Annotation of rpl/lapack/lapack/zhegvd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
! 2: $ LWORK, RWORK, LRWORK, 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, LRWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION RWORK( * ), W( * )
! 16: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
! 23: * of a complex generalized Hermitian-definite eigenproblem, of the form
! 24: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
! 25: * B are assumed to be Hermitian and B is also positive definite.
! 26: * If eigenvectors are desired, it uses a divide and conquer algorithm.
! 27: *
! 28: * The divide and conquer algorithm makes very mild assumptions about
! 29: * floating point arithmetic. It will work on machines with a guard
! 30: * digit in add/subtract, or on those binary machines without guard
! 31: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 32: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 33: * without guard digits, but we know of none.
! 34: *
! 35: * Arguments
! 36: * =========
! 37: *
! 38: * ITYPE (input) INTEGER
! 39: * Specifies the problem type to be solved:
! 40: * = 1: A*x = (lambda)*B*x
! 41: * = 2: A*B*x = (lambda)*x
! 42: * = 3: B*A*x = (lambda)*x
! 43: *
! 44: * JOBZ (input) CHARACTER*1
! 45: * = 'N': Compute eigenvalues only;
! 46: * = 'V': Compute eigenvalues and eigenvectors.
! 47: *
! 48: * UPLO (input) CHARACTER*1
! 49: * = 'U': Upper triangles of A and B are stored;
! 50: * = 'L': Lower triangles of A and B are stored.
! 51: *
! 52: * N (input) INTEGER
! 53: * The order of the matrices A and B. N >= 0.
! 54: *
! 55: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
! 56: * On entry, the Hermitian matrix A. If UPLO = 'U', the
! 57: * leading N-by-N upper triangular part of A contains the
! 58: * upper triangular part of the matrix A. If UPLO = 'L',
! 59: * the leading N-by-N lower triangular part of A contains
! 60: * the lower triangular part of the matrix A.
! 61: *
! 62: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 63: * matrix Z of eigenvectors. The eigenvectors are normalized
! 64: * as follows:
! 65: * if ITYPE = 1 or 2, Z**H*B*Z = I;
! 66: * if ITYPE = 3, Z**H*inv(B)*Z = I.
! 67: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
! 68: * or the lower triangle (if UPLO='L') of A, including the
! 69: * diagonal, is destroyed.
! 70: *
! 71: * LDA (input) INTEGER
! 72: * The leading dimension of the array A. LDA >= max(1,N).
! 73: *
! 74: * B (input/output) COMPLEX*16 array, dimension (LDB, N)
! 75: * On entry, the Hermitian matrix B. If UPLO = 'U', the
! 76: * leading N-by-N upper triangular part of B contains the
! 77: * upper triangular part of the matrix B. If UPLO = 'L',
! 78: * the leading N-by-N lower triangular part of B contains
! 79: * the lower triangular part of the matrix B.
! 80: *
! 81: * On exit, if INFO <= N, the part of B containing the matrix is
! 82: * overwritten by the triangular factor U or L from the Cholesky
! 83: * factorization B = U**H*U or B = L*L**H.
! 84: *
! 85: * LDB (input) INTEGER
! 86: * The leading dimension of the array B. LDB >= max(1,N).
! 87: *
! 88: * W (output) DOUBLE PRECISION array, dimension (N)
! 89: * If INFO = 0, the eigenvalues in ascending order.
! 90: *
! 91: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 92: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 93: *
! 94: * LWORK (input) INTEGER
! 95: * The length of the array WORK.
! 96: * If N <= 1, LWORK >= 1.
! 97: * If JOBZ = 'N' and N > 1, LWORK >= N + 1.
! 98: * If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.
! 99: *
! 100: * If LWORK = -1, then a workspace query is assumed; the routine
! 101: * only calculates the optimal sizes of the WORK, RWORK and
! 102: * IWORK arrays, returns these values as the first entries of
! 103: * the WORK, RWORK and IWORK arrays, and no error message
! 104: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 105: *
! 106: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
! 107: * On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
! 108: *
! 109: * LRWORK (input) INTEGER
! 110: * The dimension of the array RWORK.
! 111: * If N <= 1, LRWORK >= 1.
! 112: * If JOBZ = 'N' and N > 1, LRWORK >= N.
! 113: * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
! 114: *
! 115: * If LRWORK = -1, then a workspace query is assumed; the
! 116: * routine only calculates the optimal sizes of the WORK, RWORK
! 117: * and IWORK arrays, returns these values as the first entries
! 118: * of the WORK, RWORK and IWORK arrays, and no error message
! 119: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 120: *
! 121: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 122: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 123: *
! 124: * LIWORK (input) INTEGER
! 125: * The dimension of the array IWORK.
! 126: * If N <= 1, LIWORK >= 1.
! 127: * If JOBZ = 'N' and N > 1, LIWORK >= 1.
! 128: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
! 129: *
! 130: * If LIWORK = -1, then a workspace query is assumed; the
! 131: * routine only calculates the optimal sizes of the WORK, RWORK
! 132: * and IWORK arrays, returns these values as the first entries
! 133: * of the WORK, RWORK and IWORK arrays, and no error message
! 134: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 135: *
! 136: * INFO (output) INTEGER
! 137: * = 0: successful exit
! 138: * < 0: if INFO = -i, the i-th argument had an illegal value
! 139: * > 0: ZPOTRF or ZHEEVD returned an error code:
! 140: * <= N: if INFO = i and JOBZ = 'N', then the algorithm
! 141: * failed to converge; i off-diagonal elements of an
! 142: * intermediate tridiagonal form did not converge to
! 143: * zero;
! 144: * if INFO = i and JOBZ = 'V', then the algorithm
! 145: * failed to compute an eigenvalue while working on
! 146: * the submatrix lying in rows and columns INFO/(N+1)
! 147: * through mod(INFO,N+1);
! 148: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 149: * minor of order i of B is not positive definite.
