SUBROUTINE SSPGST( ITYPE, UPLO, N, AP, BP, INFO ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, N * .. * .. Array Arguments .. REAL AP( * ), BP( * ) * .. * * Purpose * ======= * * SSPGST 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 SPPTRF. * * 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) REAL 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) REAL 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 SPPTRF. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. REAL ONE, HALF PARAMETER ( ONE = 1.0, HALF = 0.5 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK REAL AJJ, AKK, BJJ, BKK, CT * .. * .. External Subroutines .. EXTERNAL SAXPY, SSCAL, SSPMV, SSPR2, STPMV, STPSV, \$ XERBLA * .. * .. External Functions .. LOGICAL LSAME REAL SDOT EXTERNAL LSAME, SDOT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SSPGST', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U')*A*inv(U) * * J1 and JJ are the indices of A(1,j) and A(j,j) * JJ = 0 DO 10 J = 1, N J1 = JJ + 1 JJ = JJ + J * * Compute the j-th column of the upper triangle of A * BJJ = BP( JJ ) CALL STPSV( UPLO, 'Transpose', 'Nonunit', J, BP, \$ AP( J1 ), 1 ) CALL SSPMV( UPLO, J-1, -ONE, AP, BP( J1 ), 1, ONE, \$ AP( J1 ), 1 ) CALL SSCAL( J-1, ONE / BJJ, AP( J1 ), 1 ) AP( JJ ) = ( AP( JJ )-SDOT( J-1, AP( J1 ), 1, BP( J1 ), \$ 1 ) ) / BJJ 10 CONTINUE 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 DO 20 K = 1, N K1K1 = KK + N - K + 1 * * Update the lower triangle of A(k:n,k:n) * AKK = AP( KK ) BKK = BP( KK ) AKK = AKK / BKK**2 AP( KK ) = AKK IF( K.LT.N ) THEN CALL SSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 ) CT = -HALF*AKK CALL SAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL SSPR2( UPLO, N-K, -ONE, AP( KK+1 ), 1, \$ BP( KK+1 ), 1, AP( K1K1 ) ) CALL SAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL STPSV( UPLO, 'No transpose', 'Non-unit', N-K, \$ BP( K1K1 ), AP( KK+1 ), 1 ) END IF KK = K1K1 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U' * * K1 and KK are the indices of A(1,k) and A(k,k) * KK = 0 DO 30 K = 1, N K1 = KK + 1 KK = KK + K * * Update the upper triangle of A(1:k,1:k) * AKK = AP( KK ) BKK = BP( KK ) CALL STPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP, \$ AP( K1 ), 1 ) CT = HALF*AKK CALL SAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL SSPR2( UPLO, K-1, ONE, AP( K1 ), 1, BP( K1 ), 1, \$ AP ) CALL SAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL SSCAL( K-1, BKK, AP( K1 ), 1 ) AP( KK ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L'*A*L * * JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) * JJ = 1 DO 40 J = 1, N J1J1 = JJ + N - J + 1 * * Compute the j-th column of the lower triangle of A * AJJ = AP( JJ ) BJJ = BP( JJ ) AP( JJ ) = AJJ*BJJ + SDOT( N-J, AP( JJ+1 ), 1, \$ BP( JJ+1 ), 1 ) CALL SSCAL( N-J, BJJ, AP( JJ+1 ), 1 ) CALL SSPMV( UPLO, N-J, ONE, AP( J1J1 ), BP( JJ+1 ), 1, \$ ONE, AP( JJ+1 ), 1 ) CALL STPMV( UPLO, 'Transpose', 'Non-unit', N-J+1, \$ BP( JJ ), AP( JJ ), 1 ) JJ = J1J1 40 CONTINUE END IF END IF RETURN * * End of SSPGST * END