 ZGBTRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* X (input) COMPLEX*16 array, dimension (N) */
/* The vector X in the formula op(A) * diag(X). */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* i > 0: The ith argument is invalid. */
/* WORK (input) COMPLEX*16 array, dimension (2*N). */
/* Workspace. */
/* RWORK (input) DOUBLE PRECISION array, dimension (N). */
/* Workspace. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. 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;
--x;
--work;
--rwork;
/* Function Body */
ret_val = 0.;
*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_("ZLA_GBRCOND_X", &i__1);
return ret_val;
}
/* Compute norm of op(A)*op2(C). */
kd = *ku + 1;
ke = *kl + 1;
anorm = 0.;
if (notrans) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 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) {
i__2 = kd + i__ - j + j * ab_dim1;
i__4 = j;
z__2.r = ab[i__2].r * x[i__4].r - ab[i__2].i * x[i__4].i,
z__2.i = ab[i__2].r * x[i__4].i + ab[i__2].i * x[i__4]
.r;
z__1.r = z__2.r, z__1.i = z__2.i;
tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1),
abs(d__2));
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 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) {
i__3 = ke - i__ + j + i__ * ab_dim1;
i__4 = j;
z__2.r = ab[i__3].r * x[i__4].r - ab[i__3].i * x[i__4].i,
z__2.i = ab[i__3].r * x[i__4].i + ab[i__3].i * x[i__4]
.r;
z__1.r = z__2.r, z__1.i = z__2.i;
tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1),
abs(d__2));
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
}
/* Quick return if possible. */
if (*n == 0) {
ret_val = 1.;
return ret_val;
} else if (anorm == 0.) {
return ret_val;
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.;
kase = 0;
L10:
zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == 2) {
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
if (notrans) {
zgbtrs_("No transpose", n, kl, ku, &c__1, &afb[afb_offset],
ldafb, &ipiv[1], &work[1], n, info);
} else {
zgbtrs_("Conjugate transpose", n, kl, ku, &c__1, &afb[
afb_offset], ldafb, &ipiv[1], &work[1], n, info);
}
/* Multiply by inv(X). */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
z_div(&z__1, &work[i__], &x[i__]);
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
} else {
/* Multiply by inv(X'). */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
z_div(&z__1, &work[i__], &x[i__]);
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
if (notrans) {
zgbtrs_("Conjugate transpose", n, kl, ku, &c__1, &afb[
afb_offset], ldafb, &ipiv[1], &work[1], n, info);
} else {
zgbtrs_("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__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
ret_val = 1. / ainvnm;
}
return ret_val;
} /* zla_gbrcond_x__ */
/* Subroutine */ int zerrge_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublecomplex a[16] /* was [4][4] */, b[4];
integer i__, j;
doublereal r__[4];
doublecomplex w[8], x[4];
char c2[2];
doublereal r1[4], r2[4];
doublecomplex af[16] /* was [4][4] */;
integer ip[4], info;
doublereal anrm, ccond, rcond;
extern /* Subroutine */ int zgbtf2_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *, integer *),
zgetf2_(integer *, integer *, doublecomplex *, integer *, integer
*, integer *), alaesm_(char *, logical *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer
*, doublecomplex *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, doublereal *, integer *),
chkxer_(char *, integer *, integer *, logical *, logical *), zgecon_(char *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zgbequ_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *), zgbrfs_(
char *, integer *, integer *, integer *, integer *, doublecomplex
*, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zgbtrf_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *, integer *),
zgeequ_(integer *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *), zgerfs_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zgetrf_(integer *, integer *, doublecomplex *,
integer *, integer *, integer *), zgetri_(integer *,
doublecomplex *, integer *, integer *, doublecomplex *, integer *,
integer *), zgbtrs_(char *, integer *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *, doublecomplex *,
integer *, integer *), zgetrs_(char *, integer *,
integer *, doublecomplex *, integer *, integer *, doublecomplex *,
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 */
/* ======= */
/* ZERRGE tests the error exits for the COMPLEX*16 routines */
/* for general matrices. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (j << 2) - 5;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = i__ + (j << 2) - 5;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