! 150: * The factorization of B could not be completed and
! 151: * no eigenvalues or eigenvectors were computed.
! 152: *
! 153: * Further Details
! 154: * ===============
! 155: *
! 156: * Based on contributions by
! 157: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 158: *
! 159: * Modified so that no backsubstitution is performed if ZHEEVD fails to
! 160: * converge (NEIG in old code could be greater than N causing out of
! 161: * bounds reference to A - reported by Ralf Meyer). Also corrected the
! 162: * description of INFO and the test on ITYPE. Sven, 16 Feb 05.
! 163: * =====================================================================
! 164: *
! 165: * .. Parameters ..
! 166: COMPLEX*16 CONE
! 167: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 168: * ..
! 169: * .. Local Scalars ..
! 170: LOGICAL LQUERY, UPPER, WANTZ
! 171: CHARACTER TRANS
! 172: INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN
! 173: * ..
! 174: * .. External Functions ..
! 175: LOGICAL LSAME
! 176: EXTERNAL LSAME
! 177: * ..
! 178: * .. External Subroutines ..
! 179: EXTERNAL XERBLA, ZHEEVD, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
! 180: * ..
! 181: * .. Intrinsic Functions ..
! 182: INTRINSIC DBLE, MAX
! 183: * ..
! 184: * .. Executable Statements ..
! 185: *
! 186: * Test the input parameters.
! 187: *
! 188: WANTZ = LSAME( JOBZ, 'V' )
! 189: UPPER = LSAME( UPLO, 'U' )
! 190: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 191: *
! 192: INFO = 0
! 193: IF( N.LE.1 ) THEN
! 194: LWMIN = 1
! 195: LRWMIN = 1
! 196: LIWMIN = 1
! 197: ELSE IF( WANTZ ) THEN
! 198: LWMIN = 2*N + N*N
! 199: LRWMIN = 1 + 5*N + 2*N*N
! 200: LIWMIN = 3 + 5*N
! 201: ELSE
! 202: LWMIN = N + 1
! 203: LRWMIN = N
! 204: LIWMIN = 1
! 205: END IF
! 206: LOPT = LWMIN
! 207: LROPT = LRWMIN
! 208: LIOPT = LIWMIN
! 209: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 210: INFO = -1
! 211: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 212: INFO = -2
! 213: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 214: INFO = -3
! 215: ELSE IF( N.LT.0 ) THEN
! 216: INFO = -4
! 217: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 218: INFO = -6
! 219: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 220: INFO = -8
! 221: END IF
! 222: *
! 223: IF( INFO.EQ.0 ) THEN
! 224: WORK( 1 ) = LOPT
! 225: RWORK( 1 ) = LROPT
! 226: IWORK( 1 ) = LIOPT
! 227: *
! 228: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 229: INFO = -11
! 230: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
! 231: INFO = -13
! 232: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 233: INFO = -15
! 234: END IF
! 235: END IF
! 236: *
! 237: IF( INFO.NE.0 ) THEN
! 238: CALL XERBLA( 'ZHEGVD', -INFO )
! 239: RETURN
! 240: ELSE IF( LQUERY ) THEN
! 241: RETURN
! 242: END IF
! 243: *
! 244: * Quick return if possible
! 245: *
! 246: IF( N.EQ.0 )
! 247: $ RETURN
! 248: *
! 249: * Form a Cholesky factorization of B.
! 250: *
! 251: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
! 252: IF( INFO.NE.0 ) THEN
! 253: INFO = N + INFO
! 254: RETURN
! 255: END IF
! 256: *
! 257: * Transform problem to standard eigenvalue problem and solve.
! 258: *
! 259: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 260: CALL ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
! 261: $ IWORK, LIWORK, INFO )
! 262: LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) )
! 263: LROPT = MAX( DBLE( LROPT ), DBLE( RWORK( 1 ) ) )
! 264: LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) )
! 265: *
! 266: IF( WANTZ .AND. INFO.EQ.0 ) THEN
! 267: *
! 268: * Backtransform eigenvectors to the original problem.
! 269: *
! 270: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 271: *
! 272: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 273: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 274: *
! 275: IF( UPPER ) THEN
! 276: TRANS = 'N'
! 277: ELSE
! 278: TRANS = 'C'
! 279: END IF
! 280: *
! 281: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
! 282: $ B, LDB, A, LDA )
! 283: *
! 284: ELSE IF( ITYPE.EQ.3 ) THEN
! 285: *
! 286: * For B*A*x=(lambda)*x;
! 287: * backtransform eigenvectors: x = L*y or U'*y
! 288: *
! 289: IF( UPPER ) THEN
! 290: TRANS = 'C'
! 291: ELSE
! 292: TRANS = 'N'
! 293: END IF
! 294: *
! 295: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
! 296: $ B, LDB, A, LDA )
! 297: END IF
! 298: END IF
! 299: *
! 300: WORK( 1 ) = LOPT
! 301: RWORK( 1 ) = LROPT
! 302: IWORK( 1 ) = LIOPT
! 303: *
! 304: RETURN
! 305: *
! 306: * End of ZHEGVD
! 307: *
! 308: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zhegvd.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack