int
f2c_ctpmv(char* uplo, char* trans, char* diag, integer* N,
complex* Ap,
complex* X, integer* incX)
{
ctpmv_(uplo, trans, diag,
N, Ap, X, incX);
return 0;
}
/* Subroutine */ int ctpt02_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, complex *ap, complex *x, integer *ldx, complex *b,
integer *ldb, complex *work, real *rwork, real *resid)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
real r__1, r__2;
/* Local variables */
static integer j;
extern logical lsame_(char *, char *);
static real anorm, bnorm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), ctpmv_(char *, char *, char *,
integer *, complex *, complex *, integer *);
static real xnorm;
extern doublereal slamch_(char *), clantp_(char *, char *, char *,
integer *, complex *, real *), 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
February 29, 1992
Purpose
=======
CTPT02 computes the residual for the computed solution to a
triangular system of linear equations A*x = b, A**T *x = b, or
A**H *x = b, when the triangular matrix A is stored in packed format.
Here A**T denotes the transpose of A, A**H denotes the conjugate
transpose of A, and x and b are N by NRHS matrices. The test ratio
is the maximum over the number of right hand sides of
the maximum over the number of right hand sides of
norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS (input) CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = b (No transpose)
= 'T': A**T *x = b (Transpose)
= 'C': A**H *x = b (Conjugate transpose)
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
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 X and B. NRHS >= 0.
AP (input) COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangular 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
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) COMPLEX array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK (workspace) COMPLEX array, dimension (N)
RWORK (workspace) REAL array, dimension (N)
RESID (output) REAL
The maximum over the number of right hand sides of
norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
=====================================================================
Quick exit if N = 0 or NRHS = 0
Parameter adjustments */
--ap;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--work;
--rwork;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
*resid = 0.f;
return 0;
}
/* Compute the 1-norm of A or A**H. */
if (lsame_(trans, "N")) {
anorm = clantp_("1", uplo, diag, n, &ap[1], &rwork[1]);
} else {
anorm = clantp_("I", uplo, diag, n, &ap[1], &rwork[1]);
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = slamch_("Epsilon");
if (anorm <= 0.f) {
*resid = 1.f / eps;
return 0;
}
/* Compute the maximum over the number of right hand sides of
norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). */
*resid = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ccopy_(n, &x_ref(1, j), &c__1, &work[1], &c__1);
ctpmv_(uplo, trans, diag, n, &ap[1], &work[1], &c__1);
caxpy_(n, &c_b12, &b_ref(1, j), &c__1, &work[1], &c__1);
bnorm = scasum_(n, &work[1], &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);
}
/* L10: */
}
return 0;
/* End of CTPT02 */
} /* ctpt02_ */
/* Subroutine */ int ctprfs_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, complex *ap, complex *b, integer *ldb, complex *x,
integer *ldx, real *ferr, real *berr, complex *work, real *rwork,
integer *info)
{
/* 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 */
integer i__, j, k;
real s;
integer kc;
real xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), ctpmv_(char *, char *, char *,
integer *, complex *, complex *, integer *);
logical upper;
extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *,
complex *, complex *, integer *), clacn2_(
integer *, complex *, complex *, real *, integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical notran;
char transn[1], transt[1];
logical nounit;
real lstres;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTPRFS provides error bounds and backward error estimates for the */
/* solution to a system of linear equations with a triangular packed */
/* coefficient matrix. */
/* The solution matrix X must be computed by CTPTRS or some other */
/* means before entering this routine. CTPRFS does not do iterative */
/* refinement because doing so cannot improve the backward error. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': A is upper triangular; */
/* = 'L': A is lower triangular. */
/* 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) */
/* DIAG (input) CHARACTER*1 */
/* = 'N': A is non-unit triangular; */
/* = 'U': A is unit triangular. */
/* 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 triangular 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)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* If DIAG = 'U', the diagonal elements of A are not referenced */
/* and are assumed to be 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) COMPLEX array, dimension (LDX,NRHS) */
/* The 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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
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");
notran = lsame_(trans, "N");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*nrhs < 0) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else if (*ldx < max(1,*n)) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)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 */
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) {
/* Compute residual R = B - op(A) * X, */
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
ccopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ctpmv_(uplo, trans, diag, n, &ap[1], &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
caxpy_(n, &q__1, &b[j * b_dim1 + 1], &c__1, &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__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), dabs(r__2));
/* L20: */
}
if (notran) {
/* Compute abs(A)*abs(X) + abs(B). */
if (upper) {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
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));
i__3 = k;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - 1]), dabs(
r__2))) * xk;
/* L30: */
}
kc += k;
/* L40: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
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));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - 1]), dabs(
r__2))) * xk;
