int
f2c_ztpmv(char* uplo, char* trans, char* diag, integer* N,
doublecomplex* Ap,
doublecomplex* X, integer* incX)
{
ztpmv_(uplo, trans, diag,
N, Ap, X, incX);
return 0;
}
/* Subroutine */ int ztpt01_(char *uplo, char *diag, integer *n,
doublecomplex *ap, doublecomplex *ainvp, doublereal *rcond,
doublereal *rwork, doublereal *resid)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublecomplex z__1;
/* Local variables */
integer j, jc;
doublereal eps;
extern logical lsame_(char *, char *);
doublereal anorm;
logical unitd;
extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *);
extern doublereal dlamch_(char *);
doublereal ainvnm;
extern doublereal zlantp_(char *, char *, char *, integer *,
doublecomplex *, doublereal *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTPT01 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*16 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*16 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) DOUBLE PRECISION */
/* The reciprocal condition number of A, computed as */
/* 1/(norm(A) * norm(AINV)). */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* RESID (output) DOUBLE PRECISION */
/* 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.;
*resid = 0.;
return 0;
}
/* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. */
eps = dlamch_("Epsilon");
anorm = zlantp_("1", uplo, diag, n, &ap[1], &rwork[1]);
ainvnm = zlantp_("1", uplo, diag, n, &ainvp[1], &rwork[1]);
if (anorm <= 0. || ainvnm <= 0.) {
*rcond = 0.;
*resid = 1. / eps;
return 0;
}
*rcond = 1. / 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., ainvp[i__2].i = 0.;
}
/* Form the j-th column of A*AINV. */
ztpmv_("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;
z__1.r = ainvp[i__3].r - 1., z__1.i = ainvp[i__3].i;
ainvp[i__2].r = z__1.r, ainvp[i__2].i = z__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., ainvp[i__2].i = 0.;
}
/* Form the j-th column of A*AINV. */
i__2 = *n - j + 1;
ztpmv_("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;
z__1.r = ainvp[i__3].r - 1., z__1.i = ainvp[i__3].i;
ainvp[i__2].r = z__1.r, ainvp[i__2].i = z__1.i;
jc = jc + *n - j + 1;
/* L20: */
}
}
/* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) */
*resid = zlantp_("1", uplo, "Non-unit", n, &ainvp[1], &rwork[1]);
*resid = *resid * *rcond / (doublereal) (*n) / eps;
return 0;
/* End of ZTPT01 */
} /* ztpt01_ */
/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n,
doublecomplex *ap, integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZTPTRI 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*16 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
Function Body */
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
static integer j;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
static logical upper;
extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *);
static integer jc, jj;
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer jclast;
static logical nounit;
static doublecomplex ajj;
#define AP(I) ap[(I)-1]
*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_("ZTPTRI", &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(jj).r == 0. && AP(jj).i == 0.) {
return 0;
}
/* L10: */
}
} else {
jj = 1;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = jj;
if (AP(jj).r == 0. && AP(jj).i == 0.) {
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 <= *n; ++j) {
if (nounit) {
i__2 = jc + j - 1;
z_div(&z__1, &c_b1, &AP(jc + j - 1));
AP(jc+j-1).r = z__1.r, AP(jc+j-1).i = z__1.i;
i__2 = jc + j - 1;
z__1.r = -AP(jc+j-1).r, z__1.i = -AP(jc+j-1).i;
ajj.r = z__1.r, ajj.i = z__1.i;
} else {
z__1.r = -1., z__1.i = 0.;
ajj.r = z__1.r, ajj.i = z__1.i;
}
/* Compute elements 1:j-1 of j-th column. */
i__2 = j - 1;
ztpmv_("Upper", "No transpose", diag, &i__2, &AP(1), &AP(jc), &
c__1);
i__2 = j - 1;
zscal_(&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;
z_div(&z__1, &c_b1, &AP(jc));
AP(jc).r = z__1.r, AP(jc).i = z__1.i;
i__1 = jc;
z__1.r = -AP(jc).r, z__1.i = -AP(jc).i;
ajj.r = z__1.r, ajj.i = z__1.i;
} else {
z__1.r = -1., z__1.i = 0.;
ajj.r = z__1.r, ajj.i = z__1.i;
}
if (j < *n) {
/* Compute elements j+1:n of j-th column. */
i__1 = *n - j;
ztpmv_("Lower", "No transpose", diag, &i__1, &AP(jclast), &AP(
jc + 1), &c__1);
i__1 = *n - j;
zscal_(&i__1, &ajj, &AP(jc + 1), &c__1);
}
jclast = jc;
jc = jc - *n + j - 2;
/* L40: */
}
}
return 0;
/* End of ZTPTRI */
} /* ztptri_ */
void
ztpmv(char uplo, char transa, char diag, int n, doublecomplex *ap, doublecomplex *x, int incx)
{
ztpmv_( &uplo, &transa, &diag, &n, ap, x, &incx);
}
/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n,
doublecomplex *ap, integer *info)
{
/* System generated locals */
integer i__1, i__2;
doublecomplex z__1;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
/* Local variables */
integer j, jc, jj;
doublecomplex ajj;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
logical upper;
extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *), xerbla_(char *, integer *);
integer jclast;
logical nounit;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTPTRI 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*16 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_("ZTPTRI", &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. && ap[i__2].i == 0.) {
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. && ap[i__2].i == 0.) {