af[i__1].r = z__1.r, af[i__1].i = z__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0., b[i__1].i = 0.;
r1[j - 1] = 0.;
r2[j - 1] = 0.;
i__1 = j - 1;
w[i__1].r = 0., w[i__1].i = 0.;
i__1 = j - 1;
x[i__1].r = 0., x[i__1].i = 0.;
ip[j - 1] = j;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Test error exits of the routines that use the LU decomposition */
/* of a general matrix. */
if (lsamen_(&c__2, c2, "GE")) {
/* ZGETRF */
s_copy(srnamc_1.srnamt, "ZGETRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetrf_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgetrf_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgetrf_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGETF2 */
s_copy(srnamc_1.srnamt, "ZGETF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetf2_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgetf2_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgetf2_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGETRI */
s_copy(srnamc_1.srnamt, "ZGETRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetri_(&c_n1, a, &c__1, ip, w, &c__1, &info);
chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgetri_(&c__2, a, &c__1, ip, w, &c__2, &info);
chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgetri_(&c__2, a, &c__2, ip, w, &c__1, &info);
chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGETRS */
s_copy(srnamc_1.srnamt, "ZGETRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGERFS */
s_copy(srnamc_1.srnamt, "ZGERFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGECON */
s_copy(srnamc_1.srnamt, "ZGECON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGEEQU */
s_copy(srnamc_1.srnamt, "ZGEEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Test error exits of the routines that use the LU decomposition */
/* of a general band matrix. */
} else if (lsamen_(&c__2, c2, "GB")) {
/* ZGBTRF */
s_copy(srnamc_1.srnamt, "ZGBTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBTF2 */
s_copy(srnamc_1.srnamt, "ZGBTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBTRS */
s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBRFS */
s_copy(srnamc_1.srnamt, "ZGBRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
zgbrfs_("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, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBCON */
s_copy(srnamc_1.srnamt, "ZGBCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBEQU */
s_copy(srnamc_1.srnamt, "ZGBEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &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 ZERRGE */
} /* zerrge_ */
/* Subroutine */ int zchkgb_(logical *dotype, integer *nm, integer *mval,
integer *nn, integer *nval, integer *nnb, integer *nbval, integer *
nns, integer *nsval, doublereal *thresh, logical *tsterr,
doublecomplex *a, integer *la, doublecomplex *afac, integer *lafac,
doublecomplex *b, doublecomplex *x, doublecomplex *xact,
doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(\002 *** In ZCHKGB, 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 ZCHKGB, 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 doublereal dget06_(doublereal *, doublereal *);
doublereal rcond;
extern /* Subroutine */ int zgbt01_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
integer *, doublecomplex *, doublereal *);
integer nimat, klval[4];
extern /* Subroutine */ int zgbt02_(char *, integer *, integer *, integer
*, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *), zgbt05_(char *, integer *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *
, doublereal *, doublereal *, doublereal *);
doublereal anorm;
integer itran;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
integer kuval[4];
char trans[1];
integer izero, nerrs;
logical zerot;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
char xtype[1];
extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, char *);
integer ldafac;
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *);
doublereal rcondc;
extern doublereal zlangb_(char *, integer *, integer *, integer *,
doublecomplex *, integer *, doublereal *);
doublereal rcondi;
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *);
doublereal cndnum, anormi, rcondo;
extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer
*, doublecomplex *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, doublereal *, integer *);
doublereal ainvnm;
logical trfcon;
doublereal anormo;
extern /* Subroutine */ int xlaenv_(integer *, integer *), zerrge_(char *,
integer *), zgbrfs_(char *, integer *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublereal *, doublereal *, doublecomplex *,
