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/* dsygs2.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 doublereal c_b6 = -1.;
static integer c__1 = 1;
static doublereal c_b27 = 1.;
/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n,
doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
doublereal d__1;
/* Local variables */
integer k;
doublereal ct, akk, bkk;
extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *), dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
logical upper;
extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *,
doublereal *, integer *, doublereal *, integer *), dtrsv_(char *, char *, char *, integer *, doublereal *,
integer *, 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 */
/* ======= */
/* DSYGS2 reduces a real symmetric-definite generalized eigenproblem */
/* to standard form. */
/* If ITYPE = 1, the problem is A*x = lambda*B*x, */
/* and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') */
/* 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` or L'*A*L. */
/* B must have been previously factorized as U'*U or L*L' by DPOTRF. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); */
/* = 2 or 3: compute U*A*U' or L'*A*L. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* symmetric matrix A is stored, and how B has been factorized. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
/* n by n upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading n by n lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit, if INFO = 0, the transformed matrix, stored in the */
/* same format as A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input) DOUBLE PRECISION array, dimension (LDB,N) */
/* The triangular factor from the Cholesky factorization of B, */
/* as returned by DPOTRF. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* 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 */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* 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;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSYGS2", &i__1);
return 0;
}
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the upper triangle of A(k:n,k:n) */
akk = a[k + k * a_dim1];
bkk = b[k + k * b_dim1];
/* Computing 2nd power */
d__1 = bkk;
akk /= d__1 * d__1;
a[k + k * a_dim1] = akk;
if (k < *n) {
i__2 = *n - k;
d__1 = 1. / bkk;
dscal_(&i__2, &d__1, &a[k + (k + 1) * a_dim1], lda);
ct = akk * -.5;
i__2 = *n - k;
daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (
k + 1) * a_dim1], lda);
i__2 = *n - k;
dsyr2_(uplo, &i__2, &c_b6, &a[k + (k + 1) * a_dim1], lda,
&b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1)
* a_dim1], lda);
i__2 = *n - k;
daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (
k + 1) * a_dim1], lda);
i__2 = *n - k;
dtrsv_(uplo, "Transpose", "Non-unit", &i__2, &b[k + 1 + (
k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1],
lda);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the lower triangle of A(k:n,k:n) */
akk = a[k + k * a_dim1];
bkk = b[k + k * b_dim1];
/* Computing 2nd power */
d__1 = bkk;
akk /= d__1 * d__1;
a[k + k * a_dim1] = akk;
if (k < *n) {
i__2 = *n - k;
d__1 = 1. / bkk;
dscal_(&i__2, &d__1, &a[k + 1 + k * a_dim1], &c__1);
ct = akk * -.5;
i__2 = *n - k;
daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k +
1 + k * a_dim1], &c__1);
i__2 = *n - k;
dsyr2_(uplo, &i__2, &c_b6, &a[k + 1 + k * a_dim1], &c__1,
&b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1)
* a_dim1], lda);
i__2 = *n - k;
daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k +
1 + k * a_dim1], &c__1);
i__2 = *n - k;
dtrsv_(uplo, "No transpose", "Non-unit", &i__2, &b[k + 1
+ (k + 1) * b_dim1], ldb, &a[k + 1 + k * a_dim1],
&c__1);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the upper triangle of A(1:k,1:k) */
akk = a[k + k * a_dim1];
bkk = b[k + k * b_dim1];
i__2 = k - 1;
dtrmv_(uplo, "No transpose", "Non-unit", &i__2, &b[b_offset],
ldb, &a[k * a_dim1 + 1], &c__1);
ct = akk * .5;
i__2 = k - 1;
daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 +
1], &c__1);
i__2 = k - 1;
dsyr2_(uplo, &i__2, &c_b27, &a[k * a_dim1 + 1], &c__1, &b[k *
b_dim1 + 1], &c__1, &a[a_offset], lda);
i__2 = k - 1;
daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 +
1], &c__1);
i__2 = k - 1;
dscal_(&i__2, &bkk, &a[k * a_dim1 + 1], &c__1);
/* Computing 2nd power */
d__1 = bkk;
a[k + k * a_dim1] = akk * (d__1 * d__1);
/* L30: */
}
} else {
/* Compute L'*A*L */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the lower triangle of A(1:k,1:k) */
akk = a[k + k * a_dim1];
bkk = b[k + k * b_dim1];
i__2 = k - 1;
dtrmv_(uplo, "Transpose", "Non-unit", &i__2, &b[b_offset],
ldb, &a[k + a_dim1], lda);
ct = akk * .5;
i__2 = k - 1;
daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda);
i__2 = k - 1;
dsyr2_(uplo, &i__2, &c_b27, &a[k + a_dim1], lda, &b[k +
b_dim1], ldb, &a[a_offset], lda);
i__2 = k - 1;
daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda);
i__2 = k - 1;
dscal_(&i__2, &bkk, &a[k + a_dim1], lda);
/* Computing 2nd power */
d__1 = bkk;
a[k + k * a_dim1] = akk * (d__1 * d__1);
/* L40: */
}
}
}
return 0;
/* End of DSYGS2 */
} /* dsygs2_ */
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