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;
z_div(&z__1, &c_b1, &ap[jc + j - 1]);
ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
i__2 = jc + j - 1;
z__1.r = -ap[i__2].r, z__1.i = -ap[i__2].i;
ajj.r = z__1.r, ajj.i = z__1.i;
} else {
z__1.r = -1., z__1.i = -0.;
ajj.r = z__1.r, ajj.i = z__1.i;
}
/* Compute elements 1:j-1 of j-th column. */
i__2 = j - 1;
ztpmv_("Upper", "No transpose", diag, &i__2, &ap[1], &ap[jc], &
c__1);
i__2 = j - 1;
zscal_(&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;
z_div(&z__1, &c_b1, &ap[jc]);
ap[i__1].r = z__1.r, ap[i__1].i = z__1.i;
i__1 = jc;
z__1.r = -ap[i__1].r, z__1.i = -ap[i__1].i;
ajj.r = z__1.r, ajj.i = z__1.i;
} else {
z__1.r = -1., z__1.i = -0.;
ajj.r = z__1.r, ajj.i = z__1.i;
}
if (j < *n) {
/* Compute elements j+1:n of j-th column. */
i__1 = *n - j;
ztpmv_("Lower", "No transpose", diag, &i__1, &ap[jclast], &ap[
jc + 1], &c__1);
i__1 = *n - j;
zscal_(&i__1, &ajj, &ap[jc + 1], &c__1);
}
jclast = jc;
jc = jc - *n + j - 2;
/* L40: */
}
}
return 0;
/* End of ZTPTRI */
} /* ztptri_ */
/* Subroutine */ int zhpgst_(integer *itype, char *uplo, integer *n,
doublecomplex *ap, doublecomplex *bp, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3;
/* Local variables */
integer j, k, j1, k1, jj, kk;
doublecomplex ct;
doublereal ajj;
integer j1j1;
doublereal akk;
integer k1k1;
doublereal bjj, bkk;
extern /* Subroutine */ int zhpr2_(char *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *);
extern logical lsame_(char *, char *);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
logical upper;
extern /* Subroutine */ int zhpmv_(char *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *), zaxpy_(integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), ztpmv_(char *, char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex *
, doublecomplex *, integer *), xerbla_(
char *, integer *), zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHPGST 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 ZPPTRF. */
/* 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*1 */
/* = '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*16 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*16 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 ZPPTRF. */
/* 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");
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_("ZHPGST", &i__1);
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;
d__1 = ap[i__3].r;
ap[i__2].r = d__1, ap[i__2].i = 0.;
i__2 = jj;
bjj = bp[i__2].r;
ztpsv_(uplo, "Conjugate transpose", "Non-unit", &j, &bp[1], &
ap[j1], &c__1);
i__2 = j - 1;
z__1.r = -1., z__1.i = -0.;
zhpmv_(uplo, &i__2, &z__1, &ap[1], &bp[j1], &c__1, &c_b1, &ap[
j1], &c__1);
i__2 = j - 1;
d__1 = 1. / bjj;
zdscal_(&i__2, &d__1, &ap[j1], &c__1);
i__2 = jj;
i__3 = jj;
i__4 = j - 1;
zdotc_(&z__3, &i__4, &ap[j1], &c__1, &bp[j1], &c__1);
z__2.r = ap[i__3].r - z__3.r, z__2.i = ap[i__3].i - z__3.i;
z__1.r = z__2.r / bjj, z__1.i = z__2.i / bjj;
ap[i__2].r = z__1.r, ap[i__2].i = z__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 */
d__1 = bkk;
akk /= d__1 * d__1;
i__2 = kk;
ap[i__2].r = akk, ap[i__2].i = 0.;
if (k < *n) {
i__2 = *n - k;
d__1 = 1. / bkk;
zdscal_(&i__2, &d__1, &ap[kk + 1], &c__1);
d__1 = akk * -.5;
ct.r = d__1, ct.i = 0.;
i__2 = *n - k;
zaxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
z__1.r = -1., z__1.i = -0.;
zhpr2_(uplo, &i__2, &z__1, &ap[kk + 1], &c__1, &bp[kk + 1]
, &c__1, &ap[k1k1]);
i__2 = *n - k;
zaxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
ztpsv_(uplo, "No transpose", "Non-unit", &i__2, &bp[k1k1],
&ap[kk + 1], &c__1);
}
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;
ztpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[
k1], &c__1);
d__1 = akk * .5;
ct.r = d__1, ct.i = 0.;
i__2 = k - 1;
zaxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
zhpr2_(uplo, &i__2, &c_b1, &ap[k1], &c__1, &bp[k1], &c__1, &
ap[1]);
i__2 = k - 1;
zaxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
zdscal_(&i__2, &bkk, &ap[k1], &c__1);
i__2 = kk;
/* Computing 2nd power */
d__2 = bkk;
d__1 = akk * (d__2 * d__2);
ap[i__2].r = d__1, ap[i__2].i = 0.;
/* 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;
d__1 = ajj * bjj;
i__3 = *n - j;
zdotc_(&z__2, &i__3, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1);
z__1.r = d__1 + z__2.r, z__1.i = z__2.i;
ap[i__2].r = z__1.r, ap[i__2].i = z__1.i;
i__2 = *n - j;
zdscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
i__2 = *n - j;
zhpmv_(uplo, &i__2, &c_b1, &ap[j1j1], &bp[jj + 1], &c__1, &
c_b1, &ap[jj + 1], &c__1);
i__2 = *n - j + 1;
ztpmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &bp[jj]
, &ap[jj], &c__1);
jj = j1j1;
/* L40: */
}
}
}
return 0;
/* End of ZHPGST */
} /* zhpgst_ */
/* Subroutine */ int ztprfs_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, doublecomplex *ap, doublecomplex *b, integer *ldb,
doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr,
doublecomplex *work, doublereal *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;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
integer i__, j, k;
doublereal s;
integer kc;
doublereal xk;
integer nz;
doublereal eps;
integer kase;
doublereal safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
logical upper;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), ztpmv_(
