SUBROUTINE CHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO ) * * -- LAPACK driver routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL RWORK( * ), W( * ) COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) * .. * * Purpose * ======= * * CHPGVD computes all the eigenvalues and, optionally, the eigenvectors * of a complex generalized Hermitian-definite eigenproblem, of the form * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and * B are assumed to be Hermitian, stored in packed format, and B is also * positive definite. * If eigenvectors are desired, it uses a divide and conquer algorithm. * * The divide and conquer algorithm makes very mild assumptions about * floating point arithmetic. It will work on machines with a guard * digit in add/subtract, or on those binary machines without guard * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or * Cray-2. It could conceivably fail on hexadecimal or decimal machines * without guard digits, but we know of none. * * Arguments * ========= * * ITYPE (input) INTEGER * Specifies the problem type to be solved: * = 1: A*x = (lambda)*B*x * = 2: A*B*x = (lambda)*x * = 3: B*A*x = (lambda)*x * * JOBZ (input) CHARACTER*1 * = 'N': Compute eigenvalues only; * = 'V': Compute eigenvalues and eigenvectors. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangles of A and B are stored; * = 'L': Lower triangles of A and B are stored. * * N (input) INTEGER * The order of the matrices A and B. N >= 0. * * AP (input/output) COMPLEX array, dimension (N*(N+1)/2) * On entry, the upper or lower triangle of the Hermitian 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. * * On exit, the contents of AP are destroyed. * * BP (input/output) COMPLEX array, dimension (N*(N+1)/2) * On entry, the upper or lower triangle of the Hermitian matrix * B, packed columnwise in a linear array. The j-th column of B * is stored in the array BP as follows: * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. * * On exit, the triangular factor U or L from the Cholesky * factorization B = U**H*U or B = L*L**H, in the same storage * format as B. * * W (output) REAL array, dimension (N) * If INFO = 0, the eigenvalues in ascending order. * * Z (output) COMPLEX array, dimension (LDZ, N) * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of * eigenvectors. The eigenvectors are normalized as follows: * if ITYPE = 1 or 2, Z**H*B*Z = I; * if ITYPE = 3, Z**H*inv(B)*Z = I. * If JOBZ = 'N', then Z is not referenced. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1, and if * JOBZ = 'V', LDZ >= max(1,N). * * WORK (workspace) COMPLEX array, dimension (MAX(1,LWORK)) * On exit, if INFO = 0, WORK(1) returns the required LWORK. * * LWORK (input) INTEGER * The dimension of array WORK. * If N <= 1, LWORK >= 1. * If JOBZ = 'N' and N > 1, LWORK >= N. * If JOBZ = 'V' and N > 1, LWORK >= 2*N. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the required sizes of the WORK, RWORK and * IWORK arrays, returns these values as the first entries of * the WORK, RWORK and IWORK arrays, and no error message * related to LWORK or LRWORK or LIWORK is issued by XERBLA. * * RWORK (workspace) REAL array, dimension (MAX(1,LRWORK)) * On exit, if INFO = 0, RWORK(1) returns the required LRWORK. * * LRWORK (input) INTEGER * The dimension of array RWORK. * If N <= 1, LRWORK >= 1. * If JOBZ = 'N' and N > 1, LRWORK >= N. * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. * * If LRWORK = -1, then a workspace query is assumed; the * routine only calculates the required sizes of the WORK, RWORK * and IWORK arrays, returns these values as the first entries * of the WORK, RWORK and IWORK arrays, and no error message * related to LWORK or LRWORK or LIWORK is issued by XERBLA. * * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) * On exit, if INFO = 0, IWORK(1) returns the required LIWORK. * * LIWORK (input) INTEGER * The dimension of array IWORK. * If JOBZ = 'N' or N <= 1, LIWORK >= 1. * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. * * If LIWORK = -1, then a workspace query is assumed; the * routine only calculates the required sizes of the WORK, RWORK * and IWORK arrays, returns these values as the first entries * of the WORK, RWORK and IWORK arrays, and no error message * related to LWORK or LRWORK or LIWORK is issued by XERBLA. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: CPPTRF or CHPEVD returned an error code: * <= N: if INFO = i, CHPEVD failed to converge; * i off-diagonal elements of an intermediate * tridiagonal form did not convergeto zero; * > N: if INFO = N + i, for 1 <= i <= n, then the leading * minor of order i of B is not positive definite. * The factorization of B could not be completed and * no eigenvalues or eigenvectors were computed. * * Further Details * =============== * * Based on contributions by * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA * * ===================================================================== * * .. Local Scalars .. LOGICAL LQUERY, UPPER, WANTZ CHARACTER TRANS INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CHPEVD, CHPGST, CPPTRF, CTPMV, CTPSV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, REAL * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * INFO = 0 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -2 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -9 END IF * IF( INFO.EQ.0 ) THEN IF( N.LE.1 ) THEN LWMIN = 1 LIWMIN = 1 LRWMIN = 1 ELSE IF( WANTZ ) THEN LWMIN = 2*N LRWMIN = 1 + 5*N + 2*N**2 LIWMIN = 3 + 5*N ELSE LWMIN = N LRWMIN = N LIWMIN = 1 END IF END IF WORK( 1 ) = LWMIN RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -11 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN INFO = -13 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -15 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHPGVD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Form a Cholesky factorization of B. * CALL CPPTRF( UPLO, N, BP, INFO ) IF( INFO.NE.0 ) THEN INFO = N + INFO RETURN END IF * * Transform problem to standard eigenvalue problem and solve. * CALL CHPGST( ITYPE, UPLO, N, AP, BP, INFO ) CALL CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, $ LRWORK, IWORK, LIWORK, INFO ) LWMIN = MAX( REAL( LWMIN ), REAL( WORK( 1 ) ) ) LRWMIN = MAX( REAL( LRWMIN ), REAL( RWORK( 1 ) ) ) LIWMIN = MAX( REAL( LIWMIN ), REAL( IWORK( 1 ) ) ) * IF( WANTZ ) THEN * * Backtransform eigenvectors to the original problem. * NEIG = N IF( INFO.GT.0 ) $ NEIG = INFO - 1 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN * * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y * IF( UPPER ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * DO 10 J = 1, NEIG CALL CTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), $ 1 ) 10 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * For B*A*x=(lambda)*x; * backtransform eigenvectors: x = L*y or U'*y * IF( UPPER ) THEN TRANS = 'C' ELSE TRANS = 'N' END IF * DO 20 J = 1, NEIG CALL CTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), $ 1 ) 20 CONTINUE END IF END IF * WORK( 1 ) = LWMIN RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN RETURN * * End of CHPGVD * END