/* L50: */
}
rwork[k] += xk;
kc += k;
/* L60: */
}
}
} else {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
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));
i__3 = *n;
for (i__ = k; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - k]), dabs(
r__2))) * xk;
/* L70: */
}
kc = kc + *n - k + 1;
/* L80: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
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));
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
rwork[i__] += ((r__1 = ap[i__4].r, dabs(r__1)) + (
r__2 = r_imag(&ap[kc + i__ - k]), dabs(
r__2))) * xk;
/* L90: */
}
rwork[k] += xk;
kc = kc + *n - k + 1;
/* L100: */
}
}
}
} else {
/* Compute abs(A**H)*abs(X) + abs(B). */
if (upper) {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = k;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - 1]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L110: */
}
rwork[k] += s;
kc += k;
/* L120: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
s = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - 1]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L130: */
}
rwork[k] += s;
kc += k;
/* L140: */
}
}
} else {
kc = 1;
if (nounit) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = *n;
for (i__ = k; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - k]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L150: */
}
rwork[k] += s;
kc = kc + *n - k + 1;
/* L160: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
s = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
x[k + j * x_dim1]), dabs(r__2));
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
i__5 = i__ + j * x_dim1;
s += ((r__1 = ap[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&ap[kc + i__ - k]), dabs(r__2))) *
((r__3 = x[i__5].r, dabs(r__3)) + (r__4 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__4)))
;
/* L170: */
}
rwork[k] += s;
kc = kc + *n - k + 1;
/* L180: */
}
}
}
}
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);
}
/* L190: */
}
berr[j] = s;
/* 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 CLACN2 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__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;
}
/* L200: */
}
kase = 0;
L210:
clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**H). */
ctpsv_(uplo, transt, diag, n, &ap[1], &work[1], &c__1);
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;
/* L220: */
}
} else {
/* Multiply by inv(op(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;
/* L230: */
}
ctpsv_(uplo, transn, diag, n, &ap[1], &work[1], &c__1);
}
goto L210;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L240: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L250: */
}
return 0;
/* End of CTPRFS */
} /* ctprfs_ */
void
ctpmv(char uplo, char transa, char diag, int n, complex *ap, complex *x, int incx)
{
ctpmv_( &uplo, &transa, &diag, &n, ap, x, &incx);
}
/* Subroutine */ int chpgst_(integer *itype, char *uplo, integer *n, complex *
ap, complex *bp, integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
static integer j, k, j1, k1, jj, kk;
static complex ct;
static real ajj;
static integer j1j1;
static real akk;
static integer k1k1;
static real bjj, bkk;
extern /* Subroutine */ int chpr2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, ftnlen);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int chpmv_(char *, integer *, complex *, complex *
, complex *, integer *, complex *, complex *, integer *, ftnlen),
caxpy_(integer *, complex *, complex *, integer *, complex *,
integer *), ctpmv_(char *, char *, char *, integer *, complex *,
complex *, integer *, ftnlen, ftnlen, ftnlen);
static logical upper;
extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *,
complex *, complex *, integer *, ftnlen, ftnlen, ftnlen), csscal_(
integer *, real *, complex *, integer *), xerbla_(char *, integer
*, ftnlen);
/* -- 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 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHPGST reduces a complex Hermitian-definite generalized */
/* eigenproblem to standard form, using packed storage. */
/* If ITYPE = 1, the problem is A*x = lambda*B*x, */
/* and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) */
/* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */
/* B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. */
/* B must have been previously factorized as U**H*U or L*L**H by CPPTRF. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); */
/* = 2 or 3: compute U*A*U**H or L**H*A*L. */
/* UPLO (input) CHARACTER */
/* = 'U': Upper triangle of A is stored and B is factored as */
/* U**H*U; */
/* = 'L': Lower triangle of A is stored and B is factored as */
/* L*L**H. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the Hermitian 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)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* On exit, if INFO = 0, the transformed matrix, stored in the */
/* same format as A. */
/* BP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The triangular factor from the Cholesky factorization of B, */
/* stored in the same format as A, as returned by CPPTRF. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--bp;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
*info = -2;
} else if (*n < 0) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHPGST", &i__1, (ftnlen)6);
return 0;
}
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
/* J1 and JJ are the indices of A(1,j) and A(j,j) */
jj = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
j1 = jj + 1;
jj += j;
/* Compute the j-th column of the upper triangle of A */
i__2 = jj;
i__3 = jj;
r__1 = ap[i__3].r;
ap[i__2].r = r__1, ap[i__2].i = 0.f;
i__2 = jj;
bjj = bp[i__2].r;
ctpsv_(uplo, "Conjugate transpose", "Non-unit", &j, &bp[1], &
ap[j1], &c__1, (ftnlen)1, (ftnlen)19, (ftnlen)8);
i__2 = j - 1;
q__1.r = -1.f, q__1.i = -0.f;
chpmv_(uplo, &i__2, &q__1, &ap[1], &bp[j1], &c__1, &c_b1, &ap[
j1], &c__1, (ftnlen)1);
i__2 = j - 1;
r__1 = 1.f / bjj;
csscal_(&i__2, &r__1, &ap[j1], &c__1);
i__2 = jj;
i__3 = jj;
i__4 = j - 1;
cdotc_(&q__3, &i__4, &ap[j1], &c__1, &bp[j1], &c__1);
q__2.r = ap[i__3].r - q__3.r, q__2.i = ap[i__3].i - q__3.i;
q__1.r = q__2.r / bjj, q__1.i = q__2.i / bjj;
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
/* KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) */
kk = 1;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
k1k1 = kk + *n - k + 1;
