Annotation of rpl/lapack/lapack/dstevd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
! 2: $ 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
! 11: INTEGER INFO, LDZ, LIWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
! 22: * real symmetric tridiagonal matrix. If eigenvectors are desired, it
! 23: * uses a divide and conquer algorithm.
! 24: *
! 25: * The divide and conquer algorithm makes very mild assumptions about
! 26: * floating point arithmetic. It will work on machines with a guard
! 27: * digit in add/subtract, or on those binary machines without guard
! 28: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 29: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 30: * without guard digits, but we know of none.
! 31: *
! 32: * Arguments
! 33: * =========
! 34: *
! 35: * JOBZ (input) CHARACTER*1
! 36: * = 'N': Compute eigenvalues only;
! 37: * = 'V': Compute eigenvalues and eigenvectors.
! 38: *
! 39: * N (input) INTEGER
! 40: * The order of the matrix. N >= 0.
! 41: *
! 42: * D (input/output) DOUBLE PRECISION array, dimension (N)
! 43: * On entry, the n diagonal elements of the tridiagonal matrix
! 44: * A.
! 45: * On exit, if INFO = 0, the eigenvalues in ascending order.
! 46: *
! 47: * E (input/output) DOUBLE PRECISION array, dimension (N-1)
! 48: * On entry, the (n-1) subdiagonal elements of the tridiagonal
! 49: * matrix A, stored in elements 1 to N-1 of E.
! 50: * On exit, the contents of E are destroyed.
! 51: *
! 52: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
! 53: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 54: * eigenvectors of the matrix A, with the i-th column of Z
! 55: * holding the eigenvector associated with D(i).
! 56: * If JOBZ = 'N', then Z is not referenced.
! 57: *
! 58: * LDZ (input) INTEGER
! 59: * The leading dimension of the array Z. LDZ >= 1, and if
! 60: * JOBZ = 'V', LDZ >= max(1,N).
! 61: *
! 62: * WORK (workspace/output) DOUBLE PRECISION array,
! 63: * dimension (LWORK)
! 64: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 65: *
! 66: * LWORK (input) INTEGER
! 67: * The dimension of the array WORK.
! 68: * If JOBZ = 'N' or N <= 1 then LWORK must be at least 1.
! 69: * If JOBZ = 'V' and N > 1 then LWORK must be at least
! 70: * ( 1 + 4*N + N**2 ).
! 71: *
! 72: * If LWORK = -1, then a workspace query is assumed; the routine
! 73: * only calculates the optimal sizes of the WORK and IWORK
! 74: * arrays, returns these values as the first entries of the WORK
! 75: * and IWORK arrays, and no error message related to LWORK or
! 76: * LIWORK is issued by XERBLA.
! 77: *
! 78: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 79: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
! 80: *
! 81: * LIWORK (input) INTEGER
! 82: * The dimension of the array IWORK.
! 83: * If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1.
! 84: * If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N.
! 85: *
! 86: * If LIWORK = -1, then a workspace query is assumed; the
! 87: * routine only calculates the optimal sizes of the WORK and
! 88: * IWORK arrays, returns these values as the first entries of
! 89: * the WORK and IWORK arrays, and no error message related to
! 90: * LWORK or LIWORK is issued by XERBLA.
! 91: *
! 92: * INFO (output) INTEGER
! 93: * = 0: successful exit
! 94: * < 0: if INFO = -i, the i-th argument had an illegal value
! 95: * > 0: if INFO = i, the algorithm failed to converge; i
! 96: * off-diagonal elements of E did not converge to zero.
! 97: *
! 98: * =====================================================================
! 99: *
! 100: * .. Parameters ..
! 101: DOUBLE PRECISION ZERO, ONE
! 102: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 103: * ..
! 104: * .. Local Scalars ..
! 105: LOGICAL LQUERY, WANTZ
! 106: INTEGER ISCALE, LIWMIN, LWMIN
! 107: DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
! 108: $ TNRM
! 109: * ..
