int
f2c_chbmv(char* uplo, integer* N, integer* K,
complex* alpha,
complex* A, integer* lda,
complex* X, integer* incX,
complex* beta,
complex* Y, integer* incY)
{
chbmv_(uplo, N, K, alpha, A, lda,
X, incX, beta, Y, incY);
return 0;
}
void
chbmv(char uplo, int n, int k, complex *alpha, complex *a, int lda, complex *x, int incx, complex *beta, complex *y, int incy )
{
chbmv_( &uplo, &n, &k, alpha, a, &lda, x, &incx, beta, y, &incy );
}
/* Subroutine */ int cpbt02_(char *uplo, integer *n, integer *kd, integer *
nrhs, complex *a, integer *lda, complex *x, integer *ldx, complex *b,
integer *ldb, real *rwork, real *resid)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
real r__1, r__2;
complex q__1;
/* Local variables */
static integer j;
extern /* Subroutine */ int chbmv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
static real anorm, bnorm, xnorm;
extern doublereal clanhb_(char *, char *, integer *, integer *, complex *,
integer *, real *), slamch_(char *),
scasum_(integer *, complex *, integer *);
static real eps;
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CPBT02 computes the residual for a solution of a Hermitian banded
system of equations A*x = b:
RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
where EPS is the machine precision.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The number of rows and columns of the matrix A. N >= 0.
KD (input) INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
A (input) COMPLEX array, dimension (LDA,N)
The original Hermitian band matrix A. If UPLO = 'U', the
upper triangular part of A is stored as a band matrix; if
UPLO = 'L', the lower triangular part of A is stored. The
columns of the appropriate triangle are stored in the columns
of A and the diagonals of the triangle are stored in the rows
of A. See CPBTRF for further details.
LDA (input) INTEGER.
The leading dimension of the array A. LDA >= max(1,KD+1).
X (input) COMPLEX array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B (input/output) COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RWORK (workspace) REAL array, dimension (N)
RESID (output) REAL
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
=====================================================================
Quick exit if N = 0 or NRHS = 0.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--rwork;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
*resid = 0.f;
return 0;
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = slamch_("Epsilon");
anorm = clanhb_("1", uplo, n, kd, &a[a_offset], lda, &rwork[1]);
if (anorm <= 0.f) {
*resid = 1.f / eps;
return 0;
}
/* Compute B - A*X */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
q__1.r = -1.f, q__1.i = 0.f;
chbmv_(uplo, n, kd, &q__1, &a[a_offset], lda, &x_ref(1, j), &c__1, &
c_b1, &b_ref(1, j), &c__1);
/* L10: */
}
/* Compute the maximum over the number of right hand sides of
norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) */
*resid = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
bnorm = scasum_(n, &b_ref(1, j), &c__1);
xnorm = scasum_(n, &x_ref(1, j), &c__1);
if (xnorm <= 0.f) {
*resid = 1.f / eps;
} else {
/* Computing MAX */
r__1 = *resid, r__2 = bnorm / anorm / xnorm / eps;
*resid = dmax(r__1,r__2);
}
/* L20: */
}
return 0;
/* End of CPBT02 */
} /* cpbt02_ */
/* Subroutine */ int cpbrfs_(char *uplo, integer *n, integer *kd, integer *
nrhs, complex *ab, integer *ldab, complex *afb, integer *ldafb,
complex *b, integer *ldb, complex *x, integer *ldx, real *ferr, real *
berr, complex *work, real *rwork, integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CPBRFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian positive definite
and banded, and provides error bounds and backward error estimates
for the solution.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
AB (input) REAL array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian band matrix A,
stored in the first KD+1 rows of the array. The j-th column
of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
AFB (input) COMPLEX array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A as computed by
CPBTRF, in the same storage format as A (see AB).
LDAFB (input) INTEGER
The leading dimension of the array AFB. LDAFB >= KD+1.
B (input) COMPLEX 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 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CPBTRS.
On exit, the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Internal Parameters
===================
ITMAX is the maximum number of steps of iterative refinement.
=====================================================================
Test the input parameters.