doublereal *, integer *), zgbtrf_(integer *, integer *,
integer *, integer *, doublecomplex *, integer *, integer *,
integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zlarhs_(char *,
char *, char *, char *, integer *, integer *, integer *, integer *
, integer *, doublecomplex *, integer *, doublecomplex *, integer
*, doublecomplex *, integer *, integer *, integer *), zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zgbtrs_(char *, integer *, integer *, integer *, integer
*, doublecomplex *, integer *, integer *, doublecomplex *,
integer *, integer *), zlatms_(integer *, integer *, char
*, integer *, char *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *, char *, doublecomplex *,
integer *, doublecomplex *, integer *);
doublereal 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 */
/* ======= */
/* ZCHKGB tests ZGBTRF, -TRS, -RFS, and -CON */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NM (input) INTEGER */
/* The number of values of M contained in the vector MVAL. */
/* MVAL (input) INTEGER array, dimension (NM) */
/* The values of the matrix row dimension M. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NBVAL) */
/* The values of the blocksize NB. */
/* NNS (input) INTEGER */
/* The number of values of NRHS contained in the vector NSVAL. */
/* NSVAL (input) INTEGER array, dimension (NNS) */
/* The values of the number of right hand sides NRHS. */
/* THRESH (input) DOUBLE PRECISION */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* A (workspace) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* WORK (workspace) COMPLEX*16 array, dimension */
/* (NMAX*max(3,NSMAX,NMAX)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* IWORK (workspace) INTEGER array, dimension (NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. 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, "Zomplex precision", (ftnlen)1, (ftnlen)17);
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) {
zerrge_(path, nout);
}
infoc_1.infot = 0;
/* 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 ZLATB4 and generate a */
/* test matrix with ZLATMS. */
zlatb4_(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__) {
i__7 = i__;
a[i__7].r = 0., a[i__7].i = 0.;
/* L20: */
}
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (
ftnlen)6);
zlatms_(&m, &n, dist, iseed, type__, &rwork[1], &
mode, &cndnum, &anorm, &kl, &ku, "Z", &a[
koff], &lda, &work[1], &info);
/* Check the error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &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;
zcopy_(&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;
zcopy_(&i__6, &a[ioff + i1], &c__1, &b[1], &
c__1);
i__6 = i2;
for (i__ = i1; i__ <= i__6; ++i__) {
i__7 = ioff + i__;
a[i__7].r = 0., a[i__7].i = 0.;
/* 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__) {
i__7 = ioff + i__;
a[i__7].r = 0., a[i__7].i = 0.;
/* 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 = ZLANGB( 'O', N, KL, KU, A, LDA, RWORK ) */
/* ANORMI = ZLANGB( '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;
zlacpy_("Full", &i__9, &n, &a[1], &lda, &afac[
kl + 1], &ldafac);
}
s_copy(srnamc_1.srnamt, "ZGBTRF", (ftnlen)6, (
ftnlen)6);
zgbtrf_(&m, &n, &kl, &ku, &afac[1], &ldafac, &
iwork[1], &info);
/* Check error code from ZGBTRF. */
if (info != izero) {
alaerh_(path, "ZGBTRF", &info, &izero, " ", &
m, &n, &kl, &ku, &nb, &imat, &nfail, &
nerrs, nout);
}
trfcon = FALSE_;
/* + TEST 1 */
/* Reconstruct matrix from factors and compute */
/* residual. */
zgbt01_(&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(doublereal));
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 = zlangb_("O", &n, &kl, &ku, &a[1], &lda, &
rwork[1]);
anormi = zlangb_("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);
zlaset_("Full", &n, &n, &c_b61, &c_b62, &work[
1], &ldb);
s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)6, (
ftnlen)6);
zgbtrs_("No transpose", &n, &kl, &ku, &n, &
afac[1], &ldafac, &iwork[1], &work[1],
&ldb, &info);
/* Compute the 1-norm condition number of A. */
ainvnm = zlange_("O", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormo <= 0. || ainvnm <= 0.) {
rcondo = 1.;
} else {
rcondo = 1. / anormo / ainvnm;
}
/* Compute the infinity-norm condition number of */
/* A. */
ainvnm = zlange_("I", &n, &n, &work[1], &ldb,
&rwork[1]);
if (anormi <= 0. || ainvnm <= 0.) {
rcondi = 1.;
} else {
rcondi = 1. / anormi / ainvnm;
}
} else {
/* Do only the condition estimate if INFO.NE.0. */
trfcon = TRUE_;
rcondo = 0.;
rcondi = 0.;
}
/* 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, "ZLARHS", (ftnlen)
6, (ftnlen)6);