char *, char *, char *, integer *, doublecomplex *, doublecomplex
*, integer *), ztpsv_(char *, char *,
char *, integer *, doublecomplex *, doublecomplex *, integer *), zlacn2_(integer *, doublecomplex *,
doublecomplex *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
doublereal safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical notran;
char transn[1], transt[1];
logical nounit;
doublereal lstres;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTPRFS 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 ZTPTRS or some other */
/* means before entering this routine. ZTPRFS 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*16 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*16 array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (input) COMPLEX*16 array, dimension (LDX,NRHS) */
/* The solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. 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_("ZTPRFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.;
berr[j] = 0.;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)transn = 'N';
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transn = 'C';
*(unsigned char *)transt = 'N';
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
/* Compute residual R = B - op(A) * X, */
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
zcopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ztpmv_(uplo, trans, diag, n, &ap[1], &work[1], &c__1);
z__1.r = -1., z__1.i = -0.;
zaxpy_(n, &z__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__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[
i__ + j * b_dim1]), abs(d__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 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&
x[k + j * x_dim1]), abs(d__2));
i__3 = k;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
rwork[i__] += ((d__1 = ap[i__4].r, abs(d__1)) + (
d__2 = d_imag(&ap[kc + i__ - 1]), abs(
d__2))) * xk;
/* L30: */
}
kc += k;
/* L40: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&
x[k + j * x_dim1]), abs(d__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
rwork[i__] += ((d__1 = ap[i__4].r, abs(d__1)) + (
d__2 = d_imag(&ap[kc + i__ - 1]), abs(
d__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 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&
x[k + j * x_dim1]), abs(d__2));
i__3 = *n;
for (i__ = k; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
rwork[i__] += ((d__1 = ap[i__4].r, abs(d__1)) + (
d__2 = d_imag(&ap[kc + i__ - k]), abs(
d__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 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&
x[k + j * x_dim1]), abs(d__2));
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
rwork[i__] += ((d__1 = ap[i__4].r, abs(d__1)) + (
d__2 = d_imag(&ap[kc + i__ - k]), abs(
d__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.;
i__3 = k;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
i__5 = i__ + j * x_dim1;
s += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 =
d_imag(&ap[kc + i__ - 1]), abs(d__2))) * (
(d__3 = x[i__5].r, abs(d__3)) + (d__4 =
d_imag(&x[i__ + j * x_dim1]), abs(d__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 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[
k + j * x_dim1]), abs(d__2));
i__3 = k - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - 1;
i__5 = i__ + j * x_dim1;
s += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 =
d_imag(&ap[kc + i__ - 1]), abs(d__2))) * (
(d__3 = x[i__5].r, abs(d__3)) + (d__4 =
d_imag(&x[i__ + j * x_dim1]), abs(d__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.;
i__3 = *n;
for (i__ = k; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
i__5 = i__ + j * x_dim1;
s += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 =
d_imag(&ap[kc + i__ - k]), abs(d__2))) * (
(d__3 = x[i__5].r, abs(d__3)) + (d__4 =
d_imag(&x[i__ + j * x_dim1]), abs(d__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 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[
k + j * x_dim1]), abs(d__2));
i__3 = *n;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = kc + i__ - k;
i__5 = i__ + j * x_dim1;
s += ((d__1 = ap[i__4].r, abs(d__1)) + (d__2 =
d_imag(&ap[kc + i__ - k]), abs(d__2))) * (
(d__3 = x[i__5].r, abs(d__3)) + (d__4 =
d_imag(&x[i__ + j * x_dim1]), abs(d__4)));
/* L170: */
}
rwork[k] += s;
kc = kc + *n - k + 1;
/* L180: */
}
}
}
}
s = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2))) / rwork[i__];
s = max(d__3,d__4);
} else {
/* Computing MAX */
i__3 = i__;
d__3 = s, d__4 = ((d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__]
+ safe1);
s = max(d__3,d__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 ZLACN2 to estimate the infinity-norm of the matrix */
/* inv(op(A)) * diag(W), */
/* where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
;
} else {
i__3 = i__;
rwork[i__] = (d__1 = work[i__3].r, abs(d__1)) + (d__2 =
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
+ safe1;
}
/* L200: */
}
kase = 0;
L210:
zlacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**H). */
ztpsv_(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__;
z__1.r = rwork[i__4] * work[i__5].r, z__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = z__1.r, work[i__3].i = z__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__;