Parameter adjustments
Function Body */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer kase;
static real safe1, safe2;
static integer i, j, k, l;
static real s;
extern /* Subroutine */ int chbmv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static integer count;
static logical upper;
extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real
*, integer *);
static real xk;
extern doublereal slamch_(char *);
static integer nz;
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), cpbtrs_(
char *, integer *, integer *, integer *, complex *, integer *,
complex *, integer *, integer *);
static real lstres, eps;
#define FERR(I) ferr[(I)-1]
#define BERR(I) berr[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define AB(I,J) ab[(I)-1 + ((J)-1)* ( *ldab)]
#define AFB(I,J) afb[(I)-1 + ((J)-1)* ( *ldafb)]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
#define X(I,J) x[(I)-1 + ((J)-1)* ( *ldx)]
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldafb < *kd + 1) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
FERR(j) = 0.f;
BERR(j) = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1
Computing MIN */
i__1 = *n + 1, i__2 = (*kd << 1) + 2;
nz = min(i__1,i__2);
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied.
Compute residual R = B - A * X */
ccopy_(n, &B(1,j), &c__1, &WORK(1), &c__1);
q__1.r = -1.f, q__1.i = 0.f;
chbmv_(uplo, n, kd, &q__1, &AB(1,1), ldab, &X(1,j), &
c__1, &c_b1, &WORK(1), &c__1);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(A)*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matr
ix
or vector Z. If the i-th component of the denominator is le
ss
than SAFE2, then SAFE1 is added to the i-th components of th
e
numerator and denominator before dividing. */
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__3 = i + j * b_dim1;
RWORK(i) = (r__1 = B(i,j).r, dabs(r__1)) + (r__2 = r_imag(&B(i,j)), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= *n; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = X(k,j).r, dabs(r__1)) + (r__2 = r_imag(&X(k,j)), dabs(r__2));
l = *kd + 1 - k;
/* Computing MAX */
i__3 = 1, i__4 = k - *kd;
i__5 = k - 1;
for (i = max(1,k-*kd); i <= k-1; ++i) {
i__3 = l + i + k * ab_dim1;
RWORK(i) += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 =
r_imag(&AB(l+i,k)), dabs(r__2))) *
xk;
i__3 = l + i + k * ab_dim1;
i__4 = i + j * x_dim1;
s += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 = r_imag(&
AB(l+i,k)), dabs(r__2))) * ((r__3 =
X(i,j).r, dabs(r__3)) + (r__4 = r_imag(&X(i,j)), dabs(r__4)));
/* L40: */
}
i__5 = *kd + 1 + k * ab_dim1;
RWORK(k) = RWORK(k) + (r__1 = AB(*kd+1,k).r, dabs(r__1)) * xk +
s;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= *n; ++k) {
s = 0.f;
i__5 = k + j * x_dim1;
xk = (r__1 = X(k,j).r, dabs(r__1)) + (r__2 = r_imag(&X(k,j)), dabs(r__2));
i__5 = k * ab_dim1 + 1;
RWORK(k) += (r__1 = AB(1,k).r, dabs(r__1)) * xk;
l = 1 - k;
/* Computing MIN */
i__3 = *n, i__4 = k + *kd;
i__5 = min(i__3,i__4);
for (i = k + 1; i <= min(*n,k+*kd); ++i) {
i__3 = l + i + k * ab_dim1;
RWORK(i) += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 =
r_imag(&AB(l+i,k)), dabs(r__2))) *
xk;
i__3 = l + i + k * ab_dim1;
i__4 = i + j * x_dim1;
s += ((r__1 = AB(l+i,k).r, dabs(r__1)) + (r__2 = r_imag(&
AB(l+i,k)), dabs(r__2))) * ((r__3 =
X(i,j).r, dabs(r__3)) + (r__4 = r_imag(&X(i,j)), dabs(r__4)));
/* L60: */
}
RWORK(k) += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i = 1; i <= *n; ++i) {
if (RWORK(i) > safe2) {
/* Computing MAX */
i__5 = i;
r__3 = s, r__4 = ((r__1 = WORK(i).r, dabs(r__1)) + (r__2 =
r_imag(&WORK(i)), dabs(r__2))) / RWORK(i);
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__5 = i;
r__3 = s, r__4 = ((r__1 = WORK(i).r, dabs(r__1)) + (r__2 =
r_imag(&WORK(i)), dabs(r__2)) + safe1) / (RWORK(i) +
safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
BERR(j) = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, a
nd
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (BERR(j) > eps && BERR(j) * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
cpbtrs_(uplo, n, kd, &c__1, &AFB(1,1), ldafb, &WORK(1), n,
info);
caxpy_(n, &c_b1, &WORK(1), &c__1, &X(1,j), &c__1);
lstres = BERR(j);
++count;
goto L20;
}
/* Bound error from formula
norm(X - XTRUE) / norm(X) .le. FERR =
norm( abs(inv(A))*
( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(A) is the inverse of A
abs(Z) is the componentwise absolute value of the matrix o
r
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(A)*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(A)*abs(X) + abs(B) is less than SAFE2.
