int csptri_(char *uplo, int *n, complex *ap, int *
ipiv, complex *work, int *info)
{
/* System generated locals */
int i__1, i__2, i__3;
complex q__1, q__2, q__3;
/* Builtin functions */
void c_div(complex *, complex *, complex *);
/* Local variables */
complex d__;
int j, k;
complex t, ak;
int kc, kp, kx, kpc, npp;
complex akp1, temp, akkp1;
extern int lsame_(char *, char *);
extern int ccopy_(int *, complex *, int *,
complex *, int *);
extern /* Complex */ VOID cdotu_(complex *, int *, complex *, int
*, complex *, int *);
extern int cswap_(int *, complex *, int *,
complex *, int *);
int kstep;
extern int cspmv_(char *, int *, complex *, complex *
, complex *, int *, complex *, complex *, int *);
int upper;
extern int xerbla_(char *, int *);
int kcnext;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CSPTRI computes the inverse of a complex symmetric indefinite matrix */
/* A in packed storage using the factorization A = U*D*U**T or */
/* A = L*D*L**T computed by CSPTRF. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the details of the factorization are stored */
/* as an upper or lower triangular matrix. */
/* = 'U': Upper triangular, form is A = U*D*U**T; */
/* = 'L': Lower triangular, form is A = L*D*L**T. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the block diagonal matrix D and the multipliers */
/* used to obtain the factor U or L as computed by CSPTRF, */
/* stored as a packed triangular matrix. */
/* On exit, if INFO = 0, the (symmetric) inverse of the original */
/* matrix, stored as a packed triangular matrix. The j-th column */
/* of inv(A) is stored in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; */
/* if UPLO = 'L', */
/* AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by CSPTRF. */
/* WORK (workspace) COMPLEX array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its */
/* inverse could not be computed. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--work;
--ipiv;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSPTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Check that the diagonal matrix D is nonsingular. */
if (upper) {
/* Upper triangular storage: examine D from bottom to top */
kp = *n * (*n + 1) / 2;
for (*info = *n; *info >= 1; --(*info)) {
i__1 = kp;
if (ipiv[*info] > 0 && (ap[i__1].r == 0.f && ap[i__1].i == 0.f)) {
return 0;
}
kp -= *info;
/* L10: */
}
} else {
/* Lower triangular storage: examine D from top to bottom. */
kp = 1;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = kp;
if (ipiv[*info] > 0 && (ap[i__2].r == 0.f && ap[i__2].i == 0.f)) {
return 0;
}
kp = kp + *n - *info + 1;
/* L20: */
}
}
*info = 0;
if (upper) {
/* Compute inv(A) from the factorization A = U*D*U'. */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
k = 1;
kc = 1;
L30:
/* If K > N, exit from loop. */
if (k > *n) {
goto L50;
}
kcnext = kc + k;
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block */
/* Invert the diagonal block. */
i__1 = kc + k - 1;
c_div(&q__1, &c_b1, &ap[kc + k - 1]);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
/* Compute column K of the inverse. */
if (k > 1) {
i__1 = k - 1;
ccopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f, q__1.i = -0.f;
cspmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
ap[kc], &c__1);
i__1 = kc + k - 1;
i__2 = kc + k - 1;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
}
kstep = 1;
} else {
/* 2 x 2 diagonal block */
/* Invert the diagonal block. */
i__1 = kcnext + k - 1;
t.r = ap[i__1].r, t.i = ap[i__1].i;
c_div(&q__1, &ap[kc + k - 1], &t);
ak.r = q__1.r, ak.i = q__1.i;
c_div(&q__1, &ap[kcnext + k], &t);
akp1.r = q__1.r, akp1.i = q__1.i;
