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1 SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, |
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2 $ LDC, WORK, LWORK, INFO ) |
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3 * |
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4 * -- LAPACK routine (version 3.1) -- |
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5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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6 * November 2006 |
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7 * |
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8 * .. Scalar Arguments .. |
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9 CHARACTER SIDE, TRANS, VECT |
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10 INTEGER INFO, K, LDA, LDC, LWORK, M, N |
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11 * .. |
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12 * .. Array Arguments .. |
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13 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), 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 * If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C |
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20 * with |
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21 * SIDE = 'L' SIDE = 'R' |
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22 * TRANS = 'N': Q * C C * Q |
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23 * TRANS = 'C': Q**H * C C * Q**H |
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24 * |
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25 * If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C |
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26 * with |
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27 * SIDE = 'L' SIDE = 'R' |
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28 * TRANS = 'N': P * C C * P |
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29 * TRANS = 'C': P**H * C C * P**H |
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30 * |
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31 * Here Q and P**H are the unitary matrices determined by ZGEBRD when |
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32 * reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q |
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33 * and P**H are defined as products of elementary reflectors H(i) and |
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34 * G(i) respectively. |
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35 * |
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36 * Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the |
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37 * order of the unitary matrix Q or P**H that is applied. |
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38 * |
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39 * If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: |
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40 * if nq >= k, Q = H(1) H(2) . . . H(k); |
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41 * if nq < k, Q = H(1) H(2) . . . H(nq-1). |
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42 * |
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43 * If VECT = 'P', A is assumed to have been a K-by-NQ matrix: |
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44 * if k < nq, P = G(1) G(2) . . . G(k); |
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45 * if k >= nq, P = G(1) G(2) . . . G(nq-1). |
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46 * |
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47 * Arguments |
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48 * ========= |
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49 * |
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50 * VECT (input) CHARACTER*1 |
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51 * = 'Q': apply Q or Q**H; |
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52 * = 'P': apply P or P**H. |
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53 * |
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54 * SIDE (input) CHARACTER*1 |
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55 * = 'L': apply Q, Q**H, P or P**H from the Left; |
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56 * = 'R': apply Q, Q**H, P or P**H from the Right. |
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57 * |
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58 * TRANS (input) CHARACTER*1 |
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59 * = 'N': No transpose, apply Q or P; |
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60 * = 'C': Conjugate transpose, apply Q**H or P**H. |
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61 * |
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62 * M (input) INTEGER |
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63 * The number of rows of the matrix C. M >= 0. |
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64 * |
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65 * N (input) INTEGER |
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66 * The number of columns of the matrix C. N >= 0. |
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67 * |
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68 * K (input) INTEGER |
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69 * If VECT = 'Q', the number of columns in the original |
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70 * matrix reduced by ZGEBRD. |
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71 * If VECT = 'P', the number of rows in the original |
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72 * matrix reduced by ZGEBRD. |
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73 * K >= 0. |
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74 * |
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75 * A (input) COMPLEX*16 array, dimension |
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76 * (LDA,min(nq,K)) if VECT = 'Q' |
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77 * (LDA,nq) if VECT = 'P' |
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78 * The vectors which define the elementary reflectors H(i) and |
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79 * G(i), whose products determine the matrices Q and P, as |
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80 * returned by ZGEBRD. |
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81 * |
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82 * LDA (input) INTEGER |
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83 * The leading dimension of the array A. |
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84 * If VECT = 'Q', LDA >= max(1,nq); |
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85 * if VECT = 'P', LDA >= max(1,min(nq,K)). |
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86 * |
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87 * TAU (input) COMPLEX*16 array, dimension (min(nq,K)) |
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88 * TAU(i) must contain the scalar factor of the elementary |
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89 * reflector H(i) or G(i) which determines Q or P, as returned |
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90 * by ZGEBRD in the array argument TAUQ or TAUP. |
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91 * |
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92 * C (input/output) COMPLEX*16 array, dimension (LDC,N) |
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93 * On entry, the M-by-N matrix C. |
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94 * On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q |
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95 * or P*C or P**H*C or C*P or C*P**H. |
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96 * |
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97 * LDC (input) INTEGER |
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98 * The leading dimension of the array C. LDC >= max(1,M). |
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99 * |
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100 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
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101 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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102 * |
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103 * LWORK (input) INTEGER |
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104 * The dimension of the array WORK. |
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105 * If SIDE = 'L', LWORK >= max(1,N); |
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106 * if SIDE = 'R', LWORK >= max(1,M); |
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107 * if N = 0 or M = 0, LWORK >= 1. |
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108 * For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', |
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109 * and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the |
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110 * optimal blocksize. (NB = 0 if M = 0 or N = 0.) |
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111 * |
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112 * If LWORK = -1, then a workspace query is assumed; the routine |
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113 * only calculates the optimal size of the WORK array, returns |
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114 * this value as the first entry of the WORK array, and no error |
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115 * message related to LWORK is issued by XERBLA. |
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116 * |
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117 * INFO (output) INTEGER |
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118 * = 0: successful exit |
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119 * < 0: if INFO = -i, the i-th argument had an illegal value |
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120 * |
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121 * ===================================================================== |
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122 * |
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123 * .. Local Scalars .. |
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124 LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN |
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125 CHARACTER TRANST |
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126 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW |
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127 * .. |
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128 * .. External Functions .. |
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129 LOGICAL LSAME |
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130 INTEGER ILAENV |
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131 EXTERNAL LSAME, ILAENV |
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132 * .. |
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133 * .. External Subroutines .. |
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134 EXTERNAL XERBLA, ZUNMLQ, ZUNMQR |
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135 * .. |
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136 * .. Intrinsic Functions .. |