zlarhs_(path, xtype, " ", trans, &n, &n, &
kl, &ku, &nrhs, &a[1], &lda, &
xact[1], &ldb, &b[1], &ldb, iseed,
&info);
*(unsigned char *)xtype = 'C';
zlacpy_("Full", &n, &nrhs, &b[1], &ldb, &
x[1], &ldb);
s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)
6, (ftnlen)6);
zgbtrs_(trans, &n, &kl, &ku, &nrhs, &afac[
1], &ldafac, &iwork[1], &x[1], &
ldb, &info);
/* Check error code from ZGBTRS. */
if (info != 0) {
alaerh_(path, "ZGBTRS", &info, &c__0,
trans, &n, &n, &kl, &ku, &
c_n1, &imat, &nfail, &nerrs,
nout);
}
zlacpy_("Full", &n, &nrhs, &b[1], &ldb, &
work[1], &ldb);
zgbt02_(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. */
zget04_(&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, "ZGBRFS", (ftnlen)
6, (ftnlen)6);
zgbrfs_(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], &rwork[(nrhs << 1) + 1], &
info);
/* Check error code from ZGBRFS. */
if (info != 0) {
alaerh_(path, "ZGBRFS", &info, &c__0,
trans, &n, &n, &kl, &ku, &
nrhs, &imat, &nfail, &nerrs,
nout);
}
zget04_(&n, &nrhs, &x[1], &ldb, &xact[1],
&ldb, &rcondc, &result[3]);
zgbt05_(trans, &n, &kl, &ku, &nrhs, &a[1],
&lda, &b[1], &ldb, &x[1], &ldb, &
xact[1], &ldb, &rwork[1], &rwork[
nrhs + 1], &result[4]);
/* Print information about the tests that did */
/* not pass the threshold. */
for (k = 2; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___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(
doublereal));
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, "ZGBCON", (ftnlen)6, (
ftnlen)6);
zgbcon_(norm, &n, &kl, &ku, &afac[1], &ldafac,
&iwork[1], &anorm, &rcond, &work[1],
&rwork[1], &info);
/* Check error code from ZGBCON. */
if (info != 0) {
alaerh_(path, "ZGBCON", &info, &c__0,
norm, &n, &n, &kl, &ku, &c_n1, &
imat, &nfail, &nerrs, nout);
}
result[6] = dget06_(&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(doublereal));
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 ZCHKGB */
} /* zchkgb_ */
/* Subroutine */ int zgbsvxx_(char *fact, char *trans, integer *n, integer *
kl, integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab,
doublecomplex *afb, integer *ldafb, integer *ipiv, char *equed,
doublereal *r__, doublereal *c__, doublecomplex *b, integer *ldb,
doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw,
doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__,
doublereal *err_bnds_comp__, integer *nparams, doublereal *params,
doublecomplex *work, doublereal *rwork, 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, i__3, i__4;
doublereal d__1, d__2;
/* Local variables */
integer i__, j;
doublereal amax;
extern doublereal zla_gbrpvgrw__(integer *, integer *, integer *, integer
*, doublecomplex *, integer *, doublecomplex *, integer *);
extern logical lsame_(char *, char *);
doublereal rcmin, rcmax;
logical equil;
extern doublereal dlamch_(char *);
doublereal colcnd;
logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *), zlaqgb_(
integer *, integer *, integer *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, char *);
doublereal bignum;
integer infequ;
logical colequ;
doublereal rowcnd;
extern /* Subroutine */ int zgbtrf_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *, integer *);
logical notran;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal smlnum;
extern /* Subroutine */ int zgbtrs_(char *, integer *, integer *, integer
*, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, integer *);
logical rowequ;
extern /* Subroutine */ int zlascl2_(integer *, integer *, doublereal *,
doublecomplex *, integer *), zgbequb_(integer *, integer *,
integer *, integer *, doublecomplex *, integer *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *, integer *)
, zgbrfsx_(char *, char *, integer *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
integer *, doublereal *, doublereal *, doublecomplex *, integer *
, doublecomplex *, integer *, doublereal *, doublereal *, integer
*, doublereal *, doublereal *, integer *, doublereal *,
doublecomplex *, doublereal *, 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 */
/* ======= */
/* ZGBSVXX uses the LU factorization to compute the solution to a */
/* complex*16 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. ZGBSVXX 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. */
/* ZGBSVXX 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 */
/* ZGBSVXX 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 ZGBSVXX would itself produce. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'E', double precision 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 ZGBTRF. 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 DGETRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the original matrix A. */
