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1 SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) |
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2 * |
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3 * -- LAPACK driver routine (version 3.0) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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5 * Courant Institute, Argonne National Lab, and Rice University |
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6 * June 30, 1999 |
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7 * |
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8 * .. Scalar Arguments .. |
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9 CHARACTER JOBZ, UPLO |
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10 INTEGER INFO, LDA, LWORK, N |
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11 * .. |
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12 * .. Array Arguments .. |
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13 DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) |
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14 * .. |
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15 * |
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16 * Purpose |
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17 * ======= |
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18 * |
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19 * DSYEV computes all eigenvalues and, optionally, eigenvectors of a |
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20 * real symmetric matrix A. |
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21 * |
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22 * Arguments |
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23 * ========= |
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24 * |
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25 * JOBZ (input) CHARACTER*1 |
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26 * = 'N': Compute eigenvalues only; |
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27 * = 'V': Compute eigenvalues and eigenvectors. |
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28 * |
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29 * UPLO (input) CHARACTER*1 |
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30 * = 'U': Upper triangle of A is stored; |
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31 * = 'L': Lower triangle of A is stored. |
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32 * |
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33 * N (input) INTEGER |
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34 * The order of the matrix A. N >= 0. |
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35 * |
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36 * A (input/output) DOUBLE PRECISION array, dimension (LDA, N) |
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37 * On entry, the symmetric matrix A. If UPLO = 'U', the |
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38 * leading N-by-N upper triangular part of A contains the |
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39 * upper triangular part of the matrix A. If UPLO = 'L', |
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40 * the leading N-by-N lower triangular part of A contains |
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41 * the lower triangular part of the matrix A. |
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42 * On exit, if JOBZ = 'V', then if INFO = 0, A contains the |
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43 * orthonormal eigenvectors of the matrix A. |
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44 * If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') |
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45 * or the upper triangle (if UPLO='U') of A, including the |
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46 * diagonal, is destroyed. |
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47 * |
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48 * LDA (input) INTEGER |
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49 * The leading dimension of the array A. LDA >= max(1,N). |
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50 * |
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51 * W (output) DOUBLE PRECISION array, dimension (N) |
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52 * If INFO = 0, the eigenvalues in ascending order. |
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53 * |
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54 * WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK) |
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55 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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56 * |
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57 * LWORK (input) INTEGER |
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58 * The length of the array WORK. LWORK >= max(1,3*N-1). |
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59 * For optimal efficiency, LWORK >= (NB+2)*N, |
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60 * where NB is the blocksize for DSYTRD returned by ILAENV. |
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61 * |
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62 * If LWORK = -1, then a workspace query is assumed; the routine |
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63 * only calculates the optimal size of the WORK array, returns |
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64 * this value as the first entry of the WORK array, and no error |
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65 * message related to LWORK is issued by XERBLA. |
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66 * |
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67 * INFO (output) INTEGER |
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68 * = 0: successful exit |
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69 * < 0: if INFO = -i, the i-th argument had an illegal value |
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70 * > 0: if INFO = i, the algorithm failed to converge; i |
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71 * off-diagonal elements of an intermediate tridiagonal |
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72 * form did not converge to zero. |
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73 * |
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74 * ===================================================================== |
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75 * |
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76 * .. Parameters .. |
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77 DOUBLE PRECISION ZERO, ONE |
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78 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) |
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79 * .. |
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80 * .. Local Scalars .. |
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81 LOGICAL LOWER, LQUERY, WANTZ |
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82 INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, |
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83 $ LLWORK, LOPT, LWKOPT, NB |
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84 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, |
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85 $ SMLNUM |
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86 * .. |
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87 * .. External Functions .. |
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88 LOGICAL LSAME |
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89 INTEGER ILAENV |
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90 DOUBLE PRECISION DLAMCH, DLANSY |
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91 EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY |
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92 * .. |
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93 * .. External Subroutines .. |
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94 EXTERNAL DLASCL, DORGTR, DSCAL, DSTEQR, DSTERF, DSYTRD, |
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95 $ XERBLA |
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96 * .. |
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97 * .. Intrinsic Functions .. |
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98 INTRINSIC MAX, SQRT |
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99 * .. |
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100 * .. Executable Statements .. |
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101 * |
