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/* dspgst.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b9 = -1.;
static doublereal c_b11 = 1.;
/* Subroutine */ int dspgst_(integer *itype, char *uplo, integer *n,
doublereal *ap, doublereal *bp, integer *info)
{
/* System generated locals */
integer i__1, i__2;
doublereal d__1;
/* Local variables */
integer j, k, j1, k1, jj, kk;
doublereal ct, ajj;
integer j1j1;
doublereal akk;
integer k1k1;
doublereal bjj, bkk;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *);
extern /* Subroutine */ int dspr2_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *), dscal_(integer *, doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *), dspmv_(char *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, integer *);
logical upper;
extern /* Subroutine */ int dtpmv_(char *, char *, char *, integer *,
doublereal *, doublereal *, integer *),
dtpsv_(char *, char *, char *, integer *, doublereal *,
doublereal *, integer *), xerbla_(char *,
integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSPGST reduces a real symmetric-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**T)*A*inv(U) or inv(L)*A*inv(L**T) */
/* 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**T or L**T*A*L. */
/* B must have been previously factorized as U**T*U or L*L**T by DPPTRF. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */
/* = 2 or 3: compute U*A*U**T or L**T*A*L. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored and B is factored as */
/* U**T*U; */
/* = 'L': Lower triangle of A is stored and B is factored as */
/* L*L**T. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the symmetric matrix */
/* A, packed columnwise in a linear array. The j-th column of A */
/* is stored in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(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) DOUBLE PRECISION 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 DPPTRF. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. 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_("DSPGST", &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 */
bjj = bp[jj];
dtpsv_(uplo, "Transpose", "Nonunit", &j, &bp[1], &ap[j1], &
c__1);
i__2 = j - 1;
dspmv_(uplo, &i__2, &c_b9, &ap[1], &bp[j1], &c__1, &c_b11, &
ap[j1], &c__1);
i__2 = j - 1;
d__1 = 1. / bjj;
dscal_(&i__2, &d__1, &ap[j1], &c__1);
i__2 = j - 1;
ap[jj] = (ap[jj] - ddot_(&i__2, &ap[j1], &c__1, &bp[j1], &
c__1)) / bjj;
/* 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) */
akk = ap[kk];
bkk = bp[kk];
/* Computing 2nd power */
d__1 = bkk;
akk /= d__1 * d__1;
ap[kk] = akk;
if (k < *n) {
i__2 = *n - k;
d__1 = 1. / bkk;
dscal_(&i__2, &d__1, &ap[kk + 1], &c__1);
ct = akk * -.5;
i__2 = *n - k;
daxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
dspr2_(uplo, &i__2, &c_b9, &ap[kk + 1], &c__1, &bp[kk + 1]
, &c__1, &ap[k1k1]);
i__2 = *n - k;
daxpy_(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
dtpsv_(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) */
akk = ap[kk];
bkk = bp[kk];
i__2 = k - 1;
dtpmv_(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[
k1], &c__1);
ct = akk * .5;
i__2 = k - 1;
daxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
dspr2_(uplo, &i__2, &c_b11, &ap[k1], &c__1, &bp[k1], &c__1, &
ap[1]);
i__2 = k - 1;
daxpy_(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
dscal_(&i__2, &bkk, &ap[k1], &c__1);
/* Computing 2nd power */
d__1 = bkk;
ap[kk] = akk * (d__1 * d__1);
/* 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 */
ajj = ap[jj];
bjj = bp[jj];
i__2 = *n - j;
ap[jj] = ajj * bjj + ddot_(&i__2, &ap[jj + 1], &c__1, &bp[jj
+ 1], &c__1);
i__2 = *n - j;
dscal_(&i__2, &bjj, &ap[jj + 1], &c__1);
i__2 = *n - j;
dspmv_(uplo, &i__2, &c_b11, &ap[j1j1], &bp[jj + 1], &c__1, &
c_b11, &ap[jj + 1], &c__1);
i__2 = *n - j + 1;
dtpmv_(uplo, "Transpose", "Non-unit", &i__2, &bp[jj], &ap[jj],
&c__1);
jj = j1j1;
/* L40: */
}
}
}
return 0;
/* End of DSPGST */
} /* dspgst_ */
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