/* Update the lower triangle of A(k:n,k:n) */
i__2 = kk;
akk = ap[i__2].r;
i__2 = kk;
bkk = bp[i__2].r;
/* Computing 2nd power */
r__1 = bkk;
akk /= r__1 * r__1;
i__2 = kk;
ap[i__2].r = akk, ap[i__2].i = 0.f;
if (k < *n) {
i__2 = *n - k;
r__1 = 1.f / bkk;
csscal_(&i__2, &r__1, &ap[kk + 1], &c__1);
r__1 = akk * -.5f;
ct.r = r__1, ct.i = 0.f;
i__2 = *n - k;
caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
q__1.r = -1.f, q__1.i = -0.f;
chpr2_(uplo, &i__2, &q__1, &ap[kk + 1], &c__1, &bp[kk + 1]
, &c__1, &ap[k1k1], (ftnlen)1);
i__2 = *n - k;
caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
ctpsv_(uplo, "No transpose", "Non-unit", &i__2, &bp[k1k1],
&ap[kk + 1], &c__1, (ftnlen)1, (ftnlen)12, (
ftnlen)8);
}
kk = k1k1;
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
/* K1 and KK are the indices of A(1,k) and A(k,k) */
kk = 0;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
k1 = kk + 1;
kk += k;
/* Update the upper triangle of A(1:k,1:k) */
i__2 = kk;
akk = ap[i__2].r;
i__2 = kk;
bkk = bp[i__2].r;
i__2 = k - 1;
ctpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[
k1], &c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8);
r__1 = akk * .5f;
ct.r = r__1, ct.i = 0.f;
i__2 = k - 1;
caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
chpr2_(uplo, &i__2, &c_b1, &ap[k1], &c__1, &bp[k1], &c__1, &
ap[1], (ftnlen)1);
i__2 = k - 1;
caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
csscal_(&i__2, &bkk, &ap[k1], &c__1);
i__2 = kk;
/* Computing 2nd power */
r__2 = bkk;
r__1 = akk * (r__2 * r__2);
ap[i__2].r = r__1, ap[i__2].i = 0.f;
/* L30: */
}
} else {
/* Compute L'*A*L */
/* JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) */
jj = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
j1j1 = jj + *n - j + 1;
/* Compute the j-th column of the lower triangle of A */
i__2 = jj;
ajj = ap[i__2].r;
i__2 = jj;
bjj = bp[i__2].r;
i__2 = jj;
r__1 = ajj * bjj;
i__3 = *n - j;
cdotc_(&q__2, &i__3, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1);
q__1.r = r__1 + q__2.r, q__1.i = q__2.i;
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
i__2 = *n - j;
csscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
i__2 = *n - j;
chpmv_(uplo, &i__2, &c_b1, &ap[j1j1], &bp[jj + 1], &c__1, &
c_b1, &ap[jj + 1], &c__1, (ftnlen)1);
i__2 = *n - j + 1;
ctpmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &bp[jj]
, &ap[jj], &c__1, (ftnlen)1, (ftnlen)19, (ftnlen)8);
jj = j1j1;
/* L40: */
}
}
}
return 0;
/* End of CHPGST */
} /* chpgst_ */
/* Subroutine */ int chpgv_(integer *itype, char *jobz, char *uplo, integer *
n, complex *ap, complex *bp, real *w, complex *z__, integer *ldz,
complex *work, real *rwork, integer *info, ftnlen jobz_len, ftnlen
uplo_len)
{
/* System generated locals */
integer z_dim1, z_offset, i__1;
/* Local variables */
static integer j, neig;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int chpev_(char *, char *, integer *, complex *,
real *, complex *, integer *, complex *, real *, integer *,
ftnlen, ftnlen);
static char trans[1];
extern /* Subroutine */ int ctpmv_(char *, char *, char *, integer *,
complex *, complex *, integer *, ftnlen, ftnlen, ftnlen);
static logical upper;
extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *,
complex *, complex *, integer *, ftnlen, ftnlen, ftnlen);
static logical wantz;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), chpgst_(
integer *, char *, integer *, complex *, complex *, integer *,
ftnlen), cpptrf_(char *, integer *, complex *, integer *, ftnlen);
/* -- LAPACK driver routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHPGV computes all the eigenvalues and, optionally, the eigenvectors */
/* of a complex generalized Hermitian-definite eigenproblem, of the form */
/* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. */
/* Here A and B are assumed to be Hermitian, stored in packed format, */
/* and B is also positive definite. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* Specifies the problem type to be solved: */
/* = 1: A*x = (lambda)*B*x */
/* = 2: A*B*x = (lambda)*x */
/* = 3: B*A*x = (lambda)*x */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangles of A and B are stored; */
/* = 'L': Lower triangles of A and B are stored. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the Hermitian 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. */
/* On exit, the contents of AP are destroyed. */
/* BP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the Hermitian matrix */
/* B, packed columnwise in a linear array. The j-th column of B */
/* is stored in the array BP as follows: */
/* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; */
/* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. */
/* On exit, the triangular factor U or L from the Cholesky */
/* factorization B = U**H*U or B = L*L**H, in the same storage */
/* format as B. */
/* W (output) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX array, dimension (LDZ, N) */
/* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */
/* eigenvectors. The eigenvectors are normalized as follows: */
/* if ITYPE = 1 or 2, Z**H*B*Z = I; */
/* if ITYPE = 3, Z**H*inv(B)*Z = I. */
/* If JOBZ = 'N', then Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1, and if */
/* JOBZ = 'V', LDZ >= max(1,N). */
/* WORK (workspace) COMPLEX array, dimension (max(1, 2*N-1)) */
/* RWORK (workspace) REAL array, dimension (max(1, 3*N-2)) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: CPPTRF or CHPEV returned an error code: */
/* <= N: if INFO = i, CHPEV failed to converge; */
/* i off-diagonal elements of an intermediate */
/* tridiagonal form did not convergeto zero; */
/* > N: if INFO = N + i, for 1 <= i <= n, then the leading */
/* minor of order i of B is not positive definite. */
/* The factorization of B could not be completed and */
/* no eigenvalues or eigenvectors were computed. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--bp;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
/* Function Body */
wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1);
upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
*info = 0;
if (*itype < 0 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) {
*info = -2;
} else if (! (upper || lsame_(uplo, "L", (ftnlen)1, (ftnlen)1))) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHPGV ", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
