LAPACK 3.3.1
Linear Algebra PACKage

cpteqr.f

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00001       SUBROUTINE CPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          COMPZ
00010       INTEGER            INFO, LDZ, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       REAL               D( * ), E( * ), WORK( * )
00014       COMPLEX            Z( LDZ, * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
00021 *  symmetric positive definite tridiagonal matrix by first factoring the
00022 *  matrix using SPTTRF and then calling CBDSQR to compute the singular
00023 *  values of the bidiagonal factor.
00024 *
00025 *  This routine computes the eigenvalues of the positive definite
00026 *  tridiagonal matrix to high relative accuracy.  This means that if the
00027 *  eigenvalues range over many orders of magnitude in size, then the
00028 *  small eigenvalues and corresponding eigenvectors will be computed
00029 *  more accurately than, for example, with the standard QR method.
00030 *
00031 *  The eigenvectors of a full or band positive definite Hermitian matrix
00032 *  can also be found if CHETRD, CHPTRD, or CHBTRD has been used to
00033 *  reduce this matrix to tridiagonal form.  (The reduction to
00034 *  tridiagonal form, however, may preclude the possibility of obtaining
00035 *  high relative accuracy in the small eigenvalues of the original
00036 *  matrix, if these eigenvalues range over many orders of magnitude.)
00037 *
00038 *  Arguments
00039 *  =========
00040 *
00041 *  COMPZ   (input) CHARACTER*1
00042 *          = 'N':  Compute eigenvalues only.
00043 *          = 'V':  Compute eigenvectors of original Hermitian
00044 *                  matrix also.  Array Z contains the unitary matrix
00045 *                  used to reduce the original matrix to tridiagonal
00046 *                  form.
00047 *          = 'I':  Compute eigenvectors of tridiagonal matrix also.
00048 *
00049 *  N       (input) INTEGER
00050 *          The order of the matrix.  N >= 0.
00051 *
00052 *  D       (input/output) REAL array, dimension (N)
00053 *          On entry, the n diagonal elements of the tridiagonal matrix.
00054 *          On normal exit, D contains the eigenvalues, in descending
00055 *          order.
00056 *
00057 *  E       (input/output) REAL array, dimension (N-1)
00058 *          On entry, the (n-1) subdiagonal elements of the tridiagonal
00059 *          matrix.
00060 *          On exit, E has been destroyed.
00061 *
00062 *  Z       (input/output) COMPLEX array, dimension (LDZ, N)
00063 *          On entry, if COMPZ = 'V', the unitary matrix used in the
00064 *          reduction to tridiagonal form.
00065 *          On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
00066 *          original Hermitian matrix;
00067 *          if COMPZ = 'I', the orthonormal eigenvectors of the
00068 *          tridiagonal matrix.
00069 *          If INFO > 0 on exit, Z contains the eigenvectors associated
00070 *          with only the stored eigenvalues.
00071 *          If  COMPZ = 'N', then Z is not referenced.
00072 *
00073 *  LDZ     (input) INTEGER
00074 *          The leading dimension of the array Z.  LDZ >= 1, and if
00075 *          COMPZ = 'V' or 'I', LDZ >= max(1,N).
00076 *
00077 *  WORK    (workspace) REAL array, dimension (4*N)
00078 *
00079 *  INFO    (output) INTEGER
00080 *          = 0:  successful exit.
00081 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
00082 *          > 0:  if INFO = i, and i is:
00083 *                <= N  the Cholesky factorization of the matrix could
00084 *                      not be performed because the i-th principal minor
00085 *                      was not positive definite.
00086 *                > N   the SVD algorithm failed to converge;
00087 *                      if INFO = N+i, i off-diagonal elements of the
00088 *                      bidiagonal factor did not converge to zero.
00089 *
00090 *  ====================================================================
00091 *
00092 *     .. Parameters ..
00093       COMPLEX            CZERO, CONE
00094       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
00095      $                   CONE = ( 1.0E+0, 0.0E+0 ) )
00096 *     ..
00097 *     .. External Functions ..
00098       LOGICAL            LSAME
00099       EXTERNAL           LSAME
00100 *     ..
00101 *     .. External Subroutines ..
00102       EXTERNAL           CBDSQR, CLASET, SPTTRF, XERBLA
00103 *     ..
00104 *     .. Local Arrays ..
00105       COMPLEX            C( 1, 1 ), VT( 1, 1 )
00106 *     ..
00107 *     .. Local Scalars ..
00108       INTEGER            I, ICOMPZ, NRU
00109 *     ..
00110 *     .. Intrinsic Functions ..
00111       INTRINSIC          MAX, SQRT
00112 *     ..
00113 *     .. Executable Statements ..
00114 *
00115 *     Test the input parameters.
00116 *
00117       INFO = 0
00118 *
00119       IF( LSAME( COMPZ, 'N' ) ) THEN
00120          ICOMPZ = 0
00121       ELSE IF( LSAME( COMPZ, 'V' ) ) THEN
00122          ICOMPZ = 1
00123       ELSE IF( LSAME( COMPZ, 'I' ) ) THEN
00124          ICOMPZ = 2
00125       ELSE
00126          ICOMPZ = -1
00127       END IF
00128       IF( ICOMPZ.LT.0 ) THEN
00129          INFO = -1
00130       ELSE IF( N.LT.0 ) THEN
00131          INFO = -2
00132       ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1,
00133      $         N ) ) ) THEN
00134          INFO = -6
00135       END IF
00136       IF( INFO.NE.0 ) THEN
00137          CALL XERBLA( 'CPTEQR', -INFO )
00138          RETURN
00139       END IF
00140 *
00141 *     Quick return if possible
00142 *
00143       IF( N.EQ.0 )
00144      $   RETURN
00145 *
00146       IF( N.EQ.1 ) THEN
00147          IF( ICOMPZ.GT.0 )
00148      $      Z( 1, 1 ) = CONE
00149          RETURN
00150       END IF
00151       IF( ICOMPZ.EQ.2 )
00152      $   CALL CLASET( 'Full', N, N, CZERO, CONE, Z, LDZ )
00153 *
00154 *     Call SPTTRF to factor the matrix.
00155 *
00156       CALL SPTTRF( N, D, E, INFO )
00157       IF( INFO.NE.0 )
00158      $   RETURN
00159       DO 10 I = 1, N
00160          D( I ) = SQRT( D( I ) )
00161    10 CONTINUE
00162       DO 20 I = 1, N - 1
00163          E( I ) = E( I )*D( I )
00164    20 CONTINUE
00165 *
00166 *     Call CBDSQR to compute the singular values/vectors of the
00167 *     bidiagonal factor.
00168 *
00169       IF( ICOMPZ.GT.0 ) THEN
00170          NRU = N
00171       ELSE
00172          NRU = 0
00173       END IF
00174       CALL CBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1,
00175      $             WORK, INFO )
00176 *
00177 *     Square the singular values.
00178 *
00179       IF( INFO.EQ.0 ) THEN
00180          DO 30 I = 1, N
00181             D( I ) = D( I )*D( I )
00182    30    CONTINUE
00183       ELSE
00184          INFO = N + INFO
00185       END IF
00186 *
00187       RETURN
00188 *
00189 *     End of CPTEQR
00190 *
00191       END
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