Use CLACON to estimate the infinity-norm of the matrix
inv(A) * diag(W),
where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
i__2 = *n;
for (i = 1; i <= *n; ++i) {
if (RWORK(i) > safe2) {
i__5 = i;
RWORK(i) = (r__1 = WORK(i).r, dabs(r__1)) + (r__2 = r_imag(
&WORK(i)), dabs(r__2)) + nz * eps * RWORK(i);
} else {
i__5 = i;
RWORK(i) = (r__1 = WORK(i).r, dabs(r__1)) + (r__2 = r_imag(
&WORK(i)), dabs(r__2)) + nz * eps * RWORK(i) + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacon_(n, &WORK(*n + 1), &WORK(1), &FERR(j), &kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
cpbtrs_(uplo, n, kd, &c__1, &AFB(1,1), ldafb, &WORK(1),
n, info);
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__5 = i;
i__3 = i;
i__4 = i;
q__1.r = RWORK(i) * WORK(i).r, q__1.i = RWORK(i)
* WORK(i).i;
WORK(i).r = q__1.r, WORK(i).i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__5 = i;
i__3 = i;
i__4 = i;
q__1.r = RWORK(i) * WORK(i).r, q__1.i = RWORK(i)
* WORK(i).i;
WORK(i).r = q__1.r, WORK(i).i = q__1.i;
/* L120: */
}
cpbtrs_(uplo, n, kd, &c__1, &AFB(1,1), ldafb, &WORK(1),
n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i = 1; i <= *n; ++i) {
/* Computing MAX */
i__5 = i + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = X(i,j).r, dabs(r__1)) + (r__2 =
r_imag(&X(i,j)), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
FERR(j) /= lstres;
}
/* L140: */
}
return 0;
/* End of CPBRFS */
} /* cpbrfs_ */
/* Subroutine */ int clarhs_(char *path, char *xtype, char *uplo, char *trans,
integer *m, integer *n, integer *kl, integer *ku, integer *nrhs,
complex *a, integer *lda, complex *x, integer *ldx, complex *b,
integer *ldb, integer *iseed, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
integer j;
char c1[1], c2[2];
integer mb, nx;
logical gen, tri, qrs, sym, band;
char diag[1];
logical tran;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *), chemm_(char *,
char *, integer *, integer *, complex *, complex *, integer *,
complex *, integer *, complex *, complex *, integer *), cgbmv_(char *, integer *, integer *, integer *, integer *
, complex *, complex *, integer *, complex *, integer *, complex *
, complex *, integer *), chbmv_(char *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *);
extern /* Subroutine */ int csbmv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *), ctbmv_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, integer *), chpmv_(char *, integer *, complex *, complex *,
complex *, integer *, complex *, complex *, integer *),
ctrmm_(char *, char *, char *, char *, integer *, integer *,
complex *, complex *, integer *, complex *, integer *), cspmv_(char *, integer *, complex *,
complex *, complex *, integer *, complex *, complex *, integer *), csymm_(char *, char *, integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, complex *,
integer *), ctpmv_(char *, char *, char *,
integer *, complex *, complex *, integer *), clacpy_(char *, integer *, integer *, complex *, integer
*, complex *, integer *), xerbla_(char *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int clarnv_(integer *, integer *, integer *,
complex *);
logical notran;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLARHS chooses a set of NRHS random solution vectors and sets */
/* up the right hand sides for the linear system */
/* op( A ) * X = B, */
/* where op( A ) may be A, A**T (transpose of A), or A**H (conjugate */
/* transpose of A). */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The type of the complex matrix A. PATH may be given in any */
/* combination of upper and lower case. Valid paths include */
/* xGE: General m x n matrix */
/* xGB: General banded matrix */
/* xPO: Hermitian positive definite, 2-D storage */
/* xPP: Hermitian positive definite packed */
/* xPB: Hermitian positive definite banded */
/* xHE: Hermitian indefinite, 2-D storage */
/* xHP: Hermitian indefinite packed */
/* xHB: Hermitian indefinite banded */
/* xSY: Symmetric indefinite, 2-D storage */
/* xSP: Symmetric indefinite packed */
/* xSB: Symmetric indefinite banded */
/* xTR: Triangular */
/* xTP: Triangular packed */
/* xTB: Triangular banded */
/* xQR: General m x n matrix */
/* xLQ: General m x n matrix */
/* xQL: General m x n matrix */
/* xRQ: General m x n matrix */