c_div(&q__1, &ap[kcnext + k - 1], &t);
akkp1.r = q__1.r, akkp1.i = q__1.i;
q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i +
ak.i * akp1.r;
q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i
* q__2.r;
d__.r = q__1.r, d__.i = q__1.i;
i__1 = kc + k - 1;
c_div(&q__1, &akp1, &d__);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = kcnext + k;
c_div(&q__1, &ak, &d__);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = kcnext + k - 1;
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
c_div(&q__1, &q__2, &d__);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
/* Compute columns K and K+1 of the inverse. */
if (k > 1) {
i__1 = k - 1;
ccopy_(&i__1, &ap[kc], &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f, q__1.i = -0.f;
cspmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
ap[kc], &c__1);
i__1 = kc + k - 1;
i__2 = kc + k - 1;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc], &c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = kcnext + k - 1;
i__2 = kcnext + k - 1;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &ap[kc], &c__1, &ap[kcnext], &c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = k - 1;
ccopy_(&i__1, &ap[kcnext], &c__1, &work[1], &c__1);
i__1 = k - 1;
q__1.r = -1.f, q__1.i = -0.f;
cspmv_(uplo, &i__1, &q__1, &ap[1], &work[1], &c__1, &c_b2, &
ap[kcnext], &c__1);
i__1 = kcnext + k;
i__2 = kcnext + k;
i__3 = k - 1;
cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kcnext], &c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
}
kstep = 2;
kcnext = kcnext + k + 1;
}
kp = (i__1 = ipiv[k], ABS(i__1));
if (kp != k) {
/* Interchange rows and columns K and KP in the leading */
/* submatrix A(1:k+1,1:k+1) */
kpc = (kp - 1) * kp / 2 + 1;
i__1 = kp - 1;
cswap_(&i__1, &ap[kc], &c__1, &ap[kpc], &c__1);
kx = kpc + kp - 1;
i__1 = k - 1;
for (j = kp + 1; j <= i__1; ++j) {
kx = kx + j - 1;
i__2 = kc + j - 1;
temp.r = ap[i__2].r, temp.i = ap[i__2].i;
i__2 = kc + j - 1;
i__3 = kx;
ap[i__2].r = ap[i__3].r, ap[i__2].i = ap[i__3].i;
i__2 = kx;
ap[i__2].r = temp.r, ap[i__2].i = temp.i;
/* L40: */
}
i__1 = kc + k - 1;
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
i__1 = kc + k - 1;
i__2 = kpc + kp - 1;
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
i__1 = kpc + kp - 1;
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
if (kstep == 2) {
i__1 = kc + k + k - 1;
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
i__1 = kc + k + k - 1;
i__2 = kc + k + kp - 1;
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
i__1 = kc + k + kp - 1;
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
}
}
k += kstep;
kc = kcnext;
goto L30;
L50:
;
} else {
/* Compute inv(A) from the factorization A = L*D*L'. */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
npp = *n * (*n + 1) / 2;
k = *n;
kc = npp;
L60:
/* If K < 1, exit from loop. */
if (k < 1) {
goto L80;
}
kcnext = kc - (*n - k + 2);
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block */
/* Invert the diagonal block. */
i__1 = kc;
c_div(&q__1, &c_b1, &ap[kc]);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
/* Compute column K of the inverse. */
if (k < *n) {
i__1 = *n - k;
ccopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f, q__1.i = -0.f;
cspmv_(uplo, &i__1, &q__1, &ap[kc + *n - k + 1], &work[1], &
c__1, &c_b2, &ap[kc + 1], &c__1);
i__1 = kc;
i__2 = kc;
i__3 = *n - k;
cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
}
kstep = 1;
} else {
/* 2 x 2 diagonal block */
/* Invert the diagonal block. */
i__1 = kcnext + 1;
t.r = ap[i__1].r, t.i = ap[i__1].i;
c_div(&q__1, &ap[kcnext], &t);
ak.r = q__1.r, ak.i = q__1.i;