z__1.r = rwork[i__4] * work[i__5].r, z__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* L230: */
}
ztpsv_(uplo, transn, diag, n, &ap[1], &work[1], &c__1);
}
goto L210;
}
/* Normalize error. */
lstres = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
d__3 = lstres, d__4 = (d__1 = x[i__3].r, abs(d__1)) + (d__2 =
d_imag(&x[i__ + j * x_dim1]), abs(d__2));
lstres = max(d__3,d__4);
/* L240: */
}
if (lstres != 0.) {
ferr[j] /= lstres;
}
/* L250: */
}
return 0;
/* End of ZTPRFS */
} /* ztprfs_ */
/* Subroutine */ int zhpgvx_(integer *itype, char *jobz, char *range, char *
uplo, integer *n, doublecomplex *ap, doublecomplex *bp, doublereal *
vl, doublereal *vu, integer *il, integer *iu, doublereal *abstol,
integer *m, doublereal *w, doublecomplex *z__, integer *ldz,
doublecomplex *work, doublereal *rwork, integer *iwork, integer *
ifail, integer *info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1;
/* Local variables */
integer j;
char trans[1];
logical upper, wantz;
logical alleig, indeig, valeig;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* ZHPGVX computes selected eigenvalues and, optionally, 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. Eigenvalues and eigenvectors can be selected by */
/* specifying either a range of values or a range of indices for the */
/* desired eigenvalues. */
/* 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. */
/* RANGE (input) CHARACTER*1 */
/* = 'A': all eigenvalues will be found; */
/* = 'V': all eigenvalues in the half-open interval (VL,VU] */
/* will be found; */
/* = 'I': the IL-th through IU-th eigenvalues will be found. */
/* 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*16 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*16 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. */
/* VL (input) DOUBLE PRECISION */
/* VU (input) DOUBLE PRECISION */
/* If RANGE='V', the lower and upper bounds of the interval to */
/* be searched for eigenvalues. VL < VU. */
/* Not referenced if RANGE = 'A' or 'I'. */
/* IL (input) INTEGER */
/* IU (input) INTEGER */
/* If RANGE='I', the indices (in ascending order) of the */
/* smallest and largest eigenvalues to be returned. */
/* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* Not referenced if RANGE = 'A' or 'V'. */
/* ABSTOL (input) DOUBLE PRECISION */
/* The absolute error tolerance for the eigenvalues. */
/* An approximate eigenvalue is accepted as converged */
/* when it is determined to lie in an interval [a,b] */
/* of width less than or equal to */
/* ABSTOL + EPS * max( |a|,|b| ) , */
/* where EPS is the machine precision. If ABSTOL is less than */
/* or equal to zero, then EPS*|T| will be used in its place, */
/* where |T| is the 1-norm of the tridiagonal matrix obtained */
/* by reducing AP to tridiagonal form. */
/* Eigenvalues will be computed most accurately when ABSTOL is */
/* set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
/* If this routine returns with INFO>0, indicating that some */
/* eigenvectors did not converge, try setting ABSTOL to */
/* 2*DLAMCH('S'). */
/* M (output) INTEGER */
/* The total number of eigenvalues found. 0 <= M <= N. */
/* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
/* W (output) DOUBLE PRECISION array, dimension (N) */
/* On normal exit, the first M elements contain the selected */
/* eigenvalues in ascending order. */
/* Z (output) COMPLEX*16 array, dimension (LDZ, N) */
/* If JOBZ = 'N', then Z is not referenced. */
/* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
/* contain the orthonormal eigenvectors of the matrix A */
/* corresponding to the selected eigenvalues, with the i-th */
/* column of Z holding the eigenvector associated with W(i). */
/* 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 an eigenvector fails to converge, then that column of Z */
/* contains the latest approximation to the eigenvector, and the */
/* index of the eigenvector is returned in IFAIL. */
/* Note: the user must ensure that at least max(1,M) columns are */
/* supplied in the array Z; if RANGE = 'V', the exact value of M */
/* is not known in advance and an upper bound must be used. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1, and if */
/* JOBZ = 'V', LDZ >= max(1,N). */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (7*N) */
/* IWORK (workspace) INTEGER array, dimension (5*N) */
/* IFAIL (output) INTEGER array, dimension (N) */
/* If JOBZ = 'V', then if INFO = 0, the first M elements of */
/* IFAIL are zero. If INFO > 0, then IFAIL contains the */
/* indices of the eigenvectors that failed to converge. */
/* If JOBZ = 'N', then IFAIL is not referenced. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: ZPPTRF or ZHPEVX returned an error code: */
/* <= N: if INFO = i, ZHPEVX failed to converge; */
/* i eigenvectors failed to converge. Their indices */
/* are stored in array IFAIL. */
/* > 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. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* ===================================================================== */
/* 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_("ZHPGVX", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
zpptrf_(uplo, n, &bp[1], info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
zhpgst_(itype, uplo, n, &ap[1], &bp[1], info);
