197 lines
6.2 KiB
FortranFixed
197 lines
6.2 KiB
FortranFixed
SUBROUTINE CHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
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$ RWORK, INFO )
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*
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* -- LAPACK driver routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER JOBZ, UPLO
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INTEGER INFO, ITYPE, LDZ, N
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* ..
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* .. Array Arguments ..
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REAL RWORK( * ), W( * )
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COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
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* ..
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*
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* Purpose
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* =======
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*
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* CHPGV computes all the eigenvalues and, optionally, the eigenvectors
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* of a complex generalized Hermitian-definite eigenproblem, of the form
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* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
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* Here A and B are assumed to be Hermitian, stored in packed format,
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* and B is also positive definite.
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*
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* Arguments
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* =========
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*
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* ITYPE (input) INTEGER
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* Specifies the problem type to be solved:
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* = 1: A*x = (lambda)*B*x
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* = 2: A*B*x = (lambda)*x
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* = 3: B*A*x = (lambda)*x
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*
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* JOBZ (input) CHARACTER*1
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* = 'N': Compute eigenvalues only;
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* = 'V': Compute eigenvalues and eigenvectors.
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*
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* UPLO (input) CHARACTER*1
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* = 'U': Upper triangles of A and B are stored;
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* = 'L': Lower triangles of A and B are stored.
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*
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* N (input) INTEGER
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* The order of the matrices A and B. N >= 0.
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*
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* AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
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* On entry, the upper or lower triangle of the Hermitian matrix
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* A, packed columnwise in a linear array. The j-th column of A
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* is stored in the array AP as follows:
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* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
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* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
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*
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* On exit, the contents of AP are destroyed.
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*
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* BP (input/output) COMPLEX array, dimension (N*(N+1)/2)
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* On entry, the upper or lower triangle of the Hermitian matrix
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* B, packed columnwise in a linear array. The j-th column of B
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* is stored in the array BP as follows:
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* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
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* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
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*
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* On exit, the triangular factor U or L from the Cholesky
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* factorization B = U**H*U or B = L*L**H, in the same storage
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* format as B.
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*
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* W (output) REAL array, dimension (N)
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* If INFO = 0, the eigenvalues in ascending order.
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*
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* Z (output) COMPLEX array, dimension (LDZ, N)
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* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
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* eigenvectors. The eigenvectors are normalized as follows:
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* if ITYPE = 1 or 2, Z**H*B*Z = I;
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* if ITYPE = 3, Z**H*inv(B)*Z = I.
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* If JOBZ = 'N', then Z is not referenced.
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*
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* LDZ (input) INTEGER
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* The leading dimension of the array Z. LDZ >= 1, and if
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* JOBZ = 'V', LDZ >= max(1,N).
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*
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* WORK (workspace) COMPLEX array, dimension (max(1, 2*N-1))
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*
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* RWORK (workspace) REAL array, dimension (max(1, 3*N-2))
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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* > 0: CPPTRF or CHPEV returned an error code:
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* <= N: if INFO = i, CHPEV failed to converge;
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* i off-diagonal elements of an intermediate
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* tridiagonal form did not convergeto zero;
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* > N: if INFO = N + i, for 1 <= i <= n, then the leading
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* minor of order i of B is not positive definite.
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* The factorization of B could not be completed and
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* no eigenvalues or eigenvectors were computed.
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL UPPER, WANTZ
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CHARACTER TRANS
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INTEGER J, NEIG
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL CHPEV, CHPGST, CPPTRF, CTPMV, CTPSV, XERBLA
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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WANTZ = LSAME( JOBZ, 'V' )
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UPPER = LSAME( UPLO, 'U' )
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*
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INFO = 0
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IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
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INFO = -1
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ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
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INFO = -2
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ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
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INFO = -9
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CHPGV ', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Form a Cholesky factorization of B.
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*
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CALL CPPTRF( UPLO, N, BP, INFO )
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IF( INFO.NE.0 ) THEN
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INFO = N + INFO
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RETURN
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END IF
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*
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* Transform problem to standard eigenvalue problem and solve.
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*
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CALL CHPGST( ITYPE, UPLO, N, AP, BP, INFO )
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CALL CHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )
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*
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IF( WANTZ ) THEN
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*
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* Backtransform eigenvectors to the original problem.
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*
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NEIG = N
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IF( INFO.GT.0 )
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$ NEIG = INFO - 1
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IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
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*
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* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
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* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
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*
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IF( UPPER ) THEN
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TRANS = 'N'
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ELSE
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TRANS = 'C'
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END IF
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*
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DO 10 J = 1, NEIG
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CALL CTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
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$ 1 )
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10 CONTINUE
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*
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ELSE IF( ITYPE.EQ.3 ) THEN
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*
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* For B*A*x=(lambda)*x;
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* backtransform eigenvectors: x = L*y or U'*y
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*
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IF( UPPER ) THEN
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TRANS = 'C'
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ELSE
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TRANS = 'N'
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END IF
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*
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DO 20 J = 1, NEIG
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CALL CTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
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$ 1 )
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20 CONTINUE
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END IF
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END IF
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RETURN
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*
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* End of CHPGV
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*
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END
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