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Diffstat (limited to 'SRC/dspgvd.f')
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diff --git a/SRC/dspgvd.f b/SRC/dspgvd.f new file mode 100644 index 00000000..23850cf7 --- /dev/null +++ b/SRC/dspgvd.f @@ -0,0 +1,277 @@ + SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, + $ LWORK, 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, LWORK, N +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ), + $ Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* DSPGVD computes all the eigenvalues, and optionally, the eigenvectors +* of a real generalized symmetric-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 symmetric, 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) 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)*(2*n-j)/2) = A(i,j) for j<=i<=n. +* +* On exit, the contents of AP are destroyed. +* +* BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) +* On entry, the upper or lower triangle of the symmetric 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**T*U or B = L*L**T, in the same storage +* format as B. +* +* W (output) DOUBLE PRECISION array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* Z (output) DOUBLE PRECISION 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**T*B*Z = I; +* if ITYPE = 3, Z**T*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/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the required LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. +* If N <= 1, LWORK >= 1. +* If JOBZ = 'N' and N > 1, LWORK >= 2*N. +* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the required sizes of the WORK and IWORK +* arrays, returns these values as the first entries of the WORK +* and IWORK arrays, and no error message related to LWORK 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 the 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 and +* IWORK arrays, returns these values as the first entries of +* the WORK and IWORK arrays, and no error message related to +* LWORK 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: DPPTRF or DSPEVD returned an error code: +* <= N: if INFO = i, DSPEVD failed to converge; +* i off-diagonal elements of an intermediate +* tridiagonal form did not converge to 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 +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION TWO + PARAMETER ( TWO = 2.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, UPPER, WANTZ + CHARACTER TRANS + INTEGER J, LIWMIN, LWMIN, NEIG +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE, MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + UPPER = LSAME( UPLO, 'U' ) + LQUERY = ( LWORK.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 + LIWMIN = 1 + LWMIN = 1 + ELSE + IF( WANTZ ) THEN + LIWMIN = 3 + 5*N + LWMIN = 1 + 6*N + 2*N**2 + ELSE + LIWMIN = 1 + LWMIN = 2*N + END IF + END IF + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN +* + IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -11 + ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN + INFO = -13 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSPGVD', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* Form a Cholesky factorization of BP. +* + CALL DPPTRF( UPLO, N, BP, INFO ) + IF( INFO.NE.0 ) THEN + INFO = N + INFO + RETURN + END IF +* +* Transform problem to standard eigenvalue problem and solve. +* + CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO ) + CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, + $ LIWORK, INFO ) + LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) ) + LIWMIN = MAX( DBLE( LIWMIN ), DBLE( 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 = 'T' + END IF +* + DO 10 J = 1, NEIG + CALL DTPSV( 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 = 'T' + ELSE + TRANS = 'N' + END IF +* + DO 20 J = 1, NEIG + CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), + $ 1 ) + 20 CONTINUE + END IF + END IF +* + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN +* + RETURN +* +* End of DSPGVD +* + END |