Annotation of rpl/lapack/lapack/dsyev.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
! 2: *
! 3: * -- LAPACK driver routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER JOBZ, UPLO
! 10: INTEGER INFO, LDA, LWORK, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DSYEV computes all eigenvalues and, optionally, eigenvectors of a
! 20: * real symmetric matrix A.
! 21: *
! 22: * Arguments
! 23: * =========
! 24: *
! 25: * JOBZ (input) CHARACTER*1
! 26: * = 'N': Compute eigenvalues only;
! 27: * = 'V': Compute eigenvalues and eigenvectors.
! 28: *
! 29: * UPLO (input) CHARACTER*1
! 30: * = 'U': Upper triangle of A is stored;
! 31: * = 'L': Lower triangle of A is stored.
! 32: *
! 33: * N (input) INTEGER
! 34: * The order of the matrix A. N >= 0.
! 35: *
! 36: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
! 37: * On entry, the symmetric matrix A. If UPLO = 'U', the
! 38: * leading N-by-N upper triangular part of A contains the
! 39: * upper triangular part of the matrix A. If UPLO = 'L',
! 40: * the leading N-by-N lower triangular part of A contains
! 41: * the lower triangular part of the matrix A.
! 42: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
! 43: * orthonormal eigenvectors of the matrix A.
! 44: * If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
! 45: * or the upper triangle (if UPLO='U') of A, including the
! 46: * diagonal, is destroyed.
! 47: *
! 48: * LDA (input) INTEGER
! 49: * The leading dimension of the array A. LDA >= max(1,N).
! 50: *
! 51: * W (output) DOUBLE PRECISION array, dimension (N)
! 52: * If INFO = 0, the eigenvalues in ascending order.
! 53: *
! 54: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 55: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 56: *
! 57: * LWORK (input) INTEGER
! 58: * The length of the array WORK. LWORK >= max(1,3*N-1).
! 59: * For optimal efficiency, LWORK >= (NB+2)*N,
! 60: * where NB is the blocksize for DSYTRD returned by ILAENV.
! 61: *
! 62: * If LWORK = -1, then a workspace query is assumed; the routine
! 63: * only calculates the optimal size of the WORK array, returns
! 64: * this value as the first entry of the WORK array, and no error
! 65: * message related to LWORK is issued by XERBLA.
! 66: *
! 67: * INFO (output) INTEGER
! 68: * = 0: successful exit
! 69: * < 0: if INFO = -i, the i-th argument had an illegal value
! 70: * > 0: if INFO = i, the algorithm failed to converge; i
! 71: * off-diagonal elements of an intermediate tridiagonal
! 72: * form did not converge to zero.
! 73: *
! 74: * =====================================================================
! 75: *
! 76: * .. Parameters ..
! 77: DOUBLE PRECISION ZERO, ONE
! 78: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 79: * ..
! 80: * .. Local Scalars ..
! 81: LOGICAL LOWER, LQUERY, WANTZ
! 82: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
! 83: $ LLWORK, LWKOPT, NB
! 84: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 85: $ SMLNUM
! 86: * ..
! 87: * .. External Functions ..
! 88: LOGICAL LSAME
! 89: INTEGER ILAENV
! 90: DOUBLE PRECISION DLAMCH, DLANSY
! 91: EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY
! 92: * ..
! 93: * .. External Subroutines ..
! 94: EXTERNAL DLASCL, DORGTR, DSCAL, DSTEQR, DSTERF, DSYTRD,
! 95: $ XERBLA
! 96: * ..
! 97: * .. Intrinsic Functions ..
! 98: INTRINSIC MAX, SQRT
! 99: * ..
! 100: * .. Executable Statements ..
! 101: *
! 102: * Test the input parameters.
! 103: *
! 104: WANTZ = LSAME( JOBZ, 'V' )
! 105: LOWER = LSAME( UPLO, 'L' )
! 106: LQUERY = ( LWORK.EQ.-1 )
! 107: *
! 108: INFO = 0
! 109: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 110: INFO = -1
! 111: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 112: INFO = -2
! 113: ELSE IF( N.LT.0 ) THEN
! 114: INFO = -3
! 115: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 116: INFO = -5
! 117: END IF
! 118: *
! 119: IF( INFO.EQ.0 ) THEN
! 120: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
! 121: LWKOPT = MAX( 1, ( NB+2 )*N )
! 122: WORK( 1 ) = LWKOPT
! 123: *
! 124: IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY )
! 125: $ INFO = -8
! 126: END IF
! 127: *
! 128: IF( INFO.NE.0 ) THEN
! 129: CALL XERBLA( 'DSYEV ', -INFO )
! 130: RETURN
! 131: ELSE IF( LQUERY ) THEN
! 132: RETURN
! 133: END IF
! 134: *
! 135: * Quick return if possible
! 136: *
! 137: IF( N.EQ.0 ) THEN
! 138: RETURN
! 139: END IF
! 140: *
! 141: IF( N.EQ.1 ) THEN
! 142: W( 1 ) = A( 1, 1 )
! 143: WORK( 1 ) = 2
! 144: IF( WANTZ )
! 145: $ A( 1, 1 ) = ONE
! 146: RETURN
! 147: END IF
! 148: *
! 149: * Get machine constants.
! 150: *
! 151: SAFMIN = DLAMCH( 'Safe minimum' )
! 152: EPS = DLAMCH( 'Precision' )
! 153: SMLNUM = SAFMIN / EPS
! 154: BIGNUM = ONE / SMLNUM
! 155: RMIN = SQRT( SMLNUM )
! 156: RMAX = SQRT( BIGNUM )
! 157: *
! 158: * Scale matrix to allowable range, if necessary.
! 159: *
! 160: ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
! 161: ISCALE = 0
! 162: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 163: ISCALE = 1
! 164: SIGMA = RMIN / ANRM
! 165: ELSE IF( ANRM.GT.RMAX ) THEN
! 166: ISCALE = 1
! 167: SIGMA = RMAX / ANRM
! 168: END IF
! 169: IF( ISCALE.EQ.1 )
! 170: $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
! 171: *
! 172: * Call DSYTRD to reduce symmetric matrix to tridiagonal form.
! 173: *
! 174: INDE = 1
! 175: INDTAU = INDE + N
! 176: INDWRK = INDTAU + N
! 177: LLWORK = LWORK - INDWRK + 1
! 178: CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
! 179: $ WORK( INDWRK ), LLWORK, IINFO )
! 180: *
! 181: * For eigenvalues only, call DSTERF. For eigenvectors, first call
! 182: * DORGTR to generate the orthogonal matrix, then call DSTEQR.
! 183: *
! 184: IF( .NOT.WANTZ ) THEN
! 185: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 186: ELSE
! 187: CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
! 188: $ LLWORK, IINFO )
! 189: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ),
! 190: $ INFO )
! 191: END IF
! 192: *
! 193: * If matrix was scaled, then rescale eigenvalues appropriately.
! 194: *
! 195: IF( ISCALE.EQ.1 ) THEN
! 196: IF( INFO.EQ.0 ) THEN
! 197: IMAX = N
! 198: ELSE
! 199: IMAX = INFO - 1
! 200: END IF
! 201: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 202: END IF
! 203: *
! 204: * Set WORK(1) to optimal workspace size.
! 205: *
! 206: WORK( 1 ) = LWKOPT
! 207: *
! 208: RETURN
! 209: *
! 210: * End of DSYEV
! 211: *
! 212: END
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