zhpevx_(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)'*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) {
ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &c__1);
}
} 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 = *m;
for (j = 1; j <= i__1; ++j) {
ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &c__1);
}
}
}
return 0;
/* End of ZHPGVX */
} /* zhpgvx_ */
/* Subroutine */ int ztpt03_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, doublecomplex *ap, doublereal *scale, doublereal *
cnorm, doublereal *tscal, doublecomplex *x, integer *ldx,
doublecomplex *b, integer *ldb, doublecomplex *work, doublereal *
resid)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
doublereal d__1, d__2;
doublecomplex z__1;
/* Local variables */
integer j, jj, ix;
doublereal eps, err;
doublereal xscal, tnorm, xnorm;
doublereal smlnum;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTPT03 computes the residual for the solution to a scaled triangular */
/* system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*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, s is a scalar, and x and b are N by NRHS matrices. The test ratio */
/* is the maximum over the number of right hand sides of */
/* norm(s*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 = s*b (No transpose) */
/* = 'T': A**T *x = s*b (Transpose) */
/* = 'C': A**H *x = s*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*16 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. */
/* SCALE (input) DOUBLE PRECISION */
/* The scaling factor s used in solving the triangular system. */
/* CNORM (input) DOUBLE PRECISION array, dimension (N) */
/* The 1-norms of the columns of A, not counting the diagonal. */
/* TSCAL (input) DOUBLE PRECISION */
/* The scaling factor used in computing the 1-norms in CNORM. */
/* CNORM actually contains the column norms of TSCAL*A. */
/* X (input) COMPLEX*16 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*16 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*16 array, dimension (N) */
/* RESID (output) DOUBLE PRECISION */
/* The maximum over the number of right hand sides of */
/* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0. */
/* Parameter adjustments */
--ap;
--cnorm;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
*resid = 0.;
return 0;
}
eps = dlamch_("Epsilon");
smlnum = dlamch_("Safe minimum");
/* Compute the norm of the triangular matrix A using the column */
/* norms already computed by ZLATPS. */
tnorm = 0.;
if (lsame_(diag, "N")) {
if (lsame_(uplo, "U")) {
jj = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__1 = tnorm, d__2 = *tscal * z_abs(&ap[jj]) + cnorm[j];
tnorm = max(d__1,d__2);
jj += j;
/* L10: */
}
} else {
jj = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__1 = tnorm, d__2 = *tscal * z_abs(&ap[jj]) + cnorm[j];
tnorm = max(d__1,d__2);
jj = jj + *n - j + 1;
/* L20: */
}
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__1 = tnorm, d__2 = *tscal + cnorm[j];
tnorm = max(d__1,d__2);
/* L30: */
}
}
/* Compute the maximum over the number of right hand sides of */
/* norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ). */
*resid = 0.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
zcopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ix = izamax_(n, &work[1], &c__1);
/* Computing MAX */
d__1 = 1., d__2 = z_abs(&x[ix + j * x_dim1]);
xnorm = max(d__1,d__2);
xscal = 1. / xnorm / (doublereal) (*n);
zdscal_(n, &xscal, &work[1], &c__1);
ztpmv_(uplo, trans, diag, n, &ap[1], &work[1], &c__1);
d__1 = -(*scale) * xscal;
z__1.r = d__1, z__1.i = 0.;
zaxpy_(n, &z__1, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
ix = izamax_(n, &work[1], &c__1);
err = *tscal * z_abs(&work[ix]);
ix = izamax_(n, &x[j * x_dim1 + 1], &c__1);
xnorm = z_abs(&x[ix + j * x_dim1]);
if (err * smlnum <= xnorm) {
if (xnorm > 0.) {
err /= xnorm;
}
} else {
if (err > 0.) {
err = 1. / eps;
}
}
if (err * smlnum <= tnorm) {
if (tnorm > 0.) {
err /= tnorm;
}
} else {
if (err > 0.) {
err = 1. / eps;
}
}
*resid = max(*resid,err);
/* L40: */
}
return 0;
/* End of ZTPT03 */
} /* ztpt03_ */
/* Subroutine */ int zlarhs_(char *path, char *xtype, char *uplo, char *trans,
integer *m, integer *n, integer *kl, integer *ku, integer *nrhs,
doublecomplex *a, integer *lda, doublecomplex *x, integer *ldx,
doublecomplex *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 zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zhemm_(char *, char *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zgbmv_(char *, integer *, integer *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zhbmv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *),
zsbmv_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *), ztbmv_(char
*, char *, char *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, integer *), zhpmv_(
char *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), ztrmm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *),
zspmv_(char *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zsymm_(char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), ztpmv_(char *, char *, char *, integer *, doublecomplex *
, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern logical lsamen_(integer *, char *, char *);
