#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int chpgst_(integer *itype, char *uplo, integer *n, complex *
ap, complex *bp, 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
=======
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
=====================================================================
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, i__3, i__4;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
extern /* Subroutine */ int chpr2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *);
static integer j, k;
extern /* Complex */ VOID cdotc_(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 *);
static logical upper;
static integer j1, k1;
extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *,
complex *, complex *, integer *);
static integer jj, kk;
static complex ct;
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*), xerbla_(char *, integer *);
static real ajj;
static integer j1j1;
static real akk;
static integer k1k1;
static real bjj, bkk;
--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')*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);
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);
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]);
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'
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;
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;
/* 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);
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 */
} /* chpgst_ */