/* where the leading character indicates the precision. */
/* XTYPE (input) CHARACTER*1 */
/* Specifies how the exact solution X will be determined: */
/* = 'N': New solution; generate a random X. */
/* = 'C': Computed; use value of X on entry. */
/* UPLO (input) CHARACTER*1 */
/* Used only if A is symmetric or triangular; specifies whether */
/* the upper or lower triangular part of the matrix A is stored. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* TRANS (input) CHARACTER*1 */
/* Used only if A is nonsymmetric; specifies the operation */
/* applied to the matrix A. */
/* = 'N': B := A * X */
/* = 'T': B := A**T * X */
/* = 'C': B := A**H * X */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* KL (input) INTEGER */
/* Used only if A is a band matrix; specifies the number of */
/* subdiagonals of A if A is a general band matrix or if A is */
/* symmetric or triangular and UPLO = 'L'; specifies the number */
/* of superdiagonals of A if A is symmetric or triangular and */
/* UPLO = 'U'. 0 <= KL <= M-1. */
/* KU (input) INTEGER */
/* Used only if A is a general band matrix or if A is */
/* triangular. */
/* If PATH = xGB, specifies the number of superdiagonals of A, */
/* and 0 <= KU <= N-1. */
/* If PATH = xTR, xTP, or xTB, specifies whether or not the */
/* matrix has unit diagonal: */
/* = 1: matrix has non-unit diagonal (default) */
/* = 2: matrix has unit diagonal */
/* NRHS (input) INTEGER */
/* The number of right hand side vectors in the system A*X = B. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The test matrix whose type is given by PATH. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. */
/* If PATH = xGB, LDA >= KL+KU+1. */
/* If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1. */
/* Otherwise, LDA >= max(1,M). */
/* X (input or output) COMPLEX array, dimension (LDX,NRHS) */
/* On entry, if XTYPE = 'C' (for 'Computed'), then X contains */
/* the exact solution to the system of linear equations. */
/* On exit, if XTYPE = 'N' (for 'New'), then X is initialized */
/* with random values. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. If TRANS = 'N', */
/* LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M). */
/* B (output) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side vector(s) for the system of equations, */
/* computed from B = op(A) * X, where op(A) is determined by */
/* TRANS. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. If TRANS = 'N', */
/* LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N). */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* The seed vector for the random number generator (used in */
/* CLATMS). Modified on exit. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--iseed;
/* Function Body */
*info = 0;
*(unsigned char *)c1 = *(unsigned char *)path;
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
tran = lsame_(trans, "T") || lsame_(trans, "C");
notran = ! tran;
gen = lsame_(path + 1, "G");
qrs = lsame_(path + 1, "Q") || lsame_(path + 2,
"Q");
sym = lsame_(path + 1, "P") || lsame_(path + 1,
"S") || lsame_(path + 1, "H");
tri = lsame_(path + 1, "T");
band = lsame_(path + 2, "B");
if (! lsame_(c1, "Complex precision")) {
*info = -1;
} else if (! (lsame_(xtype, "N") || lsame_(xtype,
"C"))) {
*info = -2;
} else if ((sym || tri) && ! (lsame_(uplo, "U") ||
lsame_(uplo, "L"))) {
*info = -3;
} else if ((gen || qrs) && ! (tran || lsame_(trans, "N"))) {
*info = -4;
} else if (*m < 0) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (band && *kl < 0) {
*info = -7;
} else if (band && *ku < 0) {
*info = -8;
} else if (*nrhs < 0) {
*info = -9;
} else if (! band && *lda < max(1,*m) || band && (sym || tri) && *lda < *
kl + 1 || band && gen && *lda < *kl + *ku + 1) {
*info = -11;
} else if (notran && *ldx < max(1,*n) || tran && *ldx < max(1,*m)) {
*info = -13;
} else if (notran && *ldb < max(1,*m) || tran && *ldb < max(1,*n)) {
*info = -15;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLARHS", &i__1);
return 0;
}
/* Initialize X to NRHS random vectors unless XTYPE = 'C'. */
if (tran) {
nx = *m;
mb = *n;
} else {
nx = *n;
mb = *m;
}
if (! lsame_(xtype, "C")) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
clarnv_(&c__2, &iseed[1], n, &x[j * x_dim1 + 1]);
/* L10: */
}
}
