Annotation of rpl/lapack/lapack/dsygv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
! 2: $ LWORK, INFO )
! 3: *
! 4: * -- LAPACK driver routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER JOBZ, UPLO
! 11: INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DSYGV computes all the eigenvalues, and optionally, the eigenvectors
! 21: * of a real generalized symmetric-definite eigenproblem, of the form
! 22: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
! 23: * Here A and B are assumed to be symmetric and B is also
! 24: * positive definite.
! 25: *
! 26: * Arguments
! 27: * =========
! 28: *
! 29: * ITYPE (input) INTEGER
! 30: * Specifies the problem type to be solved:
! 31: * = 1: A*x = (lambda)*B*x
! 32: * = 2: A*B*x = (lambda)*x
! 33: * = 3: B*A*x = (lambda)*x
! 34: *
! 35: * JOBZ (input) CHARACTER*1
! 36: * = 'N': Compute eigenvalues only;
! 37: * = 'V': Compute eigenvalues and eigenvectors.
! 38: *
! 39: * UPLO (input) CHARACTER*1
! 40: * = 'U': Upper triangles of A and B are stored;
! 41: * = 'L': Lower triangles of A and B are stored.
! 42: *
! 43: * N (input) INTEGER
! 44: * The order of the matrices A and B. N >= 0.
! 45: *
! 46: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
! 47: * On entry, the symmetric matrix A. If UPLO = 'U', the
! 48: * leading N-by-N upper triangular part of A contains the
! 49: * upper triangular part of the matrix A. If UPLO = 'L',
! 50: * the leading N-by-N lower triangular part of A contains
! 51: * the lower triangular part of the matrix A.
! 52: *
! 53: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 54: * matrix Z of eigenvectors. The eigenvectors are normalized
! 55: * as follows:
! 56: * if ITYPE = 1 or 2, Z**T*B*Z = I;
! 57: * if ITYPE = 3, Z**T*inv(B)*Z = I.
! 58: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
! 59: * or the lower triangle (if UPLO='L') of A, including the
! 60: * diagonal, is destroyed.
! 61: *
! 62: * LDA (input) INTEGER
! 63: * The leading dimension of the array A. LDA >= max(1,N).
! 64: *
! 65: * B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
! 66: * On entry, the symmetric positive definite matrix B.
! 67: * If UPLO = 'U', the leading N-by-N upper triangular part of B
! 68: * contains the upper triangular part of the matrix B.
! 69: * If UPLO = 'L', the leading N-by-N lower triangular part of B
! 70: * contains the lower triangular part of the matrix B.
! 71: *
! 72: * On exit, if INFO <= N, the part of B containing the matrix is
! 73: * overwritten by the triangular factor U or L from the Cholesky
! 74: * factorization B = U**T*U or B = L*L**T.
! 75: *
! 76: * LDB (input) INTEGER
! 77: * The leading dimension of the array B. LDB >= max(1,N).
! 78: *
! 79: * W (output) DOUBLE PRECISION array, dimension (N)
! 80: * If INFO = 0, the eigenvalues in ascending order.
! 81: *
! 82: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 83: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 84: *
! 85: * LWORK (input) INTEGER
! 86: * The length of the array WORK. LWORK >= max(1,3*N-1).
! 87: * For optimal efficiency, LWORK >= (NB+2)*N,
! 88: * where NB is the blocksize for DSYTRD returned by ILAENV.
! 89: *
! 90: * If LWORK = -1, then a workspace query is assumed; the routine
! 91: * only calculates the optimal size of the WORK array, returns
! 92: * this value as the first entry of the WORK array, and no error
! 93: * message related to LWORK is issued by XERBLA.
! 94: *
! 95: * INFO (output) INTEGER
! 96: * = 0: successful exit
! 97: * < 0: if INFO = -i, the i-th argument had an illegal value
! 98: * > 0: DPOTRF or DSYEV returned an error code:
! 99: * <= N: if INFO = i, DSYEV failed to converge;
! 100: * i off-diagonal elements of an intermediate
! 101: * tridiagonal form did not converge to zero;
! 102: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 103: * minor of order i of B is not positive definite.