logical notran;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlarnv_(integer *, integer *, integer *, doublecomplex *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLARHS 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*16 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*16 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*16 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 */
/* ZLATMS). 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, "Zomplex 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_("ZLARHS", &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) {
zlarnv_(&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 */
zgemm_(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 */
zhemm_("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 */
zsymm_("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) {
zgbmv_(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) {
zhbmv_(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) {
zsbmv_(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) {
zhpmv_(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) {
zspmv_(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 */
zlacpy_("Full", n, nrhs, &x[x_offset], ldx, &b[b_offset], ldb);
if (*ku == 2) {
*(unsigned char *)diag = 'U';
} else {
*(unsigned char *)diag = 'N';
}
ztrmm_("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 */
zlacpy_("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) {
ztpmv_(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 */
zlacpy_("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) {
ztbmv_(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_("ZLARHS", &i__1);
}
return 0;
/* End of ZLARHS */
} /* zlarhs_ */
/* Subroutine */ int zhpgvd_(integer *itype, char *jobz, char *uplo, integer *
n, doublecomplex *ap, doublecomplex *bp, doublereal *w, doublecomplex
*z__, integer *ldz, doublecomplex *work, integer *lwork, doublereal *
rwork, integer *lrwork, integer *iwork, integer *liwork, integer *
info)
{
/* System generated locals */
integer z_dim1, z_offset, i__1;
doublereal d__1, d__2;
/* Local variables */
integer j, neig;
integer lwmin;
char trans[1];
logical upper, wantz;
integer liwmin;
integer lrwmin;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* ZHPGVD 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. */
/* If eigenvectors are desired, it uses a divide and conquer algorithm. */
/* The divide and conquer algorithm makes very mild assumptions about */
/* floating point arithmetic. It will work on machines with a guard */
/* digit in add/subtract, or on those binary machines without guard */
/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* without guard digits, but we know of none. */
/* 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*16 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*16 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) DOUBLE PRECISION array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX*16 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*16 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the required LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of array WORK. */
/* If N <= 1, LWORK >= 1. */
/* If JOBZ = 'N' and N > 1, LWORK >= N. */
/* If JOBZ = 'V' and N > 1, LWORK >= 2*N. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the required sizes of the WORK, RWORK and */
/* IWORK arrays, returns these values as the first entries of */
/* the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
/* On exit, if INFO = 0, RWORK(1) returns the required LRWORK. */
/* LRWORK (input) INTEGER */
/* The dimension of array RWORK. */
/* If N <= 1, LRWORK >= 1. */
/* If JOBZ = 'N' and N > 1, LRWORK >= N. */
/* If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. */
/* If LRWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the required sizes of the WORK, RWORK */
/* and IWORK arrays, returns these values as the first entries */
/* of the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the required LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of array IWORK. */
/* If JOBZ = 'N' or N <= 1, LIWORK >= 1. */
/* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the required sizes of the WORK, RWORK */
/* and IWORK arrays, returns these values as the first entries */
/* of the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: ZPPTRF or ZHPEVD returned an error code: */
/* <= N: if INFO = i, ZHPEVD 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. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
--bp;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -9;
}
if (*info == 0) {
if (*n <= 1) {
lwmin = 1;
liwmin = 1;
lrwmin = 1;
} else {
if (wantz) {
lwmin = *n << 1;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
} else {
lwmin = *n;
lrwmin = *n;
liwmin = 1;
}
}
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -11;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -13;
} else if (*liwork < liwmin && ! lquery) {
*info = -15;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHPGVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
zpptrf_(uplo, n, &bp[1], info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
zhpgst_(itype, uplo, n, &ap[1], &bp[1], info);
zhpevd_(jobz, uplo, n, &ap[1], &w[1], &z__[z_offset], ldz, &work[1],
lwork, &rwork[1], lrwork, &iwork[1], liwork, info);
/* Computing MAX */
d__1 = (doublereal) lwmin, d__2 = work[1].r;
lwmin = (integer) max(d__1,d__2);
/* Computing MAX */
