Annotation of rpl/lapack/lapack/zhegv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
! 2: $ LWORK, RWORK, 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 RWORK( * ), W( * )
! 15: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZHEGV computes all the eigenvalues, and optionally, the eigenvectors
! 22: * of a complex generalized Hermitian-definite eigenproblem, of the form
! 23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
! 24: * Here A and B are assumed to be Hermitian and B is also
! 25: * positive definite.
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * ITYPE (input) INTEGER
! 31: * Specifies the problem type to be solved:
! 32: * = 1: A*x = (lambda)*B*x
! 33: * = 2: A*B*x = (lambda)*x
! 34: * = 3: B*A*x = (lambda)*x
! 35: *
! 36: * JOBZ (input) CHARACTER*1
! 37: * = 'N': Compute eigenvalues only;
! 38: * = 'V': Compute eigenvalues and eigenvectors.
! 39: *
! 40: * UPLO (input) CHARACTER*1
! 41: * = 'U': Upper triangles of A and B are stored;
! 42: * = 'L': Lower triangles of A and B are stored.
! 43: *
! 44: * N (input) INTEGER
! 45: * The order of the matrices A and B. N >= 0.
! 46: *
! 47: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
! 48: * On entry, the Hermitian matrix A. If UPLO = 'U', the
! 49: * leading N-by-N upper triangular part of A contains the
! 50: * upper triangular part of the matrix A. If UPLO = 'L',
! 51: * the leading N-by-N lower triangular part of A contains
! 52: * the lower triangular part of the matrix A.
! 53: *
! 54: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 55: * matrix Z of eigenvectors. The eigenvectors are normalized
! 56: * as follows:
! 57: * if ITYPE = 1 or 2, Z**H*B*Z = I;
! 58: * if ITYPE = 3, Z**H*inv(B)*Z = I.
! 59: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
! 60: * or the lower triangle (if UPLO='L') of A, including the
! 61: * diagonal, is destroyed.
! 62: *
! 63: * LDA (input) INTEGER
! 64: * The leading dimension of the array A. LDA >= max(1,N).
! 65: *
! 66: * B (input/output) COMPLEX*16 array, dimension (LDB, N)
! 67: * On entry, the Hermitian positive definite matrix B.
! 68: * If UPLO = 'U', the leading N-by-N upper triangular part of B
! 69: * contains the upper triangular part of the matrix B.
! 70: * If UPLO = 'L', the leading N-by-N lower triangular part of B
! 71: * contains the lower triangular part of the matrix B.
! 72: *
! 73: * On exit, if INFO <= N, the part of B containing the matrix is
! 74: * overwritten by the triangular factor U or L from the Cholesky
! 75: * factorization B = U**H*U or B = L*L**H.
! 76: *
! 77: * LDB (input) INTEGER
! 78: * The leading dimension of the array B. LDB >= max(1,N).
! 79: *
! 80: * W (output) DOUBLE PRECISION array, dimension (N)
! 81: * If INFO = 0, the eigenvalues in ascending order.
! 82: *
! 83: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 84: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 85: *
! 86: * LWORK (input) INTEGER
! 87: * The length of the array WORK. LWORK >= max(1,2*N-1).
! 88: * For optimal efficiency, LWORK >= (NB+1)*N,
! 89: * where NB is the blocksize for ZHETRD returned by ILAENV.
! 90: *
! 91: * If LWORK = -1, then a workspace query is assumed; the routine
! 92: * only calculates the optimal size of the WORK array, returns
! 93: * this value as the first entry of the WORK array, and no error
! 94: * message related to LWORK is issued by XERBLA.
! 95: *
! 96: * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
! 97: *
! 98: * INFO (output) INTEGER
! 99: * = 0: successful exit
! 100: * < 0: if INFO = -i, the i-th argument had an illegal value
! 101: * > 0: ZPOTRF or ZHEEV returned an error code:
! 102: * <= N: if INFO = i, ZHEEV failed to converge;
! 103: * i off-diagonal elements of an intermediate
! 104: * tridiagonal form did not converge to zero;
! 105: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
! 106: * minor of order i of B is not positive definite.
