Annotation of rpl/lapack/lapack/dsygvd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
! 2: $ LWORK, IWORK, LIWORK, 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, LIWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DSYGVD computes all the eigenvalues, and optionally, the eigenvectors
! 22: * of a real generalized symmetric-definite eigenproblem, of the form
! 23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
! 24: * B are assumed to be symmetric and B is also positive definite.
! 25: * If eigenvectors are desired, it uses a divide and conquer algorithm.
! 26: *
! 27: * The divide and conquer algorithm makes very mild assumptions about
! 28: * floating point arithmetic. It will work on machines with a guard
! 29: * digit in add/subtract, or on those binary machines without guard
! 30: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 31: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 32: * without guard digits, but we know of none.
! 33: *
! 34: * Arguments
! 35: * =========
! 36: *
! 37: * ITYPE (input) INTEGER
! 38: * Specifies the problem type to be solved:
! 39: * = 1: A*x = (lambda)*B*x
! 40: * = 2: A*B*x = (lambda)*x
! 41: * = 3: B*A*x = (lambda)*x
! 42: *
! 43: * JOBZ (input) CHARACTER*1
! 44: * = 'N': Compute eigenvalues only;
! 45: * = 'V': Compute eigenvalues and eigenvectors.
! 46: *
! 47: * UPLO (input) CHARACTER*1
! 48: * = 'U': Upper triangles of A and B are stored;
! 49: * = 'L': Lower triangles of A and B are stored.
! 50: *
! 51: * N (input) INTEGER
! 52: * The order of the matrices A and B. N >= 0.
! 53: *
! 54: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
! 55: * On entry, the symmetric matrix A. If UPLO = 'U', the
! 56: * leading N-by-N upper triangular part of A contains the
! 57: * upper triangular part of the matrix A. If UPLO = 'L',
! 58: * the leading N-by-N lower triangular part of A contains
! 59: * the lower triangular part of the matrix A.
! 60: *
! 61: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 62: * matrix Z of eigenvectors. The eigenvectors are normalized
! 63: * as follows:
! 64: * if ITYPE = 1 or 2, Z**T*B*Z = I;
! 65: * if ITYPE = 3, Z**T*inv(B)*Z = I.
! 66: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
! 67: * or the lower triangle (if UPLO='L') of A, including the
! 68: * diagonal, is destroyed.
! 69: *
! 70: * LDA (input) INTEGER
! 71: * The leading dimension of the array A. LDA >= max(1,N).
! 72: *
! 73: * B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
! 74: * On entry, the symmetric matrix B. If UPLO = 'U', the
! 75: * leading N-by-N upper triangular part of B contains the
! 76: * upper triangular part of the matrix B. If UPLO = 'L',
! 77: * the leading N-by-N lower triangular part of B contains
! 78: * the lower triangular part of the matrix B.
! 79: *
! 80: * On exit, if INFO <= N, the part of B containing the matrix is
! 81: * overwritten by the triangular factor U or L from the Cholesky
! 82: * factorization B = U**T*U or B = L*L**T.
! 83: *
! 84: * LDB (input) INTEGER
! 85: * The leading dimension of the array B. LDB >= max(1,N).
! 86: *
! 87: * W (output) DOUBLE PRECISION array, dimension (N)
! 88: * If INFO = 0, the eigenvalues in ascending order.
! 89: *
! 90: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 91: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 92: *
! 93: * LWORK (input) INTEGER
! 94: * The dimension of the array WORK.
! 95: * If N <= 1, LWORK >= 1.
! 96: * If JOBZ = 'N' and N > 1, LWORK >= 2*N+1.
! 97: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
! 98: *
! 99: * If LWORK = -1, then a workspace query is assumed; the routine
! 100: * only calculates the optimal sizes of the WORK and IWORK
! 101: * arrays, returns these values as the first entries of the WORK
! 102: * and IWORK arrays, and no error message related to LWORK or
! 103: * LIWORK is issued by XERBLA.
! 104: *
! 105: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 106: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 107: *
! 108: * LIWORK (input) INTEGER
! 109: * The dimension of the array IWORK.
! 110: * If N <= 1, LIWORK >= 1.
! 111: * If JOBZ = 'N' and N > 1, LIWORK >= 1.
! 112: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 113: *
! 114: * If LIWORK = -1, then a workspace query is assumed; the
! 115: * routine only calculates the optimal sizes of the WORK and
! 116: * IWORK arrays, returns these values as the first entries of
! 117: * the WORK and IWORK arrays, and no error message related to
! 118: * LWORK or LIWORK is issued by XERBLA.
! 119: *
! 120: * INFO (output) INTEGER
! 121: * = 0: successful exit
! 122: * < 0: if INFO = -i, the i-th argument had an illegal value
! 123: * > 0: DPOTRF or DSYEVD returned an error code:
! 124: * <= N: if INFO = i and JOBZ = 'N', then the algorithm
! 125: * failed to converge; i off-diagonal elements of an
! 126: * intermediate tridiagonal form did not converge to
! 127: * zero;
! 128: * if INFO = i and JOBZ = 'V', then the algorithm
! 129: * failed to compute an eigenvalue while working on
! 130: * the submatrix lying in rows and columns INFO/(N+1)
! 131: * through mod(INFO,N+1);
! 132: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 133: * minor of order i of B is not positive definite.
! 134: * The factorization of B could not be completed and
! 135: * no eigenvalues or eigenvectors were computed.
! 136: *
! 137: * Further Details
! 138: * ===============
! 139: *
! 140: * Based on contributions by
! 141: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 142: *
! 143: * Modified so that no backsubstitution is performed if DSYEVD fails to
! 144: * converge (NEIG in old code could be greater than N causing out of
! 145: * bounds reference to A - reported by Ralf Meyer). Also corrected the
! 146: * description of INFO and the test on ITYPE. Sven, 16 Feb 05.
! 147: * =====================================================================
! 148: *
! 149: * .. Parameters ..
! 150: DOUBLE PRECISION ONE
! 151: PARAMETER ( ONE = 1.0D+0 )
! 152: * ..
! 153: * .. Local Scalars ..
! 154: LOGICAL LQUERY, UPPER, WANTZ
! 155: CHARACTER TRANS
! 156: INTEGER LIOPT, LIWMIN, LOPT, LWMIN
! 157: * ..
! 158: * .. External Functions ..
! 159: LOGICAL LSAME
! 160: EXTERNAL LSAME
! 161: * ..
! 162: * .. External Subroutines ..
! 163: EXTERNAL DPOTRF, DSYEVD, DSYGST, DTRMM, DTRSM, XERBLA
! 164: * ..
! 165: * .. Intrinsic Functions ..
! 166: INTRINSIC DBLE, MAX
! 167: * ..
! 168: * .. Executable Statements ..
! 169: *
! 170: * Test the input parameters.
! 171: *
! 172: WANTZ = LSAME( JOBZ, 'V' )
! 173: UPPER = LSAME( UPLO, 'U' )
! 174: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 175: *
! 176: INFO = 0
! 177: IF( N.LE.1 ) THEN
! 178: LIWMIN = 1
! 179: LWMIN = 1
! 180: ELSE IF( WANTZ ) THEN
! 181: LIWMIN = 3 + 5*N
! 182: LWMIN = 1 + 6*N + 2*N**2
! 183: ELSE
! 184: LIWMIN = 1
! 185: LWMIN = 2*N + 1
! 186: END IF
! 187: LOPT = LWMIN
! 188: LIOPT = LIWMIN
! 189: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 190: INFO = -1
! 191: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 192: INFO = -2
! 193: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 194: INFO = -3
! 195: ELSE IF( N.LT.0 ) THEN
! 196: INFO = -4
! 197: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 198: INFO = -6
! 199: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 200: INFO = -8
! 201: END IF
! 202: *
! 203: IF( INFO.EQ.0 ) THEN
! 204: WORK( 1 ) = LOPT
! 205: IWORK( 1 ) = LIOPT
! 206: *
! 207: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 208: INFO = -11
! 209: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 210: INFO = -13
! 211: END IF
! 212: END IF
! 213: *
! 214: IF( INFO.NE.0 ) THEN
! 215: CALL XERBLA( 'DSYGVD', -INFO )
! 216: RETURN
! 217: ELSE IF( LQUERY ) THEN
! 218: RETURN
! 219: END IF
! 220: *
! 221: * Quick return if possible
! 222: *
! 223: IF( N.EQ.0 )
! 224: $ RETURN
! 225: *
! 226: * Form a Cholesky factorization of B.
! 227: *
! 228: CALL DPOTRF( UPLO, N, B, LDB, INFO )
! 229: IF( INFO.NE.0 ) THEN
! 230: INFO = N + INFO
! 231: RETURN
! 232: END IF
! 233: *
! 234: * Transform problem to standard eigenvalue problem and solve.
! 235: *
! 236: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 237: CALL DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK,
! 238: $ INFO )
! 239: LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) )
! 240: LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) )
! 241: *
! 242: IF( WANTZ .AND. INFO.EQ.0 ) THEN
! 243: *
! 244: * Backtransform eigenvectors to the original problem.
! 245: *
! 246: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 247: *
! 248: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 249: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 250: *
! 251: IF( UPPER ) THEN
! 252: TRANS = 'N'
! 253: ELSE
! 254: TRANS = 'T'
! 255: END IF
! 256: *
! 257: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
! 258: $ B, LDB, A, LDA )
! 259: *
! 260: ELSE IF( ITYPE.EQ.3 ) THEN
! 261: *
! 262: * For B*A*x=(lambda)*x;
! 263: * backtransform eigenvectors: x = L*y or U'*y
! 264: *
! 265: IF( UPPER ) THEN
! 266: TRANS = 'T'
! 267: ELSE
! 268: TRANS = 'N'
! 269: END IF
! 270: *
! 271: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
! 272: $ B, LDB, A, LDA )
! 273: END IF
! 274: END IF
! 275: *
! 276: WORK( 1 ) = LOPT
! 277: IWORK( 1 ) = LIOPT
! 278: *
! 279: RETURN
! 280: *
! 281: * End of DSYGVD
! 282: *
! 283: END
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