/* If FACT = 'E', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the equilibrated matrix A. */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'R': Row equilibration, i.e., A has been premultiplied by */
/* diag(R). */
/* = 'C': Column equilibration, i.e., A has been postmultiplied */
/* by diag(C). */
/* = 'B': Both row and column equilibration, i.e., A has been */
/* replaced by diag(R) * A * diag(C). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* R (input or output) DOUBLE PRECISION array, dimension (N) */
/* The row scale factors for A. If EQUED = 'R' or 'B', A is */
/* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
/* is not accessed. R is an input argument if FACT = 'F'; */
/* otherwise, R is an output argument. If FACT = 'F' and */
/* EQUED = 'R' or 'B', each element of R must be positive. */
/* 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) DOUBLE PRECISION array, dimension (N) */
/* The column scale factors for A. If EQUED = 'C' or 'B', A is */
/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
/* is not accessed. C is an input argument if FACT = 'F'; */
/* otherwise, C is an output argument. If FACT = 'F' and */
/* EQUED = 'C' or 'B', each element of C must be positive. */
/* 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) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, */
/* if EQUED = 'N', B is not modified; */
/* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
/* diag(R)*B; */
/* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
/* overwritten by diag(C)*B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* If INFO = 0, the N-by-NRHS solution matrix X to the original */
/* system of equations. Note that A and B are modified on exit */
/* if EQUED .ne. 'N', and the solution to the equilibrated system is */
/* inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */
/* inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* 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) DOUBLE PRECISION */
/* 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 DGESVX, this quantity is */
/* returned in WORK(1). */
/* BERR (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) * dlamch('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) * dlamch('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) * dlamch('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) DOUBLE PRECISION 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) * dlamch('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) * dlamch('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) * dlamch('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) DOUBLE PRECISION 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: 1.0D+0 */
/* = 0.0 : No refinement is performed, and no error bounds are */
/* computed. */
/* = 1.0 : Use the extra-precise refinement algorithm. */
/* (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) DOUBLE PRECISION 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;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
smlnum = dlamch_("Safe minimum");
bignum = 1. / 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 ZGBRFSX. */
*rpvgrw = 0.;
/* Test the input parameters. PARAMS is not tested until DGERFSX. */
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.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = rcmin, d__2 = r__[j];
rcmin = min(d__1,d__2);
/* Computing MAX */
d__1 = rcmax, d__2 = r__[j];
rcmax = max(d__1,d__2);
/* L10: */
}
if (rcmin <= 0.) {
*info = -13;
} else if (*n > 0) {
rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
} else {
rowcnd = 1.;
}
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = rcmin, d__2 = c__[j];
rcmin = min(d__1,d__2);
/* Computing MAX */
d__1 = rcmax, d__2 = c__[j];
rcmax = max(d__1,d__2);
/* L20: */
}
if (rcmin <= 0.) {
*info = -14;
} else if (*n > 0) {
colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
} else {
colcnd = 1.;
}
}
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_("ZGBSVXX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
zgbequb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &
rowcnd, &colcnd, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
zlaqgb_(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.;
}
}
if (! colequ) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
c__[j] = 1.;
}
}
}
/* Scale the right-hand side. */
if (notran) {
if (rowequ) {
zlascl2_(n, nrhs, &r__[1], &b[b_offset], ldb);
}
} else {
if (colequ) {
zlascl2_(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__) {
i__3 = i__ + j * afb_dim1;