! 107: * The factorization of B could not be completed and
! 108: * no eigenvalues or eigenvectors were computed.
! 109: *
! 110: * =====================================================================
! 111: *
! 112: * .. Parameters ..
! 113: COMPLEX*16 ONE
! 114: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
! 115: * ..
! 116: * .. Local Scalars ..
! 117: LOGICAL LQUERY, UPPER, WANTZ
! 118: CHARACTER TRANS
! 119: INTEGER LWKOPT, NB, NEIG
! 120: * ..
! 121: * .. External Functions ..
! 122: LOGICAL LSAME
! 123: INTEGER ILAENV
! 124: EXTERNAL LSAME, ILAENV
! 125: * ..
! 126: * .. External Subroutines ..
! 127: EXTERNAL XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
! 128: * ..
! 129: * .. Intrinsic Functions ..
! 130: INTRINSIC MAX
! 131: * ..
! 132: * .. Executable Statements ..
! 133: *
! 134: * Test the input parameters.
! 135: *
! 136: WANTZ = LSAME( JOBZ, 'V' )
! 137: UPPER = LSAME( UPLO, 'U' )
! 138: LQUERY = ( LWORK.EQ.-1 )
! 139: *
! 140: INFO = 0
! 141: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
! 142: INFO = -1
! 143: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 144: INFO = -2
! 145: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
! 146: INFO = -3
! 147: ELSE IF( N.LT.0 ) THEN
! 148: INFO = -4
! 149: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 150: INFO = -6
! 151: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 152: INFO = -8
! 153: END IF
! 154: *
! 155: IF( INFO.EQ.0 ) THEN
! 156: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
! 157: LWKOPT = MAX( 1, ( NB + 1 )*N )
! 158: WORK( 1 ) = LWKOPT
! 159: *
! 160: IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN
! 161: INFO = -11
! 162: END IF
! 163: END IF
! 164: *
! 165: IF( INFO.NE.0 ) THEN
! 166: CALL XERBLA( 'ZHEGV ', -INFO )
! 167: RETURN
! 168: ELSE IF( LQUERY ) THEN
! 169: RETURN
! 170: END IF
! 171: *
! 172: * Quick return if possible
! 173: *
! 174: IF( N.EQ.0 )
! 175: $ RETURN
! 176: *
! 177: * Form a Cholesky factorization of B.
! 178: *
! 179: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
! 180: IF( INFO.NE.0 ) THEN
! 181: INFO = N + INFO
! 182: RETURN
! 183: END IF
! 184: *
! 185: * Transform problem to standard eigenvalue problem and solve.
! 186: *
! 187: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
! 188: CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
! 189: *
! 190: IF( WANTZ ) THEN
! 191: *
! 192: * Backtransform eigenvectors to the original problem.
! 193: *
! 194: NEIG = N
! 195: IF( INFO.GT.0 )
! 196: $ NEIG = INFO - 1
! 197: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
! 198: *
! 199: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
! 200: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
! 201: *
! 202: IF( UPPER ) THEN
! 203: TRANS = 'N'
! 204: ELSE
! 205: TRANS = 'C'
! 206: END IF
! 207: *
! 208: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 209: $ B, LDB, A, LDA )
! 210: *
! 211: ELSE IF( ITYPE.EQ.3 ) THEN
! 212: *
! 213: * For B*A*x=(lambda)*x;
! 214: * backtransform eigenvectors: x = L*y or U'*y
! 215: *
! 216: IF( UPPER ) THEN
! 217: TRANS = 'C'
! 218: ELSE
! 219: TRANS = 'N'
! 220: END IF
! 221: *
! 222: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
! 223: $ B, LDB, A, LDA )
! 224: END IF
! 225: END IF
! 226: *
! 227: WORK( 1 ) = LWKOPT
! 228: *
! 229: RETURN
! 230: *
! 231: * End of ZHEGV
! 232: *
! 233: END
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