cpptrf_(uplo, n, &bp[1], info, (ftnlen)1);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
chpgst_(itype, uplo, n, &ap[1], &bp[1], info, (ftnlen)1);
chpev_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1], &
rwork[1], info, (ftnlen)1, (ftnlen)1);
if (wantz) {
/* Backtransform eigenvectors to the original problem. */
neig = *n;
if (*info > 0) {
neig = *info - 1;
}
if (*itype == 1 || *itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
/* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (upper) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'C';
}
i__1 = neig;
for (j = 1; j <= i__1; ++j) {
ctpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &c__1, (ftnlen)1, (ftnlen)1, (ftnlen)8);
/* L10: */
}
} else if (*itype == 3) {
/* For B*A*x=(lambda)*x; */
/* backtransform eigenvectors: x = L*y or U'*y */
if (upper) {
*(unsigned char *)trans = 'C';
} else {
*(unsigned char *)trans = 'N';
}
i__1 = neig;
for (j = 1; j <= i__1; ++j) {
ctpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &c__1, (ftnlen)1, (ftnlen)1, (ftnlen)8);
/* L20: */
}
}
}
return 0;
/* End of CHPGV */
} /* chpgv_ */
/* Subroutine */
int chpgvx_(integer *itype, char *jobz, char *range, char * uplo, integer *n, complex *ap, complex *bp, real *vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, real *w, complex * z__, integer *ldz, complex *work, real *rwork, integer *iwork, integer *ifail, integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1;
/* Local variables */
integer j;
extern logical lsame_(char *, char *);
char trans[1];
extern /* Subroutine */
int ctpmv_(char *, char *, char *, integer *, complex *, complex *, integer *);
logical upper;
extern /* Subroutine */
int ctpsv_(char *, char *, char *, integer *, complex *, complex *, integer *);
logical wantz, alleig, indeig, valeig;
extern /* Subroutine */
int xerbla_(char *, integer *), chpgst_( integer *, char *, integer *, complex *, complex *, integer *), chpevx_(char *, char *, char *, integer *, complex *, real *, real *, integer *, integer *, real *, integer *, real *, complex *, integer *, complex *, real *, integer *, integer *, integer *), cpptrf_(char *, integer *, complex *, integer *);
/* -- LAPACK driver routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--bp;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
--ifail;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
alleig = lsame_(range, "A");
valeig = lsame_(range, "V");
indeig = lsame_(range, "I");
*info = 0;
if (*itype < 1 || *itype > 3)
{
*info = -1;
}
else if (! (wantz || lsame_(jobz, "N")))
{
*info = -2;
}
else if (! (alleig || valeig || indeig))
{
*info = -3;
}
else if (! (upper || lsame_(uplo, "L")))
{
*info = -4;
}
else if (*n < 0)
{
*info = -5;
}
else
{
if (valeig)
{
if (*n > 0 && *vu <= *vl)
{
*info = -9;
}
}
else if (indeig)
{
if (*il < 1)
{
*info = -10;
}
else if (*iu < min(*n,*il) || *iu > *n)
{
*info = -11;
}
}
}
if (*info == 0)
{
if (*ldz < 1 || wantz && *ldz < *n)
{
*info = -16;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CHPGVX", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
return 0;
}
/* Form a Cholesky factorization of B. */
cpptrf_(uplo, n, &bp[1], info);
if (*info != 0)
{
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
chpgst_(itype, uplo, n, &ap[1], &bp[1], info);
chpevx_(jobz, range, uplo, n, &ap[1], vl, vu, il, iu, abstol, m, &w[1], & z__[z_offset], ldz, &work[1], &rwork[1], &iwork[1], &ifail[1], info);
if (wantz)
{
/* Backtransform eigenvectors to the original problem. */
if (*info > 0)
{
*m = *info - 1;
}
if (*itype == 1 || *itype == 2)
{
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
*/
/* backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y */
if (upper)
{
*(unsigned char *)trans = 'N';
}
else
{
*(unsigned char *)trans = 'C';
}
i__1 = *m;
for (j = 1;
j <= i__1;
++j)
{
ctpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 1], &c__1);
/* L10: */
}
}
else if (*itype == 3)
{
/* For B*A*x=(lambda)*x;
*/
/* backtransform eigenvectors: x = L*y or U**H*y */
if (upper)
{
*(unsigned char *)trans = 'C';
}
else
{
*(unsigned char *)trans = 'N';
}
i__1 = *m;
for (j = 1;
j <= i__1;
++j)
{
ctpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 + 1], &c__1);
/* L20: */
}
}
}
return 0;
/* End of CHPGVX */
}
void cblas_ctpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo,
const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag,
const integer N, const void *Ap, void *X, const integer incX)
{
char TA;
char UL;
char DI;
#ifdef F77_CHAR
F77_CHAR F77_TA, F77_UL, F77_DI;
#else
#define F77_TA &TA
#define F77_UL &UL
#define F77_DI &DI
#endif
#define F77_N N
#define F77_incX incX
integer n, i=0, tincX;
float *st=0,*x=(float *)X;
extern integer CBLAS_CallFromC;
extern integer RowMajorStrg;
RowMajorStrg = 0;
CBLAS_CallFromC = 1;
if (order == CblasColMajor)
{
if (Uplo == CblasUpper) UL = 'U';
else if (Uplo == CblasLower) UL = 'L';
else
{
cblas_xerbla(2, "cblas_ctpmv","Illegal Uplo setting, %d\n", Uplo);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
if (TransA == CblasNoTrans) TA = 'N';
else if (TransA == CblasTrans) TA = 'T';
else if (TransA == CblasConjTrans) TA = 'C';
else
{
cblas_xerbla(3, "cblas_ctpmv","Illegal TransA setting, %d\n", TransA);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
if (Diag == CblasUnit) DI = 'U';
else if (Diag == CblasNonUnit) DI = 'N';
else
{
cblas_xerbla(4, "cblas_ctpmv","Illegal Diag setting, %d\n", Diag);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
#ifdef F77_CHAR
F77_UL = C2F_CHAR(&UL);
F77_TA = C2F_CHAR(&TA);
F77_DI = C2F_CHAR(&DI);
#endif
ctpmv_( F77_UL, F77_TA, F77_DI, &F77_N, Ap, X, &F77_incX);
}
else if (order == CblasRowMajor)
{
RowMajorStrg = 1;
if (Uplo == CblasUpper) UL = 'L';
else if (Uplo == CblasLower) UL = 'U';
else
{
cblas_xerbla(2, "cblas_ctpmv","Illegal Uplo setting, %d\n", Uplo);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
if (TransA == CblasNoTrans) TA = 'T';
else if (TransA == CblasTrans) TA = 'N';
else if (TransA == CblasConjTrans)
{
TA = 'N';
if ( N > 0)
{
if(incX > 0)
tincX = incX;
else
tincX = -incX;
i = tincX << 1;
n = i * N;
x++;
st = x + n;
do
{
*x = -(*x);
x += i;
}
while (x != st);
x -= n;
}
}
else
{
cblas_xerbla(3, "cblas_ctpmv","Illegal TransA setting, %d\n", TransA);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
if (Diag == CblasUnit) DI = 'U';
else if (Diag == CblasNonUnit) DI = 'N';
else
{