/* Multiply X by op( A ) using an appropriate */
/* matrix multiply routine. */
if (lsamen_(&c__2, c2, "GE") || lsamen_(&c__2, c2,
"QR") || lsamen_(&c__2, c2, "LQ") || lsamen_(&c__2, c2, "QL") ||
lsamen_(&c__2, c2, "RQ")) {
/* General matrix */
cgemm_(trans, "N", &mb, nrhs, &nx, &c_b1, &a[a_offset], lda, &x[
x_offset], ldx, &c_b2, &b[b_offset], ldb);
} else if (lsamen_(&c__2, c2, "PO") || lsamen_(&
c__2, c2, "HE")) {
/* Hermitian matrix, 2-D storage */
chemm_("Left", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset],
ldx, &c_b2, &b[b_offset], ldb);
} else if (lsamen_(&c__2, c2, "SY")) {
/* Symmetric matrix, 2-D storage */
csymm_("Left", uplo, n, nrhs, &c_b1, &a[a_offset], lda, &x[x_offset],
ldx, &c_b2, &b[b_offset], ldb);
} else if (lsamen_(&c__2, c2, "GB")) {
/* General matrix, band storage */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
cgbmv_(trans, m, n, kl, ku, &c_b1, &a[a_offset], lda, &x[j *
x_dim1 + 1], &c__1, &c_b2, &b[j * b_dim1 + 1], &c__1);
/* L20: */
}
} else if (lsamen_(&c__2, c2, "PB") || lsamen_(&
c__2, c2, "HB")) {
/* Hermitian matrix, band storage */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
chbmv_(uplo, n, kl, &c_b1, &a[a_offset], lda, &x[j * x_dim1 + 1],
&c__1, &c_b2, &b[j * b_dim1 + 1], &c__1);
/* L30: */
}
} else if (lsamen_(&c__2, c2, "SB")) {
/* Symmetric matrix, band storage */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
csbmv_(uplo, n, kl, &c_b1, &a[a_offset], lda, &x[j * x_dim1 + 1],
&c__1, &c_b2, &b[j * b_dim1 + 1], &c__1);
/* L40: */
}
} else if (lsamen_(&c__2, c2, "PP") || lsamen_(&
c__2, c2, "HP")) {
/* Hermitian matrix, packed storage */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
chpmv_(uplo, n, &c_b1, &a[a_offset], &x[j * x_dim1 + 1], &c__1, &
c_b2, &b[j * b_dim1 + 1], &c__1);
/* L50: */
}
} else if (lsamen_(&c__2, c2, "SP")) {
/* Symmetric matrix, packed storage */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
cspmv_(uplo, n, &c_b1, &a[a_offset], &x[j * x_dim1 + 1], &c__1, &
c_b2, &b[j * b_dim1 + 1], &c__1);
/* L60: */
}
} else if (lsamen_(&c__2, c2, "TR")) {
/* Triangular matrix. Note that for triangular matrices, */
/* KU = 1 => non-unit triangular */
/* KU = 2 => unit triangular */
clacpy_("Full", n, nrhs, &x[x_offset], ldx, &b[b_offset], ldb);
if (*ku == 2) {
*(unsigned char *)diag = 'U';
} else {
*(unsigned char *)diag = 'N';
}
ctrmm_("Left", uplo, trans, diag, n, nrhs, &c_b1, &a[a_offset], lda, &
b[b_offset], ldb);
} else if (lsamen_(&c__2, c2, "TP")) {
/* Triangular matrix, packed storage */
clacpy_("Full", n, nrhs, &x[x_offset], ldx, &b[b_offset], ldb);
if (*ku == 2) {
*(unsigned char *)diag = 'U';
} else {
*(unsigned char *)diag = 'N';
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ctpmv_(uplo, trans, diag, n, &a[a_offset], &b[j * b_dim1 + 1], &
c__1);
/* L70: */
}
} else if (lsamen_(&c__2, c2, "TB")) {
/* Triangular matrix, banded storage */
clacpy_("Full", n, nrhs, &x[x_offset], ldx, &b[b_offset], ldb);
if (*ku == 2) {
*(unsigned char *)diag = 'U';
} else {
*(unsigned char *)diag = 'N';
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ctbmv_(uplo, trans, diag, n, kl, &a[a_offset], lda, &b[j * b_dim1
+ 1], &c__1);
/* L80: */
}
} else {
/* If none of the above, set INFO = -1 and return */
*info = -1;
i__1 = -(*info);
xerbla_("CLARHS", &i__1);
}
return 0;
/* End of CLARHS */
} /* clarhs_ */
/* Subroutine */ int cpbrfs_(char *uplo, integer *n, integer *kd, integer *
nrhs, complex *ab, integer *ldab, complex *afb, integer *ldafb,
complex *b, integer *ldb, complex *x, integer *ldx, real *ferr, real *
berr, complex *work, real *rwork, integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer i__, j, k, l;
static real s, xk;
static integer nz;
static real eps;
static integer kase;
static real safe1, safe2;
extern /* Subroutine */ int chbmv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *, ftnlen);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static integer count;
static logical upper;
extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real
*, integer *);
extern doublereal slamch_(char *, ftnlen);
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), cpbtrs_(
char *, integer *, integer *, integer *, complex *, integer *,
complex *, integer *, integer *, ftnlen);
static real lstres;
