Annotation of rpl/lapack/lapack/dsbev.f, revision 1.17

1.8       bertrand    1: *> \brief <b> DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
                      2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.14      bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.8       bertrand    7: *
                      8: *> \htmlonly
1.14      bertrand    9: *> Download DSBEV + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbev.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbev.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbev.f">
1.8       bertrand   15: *> [TXT]</a>
1.14      bertrand   16: *> \endhtmlonly
1.8       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE DSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
                     22: *                         INFO )
1.14      bertrand   23: *
1.8       bertrand   24: *       .. Scalar Arguments ..
                     25: *       CHARACTER          JOBZ, UPLO
                     26: *       INTEGER            INFO, KD, LDAB, LDZ, N
                     27: *       ..
                     28: *       .. Array Arguments ..
                     29: *       DOUBLE PRECISION   AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
                     30: *       ..
1.14      bertrand   31: *
1.8       bertrand   32: *
                     33: *> \par Purpose:
                     34: *  =============
                     35: *>
                     36: *> \verbatim
                     37: *>
                     38: *> DSBEV computes all the eigenvalues and, optionally, eigenvectors of
                     39: *> a real symmetric band matrix A.
                     40: *> \endverbatim
                     41: *
                     42: *  Arguments:
                     43: *  ==========
                     44: *
                     45: *> \param[in] JOBZ
                     46: *> \verbatim
                     47: *>          JOBZ is CHARACTER*1
                     48: *>          = 'N':  Compute eigenvalues only;
                     49: *>          = 'V':  Compute eigenvalues and eigenvectors.
                     50: *> \endverbatim
                     51: *>
                     52: *> \param[in] UPLO
                     53: *> \verbatim
                     54: *>          UPLO is CHARACTER*1
                     55: *>          = 'U':  Upper triangle of A is stored;
                     56: *>          = 'L':  Lower triangle of A is stored.
                     57: *> \endverbatim
                     58: *>
                     59: *> \param[in] N
                     60: *> \verbatim
                     61: *>          N is INTEGER
                     62: *>          The order of the matrix A.  N >= 0.
                     63: *> \endverbatim
                     64: *>
                     65: *> \param[in] KD
                     66: *> \verbatim
                     67: *>          KD is INTEGER
                     68: *>          The number of superdiagonals of the matrix A if UPLO = 'U',
                     69: *>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
                     70: *> \endverbatim
                     71: *>
                     72: *> \param[in,out] AB
                     73: *> \verbatim
                     74: *>          AB is DOUBLE PRECISION array, dimension (LDAB, N)
                     75: *>          On entry, the upper or lower triangle of the symmetric band
                     76: *>          matrix A, stored in the first KD+1 rows of the array.  The
                     77: *>          j-th column of A is stored in the j-th column of the array AB
                     78: *>          as follows:
                     79: *>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                     80: *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
                     81: *>
                     82: *>          On exit, AB is overwritten by values generated during the
                     83: *>          reduction to tridiagonal form.  If UPLO = 'U', the first
                     84: *>          superdiagonal and the diagonal of the tridiagonal matrix T
                     85: *>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
                     86: *>          the diagonal and first subdiagonal of T are returned in the
                     87: *>          first two rows of AB.
                     88: *> \endverbatim
                     89: *>
                     90: *> \param[in] LDAB
                     91: *> \verbatim
                     92: *>          LDAB is INTEGER
                     93: *>          The leading dimension of the array AB.  LDAB >= KD + 1.
                     94: *> \endverbatim
                     95: *>
                     96: *> \param[out] W
                     97: *> \verbatim
                     98: *>          W is DOUBLE PRECISION array, dimension (N)
                     99: *>          If INFO = 0, the eigenvalues in ascending order.
                    100: *> \endverbatim
                    101: *>
                    102: *> \param[out] Z
                    103: *> \verbatim
                    104: *>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
                    105: *>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
                    106: *>          eigenvectors of the matrix A, with the i-th column of Z
                    107: *>          holding the eigenvector associated with W(i).
                    108: *>          If JOBZ = 'N', then Z is not referenced.
                    109: *> \endverbatim
                    110: *>
                    111: *> \param[in] LDZ
                    112: *> \verbatim
                    113: *>          LDZ is INTEGER
                    114: *>          The leading dimension of the array Z.  LDZ >= 1, and if
                    115: *>          JOBZ = 'V', LDZ >= max(1,N).
                    116: *> \endverbatim
                    117: *>
                    118: *> \param[out] WORK
                    119: *> \verbatim
                    120: *>          WORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))
                    121: *> \endverbatim
                    122: *>
                    123: *> \param[out] INFO
                    124: *> \verbatim
                    125: *>          INFO is INTEGER
                    126: *>          = 0:  successful exit
                    127: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
                    128: *>          > 0:  if INFO = i, the algorithm failed to converge; i
                    129: *>                off-diagonal elements of an intermediate tridiagonal
                    130: *>                form did not converge to zero.
                    131: *> \endverbatim
                    132: *
                    133: *  Authors:
                    134: *  ========
                    135: *
1.14      bertrand  136: *> \author Univ. of Tennessee
                    137: *> \author Univ. of California Berkeley
                    138: *> \author Univ. of Colorado Denver
                    139: *> \author NAG Ltd.