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137 INTRINSIC MAX, MIN |
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138 * .. |
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139 * .. Executable Statements .. |
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140 * |
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141 * Test the input arguments |
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142 * |
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143 INFO = 0 |
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144 APPLYQ = LSAME( VECT, 'Q' ) |
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145 LEFT = LSAME( SIDE, 'L' ) |
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146 NOTRAN = LSAME( TRANS, 'N' ) |
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147 LQUERY = ( LWORK.EQ.-1 ) |
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148 * |
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149 * NQ is the order of Q or P and NW is the minimum dimension of WORK |
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150 * |
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151 IF( LEFT ) THEN |
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152 NQ = M |
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153 NW = N |
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154 ELSE |
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155 NQ = N |
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156 NW = M |
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157 END IF |
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158 IF( M.EQ.0 .OR. N.EQ.0 ) THEN |
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159 NW = 0 |
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160 END IF |
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161 IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN |
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162 INFO = -1 |
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163 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN |
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164 INFO = -2 |
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165 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN |
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166 INFO = -3 |
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167 ELSE IF( M.LT.0 ) THEN |
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168 INFO = -4 |
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169 ELSE IF( N.LT.0 ) THEN |
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170 INFO = -5 |
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171 ELSE IF( K.LT.0 ) THEN |
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172 INFO = -6 |
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173 ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. |
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174 $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) |
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175 $ THEN |
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176 INFO = -8 |
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177 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
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178 INFO = -11 |
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179 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN |
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180 INFO = -13 |
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181 END IF |
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182 * |
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183 IF( INFO.EQ.0 ) THEN |
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184 IF( NW.GT.0 ) THEN |
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185 IF( APPLYQ ) THEN |
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186 IF( LEFT ) THEN |
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187 NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1, |
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188 $ -1 ) |
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189 ELSE |
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190 NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1, |
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191 $ -1 ) |
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192 END IF |
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193 ELSE |
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194 IF( LEFT ) THEN |
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195 NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M-1, N, M-1, |
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196 $ -1 ) |
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197 ELSE |
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198 NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N-1, N-1, |
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199 $ -1 ) |
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200 END IF |
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201 END IF |
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202 LWKOPT = MAX( 1, NW*NB ) |
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203 ELSE |
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204 LWKOPT = 1 |
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205 END IF |
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206 WORK( 1 ) = LWKOPT |
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207 END IF |
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208 * |
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209 IF( INFO.NE.0 ) THEN |
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210 CALL XERBLA( 'ZUNMBR', -INFO ) |
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211 RETURN |
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212 ELSE IF( LQUERY ) THEN |
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213 RETURN |
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214 END IF |
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215 * |
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216 * Quick return if possible |
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217 * |
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218 IF( M.EQ.0 .OR. N.EQ.0 ) |
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219 $ RETURN |
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220 * |
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221 IF( APPLYQ ) THEN |
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222 * |
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223 * Apply Q |
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224 * |
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225 IF( NQ.GE.K ) THEN |
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226 * |
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227 * Q was determined by a call to ZGEBRD with nq >= k |
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228 * |
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229 CALL ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
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230 $ WORK, LWORK, IINFO ) |
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231 ELSE IF( NQ.GT.1 ) THEN |
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232 * |
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233 * Q was determined by a call to ZGEBRD with nq < k |
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234 * |
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235 IF( LEFT ) THEN |
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236 MI = M - 1 |
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237 NI = N |
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238 I1 = 2 |
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239 I2 = 1 |
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240 ELSE |
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241 MI = M |
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242 NI = N - 1 |
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243 I1 = 1 |
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244 I2 = 2 |
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245 END IF |
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246 CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, |
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247 $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) |
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248 END IF |
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249 ELSE |
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250 * |
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251 * Apply P |
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252 * |
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253 IF( NOTRAN ) THEN |
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254 TRANST = 'C' |
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255 ELSE |
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256 TRANST = 'N' |
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257 END IF |
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258 IF( NQ.GT.K ) THEN |
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259 * |
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260 * P was determined by a call to ZGEBRD with nq > k |
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261 * |
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262 CALL ZUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, |
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263 $ WORK, LWORK, IINFO ) |
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264 ELSE IF( NQ.GT.1 ) THEN |
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265 * |
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266 * P was determined by a call to ZGEBRD with nq <= k |
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267 * |
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268 IF( LEFT ) THEN |
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269 MI = M - 1 |
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270 NI = N |
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271 I1 = 2 |
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272 I2 = 1 |
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273 ELSE |
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274 MI = M |
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275 NI = N - 1 |
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276 I1 = 1 |
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277 I2 = 2 |
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278 END IF |
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279 CALL ZUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, |
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280 $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) |
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281 END IF |
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282 END IF |
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283 WORK( 1 ) = LWKOPT |
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284 RETURN |
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285 * |
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286 * End of ZUNMBR |
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287 * |
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288 END |
