Annotation of rpl/lapack/lapack/zhegvx.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
! 2: $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
! 3: $ LWORK, RWORK, IWORK, IFAIL, INFO )
! 4: *
! 5: * -- LAPACK driver routine (version 3.2) --
! 6: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 8: * November 2006
! 9: *
! 10: * .. Scalar Arguments ..
! 11: CHARACTER JOBZ, RANGE, UPLO
! 12: INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N
! 13: DOUBLE PRECISION ABSTOL, VL, VU
! 14: * ..
! 15: * .. Array Arguments ..
! 16: INTEGER IFAIL( * ), IWORK( * )
! 17: DOUBLE PRECISION RWORK( * ), W( * )
! 18: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
! 19: $ Z( LDZ, * )
! 20: * ..
! 21: *
! 22: * Purpose
! 23: * =======
! 24: *
! 25: * ZHEGVX computes selected eigenvalues, and optionally, eigenvectors
! 26: * of a complex generalized Hermitian-definite eigenproblem, of the form
! 27: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
! 28: * B are assumed to be Hermitian and B is also positive definite.
! 29: * Eigenvalues and eigenvectors can be selected by specifying either a
! 30: * range of values or a range of indices for the desired eigenvalues.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * ITYPE (input) INTEGER
! 36: * Specifies the problem type to be solved:
! 37: * = 1: A*x = (lambda)*B*x
! 38: * = 2: A*B*x = (lambda)*x
! 39: * = 3: B*A*x = (lambda)*x
! 40: *
! 41: * JOBZ (input) CHARACTER*1
! 42: * = 'N': Compute eigenvalues only;
! 43: * = 'V': Compute eigenvalues and eigenvectors.
! 44: *
! 45: * RANGE (input) CHARACTER*1
! 46: * = 'A': all eigenvalues will be found.
! 47: * = 'V': all eigenvalues in the half-open interval (VL,VU]
! 48: * will be found.
! 49: * = 'I': the IL-th through IU-th eigenvalues will be found.
! 50: **
! 51: * UPLO (input) CHARACTER*1
! 52: * = 'U': Upper triangles of A and B are stored;
! 53: * = 'L': Lower triangles of A and B are stored.
! 54: *
! 55: * N (input) INTEGER
! 56: * The order of the matrices A and B. N >= 0.
! 57: *
! 58: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
! 59: * On entry, the Hermitian matrix A. If UPLO = 'U', the
! 60: * leading N-by-N upper triangular part of A contains the
! 61: * upper triangular part of the matrix A. If UPLO = 'L',
! 62: * the leading N-by-N lower triangular part of A contains
! 63: * the lower triangular part of the matrix A.
! 64: *
! 65: * On exit, the lower triangle (if UPLO='L') or the upper
! 66: * triangle (if UPLO='U') of A, including the diagonal, is
! 67: * destroyed.
! 68: *
! 69: * LDA (input) INTEGER
! 70: * The leading dimension of the array A. LDA >= max(1,N).
! 71: *
! 72: * B (input/output) COMPLEX*16 array, dimension (LDB, N)
! 73: * On entry, the Hermitian matrix B. If UPLO = 'U', the
! 74: * leading N-by-N upper triangular part of B contains the
! 75: * upper triangular part of the matrix B. If UPLO = 'L',
! 76: * the leading N-by-N lower triangular part of B contains
! 77: * the lower triangular part of the matrix B.
! 78: *
! 79: * On exit, if INFO <= N, the part of B containing the matrix is
! 80: * overwritten by the triangular factor U or L from the Cholesky
! 81: * factorization B = U**H*U or B = L*L**H.
! 82: *
! 83: * LDB (input) INTEGER
! 84: * The leading dimension of the array B. LDB >= max(1,N).
! 85: *
! 86: * VL (input) DOUBLE PRECISION
! 87: * VU (input) DOUBLE PRECISION
! 88: * If RANGE='V', the lower and upper bounds of the interval to
! 89: * be searched for eigenvalues. VL < VU.
! 90: * Not referenced if RANGE = 'A' or 'I'.
! 91: *
! 92: * IL (input) INTEGER
! 93: * IU (input) INTEGER
! 94: * If RANGE='I', the indices (in ascending order) of the
! 95: * smallest and largest eigenvalues to be returned.
! 96: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
! 97: * Not referenced if RANGE = 'A' or 'V'.