! 110: * .. External Functions ..
! 111: LOGICAL LSAME
! 112: DOUBLE PRECISION DLAMCH, DLANST
! 113: EXTERNAL LSAME, DLAMCH, DLANST
! 114: * ..
! 115: * .. External Subroutines ..
! 116: EXTERNAL DSCAL, DSTEDC, DSTERF, XERBLA
! 117: * ..
! 118: * .. Intrinsic Functions ..
! 119: INTRINSIC SQRT
! 120: * ..
! 121: * .. Executable Statements ..
! 122: *
! 123: * Test the input parameters.
! 124: *
! 125: WANTZ = LSAME( JOBZ, 'V' )
! 126: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 127: *
! 128: INFO = 0
! 129: LIWMIN = 1
! 130: LWMIN = 1
! 131: IF( N.GT.1 .AND. WANTZ ) THEN
! 132: LWMIN = 1 + 4*N + N**2
! 133: LIWMIN = 3 + 5*N
! 134: END IF
! 135: *
! 136: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 137: INFO = -1
! 138: ELSE IF( N.LT.0 ) THEN
! 139: INFO = -2
! 140: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 141: INFO = -6
! 142: END IF
! 143: *
! 144: IF( INFO.EQ.0 ) THEN
! 145: WORK( 1 ) = LWMIN
! 146: IWORK( 1 ) = LIWMIN
! 147: *
! 148: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 149: INFO = -8
! 150: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 151: INFO = -10
! 152: END IF
! 153: END IF
! 154: *
! 155: IF( INFO.NE.0 ) THEN
! 156: CALL XERBLA( 'DSTEVD', -INFO )
! 157: RETURN
! 158: ELSE IF( LQUERY ) THEN
! 159: RETURN
! 160: END IF
! 161: *
! 162: * Quick return if possible
! 163: *
! 164: IF( N.EQ.0 )
! 165: $ RETURN
! 166: *
! 167: IF( N.EQ.1 ) THEN
! 168: IF( WANTZ )
! 169: $ Z( 1, 1 ) = ONE
! 170: RETURN
! 171: END IF
! 172: *
! 173: * Get machine constants.
! 174: *
! 175: SAFMIN = DLAMCH( 'Safe minimum' )
! 176: EPS = DLAMCH( 'Precision' )
! 177: SMLNUM = SAFMIN / EPS
! 178: BIGNUM = ONE / SMLNUM
! 179: RMIN = SQRT( SMLNUM )
! 180: RMAX = SQRT( BIGNUM )
! 181: *
! 182: * Scale matrix to allowable range, if necessary.
! 183: *
! 184: ISCALE = 0
! 185: TNRM = DLANST( 'M', N, D, E )
! 186: IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
! 187: ISCALE = 1
! 188: SIGMA = RMIN / TNRM
! 189: ELSE IF( TNRM.GT.RMAX ) THEN
! 190: ISCALE = 1
! 191: SIGMA = RMAX / TNRM
! 192: END IF
! 193: IF( ISCALE.EQ.1 ) THEN
! 194: CALL DSCAL( N, SIGMA, D, 1 )
! 195: CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
! 196: END IF
! 197: *
! 198: * For eigenvalues only, call DSTERF. For eigenvalues and
! 199: * eigenvectors, call DSTEDC.
! 200: *
! 201: IF( .NOT.WANTZ ) THEN
! 202: CALL DSTERF( N, D, E, INFO )
! 203: ELSE
! 204: CALL DSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
! 205: $ INFO )
! 206: END IF
! 207: *
! 208: * If matrix was scaled, then rescale eigenvalues appropriately.
! 209: *
! 210: IF( ISCALE.EQ.1 )
! 211: $ CALL DSCAL( N, ONE / SIGMA, D, 1 )
! 212: *
! 213: WORK( 1 ) = LWMIN
! 214: IWORK( 1 ) = LIWMIN
! 215: *
! 216: RETURN
! 217: *
! 218: * End of DSTEVD
! 219: *
! 220: END
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