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPBRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is Hermitian positive definite */
/* and banded, and provides error bounds and backward error estimates */
/* for the solution. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 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 array, dimension (LDAB,N) */
/* The upper or lower triangle of the Hermitian band matrix A, */
/* stored in the first KD+1 rows of the array. The j-th column */
/* of A is stored in the j-th column of the array AB as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* AFB (input) COMPLEX array, dimension (LDAFB,N) */
/* The triangular factor U or L from the Cholesky factorization */
/* A = U**H*U or A = L*L**H of the band matrix A as computed by */
/* CPBTRF, in the same storage format as A (see AB). */
/* LDAFB (input) INTEGER */
/* The leading dimension of the array AFB. LDAFB >= KD+1. */
/* B (input) COMPLEX 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 array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by CPBTRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL 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 .. */
/* .. */
/* .. 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;
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;
upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldafb < *kd + 1) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPBRFS", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
/* Computing MIN */
i__1 = *n + 1, i__2 = (*kd << 1) + 2;
nz = min(i__1,i__2);
eps = slamch_("Epsilon", (ftnlen)7);
safmin = slamch_("Safe minimum", (ftnlen)12);
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - A * X */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
chbmv_(uplo, n, kd, &q__1, &ab[ab_offset], ldab, &x[j * x_dim1 + 1], &
c__1, &c_b1, &work[1], &c__1, (ftnlen)1);
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(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__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
l = *kd + 1 - k;
/* Computing MAX */
i__3 = 1, i__4 = k - *kd;
i__5 = k - 1;
for (i__ = max(i__3,i__4); i__ <= i__5; ++i__) {
i__3 = l + i__ + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[l + i__ + k * ab_dim1]), dabs(r__2))) *
xk;
i__3 = l + i__ + k * ab_dim1;
i__4 = i__ + j * x_dim1;
s += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
ab[l + i__ + k * ab_dim1]), dabs(r__2))) * ((r__3
= x[i__4].r, dabs(r__3)) + (r__4 = r_imag(&x[i__
+ j * x_dim1]), dabs(r__4)));
/* L40: */
}
i__5 = *kd + 1 + k * ab_dim1;
rwork[k] = rwork[k] + (r__1 = ab[i__5].r, dabs(r__1)) * xk +
s;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__5 = k + j * x_dim1;
xk = (r__1 = x[i__5].r, dabs(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), dabs(r__2));
i__5 = k * ab_dim1 + 1;
rwork[k] += (r__1 = ab[i__5].r, dabs(r__1)) * xk;
l = 1 - k;
/* Computing MIN */
i__3 = *n, i__4 = k + *kd;
i__5 = min(i__3,i__4);
for (i__ = k + 1; i__ <= i__5; ++i__) {
i__3 = l + i__ + k * ab_dim1;
rwork[i__] += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&ab[l + i__ + k * ab_dim1]), dabs(r__2))) *
xk;
i__3 = l + i__ + k * ab_dim1;
i__4 = i__ + j * x_dim1;
s += ((r__1 = ab[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
ab[l + i__ + k * ab_dim1]), dabs(r__2))) * ((r__3
= x[i__4].r, dabs(r__3)) + (r__4 = r_imag(&x[i__
+ j * x_dim1]), dabs(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__5 = i__;
r__3 = s, r__4 = ((r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__5 = i__;
r__3 = s, r__4 = ((r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__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.f <= lstres && count <= 5) {
/* Update solution and try again. */
cpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[1], n,
info, (ftnlen)1);
caxpy_(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(A))* */
/* ( abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(A) is the inverse of 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(A)*abs(X)+abs(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* abs(A)*abs(X) + abs(B) is less than SAFE2. */
/* Use CLACON to estimate the infinity-norm of the matrix */