! 98: *
! 99: * ABSTOL (input) DOUBLE PRECISION
! 100: * The absolute error tolerance for the eigenvalues.
! 101: * An approximate eigenvalue is accepted as converged
! 102: * when it is determined to lie in an interval [a,b]
! 103: * of width less than or equal to
! 104: *
! 105: * ABSTOL + EPS * max( |a|,|b| ) ,
! 106: *
! 107: * where EPS is the machine precision. If ABSTOL is less than
! 108: * or equal to zero, then EPS*|T| will be used in its place,
! 109: * where |T| is the 1-norm of the tridiagonal matrix obtained
! 110: * by reducing A to tridiagonal form.
! 111: *
! 112: * Eigenvalues will be computed most accurately when ABSTOL is
! 113: * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
! 114: * If this routine returns with INFO>0, indicating that some
! 115: * eigenvectors did not converge, try setting ABSTOL to
! 116: * 2*DLAMCH('S').
! 117: *
! 118: * M (output) INTEGER
! 119: * The total number of eigenvalues found. 0 <= M <= N.
! 120: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
! 121: *
! 122: * W (output) DOUBLE PRECISION array, dimension (N)
! 123: * The first M elements contain the selected
! 124: * eigenvalues in ascending order.
! 125: *
! 126: * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
! 127: * If JOBZ = 'N', then Z is not referenced.
! 128: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
! 129: * contain the orthonormal eigenvectors of the matrix A
! 130: * corresponding to the selected eigenvalues, with the i-th
! 131: * column of Z holding the eigenvector associated with W(i).
! 132: * The eigenvectors are normalized as follows:
! 133: * if ITYPE = 1 or 2, Z**T*B*Z = I;
! 134: * if ITYPE = 3, Z**T*inv(B)*Z = I.
! 135: *
! 136: * If an eigenvector fails to converge, then that column of Z
! 137: * contains the latest approximation to the eigenvector, and the
! 138: * index of the eigenvector is returned in IFAIL.
! 139: * Note: the user must ensure that at least max(1,M) columns are
! 140: * supplied in the array Z; if RANGE = 'V', the exact value of M
! 141: * is not known in advance and an upper bound must be used.
! 142: *
! 143: * LDZ (input) INTEGER
! 144: * The leading dimension of the array Z. LDZ >= 1, and if
! 145: * JOBZ = 'V', LDZ >= max(1,N).
! 146: *
! 147: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 148: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 149: *
! 150: * LWORK (input) INTEGER
! 151: * The length of the array WORK. LWORK >= max(1,2*N).
! 152: * For optimal efficiency, LWORK >= (NB+1)*N,
! 153: * where NB is the blocksize for ZHETRD returned by ILAENV.
! 154: *
! 155: * If LWORK = -1, then a workspace query is assumed; the routine
! 156: * only calculates the optimal size of the WORK array, returns
! 157: * this value as the first entry of the WORK array, and no error
! 158: * message related to LWORK is issued by XERBLA.
! 159: *
! 160: * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
! 161: *
! 162: * IWORK (workspace) INTEGER array, dimension (5*N)
! 163: *
! 164: * IFAIL (output) INTEGER array, dimension (N)
! 165: * If JOBZ = 'V', then if INFO = 0, the first M elements of
! 166: * IFAIL are zero. If INFO > 0, then IFAIL contains the
! 167: * indices of the eigenvectors that failed to converge.
! 168: * If JOBZ = 'N', then IFAIL is not referenced.
! 169: *
! 170: * INFO (output) INTEGER
! 171: * = 0: successful exit
! 172: * < 0: if INFO = -i, the i-th argument had an illegal value
! 173: * > 0: ZPOTRF or ZHEEVX returned an error code:
! 174: * <= N: if INFO = i, ZHEEVX failed to converge;
! 175: * i eigenvectors failed to converge. Their indices
! 176: * are stored in array IFAIL.
! 177: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 178: * minor of order i of B is not positive definite.
! 179: * The factorization of B could not be completed and
! 180: * no eigenvalues or eigenvectors were computed.
! 181: *
! 182: * Further Details
! 183: * ===============
! 184: *
! 185: * Based on contributions by
! 186: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
! 187: *
! 188: * =====================================================================
! 189: *
! 190: * .. Parameters ..
! 191: COMPLEX*16 CONE
! 192: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 193: * ..
! 194: * .. Local Scalars ..