cblas_xerbla(4, "cblas_ctpmv","Illegal Diag setting, %d\n", Diag);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
#ifdef F77_CHAR
F77_UL = C2F_CHAR(&UL);
F77_TA = C2F_CHAR(&TA);
F77_DI = C2F_CHAR(&DI);
#endif
ctpmv_( F77_UL, F77_TA, F77_DI, &F77_N, Ap, X,&F77_incX);
if (TransA == CblasConjTrans)
{
if (N > 0)
{
do
{
*x = -(*x);
x += i;
}
while (x != st);
}
}
}
else cblas_xerbla(1, "cblas_ctpmv", "Illegal Order setting, %d\n", order);
CBLAS_CallFromC = 0;
RowMajorStrg = 0;
return;
}
/* 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 ctpt01_(char *uplo, char *diag, integer *n, complex *ap,
complex *ainvp, real *rcond, real *rwork, real *resid)
{
/* System generated locals */
integer i__1, i__2, i__3;
complex q__1;
/* Local variables */
integer j, jc;
real eps;
extern logical lsame_(char *, char *);
real anorm;
logical unitd;
extern /* Subroutine */ int ctpmv_(char *, char *, char *, integer *,
complex *, complex *, integer *);
extern doublereal slamch_(char *), clantp_(char *, char *, char *,
integer *, complex *, real *);
real ainvnm;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTPT01 computes the residual for a triangular matrix A times its */
/* inverse when A is stored in packed format: */
/* RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ), */
/* where EPS is the machine epsilon. */
/* Arguments */
/* ========== */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The original upper or lower triangular 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', */
/* AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. */
/* AINVP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the (triangular) inverse of the matrix A, packed */
/* columnwise in a linear array as in AP. */
/* On exit, the contents of AINVP are destroyed. */
/* RCOND (output) REAL */
/* The reciprocal condition number of A, computed as */
/* 1/(norm(A) * norm(AINV)). */
/* RWORK (workspace) REAL array, dimension (N) */
/* RESID (output) REAL */
/* norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0. */
/* Parameter adjustments */
--rwork;
--ainvp;
--ap;
/* Function Body */
if (*n <= 0) {
*rcond = 1.f;
*resid = 0.f;
return 0;
}
/* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. */
eps = slamch_("Epsilon");
anorm = clantp_("1", uplo, diag, n, &ap[1], &rwork[1]);
ainvnm = clantp_("1", uplo, diag, n, &ainvp[1], &rwork[1]);
if (anorm <= 0.f || ainvnm <= 0.f) {
*rcond = 0.f;
*resid = 1.f / eps;
return 0;
}
*rcond = 1.f / anorm / ainvnm;
/* Compute A * AINV, overwriting AINV. */
unitd = lsame_(diag, "U");
if (lsame_(uplo, "U")) {
jc = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (unitd) {
i__2 = jc + j - 1;
ainvp[i__2].r = 1.f, ainvp[i__2].i = 0.f;
}
/* Form the j-th column of A*AINV. */
ctpmv_("Upper", "No transpose", diag, &j, &ap[1], &ainvp[jc], &
c__1);
/* Subtract 1 from the diagonal to form A*AINV - I. */
i__2 = jc + j - 1;
i__3 = jc + j - 1;
q__1.r = ainvp[i__3].r - 1.f, q__1.i = ainvp[i__3].i;
ainvp[i__2].r = q__1.r, ainvp[i__2].i = q__1.i;
jc += j;
/* L10: */
}
} else {
jc = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (unitd) {
i__2 = jc;
ainvp[i__2].r = 1.f, ainvp[i__2].i = 0.f;
}
/* Form the j-th column of A*AINV. */
i__2 = *n - j + 1;
ctpmv_("Lower", "No transpose", diag, &i__2, &ap[jc], &ainvp[jc],
&c__1);
/* Subtract 1 from the diagonal to form A*AINV - I. */
i__2 = jc;
i__3 = jc;
q__1.r = ainvp[i__3].r - 1.f, q__1.i = ainvp[i__3].i;
ainvp[i__2].r = q__1.r, ainvp[i__2].i = q__1.i;
jc = jc + *n - j + 1;
/* L20: */
}
}
/* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) */
*resid = clantp_("1", uplo, "Non-unit", n, &ainvp[1], &rwork[1]);
*resid = *resid * *rcond / (real) (*n) / eps;
return 0;
/* End of CTPT01 */
} /* ctpt01_ */
int ctptri_(char *uplo, char *diag, int *n, complex *ap,
int *info)
{
/* System generated locals */
int i__1, i__2;
complex q__1;
/* Builtin functions */
void c_div(complex *, complex *, complex *);
/* Local variables */
int j, jc, jj;
complex ajj;
extern int cscal_(int *, complex *, complex *,
int *);
extern int lsame_(char *, char *);
extern int ctpmv_(char *, char *, char *, int *,
complex *, complex *, int *);
int upper;
extern int xerbla_(char *, int *);
int jclast;
int nounit;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTPTRI computes the inverse of a complex upper or lower triangular */
/* matrix A stored in packed format. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': A is upper triangular; */
/* = 'L': A is lower triangular. */
/* DIAG (input) CHARACTER*1 */
/* = 'N': A is non-unit triangular; */
/* = 'U': A is unit triangular. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangular matrix A, stored */
/* 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. */
/* See below for further details. */
/* On exit, the (triangular) inverse of the original matrix, in */
/* the same packed storage format. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, A(i,i) is exactly zero. The triangular */
/* matrix is singular and its inverse can not be computed. */
/* Further Details */
/* =============== */
/* A triangular matrix A can be transferred to packed storage using one */
/* of the following program segments: */
/* UPLO = 'U': UPLO = 'L': */
/* JC = 1 JC = 1 */
/* DO 2 J = 1, N DO 2 J = 1, N */
/* DO 1 I = 1, J DO 1 I = J, N */
/* AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) */
/* 1 CONTINUE 1 CONTINUE */
/* JC = JC + J JC = JC + N - J + 1 */
/* 2 CONTINUE 2 CONTINUE */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTPTRI", &i__1);
return 0;
}
/* Check for singularity if non-unit. */
if (nounit) {
if (upper) {
jj = 0;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
jj += *info;
i__2 = jj;
if (ap[i__2].r == 0.f && ap[i__2].i == 0.f) {
return 0;
}
/* L10: */
}
} else {
jj = 1;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = jj;
if (ap[i__2].r == 0.f && ap[i__2].i == 0.f) {
return 0;
}
jj = jj + *n - *info + 1;
/* L20: */
}
}
*info = 0;
}
if (upper) {
/* Compute inverse of upper triangular matrix. */
jc = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (nounit) {
i__2 = jc + j - 1;
c_div(&q__1, &c_b1, &ap[jc + j - 1]);
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
i__2 = jc + j - 1;
q__1.r = -ap[i__2].r, q__1.i = -ap[i__2].i;
ajj.r = q__1.r, ajj.i = q__1.i;
} else {
q__1.r = -1.f, q__1.i = -0.f;
ajj.r = q__1.r, ajj.i = q__1.i;
}
/* Compute elements 1:j-1 of j-th column. */
i__2 = j - 1;