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102 * Test the input parameters. |
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103 * |
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104 WANTZ = LSAME( JOBZ, 'V' ) |
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105 LOWER = LSAME( UPLO, 'L' ) |
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106 LQUERY = ( LWORK.EQ.-1 ) |
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107 * |
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108 INFO = 0 |
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109 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN |
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110 INFO = -1 |
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111 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN |
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112 INFO = -2 |
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113 ELSE IF( N.LT.0 ) THEN |
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114 INFO = -3 |
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115 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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116 INFO = -5 |
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117 ELSE IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY ) THEN |
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118 INFO = -8 |
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119 END IF |
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120 * |
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121 IF( INFO.EQ.0 ) THEN |
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122 NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) |
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123 LWKOPT = MAX( 1, ( NB+2 )*N ) |
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124 WORK( 1 ) = LWKOPT |
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125 END IF |
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126 * |
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127 IF( INFO.NE.0 ) THEN |
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128 CALL XERBLA( 'DSYEV ', -INFO ) |
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129 RETURN |
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130 ELSE IF( LQUERY ) THEN |
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131 RETURN |
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132 END IF |
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133 * |
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134 * Quick return if possible |
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135 * |
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136 IF( N.EQ.0 ) THEN |
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137 WORK( 1 ) = 1 |
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138 RETURN |
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139 END IF |
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140 * |
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141 IF( N.EQ.1 ) THEN |
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142 W( 1 ) = A( 1, 1 ) |
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143 WORK( 1 ) = 3 |
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144 IF( WANTZ ) |
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145 $ A( 1, 1 ) = ONE |
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146 RETURN |
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147 END IF |
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148 * |
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149 * Get machine constants. |
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150 * |
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151 SAFMIN = DLAMCH( 'Safe minimum' ) |
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152 EPS = DLAMCH( 'Precision' ) |
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153 SMLNUM = SAFMIN / EPS |
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154 BIGNUM = ONE / SMLNUM |
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155 RMIN = SQRT( SMLNUM ) |
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156 RMAX = SQRT( BIGNUM ) |
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157 * |
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158 * Scale matrix to allowable range, if necessary. |
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159 * |
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160 ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) |
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161 ISCALE = 0 |
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162 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN |
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163 ISCALE = 1 |
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164 SIGMA = RMIN / ANRM |
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165 ELSE IF( ANRM.GT.RMAX ) THEN |
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166 ISCALE = 1 |
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167 SIGMA = RMAX / ANRM |
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168 END IF |
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169 IF( ISCALE.EQ.1 ) |
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170 $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) |
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171 * |
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172 * Call DSYTRD to reduce symmetric matrix to tridiagonal form. |
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173 * |
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174 INDE = 1 |
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175 INDTAU = INDE + N |
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176 INDWRK = INDTAU + N |
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177 LLWORK = LWORK - INDWRK + 1 |
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178 CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), |
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179 $ WORK( INDWRK ), LLWORK, IINFO ) |
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180 LOPT = 2*N + WORK( INDWRK ) |
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181 * |
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182 * For eigenvalues only, call DSTERF. For eigenvectors, first call |
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183 * DORGTR to generate the orthogonal matrix, then call DSTEQR. |
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184 * |
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185 IF( .NOT.WANTZ ) THEN |
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186 CALL DSTERF( N, W, WORK( INDE ), INFO ) |
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187 ELSE |
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188 CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), |
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189 $ LLWORK, IINFO ) |
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190 CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ), |
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191 $ INFO ) |
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192 END IF |
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193 * |
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194 * If matrix was scaled, then rescale eigenvalues appropriately. |
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195 * |
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196 IF( ISCALE.EQ.1 ) THEN |
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197 IF( INFO.EQ.0 ) THEN |
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198 IMAX = N |
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199 ELSE |
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200 IMAX = INFO - 1 |
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201 END IF |
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202 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) |
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203 END IF |
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204 * |
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205 * Set WORK(1) to optimal workspace size. |
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206 * |
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207 WORK( 1 ) = LWKOPT |
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208 * |
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209 RETURN |
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210 * |
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211 * End of DSYEV |
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212 * |
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213 END |