! 195: LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ
! 196: CHARACTER TRANS
! 197: INTEGER LWKOPT, NB
! 198: * ..
! 199: * .. External Functions ..
! 200: LOGICAL LSAME
! 201: INTEGER ILAENV
! 202: EXTERNAL LSAME, ILAENV
! 203: * ..
! 204: * .. External Subroutines ..
! 205: EXTERNAL XERBLA, ZHEEVX, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
! 206: * ..
! 207: * .. Intrinsic Functions ..
! 208: INTRINSIC MAX, MIN
! 209: * ..
! 210: * .. Executable Statements ..
! 211: *
! 212: * Test the input parameters.
! 213: *
! 214: WANTZ = LSAME( JOBZ, 'V' )
! 215: UPPER = LSAME( UPLO, 'U' )
! 216: ALLEIG = LSAME( RANGE, 'A' )
! 217: VALEIG = LSAME( RANGE, 'V' )
! 218: INDEIG = LSAME( RANGE, 'I' )
! 219: LQUERY = ( LWORK.EQ.-1 )
! 220: *
! 221: INFO = 0
! 222: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 223: INFO = -1
! 224: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 225: INFO = -2
! 226: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
! 227: INFO = -3
! 228: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 229: INFO = -4
! 230: ELSE IF( N.LT.0 ) THEN
! 231: INFO = -5
! 232: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 233: INFO = -7
! 234: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 235: INFO = -9
! 236: ELSE
! 237: IF( VALEIG ) THEN
! 238: IF( N.GT.0 .AND. VU.LE.VL )
! 239: $ INFO = -11
! 240: ELSE IF( INDEIG ) THEN
! 241: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
! 242: INFO = -12
! 243: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
! 244: INFO = -13
! 245: END IF
! 246: END IF
! 247: END IF
! 248: IF (INFO.EQ.0) THEN
! 249: IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN
! 250: INFO = -18
! 251: END IF
! 252: END IF
! 253: *
! 254: IF( INFO.EQ.0 ) THEN
! 255: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
! 256: LWKOPT = MAX( 1, ( NB + 1 )*N )
! 257: WORK( 1 ) = LWKOPT
! 258: *
! 259: IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
! 260: INFO = -20
! 261: END IF
! 262: END IF
! 263: *
! 264: IF( INFO.NE.0 ) THEN
! 265: CALL XERBLA( 'ZHEGVX', -INFO )
! 266: RETURN
! 267: ELSE IF( LQUERY ) THEN
! 268: RETURN
! 269: END IF
! 270: *
! 271: * Quick return if possible
! 272: *
! 273: M = 0
! 274: IF( N.EQ.0 ) THEN
! 275: RETURN
! 276: END IF
! 277: *
! 278: * Form a Cholesky factorization of B.
! 279: *
! 280: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
! 281: IF( INFO.NE.0 ) THEN
! 282: INFO = N + INFO
! 283: RETURN
! 284: END IF
! 285: *
! 286: * Transform problem to standard eigenvalue problem and solve.
! 287: *
! 288: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 289: CALL ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,
! 290: $ M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL,
! 291: $ INFO )
! 292: *
! 293: IF( WANTZ ) THEN
! 294: *
! 295: * Backtransform eigenvectors to the original problem.
! 296: *
! 297: IF( INFO.GT.0 )
! 298: $ M = INFO - 1
! 299: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 300: *
! 301: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 302: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 303: *
! 304: IF( UPPER ) THEN
! 305: TRANS = 'N'
! 306: ELSE
! 307: TRANS = 'C'
! 308: END IF
! 309: *
! 310: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B,
! 311: $ LDB, Z, LDZ )
! 312: *
! 313: ELSE IF( ITYPE.EQ.3 ) THEN
! 314: *
! 315: * For B*A*x=(lambda)*x;
! 316: * backtransform eigenvectors: x = L*y or U'*y
! 317: *
! 318: IF( UPPER ) THEN
! 319: TRANS = 'C'
! 320: ELSE
! 321: TRANS = 'N'
! 322: END IF
! 323: *
! 324: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B,
! 325: $ LDB, Z, LDZ )
! 326: END IF
! 327: END IF
! 328: *
! 329: * Set WORK(1) to optimal complex workspace size.
! 330: *
! 331: WORK( 1 ) = LWKOPT
! 332: *
! 333: RETURN
! 334: *
! 335: * End of ZHEGVX
! 336: *
! 337: END
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