i__4 = i__ - *kl + j * ab_dim1;
afb[i__3].r = ab[i__4].r, afb[i__3].i = ab[i__4].i;
/* L30: */
}
/* L40: */
}
zgbtrf_(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 = zla_gbrpvgrw__(n, kl, ku, info, &ab[ab_offset], ldab, &
afb[afb_offset], ldafb);
return 0;
}
}
/* Compute the reciprocal pivot growth factor RPVGRW. */
*rpvgrw = zla_gbrpvgrw__(n, kl, ku, n, &ab[ab_offset], ldab, &afb[
afb_offset], ldafb);
/* Compute the solution matrix X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zgbtrs_(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. */
zgbrfsx_(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], &rwork[1],
info);
/* Scale solutions. */
if (colequ && notran) {
zlascl2_(n, nrhs, &c__[1], &x[x_offset], ldx);
} else if (rowequ && ! notran) {
zlascl2_(n, nrhs, &r__[1], &x[x_offset], ldx);
}
return 0;
/* End of ZGBSVXX */
} /* zgbsvxx_ */
/* ===================================================================== */
doublereal zla_gbrcond_x_(char *trans, integer *n, integer *kl, integer *ku, doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb, integer *ipiv, doublecomplex *x, integer *info, doublecomplex *work, doublereal *rwork)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, i__1, i__2, i__3, i__4;
doublereal ret_val, d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *);
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, kd, ke;
doublereal tmp;
integer kase;
extern logical lsame_(char *, char *);
integer isave[3];
doublereal anorm;
extern /* Subroutine */
int zlacn2_(integer *, doublecomplex *, doublecomplex *, doublereal *, integer *, integer *), xerbla_( char *, integer *);
doublereal ainvnm;
extern /* Subroutine */
int zgbtrs_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *);
logical notrans;
/* -- LAPACK computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. 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;
--x;
--work;
--rwork;
/* Function Body */
ret_val = 0.;
*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_("ZLA_GBRCOND_X", &i__1);
return ret_val;
}
/* Compute norm of op(A)*op2(C). */
kd = *ku + 1;
ke = *kl + 1;
anorm = 0.;
if (notrans)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
tmp = 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)
{
i__2 = kd + i__ - j + j * ab_dim1;
i__4 = j;
z__2.r = ab[i__2].r * x[i__4].r - ab[i__2].i * x[i__4].i;
z__2.i = ab[i__2].r * x[i__4].i + ab[i__2].i * x[i__4] .r; // , expr subst
z__1.r = z__2.r;
z__1.i = z__2.i; // , expr subst
tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), abs(d__2));
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
}
else
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
tmp = 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)
{
i__3 = ke - i__ + j + i__ * ab_dim1;
i__4 = j;
z__2.r = ab[i__3].r * x[i__4].r - ab[i__3].i * x[i__4].i;
z__2.i = ab[i__3].r * x[i__4].i + ab[i__3].i * x[i__4] .r; // , expr subst
z__1.r = z__2.r;
z__1.i = z__2.i; // , expr subst
tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), abs(d__2));
}
rwork[i__] = tmp;
anorm = max(anorm,tmp);
}
}
/* Quick return if possible. */
if (*n == 0)
{
ret_val = 1.;
return ret_val;
}
else if (anorm == 0.)
{
return ret_val;
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.;
kase = 0;
L10:
zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0)
{
if (kase == 2)
{
/* Multiply by R. */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r;
z__1.i = rwork[i__4] * work[i__3].i; // , expr subst
work[i__2].r = z__1.r;
work[i__2].i = z__1.i; // , expr subst
}
if (notrans)
{
zgbtrs_("No transpose", n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1], &work[1], n, info);
}
else
{
zgbtrs_("Conjugate transpose", n, kl, ku, &c__1, &afb[ afb_offset], ldafb, &ipiv[1], &work[1], n, info);
}
/* Multiply by inv(X). */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
z_div(&z__1, &work[i__], &x[i__]);
work[i__2].r = z__1.r;
work[i__2].i = z__1.i; // , expr subst
}
}
else
{
/* Multiply by inv(X**H). */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
z_div(&z__1, &work[i__], &x[i__]);
work[i__2].r = z__1.r;
work[i__2].i = z__1.i; // , expr subst
}
if (notrans)
{
zgbtrs_("Conjugate transpose", n, kl, ku, &c__1, &afb[ afb_offset], ldafb, &ipiv[1], &work[1], n, info);
}
else
{
zgbtrs_("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__)
{
i__2 = i__;
i__3 = i__;
i__4 = i__;
z__1.r = rwork[i__4] * work[i__3].r;
z__1.i = rwork[i__4] * work[i__3].i; // , expr subst
work[i__2].r = z__1.r;
work[i__2].i = z__1.i; // , expr subst
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.)
{
ret_val = 1. / ainvnm;
}
return ret_val;
}
int main(void)
