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1 SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) |
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2 * |
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3 * -- LAPACK routine (version 3.1) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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5 * November 2006 |
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6 * |
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7 * .. Scalar Arguments .. |
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8 INTEGER IHI, ILO, INFO, LDA, LWORK, N |
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9 * .. |
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10 * .. Array Arguments .. |
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11 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) |
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12 * .. |
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13 * |
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14 * Purpose |
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15 * ======= |
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16 * |
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17 * ZUNGHR generates a complex unitary matrix Q which is defined as the |
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18 * product of IHI-ILO elementary reflectors of order N, as returned by |
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19 * ZGEHRD: |
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20 * |
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21 * Q = H(ilo) H(ilo+1) . . . H(ihi-1). |
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22 * |
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23 * Arguments |
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24 * ========= |
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25 * |
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26 * N (input) INTEGER |
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27 * The order of the matrix Q. N >= 0. |
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28 * |
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29 * ILO (input) INTEGER |
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30 * IHI (input) INTEGER |
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31 * ILO and IHI must have the same values as in the previous call |
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32 * of ZGEHRD. Q is equal to the unit matrix except in the |
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33 * submatrix Q(ilo+1:ihi,ilo+1:ihi). |
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34 * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. |
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35 * |
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36 * A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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37 * On entry, the vectors which define the elementary reflectors, |
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38 * as returned by ZGEHRD. |
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39 * On exit, the N-by-N unitary matrix Q. |
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40 * |
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41 * LDA (input) INTEGER |
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42 * The leading dimension of the array A. LDA >= max(1,N). |
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43 * |
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44 * TAU (input) COMPLEX*16 array, dimension (N-1) |
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45 * TAU(i) must contain the scalar factor of the elementary |
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46 * reflector H(i), as returned by ZGEHRD. |
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47 * |
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48 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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49 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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50 * |
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51 * LWORK (input) INTEGER |
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52 * The dimension of the array WORK. LWORK >= IHI-ILO. |
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53 * For optimum performance LWORK >= (IHI-ILO)*NB, where NB is |
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54 * the optimal blocksize. |
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55 * |
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56 * If LWORK = -1, then a workspace query is assumed; the routine |
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57 * only calculates the optimal size of the WORK array, returns |
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58 * this value as the first entry of the WORK array, and no error |
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59 * message related to LWORK is issued by XERBLA. |
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60 * |
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61 * INFO (output) INTEGER |
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62 * = 0: successful exit |
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63 * < 0: if INFO = -i, the i-th argument had an illegal value |
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64 * |
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65 * ===================================================================== |
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66 * |
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67 * .. Parameters .. |
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68 COMPLEX*16 ZERO, ONE |
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69 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), |
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70 $ ONE = ( 1.0D+0, 0.0D+0 ) ) |
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71 * .. |
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72 * .. Local Scalars .. |
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73 LOGICAL LQUERY |
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74 INTEGER I, IINFO, J, LWKOPT, NB, NH |
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75 * .. |
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76 * .. External Subroutines .. |
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77 EXTERNAL XERBLA, ZUNGQR |
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78 * .. |
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79 * .. External Functions .. |
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80 INTEGER ILAENV |
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81 EXTERNAL ILAENV |
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82 * .. |
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83 * .. Intrinsic Functions .. |
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84 INTRINSIC MAX, MIN |
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85 * .. |
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86 * .. Executable Statements .. |
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87 * |
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88 * Test the input arguments |
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89 * |
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90 INFO = 0 |
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91 NH = IHI - ILO |
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92 LQUERY = ( LWORK.EQ.-1 ) |
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93 IF( N.LT.0 ) THEN |
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94 INFO = -1 |
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95 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN |
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96 INFO = -2 |
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97 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN |
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98 INFO = -3 |
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99 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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100 INFO = -5 |
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101 ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN |
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102 INFO = -8 |
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103 END IF |
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104 * |
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105 IF( INFO.EQ.0 ) THEN |
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106 NB = ILAENV( 1, 'ZUNGQR', ' ', NH, NH, NH, -1 ) |
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107 LWKOPT = MAX( 1, NH )*NB |
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108 WORK( 1 ) = LWKOPT |
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109 END IF |
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110 * |
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111 IF( INFO.NE.0 ) THEN |
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112 CALL XERBLA( 'ZUNGHR', -INFO ) |
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113 RETURN |
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114 ELSE IF( LQUERY ) THEN |
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115 RETURN |
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116 END IF |
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117 * |
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118 * Quick return if possible |
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119 * |
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120 IF( N.EQ.0 ) THEN |
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121 WORK( 1 ) = 1 |
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122 RETURN |
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123 END IF |
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124 * |
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125 * Shift the vectors which define the elementary reflectors one |
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126 * column to the right, and set the first ilo and the last n-ihi |
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127 * rows and columns to those of the unit matrix |
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128 * |
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129 DO 40 J = IHI, ILO + 1, -1 |
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130 DO 10 I = 1, J - 1 |
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131 A( I, J ) = ZERO |
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132 10 CONTINUE |
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133 DO 20 I = J + 1, IHI |
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134 A( I, J ) = A( I, J-1 ) |
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135 20 CONTINUE |
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136 DO 30 I = IHI + 1, N |
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137 A( I, J ) = ZERO |
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138 30 CONTINUE |
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139 40 CONTINUE |
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140 DO 60 J = 1, ILO |
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141 DO 50 I = 1, N |
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142 A( I, J ) = ZERO |
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143 50 CONTINUE |
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144 A( J, J ) = ONE |
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145 60 CONTINUE |
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146 DO 80 J = IHI + 1, N |
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147 DO 70 I = 1, N |
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148 A( I, J ) = ZERO |
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149 70 CONTINUE |
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150 A( J, J ) = ONE |
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151 80 CONTINUE |
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152 * |
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153 IF( NH.GT.0 ) THEN |
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154 * |
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155 * Generate Q(ilo+1:ihi,ilo+1:ihi) |
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156 * |
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157 CALL ZUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ), |
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158 $ WORK, LWORK, IINFO ) |
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159 END IF |
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160 WORK( 1 ) = LWKOPT |
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161 RETURN |
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162 * |
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163 * End of ZUNGHR |
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164 * |
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165 END |