! 104: * The factorization of B could not be completed and
! 105: * no eigenvalues or eigenvectors were computed.
! 106: *
! 107: * =====================================================================
! 108: *
! 109: * .. Parameters ..
! 110: DOUBLE PRECISION ONE
! 111: PARAMETER ( ONE = 1.0D+0 )
! 112: * ..
! 113: * .. Local Scalars ..
! 114: LOGICAL LQUERY, UPPER, WANTZ
! 115: CHARACTER TRANS
! 116: INTEGER LWKMIN, LWKOPT, NB, NEIG
! 117: * ..
! 118: * .. External Functions ..
! 119: LOGICAL LSAME
! 120: INTEGER ILAENV
! 121: EXTERNAL LSAME, ILAENV
! 122: * ..
! 123: * .. External Subroutines ..
! 124: EXTERNAL DPOTRF, DSYEV, DSYGST, DTRMM, DTRSM, XERBLA
! 125: * ..
! 126: * .. Intrinsic Functions ..
! 127: INTRINSIC MAX
! 128: * ..
! 129: * .. Executable Statements ..
! 130: *
! 131: * Test the input parameters.
! 132: *
! 133: WANTZ = LSAME( JOBZ, 'V' )
! 134: UPPER = LSAME( UPLO, 'U' )
! 135: LQUERY = ( LWORK.EQ.-1 )
! 136: *
! 137: INFO = 0
! 138: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 139: INFO = -1
! 140: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 141: INFO = -2
! 142: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 143: INFO = -3
! 144: ELSE IF( N.LT.0 ) THEN
! 145: INFO = -4
! 146: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 147: INFO = -6
! 148: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 149: INFO = -8
! 150: END IF
! 151: *
! 152: IF( INFO.EQ.0 ) THEN
! 153: LWKMIN = MAX( 1, 3*N - 1 )
! 154: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
! 155: LWKOPT = MAX( LWKMIN, ( NB + 2 )*N )
! 156: WORK( 1 ) = LWKOPT
! 157: *
! 158: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
! 159: INFO = -11
! 160: END IF
! 161: END IF
! 162: *
! 163: IF( INFO.NE.0 ) THEN
! 164: CALL XERBLA( 'DSYGV ', -INFO )
! 165: RETURN
! 166: ELSE IF( LQUERY ) THEN
! 167: RETURN
! 168: END IF
! 169: *
! 170: * Quick return if possible
! 171: *
! 172: IF( N.EQ.0 )
! 173: $ RETURN
! 174: *
! 175: * Form a Cholesky factorization of B.
! 176: *
! 177: CALL DPOTRF( UPLO, N, B, LDB, INFO )
! 178: IF( INFO.NE.0 ) THEN
! 179: INFO = N + INFO
! 180: RETURN
! 181: END IF
! 182: *
! 183: * Transform problem to standard eigenvalue problem and solve.
! 184: *
! 185: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 186: CALL DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
! 187: *
! 188: IF( WANTZ ) THEN
! 189: *
! 190: * Backtransform eigenvectors to the original problem.
! 191: *
! 192: NEIG = N
! 193: IF( INFO.GT.0 )
! 194: $ NEIG = INFO - 1
! 195: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 196: *
! 197: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 198: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 199: *
! 200: IF( UPPER ) THEN
! 201: TRANS = 'N'
! 202: ELSE
! 203: TRANS = 'T'
! 204: END IF
! 205: *
! 206: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 207: $ B, LDB, A, LDA )
! 208: *
! 209: ELSE IF( ITYPE.EQ.3 ) THEN
! 210: *
! 211: * For B*A*x=(lambda)*x;
! 212: * backtransform eigenvectors: x = L*y or U'*y
! 213: *
! 214: IF( UPPER ) THEN
! 215: TRANS = 'T'
! 216: ELSE
! 217: TRANS = 'N'
! 218: END IF
! 219: *
! 220: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 221: $ B, LDB, A, LDA )
! 222: END IF
! 223: END IF
! 224: *
! 225: WORK( 1 ) = LWKOPT
! 226: RETURN
! 227: *
! 228: * End of DSYGV
! 229: *
! 230: END
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