c_div(&q__1, &ap[kc], &t);
akp1.r = q__1.r, akp1.i = q__1.i;
c_div(&q__1, &ap[kcnext + 1], &t);
akkp1.r = q__1.r, akkp1.i = q__1.i;
q__3.r = ak.r * akp1.r - ak.i * akp1.i, q__3.i = ak.r * akp1.i +
ak.i * akp1.r;
q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f;
q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i
* q__2.r;
d__.r = q__1.r, d__.i = q__1.i;
i__1 = kcnext;
c_div(&q__1, &akp1, &d__);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = kc;
c_div(&q__1, &ak, &d__);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = kcnext + 1;
q__2.r = -akkp1.r, q__2.i = -akkp1.i;
c_div(&q__1, &q__2, &d__);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
/* Compute columns K-1 and K of the inverse. */
if (k < *n) {
i__1 = *n - k;
ccopy_(&i__1, &ap[kc + 1], &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f, q__1.i = -0.f;
cspmv_(uplo, &i__1, &q__1, &ap[kc + (*n - k + 1)], &work[1], &
c__1, &c_b2, &ap[kc + 1], &c__1);
i__1 = kc;
i__2 = kc;
i__3 = *n - k;
cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kc + 1], &c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = kcnext + 1;
i__2 = kcnext + 1;
i__3 = *n - k;
cdotu_(&q__2, &i__3, &ap[kc + 1], &c__1, &ap[kcnext + 2], &
c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = *n - k;
ccopy_(&i__1, &ap[kcnext + 2], &c__1, &work[1], &c__1);
i__1 = *n - k;
q__1.r = -1.f, q__1.i = -0.f;
cspmv_(uplo, &i__1, &q__1, &ap[kc + (*n - k + 1)], &work[1], &
c__1, &c_b2, &ap[kcnext + 2], &c__1);
i__1 = kcnext;
i__2 = kcnext;
i__3 = *n - k;
cdotu_(&q__2, &i__3, &work[1], &c__1, &ap[kcnext + 2], &c__1);
q__1.r = ap[i__2].r - q__2.r, q__1.i = ap[i__2].i - q__2.i;
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
}
kstep = 2;
kcnext -= *n - k + 3;
}
kp = (i__1 = ipiv[k], ABS(i__1));
if (kp != k) {
/* Interchange rows and columns K and KP in the trailing */
/* submatrix A(k-1:n,k-1:n) */
kpc = npp - (*n - kp + 1) * (*n - kp + 2) / 2 + 1;
if (kp < *n) {
i__1 = *n - kp;
cswap_(&i__1, &ap[kc + kp - k + 1], &c__1, &ap[kpc + 1], &
c__1);
}
kx = kc + kp - k;
i__1 = kp - 1;
for (j = k + 1; j <= i__1; ++j) {
kx = kx + *n - j + 1;
i__2 = kc + j - k;
temp.r = ap[i__2].r, temp.i = ap[i__2].i;
i__2 = kc + j - k;
i__3 = kx;
ap[i__2].r = ap[i__3].r, ap[i__2].i = ap[i__3].i;
i__2 = kx;
ap[i__2].r = temp.r, ap[i__2].i = temp.i;
/* L70: */
}
i__1 = kc;
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
i__1 = kc;
i__2 = kpc;
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
i__1 = kpc;
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
if (kstep == 2) {
i__1 = kc - *n + k - 1;
temp.r = ap[i__1].r, temp.i = ap[i__1].i;
i__1 = kc - *n + k - 1;
i__2 = kc - *n + kp - 1;
ap[i__1].r = ap[i__2].r, ap[i__1].i = ap[i__2].i;
i__1 = kc - *n + kp - 1;
ap[i__1].r = temp.r, ap[i__1].i = temp.i;
}
}
k -= kstep;
kc = kcnext;
goto L60;
L80:
;
}
return 0;
/* End of CSPTRI */
} /* csptri_ */
/* Subroutine */ int csprfs_(char *uplo, integer *n, integer *nrhs, complex *
ap, complex *afp, integer *ipiv, complex *b, integer *ldb, complex *x,
integer *ldx, real *ferr, real *berr, complex *work, real *rwork,
integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CSPRFS improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric indefinite
and packed, 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.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
AP (input) COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
AFP (input) COMPLEX array, dimension (N*(N+1)/2)
The factored form of the matrix A. AFP contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**T or
A = L*D*L**T as computed by CSPTRF, stored as a packed
triangular matrix.
