209 lines
6.5 KiB
FortranFixed
209 lines
6.5 KiB
FortranFixed
SUBROUTINE DSPGST( 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 ..
|
|
DOUBLE PRECISION AP( * ), BP( * )
|
|
* ..
|
|
*
|
|
* 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 ..
|
|
DOUBLE PRECISION ONE, HALF
|
|
PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL UPPER
|
|
INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK
|
|
DOUBLE PRECISION AJJ, AKK, BJJ, BKK, CT
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DAXPY, DSCAL, DSPMV, DSPR2, DTPMV, DTPSV,
|
|
$ XERBLA
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
DOUBLE PRECISION DDOT
|
|
EXTERNAL LSAME, DDOT
|
|
* ..
|
|
* .. 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( 'DSPGST', -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 DTPSV( UPLO, 'Transpose', 'Nonunit', J, BP,
|
|
$ AP( J1 ), 1 )
|
|
CALL DSPMV( UPLO, J-1, -ONE, AP, BP( J1 ), 1, ONE,
|
|
$ AP( J1 ), 1 )
|
|
CALL DSCAL( J-1, ONE / BJJ, AP( J1 ), 1 )
|
|
AP( JJ ) = ( AP( JJ )-DDOT( 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 DSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 )
|
|
CT = -HALF*AKK
|
|
CALL DAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
|
|
CALL DSPR2( UPLO, N-K, -ONE, AP( KK+1 ), 1,
|
|
$ BP( KK+1 ), 1, AP( K1K1 ) )
|
|
CALL DAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 )
|
|
CALL DTPSV( 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 DTPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP,
|
|
$ AP( K1 ), 1 )
|
|
CT = HALF*AKK
|
|
CALL DAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
|
|
CALL DSPR2( UPLO, K-1, ONE, AP( K1 ), 1, BP( K1 ), 1,
|
|
$ AP )
|
|
CALL DAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 )
|
|
CALL DSCAL( 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 + DDOT( N-J, AP( JJ+1 ), 1,
|
|
$ BP( JJ+1 ), 1 )
|
|
CALL DSCAL( N-J, BJJ, AP( JJ+1 ), 1 )
|
|
CALL DSPMV( UPLO, N-J, ONE, AP( J1J1 ), BP( JJ+1 ), 1,
|
|
$ ONE, AP( JJ+1 ), 1 )
|
|
CALL DTPMV( UPLO, 'Transpose', 'Non-unit', N-J+1,
|
|
$ BP( JJ ), AP( JJ ), 1 )
|
|
JJ = J1J1
|
|
40 CONTINUE
|
|
END IF
|
|
END IF
|
|
RETURN
|
|
*
|
|
* End of DSPGST
|
|
*
|
|
END
|