1.8       bertrand  140: *
                    141: *> \ingroup doubleOTHEReigen
                    142: *
                    143: *  =====================================================================
1.1       bertrand  144:       SUBROUTINE DSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
                    145:      $                  INFO )
                    146: *
1.17    ! bertrand  147: *  -- LAPACK driver routine --
1.1       bertrand  148: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    149: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                    150: *
                    151: *     .. Scalar Arguments ..
                    152:       CHARACTER          JOBZ, UPLO
                    153:       INTEGER            INFO, KD, LDAB, LDZ, N
                    154: *     ..
                    155: *     .. Array Arguments ..
                    156:       DOUBLE PRECISION   AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
                    157: *     ..
                    158: *
                    159: *  =====================================================================
                    160: *
                    161: *     .. Parameters ..
                    162:       DOUBLE PRECISION   ZERO, ONE
                    163:       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
                    164: *     ..
                    165: *     .. Local Scalars ..
                    166:       LOGICAL            LOWER, WANTZ
                    167:       INTEGER            IINFO, IMAX, INDE, INDWRK, ISCALE
                    168:       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
                    169:      $                   SMLNUM
                    170: *     ..
                    171: *     .. External Functions ..
                    172:       LOGICAL            LSAME
                    173:       DOUBLE PRECISION   DLAMCH, DLANSB
                    174:       EXTERNAL           LSAME, DLAMCH, DLANSB
                    175: *     ..
                    176: *     .. External Subroutines ..
                    177:       EXTERNAL           DLASCL, DSBTRD, DSCAL, DSTEQR, DSTERF, XERBLA
                    178: *     ..
                    179: *     .. Intrinsic Functions ..
                    180:       INTRINSIC          SQRT
                    181: *     ..
                    182: *     .. Executable Statements ..
                    183: *
                    184: *     Test the input parameters.
                    185: *
                    186:       WANTZ = LSAME( JOBZ, 'V' )
                    187:       LOWER = LSAME( UPLO, 'L' )
                    188: *
                    189:       INFO = 0
                    190:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
                    191:          INFO = -1
                    192:       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
                    193:          INFO = -2
                    194:       ELSE IF( N.LT.0 ) THEN
                    195:          INFO = -3
                    196:       ELSE IF( KD.LT.0 ) THEN
                    197:          INFO = -4
                    198:       ELSE IF( LDAB.LT.KD+1 ) THEN
                    199:          INFO = -6
                    200:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
                    201:          INFO = -9
                    202:       END IF
                    203: *
                    204:       IF( INFO.NE.0 ) THEN
                    205:          CALL XERBLA( 'DSBEV ', -INFO )
                    206:          RETURN
                    207:       END IF
                    208: *
                    209: *     Quick return if possible
                    210: *
                    211:       IF( N.EQ.0 )
                    212:      $   RETURN
                    213: *
                    214:       IF( N.EQ.1 ) THEN
                    215:          IF( LOWER ) THEN
                    216:             W( 1 ) = AB( 1, 1 )
                    217:          ELSE
                    218:             W( 1 ) = AB( KD+1, 1 )
                    219:          END IF
                    220:          IF( WANTZ )
                    221:      $      Z( 1, 1 ) = ONE
                    222:          RETURN
                    223:       END IF
                    224: *
                    225: *     Get machine constants.
                    226: *
                    227:       SAFMIN = DLAMCH( 'Safe minimum' )
                    228:       EPS = DLAMCH( 'Precision' )
                    229:       SMLNUM = SAFMIN / EPS
                    230:       BIGNUM = ONE / SMLNUM
                    231:       RMIN = SQRT( SMLNUM )
                    232:       RMAX = SQRT( BIGNUM )
                    233: *
                    234: *     Scale matrix to allowable range, if necessary.
                    235: *
                    236:       ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
                    237:       ISCALE = 0
                    238:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
                    239:          ISCALE = 1
                    240:          SIGMA = RMIN / ANRM
                    241:       ELSE IF( ANRM.GT.RMAX ) THEN
                    242:          ISCALE = 1
                    243:          SIGMA = RMAX / ANRM
                    244:       END IF
                    245:       IF( ISCALE.EQ.1 ) THEN
                    246:          IF( LOWER ) THEN
                    247:             CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
                    248:          ELSE
                    249:             CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
                    250:          END IF
                    251:       END IF
                    252: *
                    253: *     Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
                    254: *
                    255:       INDE = 1
                    256:       INDWRK = INDE + N
                    257:       CALL DSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, WORK( INDE ), Z, LDZ,
                    258:      $             WORK( INDWRK ), IINFO )
                    259: *
                    260: *     For eigenvalues only, call DSTERF.  For eigenvectors, call SSTEQR.
                    261: *
                    262:       IF( .NOT.WANTZ ) THEN
                    263:          CALL DSTERF( N, W, WORK( INDE ), INFO )
                    264:       ELSE
                    265:          CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
                    266:      $                INFO )
                    267:       END IF
                    268: *
                    269: *     If matrix was scaled, then rescale eigenvalues appropriately.
                    270: *
                    271:       IF( ISCALE.EQ.1 ) THEN
                    272:          IF( INFO.EQ.0 ) THEN
                    273:             IMAX = N
                    274:          ELSE
                    275:             IMAX = INFO - 1
                    276:          END IF
                    277:          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
                    278:       END IF
                    279: *
                    280:       RETURN
                    281: *
                    282: *     End of DSBEV
                    283: *
                    284:       END

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