{
/* Local scalars */
char trans, trans_i;
lapack_int n, n_i;
lapack_int kl, kl_i;
lapack_int ku, ku_i;
lapack_int nrhs, nrhs_i;
lapack_int ldab, ldab_i;
lapack_int ldab_r;
lapack_int ldb, ldb_i;
lapack_int ldb_r;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
lapack_complex_double *ab = NULL, *ab_i = NULL;
lapack_int *ipiv = NULL, *ipiv_i = NULL;
lapack_complex_double *b = NULL, *b_i = NULL;
lapack_complex_double *b_save = NULL;
lapack_complex_double *ab_r = NULL;
lapack_complex_double *b_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_zgbtrs( &trans, &n, &kl, &ku, &nrhs, &ldab, &ldb );
ldab_r = n+2;
ldb_r = nrhs+2;
trans_i = trans;
n_i = n;
kl_i = kl;
ku_i = ku;
nrhs_i = nrhs;
ldab_i = ldab;
ldb_i = ldb;
/* Allocate memory for the LAPACK routine arrays */
ab = (lapack_complex_double *)
LAPACKE_malloc( ldab*n * sizeof(lapack_complex_double) );
ipiv = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
b = (lapack_complex_double *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_double) );
/* Allocate memory for the C interface function arrays */
ab_i = (lapack_complex_double *)
LAPACKE_malloc( ldab*n * sizeof(lapack_complex_double) );
ipiv_i = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
b_i = (lapack_complex_double *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_double) );
/* Allocate memory for the backup arrays */
b_save = (lapack_complex_double *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_double) );
/* Allocate memory for the row-major arrays */
ab_r = (lapack_complex_double *)
LAPACKE_malloc( ((2*kl+ku+1)*(n+2)) * sizeof(lapack_complex_double) );
b_r = (lapack_complex_double *)
LAPACKE_malloc( n*(nrhs+2) * sizeof(lapack_complex_double) );
/* Initialize input arrays */
init_ab( ldab*n, ab );
init_ipiv( n, ipiv );
init_b( ldb*nrhs, b );
/* Backup the ouptut arrays */
for( i = 0; i < ldb*nrhs; i++ ) {
b_save[i] = b[i];
}
/* Call the LAPACK routine */
zgbtrs_( &trans, &n, &kl, &ku, &nrhs, ab, &ldab, ipiv, b, &ldb, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < ldab*n; i++ ) {
ab_i[i] = ab[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
info_i = LAPACKE_zgbtrs_work( LAPACK_COL_MAJOR, trans_i, n_i, kl_i, ku_i,
nrhs_i, ab_i, ldab_i, ipiv_i, b_i, ldb_i );
failed = compare_zgbtrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to zgbtrs\n" );
} else {
printf( "FAILED: column-major middle-level interface to zgbtrs\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < ldab*n; i++ ) {
ab_i[i] = ab[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
info_i = LAPACKE_zgbtrs( LAPACK_COL_MAJOR, trans_i, n_i, kl_i, ku_i, nrhs_i,
ab_i, ldab_i, ipiv_i, b_i, ldb_i );
failed = compare_zgbtrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to zgbtrs\n" );
} else {
printf( "FAILED: column-major high-level interface to zgbtrs\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < ldab*n; i++ ) {
ab_i[i] = ab[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
LAPACKE_zge_trans( LAPACK_COL_MAJOR, 2*kl+ku+1, n, ab_i, ldab, ab_r, n+2 );
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, nrhs, b_i, ldb, b_r, nrhs+2 );
info_i = LAPACKE_zgbtrs_work( LAPACK_ROW_MAJOR, trans_i, n_i, kl_i, ku_i,
nrhs_i, ab_r, ldab_r, ipiv_i, b_r, ldb_r );
LAPACKE_zge_trans( LAPACK_ROW_MAJOR, n, nrhs, b_r, nrhs+2, b_i, ldb );
failed = compare_zgbtrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to zgbtrs\n" );
} else {
printf( "FAILED: row-major middle-level interface to zgbtrs\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < ldab*n; i++ ) {
ab_i[i] = ab[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b_save[i];
}
/* Init row_major arrays */
LAPACKE_zge_trans( LAPACK_COL_MAJOR, 2*kl+ku+1, n, ab_i, ldab, ab_r, n+2 );
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, nrhs, b_i, ldb, b_r, nrhs+2 );
info_i = LAPACKE_zgbtrs( LAPACK_ROW_MAJOR, trans_i, n_i, kl_i, ku_i, nrhs_i,
ab_r, ldab_r, ipiv_i, b_r, ldb_r );
LAPACKE_zge_trans( LAPACK_ROW_MAJOR, n, nrhs, b_r, nrhs+2, b_i, ldb );
failed = compare_zgbtrs( b, b_i, info, info_i, ldb, nrhs );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to zgbtrs\n" );
} else {
printf( "FAILED: row-major high-level interface to zgbtrs\n" );
}
/* Release memory */
if( ab != NULL ) {
LAPACKE_free( ab );
}
if( ab_i != NULL ) {
LAPACKE_free( ab_i );
}
if( ab_r != NULL ) {
LAPACKE_free( ab_r );
}
if( ipiv != NULL ) {
LAPACKE_free( ipiv );
}
if( ipiv_i != NULL ) {
LAPACKE_free( ipiv_i );
}
if( b != NULL ) {
LAPACKE_free( b );
}
if( b_i != NULL ) {
LAPACKE_free( b_i );
}
if( b_r != NULL ) {
LAPACKE_free( b_r );
}
if( b_save != NULL ) {
LAPACKE_free( b_save );
}
return 0;
}