d__1 = (doublereal) lrwmin;
lrwmin = (integer) max(d__1,rwork[1]);
/* Computing MAX */
d__1 = (doublereal) liwmin, d__2 = (doublereal) iwork[1];
liwmin = (integer) max(d__1,d__2);
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) {
ztpsv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &c__1);
}
} 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) {
ztpmv_(uplo, trans, "Non-unit", n, &bp[1], &z__[j * z_dim1 +
1], &c__1);
}
}
}
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of ZHPGVD */
} /* zhpgvd_ */
/* Subroutine */ int ztpt02_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, doublecomplex *ap, doublecomplex *x, integer *ldx,
doublecomplex *b, integer *ldb, doublecomplex *work, doublereal *
rwork, doublereal *resid)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
doublereal d__1, d__2;
/* Local variables */
integer j;
doublereal eps;
extern logical lsame_(char *, char *);
doublereal anorm, bnorm, xnorm;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), ztpmv_(
char *, char *, char *, integer *, doublecomplex *, doublecomplex
*, integer *);
extern doublereal dlamch_(char *), dzasum_(integer *,
doublecomplex *, integer *), zlantp_(char *, char *, char *,
integer *, doublecomplex *, doublereal *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTPT02 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*16 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*16 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*16 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*16 array, dimension (N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* RESID (output) DOUBLE PRECISION */
/* 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.;
return 0;
}
/* Compute the 1-norm of A or A**H. */
if (lsame_(trans, "N")) {
anorm = zlantp_("1", uplo, diag, n, &ap[1], &rwork[1]);
} else {
anorm = zlantp_("I", uplo, diag, n, &ap[1], &rwork[1]);
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = dlamch_("Epsilon");
if (anorm <= 0.) {
*resid = 1. / 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.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
zcopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ztpmv_(uplo, trans, diag, n, &ap[1], &work[1], &c__1);
zaxpy_(n, &c_b12, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
bnorm = dzasum_(n, &work[1], &c__1);
xnorm = dzasum_(n, &x[j * x_dim1 + 1], &c__1);
if (xnorm <= 0.) {
*resid = 1. / eps;
} else {
/* Computing MAX */
d__1 = *resid, d__2 = bnorm / anorm / xnorm / eps;
*resid = max(d__1,d__2);
}
/* L10: */
}
return 0;
/* End of ZTPT02 */
} /* ztpt02_ */
/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap,
integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal d__1;
doublecomplex z__1;
/* Local variables */
static integer j, jc, jj;
static doublereal ajj;
static integer jjn;
extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *,
doublecomplex *, integer *, doublecomplex *, ftnlen);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static logical upper;
extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen,
ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *,
doublereal *, doublecomplex *, integer *), ztptri_(char *, char *,
integer *, doublecomplex *, integer *, ftnlen, ftnlen);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* March 31, 1993 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPPTRI 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 ZPPTRF. */
/* 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*16 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", (ftnlen)1, (ftnlen)1);
if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPPTRI", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Invert the triangular Cholesky factor U or L. */
ztptri_(uplo, "Non-unit", n, &ap[1], info, (ftnlen)1, (ftnlen)8);
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;
zhpr_("Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen)
5);
}
i__2 = jj;
ajj = ap[i__2].r;
zdscal_(&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;
zdotc_(&z__1, &i__3, &ap[jj], &c__1, &ap[jj], &c__1);
d__1 = z__1.r;
ap[i__2].r = d__1, ap[i__2].i = 0.;
if (j < *n) {
i__2 = *n - j;
ztpmv_("Lower", "Conjugate transpose", "Non-unit", &i__2, &ap[
jjn], &ap[jj + 1], &c__1, (ftnlen)5, (ftnlen)19, (
ftnlen)8);
}
jj = jjn;
/* L20: */
}
}
return 0;
/* End of ZPPTRI */
} /* zpptri_ */
/* Subroutine */ int zppt01_(char *uplo, integer *n, doublecomplex *a,
doublecomplex *afac, doublereal *rwork, doublereal *resid)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
doublereal d__1;
doublecomplex z__1;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
integer i__, k, kc;
doublecomplex tc;
doublereal tr, eps;
extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *,
doublecomplex *, integer *, doublecomplex *);
extern logical lsame_(char *, char *);
doublereal anorm;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *);
extern doublereal dlamch_(char *), zlanhp_(char *, char *,
integer *, doublecomplex *, doublereal *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPPT01 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*16 array, dimension (N*(N+1)/2) */
/* The original Hermitian matrix A, stored as a packed */
/* triangular matrix. */
/* AFAC (input/output) COMPLEX*16 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) DOUBLE PRECISION array, dimension (N) */
