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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZPTEQR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZPTEQR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpteqr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpteqr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpteqr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER COMPZ 00025 * INTEGER INFO, LDZ, N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION D( * ), E( * ), WORK( * ) 00029 * COMPLEX*16 Z( LDZ, * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> ZPTEQR computes all eigenvalues and, optionally, eigenvectors of a 00039 *> symmetric positive definite tridiagonal matrix by first factoring the 00040 *> matrix using DPTTRF and then calling ZBDSQR to compute the singular 00041 *> values of the bidiagonal factor. 00042 *> 00043 *> This routine computes the eigenvalues of the positive definite 00044 *> tridiagonal matrix to high relative accuracy. This means that if the 00045 *> eigenvalues range over many orders of magnitude in size, then the 00046 *> small eigenvalues and corresponding eigenvectors will be computed 00047 *> more accurately than, for example, with the standard QR method. 00048 *> 00049 *> The eigenvectors of a full or band positive definite Hermitian matrix 00050 *> can also be found if ZHETRD, ZHPTRD, or ZHBTRD has been used to 00051 *> reduce this matrix to tridiagonal form. (The reduction to 00052 *> tridiagonal form, however, may preclude the possibility of obtaining 00053 *> high relative accuracy in the small eigenvalues of the original 00054 *> matrix, if these eigenvalues range over many orders of magnitude.) 00055 *> \endverbatim 00056 * 00057 * Arguments: 00058 * ========== 00059 * 00060 *> \param[in] COMPZ 00061 *> \verbatim 00062 *> COMPZ is CHARACTER*1 00063 *> = 'N': Compute eigenvalues only. 00064 *> = 'V': Compute eigenvectors of original Hermitian 00065 *> matrix also. Array Z contains the unitary matrix 00066 *> used to reduce the original matrix to tridiagonal 00067 *> form. 00068 *> = 'I': Compute eigenvectors of tridiagonal matrix also. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] N 00072 *> \verbatim 00073 *> N is INTEGER 00074 *> The order of the matrix. N >= 0. 00075 *> \endverbatim 00076 *> 00077 *> \param[in,out] D 00078 *> \verbatim 00079 *> D is DOUBLE PRECISION array, dimension (N) 00080 *> On entry, the n diagonal elements of the tridiagonal matrix. 00081 *> On normal exit, D contains the eigenvalues, in descending 00082 *> order. 00083 *> \endverbatim 00084 *> 00085 *> \param[in,out] E 00086 *> \verbatim 00087 *> E is DOUBLE PRECISION array, dimension (N-1) 00088 *> On entry, the (n-1) subdiagonal elements of the tridiagonal 00089 *> matrix. 00090 *> On exit, E has been destroyed. 00091 *> \endverbatim 00092 *> 00093 *> \param[in,out] Z 00094 *> \verbatim 00095 *> Z is COMPLEX*16 array, dimension (LDZ, N) 00096 *> On entry, if COMPZ = 'V', the unitary matrix used in the 00097 *> reduction to tridiagonal form. 00098 *> On exit, if COMPZ = 'V', the orthonormal eigenvectors of the 00099 *> original Hermitian matrix; 00100 *> if COMPZ = 'I', the orthonormal eigenvectors of the 00101 *> tridiagonal matrix. 00102 *> If INFO > 0 on exit, Z contains the eigenvectors associated 00103 *> with only the stored eigenvalues. 00104 *> If COMPZ = 'N', then Z is not referenced. 00105 *> \endverbatim 00106 *> 00107 *> \param[in] LDZ 00108 *> \verbatim 00109 *> LDZ is INTEGER 00110 *> The leading dimension of the array Z. LDZ >= 1, and if 00111 *> COMPZ = 'V' or 'I', LDZ >= max(1,N). 