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SUBROUTINE <a name="SSYGS2.1"></a><a href="ssygs2.f.html#SSYGS2.1">SSYGS2</a>( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER UPLO
INTEGER INFO, ITYPE, LDA, LDB, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL A( LDA, * ), B( LDB, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SSYGS2.18"></a><a href="ssygs2.f.html#SSYGS2.1">SSYGS2</a> reduces a real symmetric-definite generalized eigenproblem
</span><span class="comment">*</span><span class="comment"> to standard form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If ITYPE = 1, the problem is A*x = lambda*B*x,
</span><span class="comment">*</span><span class="comment"> and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
</span><span class="comment">*</span><span class="comment"> B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B must have been previously factorized as U'*U or L*L' by <a name="SPOTRF.27"></a><a href="spotrf.f.html#SPOTRF.1">SPOTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ITYPE (input) INTEGER
</span><span class="comment">*</span><span class="comment"> = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
</span><span class="comment">*</span><span class="comment"> = 2 or 3: compute U*A*U' or L'*A*L.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment"> symmetric matrix A is stored, and how B has been factorized.
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrices A and B. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the symmetric matrix A. If UPLO = 'U', the leading
</span><span class="comment">*</span><span class="comment"> n by n upper triangular part of A contains the upper
</span><span class="comment">*</span><span class="comment"> triangular part of the matrix A, and the strictly lower
</span><span class="comment">*</span><span class="comment"> triangular part of A is not referenced. If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment"> leading n by n lower triangular part of A contains the lower
</span><span class="comment">*</span><span class="comment"> triangular part of the matrix A, and the strictly upper
</span><span class="comment">*</span><span class="comment"> triangular part of A is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, the transformed matrix, stored in the
</span><span class="comment">*</span><span class="comment"> same format as A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input) REAL array, dimension (LDB,N)
</span><span class="comment">*</span><span class="comment"> The triangular factor from the Cholesky factorization of B,
</span><span class="comment">*</span><span class="comment"> as returned by <a name="SPOTRF.62"></a><a href="spotrf.f.html#SPOTRF.1">SPOTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array B. LDB >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit.
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ONE, HALF
PARAMETER ( ONE = 1.0, HALF = 0.5 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
INTEGER K
REAL AKK, BKK, CT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL SAXPY, SSCAL, SSYR2, STRMV, STRSV, <a name="XERBLA.83"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.89"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.90"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
UPPER = <a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
INFO = -1
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