Annotation of rpl/lapack/lapack/zhbev.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
! 2: $ 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, KD, LDAB, LDZ, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION RWORK( * ), W( * )
! 15: COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
! 22: * a complex Hermitian band 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: * KD (input) INTEGER
! 39: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 40: * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 41: *
! 42: * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
! 43: * On entry, the upper or lower triangle of the Hermitian band
! 44: * matrix A, stored in the first KD+1 rows of the array. The
! 45: * j-th column of A is stored in the j-th column of the array AB
! 46: * as follows:
! 47: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 48: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 49: *
! 50: * On exit, AB is overwritten by values generated during the
! 51: * reduction to tridiagonal form. If UPLO = 'U', the first
! 52: * superdiagonal and the diagonal of the tridiagonal matrix T
! 53: * are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
! 54: * the diagonal and first subdiagonal of T are returned in the
! 55: * first two rows of AB.
! 56: *
! 57: * LDAB (input) INTEGER
! 58: * The leading dimension of the array AB. LDAB >= KD + 1.
! 59: *
! 60: * W (output) DOUBLE PRECISION array, dimension (N)
! 61: * If INFO = 0, the eigenvalues in ascending order.
! 62: *
! 63: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
! 64: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 65: * eigenvectors of the matrix A, with the i-th column of Z
! 66: * holding the eigenvector associated with W(i).
! 67: * If JOBZ = 'N', then Z is not referenced.
! 68: *
! 69: * LDZ (input) INTEGER
! 70: * The leading dimension of the array Z. LDZ >= 1, and if
! 71: * JOBZ = 'V', LDZ >= max(1,N).
! 72: *
! 73: * WORK (workspace) COMPLEX*16 array, dimension (N)
! 74: *
! 75: * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))
! 76: *
! 77: * INFO (output) INTEGER
! 78: * = 0: successful exit.
! 79: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 80: * > 0: if INFO = i, the algorithm failed to converge; i
! 81: * off-diagonal elements of an intermediate tridiagonal
! 82: * form did not converge to zero.
! 83: *
! 84: * =====================================================================
! 85: *
! 86: * .. Parameters ..
! 87: DOUBLE PRECISION ZERO, ONE
! 88: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 89: * ..
! 90: * .. Local Scalars ..
! 91: LOGICAL LOWER, WANTZ
! 92: INTEGER IINFO, IMAX, INDE, INDRWK, ISCALE
! 93: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 94: $ SMLNUM
! 95: * ..
! 96: * .. External Functions ..
! 97: LOGICAL LSAME
! 98: DOUBLE PRECISION DLAMCH, ZLANHB
! 99: EXTERNAL LSAME, DLAMCH, ZLANHB
! 100: * ..
! 101: * .. External Subroutines ..
! 102: EXTERNAL DSCAL, DSTERF, XERBLA, ZHBTRD, ZLASCL, ZSTEQR
! 103: * ..
! 104: * .. Intrinsic Functions ..
! 105: INTRINSIC SQRT
! 106: * ..
! 107: * .. Executable Statements ..
! 108: *
! 109: * Test the input parameters.
! 110: *
! 111: WANTZ = LSAME( JOBZ, 'V' )
! 112: LOWER = LSAME( UPLO, 'L' )
! 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( KD.LT.0 ) THEN
! 122: INFO = -4
! 123: ELSE IF( LDAB.LT.KD+1 ) THEN
! 124: INFO = -6
! 125: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 126: INFO = -9
! 127: END IF
! 128: *
! 129: IF( INFO.NE.0 ) THEN
! 130: CALL XERBLA( 'ZHBEV ', -INFO )
! 131: RETURN
! 132: END IF
! 133: *
! 134: * Quick return if possible
! 135: *
! 136: IF( N.EQ.0 )
! 137: $ RETURN
! 138: *
! 139: IF( N.EQ.1 ) THEN
! 140: IF( LOWER ) THEN
! 141: W( 1 ) = AB( 1, 1 )
! 142: ELSE
! 143: W( 1 ) = AB( KD+1, 1 )
! 144: END IF
! 145: IF( WANTZ )
! 146: $ Z( 1, 1 ) = ONE
! 147: RETURN
! 148: END IF
! 149: *
! 150: * Get machine constants.
! 151: *
! 152: SAFMIN = DLAMCH( 'Safe minimum' )
! 153: EPS = DLAMCH( 'Precision' )
! 154: SMLNUM = SAFMIN / EPS
! 155: BIGNUM = ONE / SMLNUM
! 156: RMIN = SQRT( SMLNUM )
! 157: RMAX = SQRT( BIGNUM )
! 158: *
! 159: * Scale matrix to allowable range, if necessary.
! 160: *
! 161: ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
! 162: ISCALE = 0
! 163: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 164: ISCALE = 1
! 165: SIGMA = RMIN / ANRM
! 166: ELSE IF( ANRM.GT.RMAX ) THEN
! 167: ISCALE = 1
! 168: SIGMA = RMAX / ANRM
! 169: END IF
! 170: IF( ISCALE.EQ.1 ) THEN
! 171: IF( LOWER ) THEN
! 172: CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 173: ELSE
! 174: CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 175: END IF
! 176: END IF
! 177: *
! 178: * Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
! 179: *
! 180: INDE = 1
! 181: CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
! 182: $ LDZ, WORK, IINFO )
! 183: *
! 184: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
! 185: *
! 186: IF( .NOT.WANTZ ) THEN
! 187: CALL DSTERF( N, W, RWORK( INDE ), INFO )
! 188: ELSE
! 189: INDRWK = INDE + N
! 190: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
! 191: $ RWORK( INDRWK ), INFO )
! 192: END IF
! 193: *
! 194: * If matrix was scaled, then rescale eigenvalues appropriately.
! 195: *
! 196: IF( ISCALE.EQ.1 ) THEN
! 197: IF( INFO.EQ.0 ) THEN
! 198: IMAX = N
! 199: ELSE
! 200: IMAX = INFO - 1
! 201: END IF
! 202: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 203: END IF
! 204: *
! 205: RETURN
! 206: *
! 207: * End of ZHBEV
! 208: *
! 209: END
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