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSPTRF.
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 CSPTRS.
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 */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer 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;
static real s;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static integer count;
extern /* Subroutine */ int cspmv_(char *, integer *, complex *, complex *
, complex *, integer *, complex *, complex *, integer *);
static logical upper;
static integer ik, kk;
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 *);
static real lstres;
extern /* Subroutine */ int csptrs_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, 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)]
--ap;
--afp;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else if (*ldx < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CSPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied.
Compute residual R = B - A * X */
ccopy_(n, &b_ref(1, j), &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = 0.f;
cspmv_(uplo, n, &q__1, &ap[1], &x_ref(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 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 = b_subscr(i__, j);
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
b_ref(i__, j)), dabs(r__2));
/* L30: */
}
/* Compute abs(A)*abs(X) + abs(B). */
kk = 1;
if (upper) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = x_subscr(k, j);
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x_ref(k,
j)), dabs(r__2));
ik = kk;
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ik;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[ik]), dabs(r__2))) * xk;
i__4 = ik;
i__5 = x_subscr(i__, j);
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
ap[ik]), dabs(r__2))) * ((r__3 = x[i__5].r, dabs(
r__3)) + (r__4 = r_imag(&x_ref(i__, j)), dabs(
r__4)));
++ik;
/* L40: */
}
i__3 = kk + k - 1;
rwork[k] = rwork[k] + ((r__1 = ap[i__3].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kk + k - 1]), dabs(r__2))) * xk + s;
kk += k;
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = x_subscr(k, j);
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x_ref(k,
j)), dabs(r__2));
i__3 = kk;
rwork[k] += ((r__1 = ap[i__3].r, dabs(r__1)) + (r__2 = r_imag(
&ap[kk]), dabs(r__2))) * xk;
ik = kk + 1;
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = ik;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[ik]), dabs(r__2))) * xk;
i__4 = ik;
i__5 = x_subscr(i__, j);
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
ap[ik]), dabs(r__2))) * ((r__3 = x[i__5].r, dabs(
r__3)) + (r__4 = r_imag(&x_ref(i__, j)), dabs(
r__4)));
++ik;
/* L60: */
}
rwork[k] += s;
kk += *n - k + 1;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].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__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].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. */
csptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[1], n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x_ref(1, j), &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula
norm(X - XTRUE) / norm(X) .le. FERR =
norm( abs(inv(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__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].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'). */
csptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].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__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L120: */
}
csptrs_(uplo, n, &c__1, &afp[1], &ipiv[1], &work[1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = x_subscr(i__, j);
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x_ref(i__, j)), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CSPRFS */
} /* csprfs_ */
/* Subroutine */ int cspt02_(char *uplo, integer *n, integer *nrhs, complex *
a, complex *x, integer *ldx, complex *b, integer *ldb, real *rwork,
real *resid)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
real r__1, r__2;
complex q__1;
/* Local variables */
integer j;
real eps, anorm, bnorm;
real xnorm;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CSPT02 computes the residual in the solution of a complex symmetric */
/* system of linear equations A*x = b when packed storage is used for */
/* the coefficient matrix. The ratio computed is */
/* 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 */
/* complex symmetric 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. */
/* NRHS (input) INTEGER */
/* The number of columns of B, the matrix of right hand sides. */
/* NRHS >= 0. */
/* A (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The original complex symmetric matrix A, stored as a packed */
/* triangular matrix. */
/* 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;
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 = clansp_("1", uplo, n, &a[1], &rwork[1]);
if (anorm <= 0.f) {
*resid = 1.f / eps;
return 0;
}
/* Compute B - A*X for the matrix of right hand sides B. */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
q__1.r = -1.f, q__1.i = -0.f;
cspmv_(uplo, n, &q__1, &a[1], &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 CSPT02 */
} /* cspt02_ */
/* 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_ */