Annotation of rpl/lapack/lapack/dsbev.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
! 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, KD, LDAB, LDZ, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DSBEV computes all the eigenvalues and, optionally, eigenvectors of
! 21: * a real symmetric band matrix A.
! 22: *
! 23: * Arguments
! 24: * =========
! 25: *
! 26: * JOBZ (input) CHARACTER*1
! 27: * = 'N': Compute eigenvalues only;
! 28: * = 'V': Compute eigenvalues and eigenvectors.
! 29: *
! 30: * UPLO (input) CHARACTER*1
! 31: * = 'U': Upper triangle of A is stored;
! 32: * = 'L': Lower triangle of A is stored.
! 33: *
! 34: * N (input) INTEGER
! 35: * The order of the matrix A. N >= 0.
! 36: *
! 37: * KD (input) INTEGER
! 38: * The number of superdiagonals of the matrix A if UPLO = 'U',
! 39: * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
! 40: *
! 41: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
! 42: * On entry, the upper or lower triangle of the symmetric band
! 43: * matrix A, stored in the first KD+1 rows of the array. The
! 44: * j-th column of A is stored in the j-th column of the array AB
! 45: * as follows:
! 46: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
! 47: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
! 48: *
! 49: * On exit, AB is overwritten by values generated during the
! 50: * reduction to tridiagonal form. If UPLO = 'U', the first
! 51: * superdiagonal and the diagonal of the tridiagonal matrix T
! 52: * are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
! 53: * the diagonal and first subdiagonal of T are returned in the
! 54: * first two rows of AB.
! 55: *
! 56: * LDAB (input) INTEGER
! 57: * The leading dimension of the array AB. LDAB >= KD + 1.
! 58: *
! 59: * W (output) DOUBLE PRECISION array, dimension (N)
! 60: * If INFO = 0, the eigenvalues in ascending order.
! 61: *
! 62: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
! 63: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 64: * eigenvectors of the matrix A, with the i-th column of Z
! 65: * holding the eigenvector associated with W(i).
! 66: * If JOBZ = 'N', then Z is not referenced.
! 67: *
! 68: * LDZ (input) INTEGER
! 69: * The leading dimension of the array Z. LDZ >= 1, and if
! 70: * JOBZ = 'V', LDZ >= max(1,N).
! 71: *
! 72: * WORK (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))
! 73: *
! 74: * INFO (output) INTEGER
! 75: * = 0: successful exit
! 76: * < 0: if INFO = -i, the i-th argument had an illegal value
! 77: * > 0: if INFO = i, the algorithm failed to converge; i
! 78: * off-diagonal elements of an intermediate tridiagonal
! 79: * form did not converge to zero.
! 80: *
! 81: * =====================================================================
! 82: *
! 83: * .. Parameters ..
! 84: DOUBLE PRECISION ZERO, ONE
! 85: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
! 86: * ..
! 87: * .. Local Scalars ..
! 88: LOGICAL LOWER, WANTZ
! 89: INTEGER IINFO, IMAX, INDE, INDWRK, ISCALE
! 90: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 91: $ SMLNUM
! 92: * ..
! 93: * .. External Functions ..
! 94: LOGICAL LSAME
! 95: DOUBLE PRECISION DLAMCH, DLANSB
! 96: EXTERNAL LSAME, DLAMCH, DLANSB
! 97: * ..
! 98: * .. External Subroutines ..
! 99: EXTERNAL DLASCL, DSBTRD, DSCAL, DSTEQR, DSTERF, XERBLA
! 100: * ..
! 101: * .. Intrinsic Functions ..
! 102: INTRINSIC SQRT
! 103: * ..
! 104: * .. Executable Statements ..
! 105: *
! 106: * Test the input parameters.
! 107: *
! 108: WANTZ = LSAME( JOBZ, 'V' )
! 109: LOWER = LSAME( UPLO, 'L' )
! 110: *
! 111: INFO = 0
! 112: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 113: INFO = -1
! 114: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
! 115: INFO = -2
! 116: ELSE IF( N.LT.0 ) THEN
! 117: INFO = -3
! 118: ELSE IF( KD.LT.0 ) THEN
! 119: INFO = -4
! 120: ELSE IF( LDAB.LT.KD+1 ) THEN
! 121: INFO = -6
! 122: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 123: INFO = -9
! 124: END IF
! 125: *
! 126: IF( INFO.NE.0 ) THEN
! 127: CALL XERBLA( 'DSBEV ', -INFO )
! 128: RETURN
! 129: END IF
! 130: *
! 131: * Quick return if possible
! 132: *
! 133: IF( N.EQ.0 )
! 134: $ RETURN
! 135: *
! 136: IF( N.EQ.1 ) THEN
! 137: IF( LOWER ) THEN
! 138: W( 1 ) = AB( 1, 1 )
! 139: ELSE
! 140: W( 1 ) = AB( KD+1, 1 )
! 141: END IF
! 142: IF( WANTZ )
! 143: $ Z( 1, 1 ) = ONE
! 144: RETURN
! 145: END IF
! 146: *
! 147: * Get machine constants.
! 148: *
! 149: SAFMIN = DLAMCH( 'Safe minimum' )
! 150: EPS = DLAMCH( 'Precision' )
! 151: SMLNUM = SAFMIN / EPS
! 152: BIGNUM = ONE / SMLNUM
! 153: RMIN = SQRT( SMLNUM )
! 154: RMAX = SQRT( BIGNUM )
! 155: *
! 156: * Scale matrix to allowable range, if necessary.
! 157: *
! 158: ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
! 159: ISCALE = 0
! 160: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 161: ISCALE = 1
! 162: SIGMA = RMIN / ANRM
! 163: ELSE IF( ANRM.GT.RMAX ) THEN
! 164: ISCALE = 1
! 165: SIGMA = RMAX / ANRM
! 166: END IF
! 167: IF( ISCALE.EQ.1 ) THEN
! 168: IF( LOWER ) THEN
! 169: CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 170: ELSE
! 171: CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
! 172: END IF
! 173: END IF
! 174: *
! 175: * Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
! 176: *
! 177: INDE = 1
! 178: INDWRK = INDE + N
! 179: CALL DSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, WORK( INDE ), Z, LDZ,
! 180: $ WORK( INDWRK ), IINFO )
! 181: *
! 182: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
! 183: *
! 184: IF( .NOT.WANTZ ) THEN
! 185: CALL DSTERF( N, W, WORK( INDE ), INFO )
! 186: ELSE
! 187: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
! 188: $ INFO )
! 189: END IF
! 190: *
! 191: * If matrix was scaled, then rescale eigenvalues appropriately.
! 192: *
! 193: IF( ISCALE.EQ.1 ) THEN
! 194: IF( INFO.EQ.0 ) THEN
! 195: IMAX = N
! 196: ELSE
! 197: IMAX = INFO - 1
! 198: END IF
! 199: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 200: END IF
! 201: *
! 202: RETURN
! 203: *
! 204: * End of DSBEV
! 205: *
! 206: END
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