ctpmv_("Upper", "No transpose", diag, &i__2, &ap[1], &ap[jc], &
c__1);
i__2 = j - 1;
cscal_(&i__2, &ajj, &ap[jc], &c__1);
jc += j;
/* L30: */
}
} else {
/* Compute inverse of lower triangular matrix. */
jc = *n * (*n + 1) / 2;
for (j = *n; j >= 1; --j) {
if (nounit) {
i__1 = jc;
c_div(&q__1, &c_b1, &ap[jc]);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = jc;
q__1.r = -ap[i__1].r, q__1.i = -ap[i__1].i;
ajj.r = q__1.r, ajj.i = q__1.i;
} else {
q__1.r = -1.f, q__1.i = -0.f;
ajj.r = q__1.r, ajj.i = q__1.i;
}
if (j < *n) {
/* Compute elements j+1:n of j-th column. */
i__1 = *n - j;
ctpmv_("Lower", "No transpose", diag, &i__1, &ap[jclast], &ap[
jc + 1], &c__1);
i__1 = *n - j;
cscal_(&i__1, &ajj, &ap[jc + 1], &c__1);
}
jclast = jc;
jc = jc - *n + j - 2;
/* L40: */
}
}
return 0;
/* End of CTPTRI */
} /* ctptri_ */
int cpptri_(char *uplo, int *n, complex *ap, int *
info)
{
/* System generated locals */
int i__1, i__2, i__3;
float r__1;
complex q__1;
/* Local variables */
int j, jc, jj;
float ajj;
int jjn;
extern int chpr_(char *, int *, float *, complex *,
int *, complex *);
extern /* Complex */ VOID cdotc_(complex *, int *, complex *, int
*, complex *, int *);
extern int lsame_(char *, char *);
extern int ctpmv_(char *, char *, char *, int *,
complex *, complex *, int *);
int upper;
extern int csscal_(int *, float *, complex *, int
*), xerbla_(char *, int *), ctptri_(char *, char *,
int *, complex *, int *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPPTRI computes the inverse of a complex Hermitian positive definite */
/* matrix A using the Cholesky factorization A = U**H*U or A = L*L**H */
/* computed by CPPTRF. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular factor is stored in AP; */
/* = 'L': Lower triangular factor is stored in AP. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H, packed columnwise as */
/* a linear array. The j-th column of U or L is stored in the */
/* array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. */
/* On exit, the upper or lower triangle of the (Hermitian) */
/* inverse of A, overwriting the input factor U or L. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the (i,i) element of the factor U or L is */
/* zero, and the inverse could not be computed. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--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_("CPPTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Invert the triangular Cholesky factor U or L. */
ctptri_(uplo, "Non-unit", n, &ap[1], info);
if (*info > 0) {
return 0;
}
if (upper) {
/* Compute the product inv(U) * inv(U)'. */
jj = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jc = jj + 1;
jj += j;
if (j > 1) {
i__2 = j - 1;
chpr_("Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1]);
}
i__2 = jj;
ajj = ap[i__2].r;
csscal_(&j, &ajj, &ap[jc], &c__1);
/* L10: */
}
} else {
/* Compute the product inv(L)' * inv(L). */
jj = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jjn = jj + *n - j + 1;
i__2 = jj;
i__3 = *n - j + 1;
cdotc_(&q__1, &i__3, &ap[jj], &c__1, &ap[jj], &c__1);
r__1 = q__1.r;
ap[i__2].r = r__1, ap[i__2].i = 0.f;
if (j < *n) {
i__2 = *n - j;
ctpmv_("Lower", "Conjugate transpose", "Non-unit", &i__2, &ap[
jjn], &ap[jj + 1], &c__1);
}
jj = jjn;
/* L20: */
}
}
return 0;
/* End of CPPTRI */
} /* cpptri_ */
/* Subroutine */ int ctptri_(char *uplo, char *diag, integer *n, complex *ap,
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
=======
CTPTRI computes the inverse of a complex upper or lower triangular
matrix A stored in packed format.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangular matrix A, stored
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.
See below for further details.
On exit, the (triangular) inverse of the original matrix, in
the same packed storage format.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.
Further Details
===============
A triangular matrix A can be transferred to packed storage using one
of the following program segments:
UPLO = 'U': UPLO = 'L':
JC = 1 JC = 1
DO 2 J = 1, N DO 2 J = 1, N
DO 1 I = 1, J DO 1 I = J, N
AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE
=====================================================================
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 i__1, i__2;
complex q__1;
/* Builtin functions */
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer j;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ctpmv_(char *, char *, char *, integer *,
complex *, complex *, integer *);
static logical upper;
static integer jc, jj;
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer jclast;
static logical nounit;
static complex ajj;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CTPTRI", &i__1);
return 0;
}
/* Check for singularity if non-unit. */
if (nounit) {
if (upper) {
jj = 0;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
jj += *info;
i__2 = jj;
if (ap[i__2].r == 0.f && ap[i__2].i == 0.f) {
return 0;
}
/* L10: */
}
} else {
jj = 1;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = jj;
if (ap[i__2].r == 0.f && ap[i__2].i == 0.f) {
return 0;
}
jj = jj + *n - *info + 1;
/* L20: */
}
}
*info = 0;
}
if (upper) {
/* Compute inverse of upper triangular matrix. */
jc = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (nounit) {
i__2 = jc + j - 1;
c_div(&q__1, &c_b1, &ap[jc + j - 1]);
ap[i__2].r = q__1.r, ap[i__2].i = q__1.i;
i__2 = jc + j - 1;
q__1.r = -ap[i__2].r, q__1.i = -ap[i__2].i;
ajj.r = q__1.r, ajj.i = q__1.i;
} else {
q__1.r = -1.f, q__1.i = 0.f;
ajj.r = q__1.r, ajj.i = q__1.i;
}
/* Compute elements 1:j-1 of j-th column. */
i__2 = j - 1;
ctpmv_("Upper", "No transpose", diag, &i__2, &ap[1], &ap[jc], &
c__1);
i__2 = j - 1;
cscal_(&i__2, &ajj, &ap[jc], &c__1);
jc += j;
/* L30: */
}
} else {
/* Compute inverse of lower triangular matrix. */
jc = *n * (*n + 1) / 2;
for (j = *n; j >= 1; --j) {
if (nounit) {
i__1 = jc;
c_div(&q__1, &c_b1, &ap[jc]);
ap[i__1].r = q__1.r, ap[i__1].i = q__1.i;
i__1 = jc;
q__1.r = -ap[i__1].r, q__1.i = -ap[i__1].i;
ajj.r = q__1.r, ajj.i = q__1.i;
} else {
q__1.r = -1.f, q__1.i = 0.f;
ajj.r = q__1.r, ajj.i = q__1.i;
}
if (j < *n) {
/* Compute elements j+1:n of j-th column. */
i__1 = *n - j;
ctpmv_("Lower", "No transpose", diag, &i__1, &ap[jclast], &ap[
jc + 1], &c__1);
i__1 = *n - j;
cscal_(&i__1, &ajj, &ap[jc + 1], &c__1);
}
jclast = jc;
jc = jc - *n + j - 2;
/* L40: */
}
}
return 0;
/* End of CTPTRI */
} /* ctptri_ */
/* Subroutine */ int cppt01_(char *uplo, integer *n, complex *a, complex *
afac, real *rwork, real *resid)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
real r__1;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, k, kc;
complex tc;
real tr, eps;
extern /* Subroutine */ int chpr_(char *, integer *, real *, complex *,
integer *, complex *), cscal_(integer *, complex *,
complex *, integer *);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern logical lsame_(char *, char *);
real anorm;
extern /* Subroutine */ int ctpmv_(char *, char *, char *, integer *,
complex *, complex *, integer *);
extern doublereal clanhp_(char *, char *, integer *, complex *, real *), slamch_(char *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CPPT01 reconstructs a Hermitian positive definite packed matrix A */
/* from its L*L' or U'*U factorization and computes the residual */
/* norm( L*L' - A ) / ( N * norm(A) * EPS ) or */
/* norm( U'*U - A ) / ( N * norm(A) * EPS ), */
/* where EPS is the machine epsilon, L' is the conjugate transpose of */
/* L, and U' is the conjugate transpose of U. */
/* 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. */
/* A (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The original Hermitian matrix A, stored as a packed */
/* triangular matrix. */
/* AFAC (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the factor L or U from the L*L' or U'*U */
/* factorization of A, stored as a packed triangular matrix. */
/* Overwritten with the reconstructed matrix, and then with the */
/* difference L*L' - A (or U'*U - A). */
/* RWORK (workspace) REAL array, dimension (N) */
/* RESID (output) REAL */
/* If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) */
/* If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0 */
/* Parameter adjustments */
--rwork;
--afac;
--a;
/* Function Body */
if (*n <= 0) {
*resid = 0.f;
return 0;
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = slamch_("Epsilon");
anorm = clanhp_("1", uplo, n, &a[1], &rwork[1]);
if (anorm <= 0.f) {
*resid = 1.f / eps;
return 0;
}
/* Check the imaginary parts of the diagonal elements and return with */
/* an error code if any are nonzero. */
kc = 1;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (r_imag(&afac[kc]) != 0.f) {
*resid = 1.f / eps;
return 0;
}
kc = kc + k + 1;
/* L10: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (r_imag(&afac[kc]) != 0.f) {
*resid = 1.f / eps;
return 0;
}
kc = kc + *n - k + 1;
/* L20: */
}
}
/* Compute the product U'*U, overwriting U. */
if (lsame_(uplo, "U")) {
kc = *n * (*n - 1) / 2 + 1;
for (k = *n; k >= 1; --k) {
/* Compute the (K,K) element of the result. */
cdotc_(&q__1, &k, &afac[kc], &c__1, &afac[kc], &c__1);
tr = q__1.r;
i__1 = kc + k - 1;
afac[i__1].r = tr, afac[i__1].i = 0.f;
/* Compute the rest of column K. */
if (k > 1) {
i__1 = k - 1;
ctpmv_("Upper", "Conjugate", "Non-unit", &i__1, &afac[1], &
afac[kc], &c__1);
kc -= k - 1;
}
/* L30: */
}
/* Compute the difference L*L' - A */
kc = 1;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = kc + i__ - 1;
i__4 = kc + i__ - 1;
i__5 = kc + i__ - 1;
q__1.r = afac[i__4].r - a[i__5].r, q__1.i = afac[i__4].i - a[
i__5].i;
afac[i__3].r = q__1.r, afac[i__3].i = q__1.i;
/* L40: */
}
i__2 = kc + k - 1;
i__3 = kc + k - 1;
i__4 = kc + k - 1;
r__1 = a[i__4].r;
q__1.r = afac[i__3].r - r__1, q__1.i = afac[i__3].i;
afac[i__2].r = q__1.r, afac[i__2].i = q__1.i;
kc += k;
/* L50: */
}
/* Compute the product L*L', overwriting L. */
} else {
kc = *n * (*n + 1) / 2;
for (k = *n; k >= 1; --k) {
/* Add a multiple of column K of the factor L to each of */
/* columns K+1 through N. */
if (k < *n) {
i__1 = *n - k;
chpr_("Lower", &i__1, &c_b19, &afac[kc + 1], &c__1, &afac[kc
+ *n - k + 1]);
}
/* Scale column K by the diagonal element. */
i__1 = kc;
tc.r = afac[i__1].r, tc.i = afac[i__1].i;
i__1 = *n - k + 1;
cscal_(&i__1, &tc, &afac[kc], &c__1);
kc -= *n - k + 2;
/* L60: */
}
/* Compute the difference U'*U - A */
kc = 1;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
i__2 = kc;
i__3 = kc;
i__4 = kc;
r__1 = a[i__4].r;
q__1.r = afac[i__3].r - r__1, q__1.i = afac[i__3].i;
afac[i__2].r = q__1.r, afac[i__2].i = q__1.i;
i__2 = *n;
for (i__ = k + 1; i__ <= i__2; ++i__) {
i__3 = kc + i__ - k;
i__4 = kc + i__ - k;
i__5 = kc + i__ - k;
q__1.r = afac[i__4].r - a[i__5].r, q__1.i = afac[i__4].i - a[
i__5].i;
afac[i__3].r = q__1.r, afac[i__3].i = q__1.i;
/* L70: */
}
kc = kc + *n - k + 1;
/* L80: */
}
}
/* Compute norm( L*U - A ) / ( N * norm(A) * EPS ) */
*resid = clanhp_("1", uplo, n, &afac[1], &rwork[1]);
*resid = *resid / (real) (*n) / anorm / eps;
return 0;
/* End of CPPT01 */
} /* cppt01_ */
/* Subroutine */ int ctpt02_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, complex *ap, complex *x, integer *ldx, complex *b,
integer *ldb, complex *work, real *rwork, real *resid)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
real r__1, r__2;
/* Local variables */
integer j;
real eps;
extern logical lsame_(char *, char *);
real anorm, bnorm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), ctpmv_(char *, char *, char *,
integer *, complex *, complex *, integer *);
real xnorm;
extern doublereal slamch_(char *), clantp_(char *, char *, char *,
integer *, complex *, real *), scasum_(
integer *, complex *, integer *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CTPT02 computes the residual for the computed solution to a */
/* triangular system of linear equations A*x = b, A**T *x = b, or */
/* A**H *x = b, when the triangular matrix A is stored in packed format. */
/* Here A**T denotes the transpose of A, A**H denotes the conjugate */
/* transpose of A, and x and b are N by NRHS matrices. The test ratio */
/* is the maximum over the number of right hand sides of */
/* the maximum over the number of right hand sides of */
/* norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), */
/* where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* TRANS (input) CHARACTER*1 */
/* Specifies the operation applied to A. */
/* = 'N': A *x = b (No transpose) */
/* = 'T': A**T *x = b (Transpose) */
/* = 'C': A**H *x = b (Conjugate transpose) */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* 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 X and B. NRHS >= 0. */
/* AP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The upper or lower triangular 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', */
/* AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. */
/* 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) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side vectors for the system of linear */
/* equations. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* WORK (workspace) COMPLEX array, dimension (N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* RESID (output) REAL */
/* The maximum over the number of right hand sides of */
/* norm(op(A)*x - b) / ( norm(op(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 */
--ap;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
--rwork;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
*resid = 0.f;
return 0;
}
/* Compute the 1-norm of A or A**H. */
if (lsame_(trans, "N")) {
anorm = clantp_("1", uplo, diag, n, &ap[1], &rwork[1]);
} else {
anorm = clantp_("I", uplo, diag, n, &ap[1], &rwork[1]);
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = slamch_("Epsilon");
if (anorm <= 0.f) {
*resid = 1.f / eps;
return 0;
}
/* Compute the maximum over the number of right hand sides of */
/* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). */
*resid = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ccopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ctpmv_(uplo, trans, diag, n, &ap[1], &work[1], &c__1);
caxpy_(n, &c_b12, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
bnorm = scasum_(n, &work[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);
}
/* L10: */
}
return 0;
/* End of CTPT02 */
} /* ctpt02_ */
/* Subroutine */
int chpgst_(integer *itype, char *uplo, integer *n, complex * ap, complex *bp, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
integer j, k, j1, k1, jj, kk;
complex ct;
real ajj;
integer j1j1;
real akk;
integer k1k1;
real bjj, bkk;
extern /* Subroutine */
int chpr2_(char *, integer *, complex *, complex * , integer *, complex *, integer *, complex *);
extern /* Complex */
VOID cdotc_f2c_(complex *, integer *, complex *, integer *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */
int chpmv_(char *, integer *, complex *, complex * , complex *, integer *, complex *, complex *, integer *), caxpy_(integer *, complex *, complex *, integer *, complex *, integer *), ctpmv_(char *, char *, char *, integer *, complex *, complex *, integer *);
logical upper;
extern /* Subroutine */
int ctpsv_(char *, char *, char *, integer *, complex *, complex *, integer *), csscal_( integer *, real *, complex *, integer *), xerbla_(char *, integer *);
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--bp;
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (*itype < 1 || *itype > 3)
{
*info = -1;
}
else if (! upper && ! lsame_(uplo, "L"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CHPGST", &i__1);
return 0;
}
if (*itype == 1)
{
if (upper)
{
/* Compute inv(U**H)*A*inv(U) */
/* J1 and JJ are the indices of A(1,j) and A(j,j) */
jj = 0;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
j1 = jj + 1;
jj += j;
/* Compute the j-th column of the upper triangle of A */
i__2 = jj;
i__3 = jj;
r__1 = ap[i__3].r;
ap[i__2].r = r__1;
ap[i__2].i = 0.f; // , expr subst
i__2 = jj;
bjj = bp[i__2].r;
ctpsv_(uplo, "Conjugate transpose", "Non-unit", &j, &bp[1], & ap[j1], &c__1);
i__2 = j - 1;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
chpmv_(uplo, &i__2, &q__1, &ap[1], &bp[j1], &c__1, &c_b1, &ap[ j1], &c__1);
i__2 = j - 1;
r__1 = 1.f / bjj;
csscal_(&i__2, &r__1, &ap[j1], &c__1);
i__2 = jj;
i__3 = jj;
i__4 = j - 1;
cdotc_f2c_(&q__3, &i__4, &ap[j1], &c__1, &bp[j1], &c__1);
q__2.r = ap[i__3].r - q__3.r;
q__2.i = ap[i__3].i - q__3.i; // , expr subst
q__1.r = q__2.r / bjj;
q__1.i = q__2.i / bjj; // , expr subst
ap[i__2].r = q__1.r;
ap[i__2].i = q__1.i; // , expr subst
/* L10: */
}
}
else
{
/* Compute inv(L)*A*inv(L**H) */
/* KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) */
kk = 1;
i__1 = *n;
for (k = 1;
k <= i__1;
++k)
{
k1k1 = kk + *n - k + 1;
/* Update the lower triangle of A(k:n,k:n) */
i__2 = kk;
akk = ap[i__2].r;
i__2 = kk;
bkk = bp[i__2].r;
/* Computing 2nd power */
r__1 = bkk;
akk /= r__1 * r__1;
i__2 = kk;
ap[i__2].r = akk;
ap[i__2].i = 0.f; // , expr subst
if (k < *n)
{
i__2 = *n - k;
r__1 = 1.f / bkk;
csscal_(&i__2, &r__1, &ap[kk + 1], &c__1);
r__1 = akk * -.5f;
ct.r = r__1;
ct.i = 0.f; // , expr subst
i__2 = *n - k;
caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ;
i__2 = *n - k;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
chpr2_(uplo, &i__2, &q__1, &ap[kk + 1], &c__1, &bp[kk + 1] , &c__1, &ap[k1k1]);
i__2 = *n - k;
caxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ;
i__2 = *n - k;
ctpsv_(uplo, "No transpose", "Non-unit", &i__2, &bp[k1k1], &ap[kk + 1], &c__1);
}
kk = k1k1;
/* L20: */
}
}
}
else
{
if (upper)
{
/* Compute U*A*U**H */
/* K1 and KK are the indices of A(1,k) and A(k,k) */
kk = 0;
i__1 = *n;
for (k = 1;
k <= i__1;
++k)
{
k1 = kk + 1;
kk += k;
/* Update the upper triangle of A(1:k,1:k) */
i__2 = kk;
akk = ap[i__2].r;
i__2 = kk;
bkk = bp[i__2].r;
i__2 = k - 1;
ctpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[ k1], &c__1);
r__1 = akk * .5f;
ct.r = r__1;
ct.i = 0.f; // , expr subst
i__2 = k - 1;
caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
chpr2_(uplo, &i__2, &c_b1, &ap[k1], &c__1, &bp[k1], &c__1, & ap[1]);
i__2 = k - 1;
caxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
csscal_(&i__2, &bkk, &ap[k1], &c__1);
i__2 = kk;
/* Computing 2nd power */
r__2 = bkk;
r__1 = akk * (r__2 * r__2);
ap[i__2].r = r__1;
ap[i__2].i = 0.f; // , expr subst
/* L30: */
}
}
else
{
/* Compute L**H *A*L */
/* JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) */
jj = 1;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
j1j1 = jj + *n - j + 1;
/* Compute the j-th column of the lower triangle of A */
i__2 = jj;
ajj = ap[i__2].r;
i__2 = jj;
bjj = bp[i__2].r;
i__2 = jj;
r__1 = ajj * bjj;
i__3 = *n - j;
cdotc_f2c_(&q__2, &i__3, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1);
q__1.r = r__1 + q__2.r;
q__1.i = q__2.i; // , expr subst
ap[i__2].r = q__1.r;
ap[i__2].i = q__1.i; // , expr subst
i__2 = *n - j;
csscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
i__2 = *n - j;
chpmv_(uplo, &i__2, &c_b1, &ap[j1j1], &bp[jj + 1], &c__1, & c_b1, &ap[jj + 1], &c__1);
i__2 = *n - j + 1;
ctpmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &bp[jj] , &ap[jj], &c__1);
jj = j1j1;
/* L40: */
}
}
}
return 0;
/* End of CHPGST */
}
