LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ cpteqr()

subroutine cpteqr ( character  COMPZ,
integer  N,
real, dimension( * )  D,
real, dimension( * )  E,
complex, dimension( ldz, * )  Z,
integer  LDZ,
real, dimension( * )  WORK,
integer  INFO 
)

CPTEQR

Download CPTEQR + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CPTEQR computes all eigenvalues and, optionally, eigenvectors of a
 symmetric positive definite tridiagonal matrix by first factoring the
 matrix using SPTTRF and then calling CBDSQR to compute the singular
 values of the bidiagonal factor.

 This routine computes the eigenvalues of the positive definite
 tridiagonal matrix to high relative accuracy.  This means that if the
 eigenvalues range over many orders of magnitude in size, then the
 small eigenvalues and corresponding eigenvectors will be computed
 more accurately than, for example, with the standard QR method.

 The eigenvectors of a full or band positive definite Hermitian matrix
 can also be found if CHETRD, CHPTRD, or CHBTRD has been used to
 reduce this matrix to tridiagonal form.  (The reduction to
 tridiagonal form, however, may preclude the possibility of obtaining
 high relative accuracy in the small eigenvalues of the original
 matrix, if these eigenvalues range over many orders of magnitude.)
Parameters
[in]COMPZ
          COMPZ is CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'V':  Compute eigenvectors of original Hermitian
                  matrix also.  Array Z contains the unitary matrix
                  used to reduce the original matrix to tridiagonal
                  form.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
[in]N
          N is INTEGER
          The order of the matrix.  N >= 0.
[in,out]D
          D is REAL array, dimension (N)
          On entry, the n diagonal elements of the tridiagonal matrix.
          On normal exit, D contains the eigenvalues, in descending
          order.
[in,out]E
          E is REAL array, dimension (N-1)
          On entry, the (n-1) subdiagonal elements of the tridiagonal
          matrix.
          On exit, E has been destroyed.
[in,out]Z
          Z is COMPLEX array, dimension (LDZ, N)
          On entry, if COMPZ = 'V', the unitary matrix used in the
          reduction to tridiagonal form.
          On exit, if COMPZ = 'V', the orthonormal eigenvectors of the
          original Hermitian matrix;
          if COMPZ = 'I', the orthonormal eigenvectors of the
          tridiagonal matrix.
          If INFO > 0 on exit, Z contains the eigenvectors associated
          with only the stored eigenvalues.
          If  COMPZ = 'N', then Z is not referenced.
[in]LDZ
          LDZ is INTEGER
          The leading dimension of the array Z.  LDZ >= 1, and if
          COMPZ = 'V' or 'I', LDZ >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (4*N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          > 0:  if INFO = i, and i is:
                <= N  the Cholesky factorization of the matrix could
                      not be performed because the i-th principal minor
                      was not positive definite.
                > N   the SVD algorithm failed to converge;
                      if INFO = N+i, i off-diagonal elements of the
                      bidiagonal factor did not converge to zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 144 of file cpteqr.f.

145 *
146 * -- LAPACK computational routine --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 *
150 * .. Scalar Arguments ..
151  CHARACTER COMPZ
152  INTEGER INFO, LDZ, N
153 * ..
154 * .. Array Arguments ..
155  REAL D( * ), E( * ), WORK( * )
156  COMPLEX Z( LDZ, * )
157 * ..
158 *
159 * ====================================================================
160 *
161 * .. Parameters ..
162  COMPLEX CZERO, CONE
163  parameter( czero = ( 0.0e+0, 0.0e+0 ),
164  $ cone = ( 1.0e+0, 0.0e+0 ) )
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  EXTERNAL lsame
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL cbdsqr, claset, spttrf, xerbla
172 * ..
173 * .. Local Arrays ..
174  COMPLEX C( 1, 1 ), VT( 1, 1 )
175 * ..
176 * .. Local Scalars ..
177  INTEGER I, ICOMPZ, NRU
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC max, sqrt
181 * ..
182 * .. Executable Statements ..
183 *
184 * Test the input parameters.
185 *
186  info = 0
187 *
188  IF( lsame( compz, 'N' ) ) THEN
189  icompz = 0
190  ELSE IF( lsame( compz, 'V' ) ) THEN
191  icompz = 1
192  ELSE IF( lsame( compz, 'I' ) ) THEN
193  icompz = 2
194  ELSE
195  icompz = -1
196  END IF
197  IF( icompz.LT.0 ) THEN
198  info = -1
199  ELSE IF( n.LT.0 ) THEN
200  info = -2
201  ELSE IF( ( ldz.LT.1 ) .OR. ( icompz.GT.0 .AND. ldz.LT.max( 1,
202  $ n ) ) ) THEN
203  info = -6
204  END IF
205  IF( info.NE.0 ) THEN
206  CALL xerbla( 'CPTEQR', -info )
207  RETURN
208  END IF
209 *
210 * Quick return if possible
211 *
212  IF( n.EQ.0 )
213  $ RETURN
214 *
215  IF( n.EQ.1 ) THEN
216  IF( icompz.GT.0 )
217  $ z( 1, 1 ) = cone
218  RETURN
219  END IF
220  IF( icompz.EQ.2 )
221  $ CALL claset( 'Full', n, n, czero, cone, z, ldz )
222 *
223 * Call SPTTRF to factor the matrix.
224 *
225  CALL spttrf( n, d, e, info )
226  IF( info.NE.0 )
227  $ RETURN
228  DO 10 i = 1, n
229  d( i ) = sqrt( d( i ) )
230  10 CONTINUE
231  DO 20 i = 1, n - 1
232  e( i ) = e( i )*d( i )
233  20 CONTINUE
234 *
235 * Call CBDSQR to compute the singular values/vectors of the
236 * bidiagonal factor.
237 *
238  IF( icompz.GT.0 ) THEN
239  nru = n
240  ELSE
241  nru = 0
242  END IF
243  CALL cbdsqr( 'Lower', n, 0, nru, 0, d, e, vt, 1, z, ldz, c, 1,
244  $ work, info )
245 *
246 * Square the singular values.
247 *
248  IF( info.EQ.0 ) THEN
249  DO 30 i = 1, n
250  d( i ) = d( i )*d( i )
251  30 CONTINUE
252  ELSE
253  info = n + info
254  END IF
255 *
256  RETURN
257 *
258 * End of CPTEQR
259 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine spttrf(N, D, E, INFO)
SPTTRF
Definition: spttrf.f:91
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine cbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, RWORK, INFO)
CBDSQR
Definition: cbdsqr.f:222
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