/* RESID (output) DOUBLE PRECISION */
/* 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.;
return 0;
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = dlamch_("Epsilon");
anorm = zlanhp_("1", uplo, n, &a[1], &rwork[1]);
if (anorm <= 0.) {
*resid = 1. / 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 (d_imag(&afac[kc]) != 0.) {
*resid = 1. / eps;
return 0;
}
kc = kc + k + 1;
/* L10: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (d_imag(&afac[kc]) != 0.) {
*resid = 1. / 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. */
zdotc_(&z__1, &k, &afac[kc], &c__1, &afac[kc], &c__1);
tr = z__1.r;
i__1 = kc + k - 1;
afac[i__1].r = tr, afac[i__1].i = 0.;
/* Compute the rest of column K. */
if (k > 1) {
i__1 = k - 1;
ztpmv_("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;
z__1.r = afac[i__4].r - a[i__5].r, z__1.i = afac[i__4].i - a[
i__5].i;
afac[i__3].r = z__1.r, afac[i__3].i = z__1.i;
/* L40: */
}
i__2 = kc + k - 1;
i__3 = kc + k - 1;
i__4 = kc + k - 1;
d__1 = a[i__4].r;
z__1.r = afac[i__3].r - d__1, z__1.i = afac[i__3].i;
afac[i__2].r = z__1.r, afac[i__2].i = z__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;
zhpr_("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;
zscal_(&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;
d__1 = a[i__4].r;
z__1.r = afac[i__3].r - d__1, z__1.i = afac[i__3].i;
afac[i__2].r = z__1.r, afac[i__2].i = z__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;
z__1.r = afac[i__4].r - a[i__5].r, z__1.i = afac[i__4].i - a[
i__5].i;
afac[i__3].r = z__1.r, afac[i__3].i = z__1.i;
/* L70: */
}
kc = kc + *n - k + 1;
/* L80: */
}
}
/* Compute norm( L*U - A ) / ( N * norm(A) * EPS ) */
*resid = zlanhp_("1", uplo, n, &afac[1], &rwork[1]);
*resid = *resid / (doublereal) (*n) / anorm / eps;
return 0;
/* End of ZPPT01 */
} /* zppt01_ */
/* Subroutine */
int zhpgst_(integer *itype, char *uplo, integer *n, doublecomplex *ap, doublecomplex *bp, integer *info)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3;
/* Local variables */
integer j, k, j1, k1, jj, kk;
doublecomplex ct;
doublereal ajj;
integer j1j1;
doublereal akk;
integer k1k1;
doublereal bjj, bkk;
extern /* Subroutine */
int zhpr2_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *);
extern logical lsame_(char *, char *);
extern /* Double Complex */
VOID zdotc_f2c_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *);
logical upper;
extern /* Subroutine */
int zhpmv_(char *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), ztpmv_(char *, char *, char *, integer *, doublecomplex *, doublecomplex *, integer *), ztpsv_(char *, char *, char *, integer *, doublecomplex * , doublecomplex *, integer *), xerbla_( char *, integer *), zdscal_(integer *, doublereal *, doublecomplex *, 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_("ZHPGST", &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;
d__1 = ap[i__3].r;
ap[i__2].r = d__1;
ap[i__2].i = 0.; // , expr subst
i__2 = jj;
bjj = bp[i__2].r;
ztpsv_(uplo, "Conjugate transpose", "Non-unit", &j, &bp[1], & ap[j1], &c__1);
i__2 = j - 1;
z__1.r = -1.;
z__1.i = -0.; // , expr subst
zhpmv_(uplo, &i__2, &z__1, &ap[1], &bp[j1], &c__1, &c_b1, &ap[ j1], &c__1);
i__2 = j - 1;
d__1 = 1. / bjj;
zdscal_(&i__2, &d__1, &ap[j1], &c__1);
i__2 = jj;
i__3 = jj;
i__4 = j - 1;
zdotc_f2c_(&z__3, &i__4, &ap[j1], &c__1, &bp[j1], &c__1);
z__2.r = ap[i__3].r - z__3.r;
z__2.i = ap[i__3].i - z__3.i; // , expr subst
z__1.r = z__2.r / bjj;
z__1.i = z__2.i / bjj; // , expr subst
ap[i__2].r = z__1.r;
ap[i__2].i = z__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 */
d__1 = bkk;
akk /= d__1 * d__1;
i__2 = kk;
ap[i__2].r = akk;
ap[i__2].i = 0.; // , expr subst
if (k < *n)
{
i__2 = *n - k;
d__1 = 1. / bkk;
zdscal_(&i__2, &d__1, &ap[kk + 1], &c__1);
d__1 = akk * -.5;
ct.r = d__1;
ct.i = 0.; // , expr subst
i__2 = *n - k;
zaxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ;
i__2 = *n - k;
z__1.r = -1.;
z__1.i = -0.; // , expr subst
zhpr2_(uplo, &i__2, &z__1, &ap[kk + 1], &c__1, &bp[kk + 1] , &c__1, &ap[k1k1]);
i__2 = *n - k;
zaxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1) ;
i__2 = *n - k;
ztpsv_(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;
ztpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[ k1], &c__1);
d__1 = akk * .5;
ct.r = d__1;
ct.i = 0.; // , expr subst
i__2 = k - 1;
zaxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
zhpr2_(uplo, &i__2, &c_b1, &ap[k1], &c__1, &bp[k1], &c__1, & ap[1]);
i__2 = k - 1;
zaxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
zdscal_(&i__2, &bkk, &ap[k1], &c__1);
i__2 = kk;
/* Computing 2nd power */
d__2 = bkk;
d__1 = akk * (d__2 * d__2);
ap[i__2].r = d__1;
ap[i__2].i = 0.; // , 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;
d__1 = ajj * bjj;
i__3 = *n - j;
zdotc_f2c_(&z__2, &i__3, &ap[jj + 1], &c__1, &bp[jj + 1], &c__1);
z__1.r = d__1 + z__2.r;
z__1.i = z__2.i; // , expr subst
ap[i__2].r = z__1.r;
ap[i__2].i = z__1.i; // , expr subst
i__2 = *n - j;
zdscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
i__2 = *n - j;
zhpmv_(uplo, &i__2, &c_b1, &ap[j1j1], &bp[jj + 1], &c__1, & c_b1, &ap[jj + 1], &c__1);
i__2 = *n - j + 1;
ztpmv_(uplo, "Conjugate transpose", "Non-unit", &i__2, &bp[jj] , &ap[jj], &c__1);
jj = j1j1;
/* L40: */
}
}
}
return 0;
/* End of ZHPGST */
}