00112 *> \endverbatim 00113 *> 00114 *> \param[out] WORK 00115 *> \verbatim 00116 *> WORK is DOUBLE PRECISION array, dimension (4*N) 00117 *> \endverbatim 00118 *> 00119 *> \param[out] INFO 00120 *> \verbatim 00121 *> INFO is INTEGER 00122 *> = 0: successful exit. 00123 *> < 0: if INFO = -i, the i-th argument had an illegal value. 00124 *> > 0: if INFO = i, and i is: 00125 *> <= N the Cholesky factorization of the matrix could 00126 *> not be performed because the i-th principal minor 00127 *> was not positive definite. 00128 *> > N the SVD algorithm failed to converge; 00129 *> if INFO = N+i, i off-diagonal elements of the 00130 *> bidiagonal factor did not converge to zero. 00131 *> \endverbatim 00132 * 00133 * Authors: 00134 * ======== 00135 * 00136 *> \author Univ. of Tennessee 00137 *> \author Univ. of California Berkeley 00138 *> \author Univ. of Colorado Denver 00139 *> \author NAG Ltd. 00140 * 00141 *> \date November 2011 00142 * 00143 *> \ingroup complex16OTHERcomputational 00144 * 00145 * ===================================================================== 00146 SUBROUTINE ZPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) 00147 * 00148 * -- LAPACK computational routine (version 3.4.0) -- 00149 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00151 * November 2011 00152 * 00153 * .. Scalar Arguments .. 00154 CHARACTER COMPZ 00155 INTEGER INFO, LDZ, N 00156 * .. 00157 * .. Array Arguments .. 00158 DOUBLE PRECISION D( * ), E( * ), WORK( * ) 00159 COMPLEX*16 Z( LDZ, * ) 00160 * .. 00161 * 00162 * ==================================================================== 00163 * 00164 * .. Parameters .. 00165 COMPLEX*16 CZERO, CONE 00166 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 00167 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 00168 * .. 00169 * .. External Functions .. 00170 LOGICAL LSAME 00171 EXTERNAL LSAME 00172 * .. 00173 * .. External Subroutines .. 00174 EXTERNAL DPTTRF, XERBLA, ZBDSQR, ZLASET 00175 * .. 00176 * .. Local Arrays .. 00177 COMPLEX*16 C( 1, 1 ), VT( 1, 1 ) 00178 * .. 00179 * .. Local Scalars .. 00180 INTEGER I, ICOMPZ, NRU 00181 * .. 00182 * .. Intrinsic Functions .. 00183 INTRINSIC MAX, SQRT 00184 * .. 00185 * .. Executable Statements .. 00186 * 00187 * Test the input parameters. 00188 * 00189 INFO = 0 00190 * 00191 IF( LSAME( COMPZ, 'N' ) ) THEN 00192 ICOMPZ = 0 00193 ELSE IF( LSAME( COMPZ, 'V' ) ) THEN 00194 ICOMPZ = 1 00195 ELSE IF( LSAME( COMPZ, 'I' ) ) THEN 00196 ICOMPZ = 2 00197 ELSE 00198 ICOMPZ = -1 00199 END IF 00200 IF( ICOMPZ.LT.0 ) THEN 00201 INFO = -1 00202 ELSE IF( N.LT.0 ) THEN 00203 INFO = -2 00204 ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, 00205 $ N ) ) ) THEN 00206 INFO = -6 00207 END IF 00208 IF( INFO.NE.0 ) THEN 00209 CALL XERBLA( 'ZPTEQR', -INFO ) 00210 RETURN 00211 END IF 00212 * 00213 * Quick return if possible 00214 * 00215 IF( N.EQ.0 ) 00216 $ RETURN 00217 * 00218 IF( N.EQ.1 ) THEN 00219 IF( ICOMPZ.GT.0 ) 00220 $ Z( 1, 1 ) = CONE 00221 RETURN 00222 END IF 00223 IF( ICOMPZ.EQ.2 ) 00224 $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ ) 00225 * 00226 * Call DPTTRF to factor the matrix. 00227 * 00228 CALL DPTTRF( N, D, E, INFO ) 00229 IF( INFO.NE.0 ) 00230 $ RETURN 00231 DO 10 I = 1, N 00232 D( I ) = SQRT( D( I ) ) 00233 10 CONTINUE 00234 DO 20 I = 1, N - 1 00235 E( I ) = E( I )*D( I ) 00236 20 CONTINUE 00237 * 00238 * Call ZBDSQR to compute the singular values/vectors of the 00239 * bidiagonal factor. 00240 * 00241 IF( ICOMPZ.GT.0 ) THEN 00242 NRU = N 00243 ELSE 00244 NRU = 0 00245 END IF 00246 CALL ZBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1, 00247 $ WORK, INFO ) 00248 * 00249 * Square the singular values. 00250 * 00251 IF( INFO.EQ.0 ) THEN 00252 DO 30 I = 1, N 00253 D( I ) = D( I )*D( I ) 00254 30 CONTINUE 00255 ELSE 00256 INFO = N + INFO 00257 END IF 00258 * 00259 RETURN 00260 * 00261 * End of ZPTEQR 00262 * 00263 END