Annotation of rpl/lapack/lapack/zheev.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
! 2: $ 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, LDA, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION RWORK( * ), W( * )
! 15: COMPLEX*16 A( LDA, * ), WORK( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
! 22: * complex Hermitian matrix A.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * JOBZ (input) CHARACTER*1
! 28: * = 'N': Compute eigenvalues only;
! 29: * = 'V': Compute eigenvalues and eigenvectors.
! 30: *
! 31: * UPLO (input) CHARACTER*1
! 32: * = 'U': Upper triangle of A is stored;
! 33: * = 'L': Lower triangle of A is stored.
! 34: *
! 35: * N (input) INTEGER
! 36: * The order of the matrix A. N >= 0.
! 37: *
! 38: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
! 39: * On entry, the Hermitian matrix A. If UPLO = 'U', the
! 40: * leading N-by-N upper triangular part of A contains the
! 41: * upper triangular part of the matrix A. If UPLO = 'L',
! 42: * the leading N-by-N lower triangular part of A contains
! 43: * the lower triangular part of the matrix A.
! 44: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 45: * orthonormal eigenvectors of the matrix A.
! 46: * If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
! 47: * or the upper triangle (if UPLO='U') of A, including the
! 48: * diagonal, is destroyed.
! 49: *
! 50: * LDA (input) INTEGER
! 51: * The leading dimension of the array A. LDA >= max(1,N).
! 52: *
! 53: * W (output) DOUBLE PRECISION array, dimension (N)
! 54: * If INFO = 0, the eigenvalues in ascending order.
! 55: *
! 56: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 57: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 58: *
! 59: * LWORK (input) INTEGER
! 60: * The length of the array WORK. LWORK >= max(1,2*N-1).
! 61: * For optimal efficiency, LWORK >= (NB+1)*N,
! 62: * where NB is the blocksize for ZHETRD returned by ILAENV.
! 63: *
! 64: * If LWORK = -1, then a workspace query is assumed; the routine
! 65: * only calculates the optimal size of the WORK array, returns
! 66: * this value as the first entry of the WORK array, and no error
! 67: * message related to LWORK is issued by XERBLA.
! 68: *
! 69: * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
! 70: *
! 71: * INFO (output) INTEGER
! 72: * = 0: successful exit
! 73: * < 0: if INFO = -i, the i-th argument had an illegal value
! 74: * > 0: if INFO = i, the algorithm failed to converge; i
! 75: * off-diagonal elements of an intermediate tridiagonal
! 76: * form did not converge to zero.
! 77: *
! 78: * =====================================================================
! 79: *
! 80: * .. Parameters ..
! 81: DOUBLE PRECISION ZERO, ONE
! 82: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 83: COMPLEX*16 CONE
! 84: PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) )
! 85: * ..
! 86: * .. Local Scalars ..
! 87: LOGICAL LOWER, LQUERY, WANTZ
! 88: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
! 89: $ LLWORK, LWKOPT, NB
! 90: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 91: $ SMLNUM
! 92: * ..
! 93: * .. External Functions ..
! 94: LOGICAL LSAME
! 95: INTEGER ILAENV
! 96: DOUBLE PRECISION DLAMCH, ZLANHE
! 97: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE
! 98: * ..
! 99: * .. External Subroutines ..
! 100: EXTERNAL DSCAL, DSTERF, XERBLA, ZHETRD, ZLASCL, ZSTEQR,
! 101: $ ZUNGTR
! 102: * ..
! 103: * .. Intrinsic Functions ..
! 104: INTRINSIC MAX, SQRT
! 105: * ..
! 106: * .. Executable Statements ..
! 107: *
! 108: * Test the input parameters.
! 109: *
! 110: WANTZ = LSAME( JOBZ, 'V' )
! 111: LOWER = LSAME( UPLO, 'L' )
! 112: LQUERY = ( LWORK.EQ.-1 )
! 113: *
! 114: INFO = 0
! 115: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 116: INFO = -1
! 117: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 118: INFO = -2
! 119: ELSE IF( N.LT.0 ) THEN
! 120: INFO = -3
! 121: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 122: INFO = -5
! 123: END IF
! 124: *
! 125: IF( INFO.EQ.0 ) THEN
! 126: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
! 127: LWKOPT = MAX( 1, ( NB+1 )*N )
! 128: WORK( 1 ) = LWKOPT
! 129: *
! 130: IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY )
! 131: $ INFO = -8
! 132: END IF
! 133: *
! 134: IF( INFO.NE.0 ) THEN
! 135: CALL XERBLA( 'ZHEEV ', -INFO )
! 136: RETURN
! 137: ELSE IF( LQUERY ) THEN
! 138: RETURN
! 139: END IF
! 140: *
! 141: * Quick return if possible
! 142: *
! 143: IF( N.EQ.0 ) THEN
! 144: RETURN
! 145: END IF
! 146: *
! 147: IF( N.EQ.1 ) THEN
! 148: W( 1 ) = A( 1, 1 )
! 149: WORK( 1 ) = 1
! 150: IF( WANTZ )
! 151: $ A( 1, 1 ) = CONE
! 152: RETURN
! 153: END IF
! 154: *
! 155: * Get machine constants.
! 156: *
! 157: SAFMIN = DLAMCH( 'Safe minimum' )
! 158: EPS = DLAMCH( 'Precision' )
! 159: SMLNUM = SAFMIN / EPS
! 160: BIGNUM = ONE / SMLNUM
! 161: RMIN = SQRT( SMLNUM )
! 162: RMAX = SQRT( BIGNUM )
! 163: *
! 164: * Scale matrix to allowable range, if necessary.
! 165: *
! 166: ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK )
! 167: ISCALE = 0
! 168: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 169: ISCALE = 1
! 170: SIGMA = RMIN / ANRM
! 171: ELSE IF( ANRM.GT.RMAX ) THEN
! 172: ISCALE = 1
! 173: SIGMA = RMAX / ANRM
! 174: END IF
! 175: IF( ISCALE.EQ.1 )
! 176: $ CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
! 177: *
! 178: * Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
! 179: *
! 180: INDE = 1
! 181: INDTAU = 1
! 182: INDWRK = INDTAU + N
! 183: LLWORK = LWORK - INDWRK + 1
! 184: CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ),
! 185: $ WORK( INDWRK ), LLWORK, IINFO )
! 186: *
! 187: * For eigenvalues only, call DSTERF. For eigenvectors, first call
! 188: * ZUNGTR to generate the unitary matrix, then call ZSTEQR.
! 189: *
! 190: IF( .NOT.WANTZ ) THEN
! 191: CALL DSTERF( N, W, RWORK( INDE ), INFO )
! 192: ELSE
! 193: CALL ZUNGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
! 194: $ LLWORK, IINFO )
! 195: INDWRK = INDE + N
! 196: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), A, LDA,
! 197: $ RWORK( INDWRK ), INFO )
! 198: END IF
! 199: *
! 200: * If matrix was scaled, then rescale eigenvalues appropriately.
! 201: *
! 202: IF( ISCALE.EQ.1 ) THEN
! 203: IF( INFO.EQ.0 ) THEN
! 204: IMAX = N
! 205: ELSE
! 206: IMAX = INFO - 1
! 207: END IF
! 208: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 209: END IF
! 210: *
! 211: * Set WORK(1) to optimal complex workspace size.
! 212: *
! 213: WORK( 1 ) = LWKOPT
! 214: *
! 215: RETURN
! 216: *
! 217: * End of ZHEEV
! 218: *
! 219: END
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