/* inv(A) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(A)*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__5 = i__;
rwork[i__] = (r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__5 = i__;
rwork[i__] = (r__1 = work[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacon_(n, &work[*n + 1], &work[1], &ferr[j], &kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(A'). */
cpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[1],
n, info, (ftnlen)1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__5 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__3] * work[i__4].r, q__1.i = rwork[i__3]
* work[i__4].i;
work[i__5].r = q__1.r, work[i__5].i = q__1.i;
/* L110: */
}
} else if (kase == 2) {
/* Multiply by inv(A)*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__5 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__3] * work[i__4].r, q__1.i = rwork[i__3]
* work[i__4].i;
work[i__5].r = q__1.r, work[i__5].i = q__1.i;
/* L120: */
}
cpbtrs_(uplo, n, kd, &c__1, &afb[afb_offset], ldafb, &work[1],
n, info, (ftnlen)1);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__5 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__5].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CPBRFS */
} /* cpbrfs_ */
/* Subroutine */ int cpbt02_(char *uplo, integer *n, integer *kd, integer *
nrhs, complex *a, integer *lda, complex *x, integer *ldx, complex *b,
integer *ldb, real *rwork, real *resid)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
real r__1, r__2;
complex q__1;
/* Local variables */
integer j;
real eps;
real anorm, bnorm, xnorm;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPBT02 computes the residual for a solution of a Hermitian banded */
/* system of equations A*x = b: */
/* RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) */
/* where EPS is the machine precision. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* Hermitian matrix A is stored: */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* N (input) INTEGER */
/* The number of rows and columns of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of super-diagonals of the matrix A if UPLO = 'U', */
/* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* The original Hermitian band matrix A. If UPLO = 'U', the */
/* upper triangular part of A is stored as a band matrix; if */
/* UPLO = 'L', the lower triangular part of A is stored. The */
/* columns of the appropriate triangle are stored in the columns */
/* of A and the diagonals of the triangle are stored in the rows */
/* of A. See CPBTRF for further details. */
/* LDA (input) INTEGER. */
/* The leading dimension of the array A. LDA >= max(1,KD+1). */
/* X (input) COMPLEX array, dimension (LDX,NRHS) */
/* The computed solution vectors for the system of linear */
/* equations. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the right hand side vectors for the system of */
/* linear equations. */
/* On exit, B is overwritten with the difference B - A*X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* RWORK (workspace) REAL array, dimension (N) */
/* RESID (output) REAL */
/* The maximum over the number of right hand sides of */
/* norm(B - A*X) / ( norm(A) * norm(X) * EPS ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0 or NRHS = 0. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--rwork;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
*resid = 0.f;
return 0;
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = slamch_("Epsilon");
anorm = clanhb_("1", uplo, n, kd, &a[a_offset], lda, &rwork[1]);
if (anorm <= 0.f) {
*resid = 1.f / eps;
return 0;
}
/* Compute B - A*X */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
q__1.r = -1.f, q__1.i = -0.f;
chbmv_(uplo, n, kd, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &
c__1, &c_b1, &b[j * b_dim1 + 1], &c__1);
/* L10: */
}
/* Compute the maximum over the number of right hand sides of */
/* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) */
*resid = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
bnorm = scasum_(n, &b[j * b_dim1 + 1], &c__1);
xnorm = scasum_(n, &x[j * x_dim1 + 1], &c__1);
if (xnorm <= 0.f) {
*resid = 1.f / eps;
} else {
/* Computing MAX */
r__1 = *resid, r__2 = bnorm / anorm / xnorm / eps;
*resid = dmax(r__1,r__2);
}
/* L20: */
}
return 0;
/* End of CPBT02 */
} /* cpbt02_ */
