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1 SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) |
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2 * |
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3 * -- LAPACK 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 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 COMPLEX*16 A( LDA, * ), 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 * ZUNGTR generates a complex unitary matrix Q which is defined as the |
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20 * product of n-1 elementary reflectors of order N, as returned by |
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21 * ZHETRD: |
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22 * |
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23 * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), |
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24 * |
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25 * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). |
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26 * |
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27 * Arguments |
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28 * ========= |
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29 * |
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30 * UPLO (input) CHARACTER*1 |
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31 * = 'U': Upper triangle of A contains elementary reflectors |
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32 * from ZHETRD; |
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33 * = 'L': Lower triangle of A contains elementary reflectors |
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34 * from ZHETRD. |
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35 * |
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36 * N (input) INTEGER |
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37 * The order of the matrix Q. N >= 0. |
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38 * |
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39 * A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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40 * On entry, the vectors which define the elementary reflectors, |
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41 * as returned by ZHETRD. |
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42 * On exit, the N-by-N unitary matrix Q. |
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43 * |
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44 * LDA (input) INTEGER |
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45 * The leading dimension of the array A. LDA >= N. |
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46 * |
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47 * TAU (input) COMPLEX*16 array, dimension (N-1) |
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48 * TAU(i) must contain the scalar factor of the elementary |
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49 * reflector H(i), as returned by ZHETRD. |
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50 * |
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51 * WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) |
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52 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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53 * |
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54 * LWORK (input) INTEGER |
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55 * The dimension of the array WORK. LWORK >= N-1. |
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56 * For optimum performance LWORK >= (N-1)*NB, where NB is |
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57 * the optimal blocksize. |
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58 * |
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59 * If LWORK = -1, then a workspace query is assumed; the routine |
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60 * only calculates the optimal size of the WORK array, returns |
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61 * this value as the first entry of the WORK array, and no error |
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62 * message related to LWORK is issued by XERBLA. |
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63 * |
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64 * INFO (output) INTEGER |
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65 * = 0: successful exit |
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66 * < 0: if INFO = -i, the i-th argument had an illegal value |
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67 * |
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68 * ===================================================================== |
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69 * |
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70 * .. Parameters .. |
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71 COMPLEX*16 ZERO, ONE |
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72 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), |
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73 $ ONE = ( 1.0D+0, 0.0D+0 ) ) |
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74 * .. |
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75 * .. Local Scalars .. |
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76 LOGICAL LQUERY, UPPER |
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77 INTEGER I, IINFO, J, LWKOPT, NB |
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78 * .. |
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79 * .. External Functions .. |
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80 LOGICAL LSAME |
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81 INTEGER ILAENV |
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82 EXTERNAL LSAME, ILAENV |
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83 * .. |
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84 * .. External Subroutines .. |
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85 EXTERNAL XERBLA, ZUNGQL, ZUNGQR |
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86 * .. |
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87 * .. Intrinsic Functions .. |
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88 INTRINSIC MAX |
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89 * .. |
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90 * .. Executable Statements .. |
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91 * |
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92 * Test the input arguments |
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93 * |
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94 INFO = 0 |
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95 LQUERY = ( LWORK.EQ.-1 ) |
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96 UPPER = LSAME( UPLO, 'U' ) |
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97 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
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98 INFO = -1 |
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99 ELSE IF( N.LT.0 ) THEN |
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100 INFO = -2 |
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101 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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102 INFO = -4 |
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103 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN |
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104 INFO = -7 |
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105 END IF |
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106 * |
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107 IF( INFO.EQ.0 ) THEN |
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108 IF( UPPER ) THEN |
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109 NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 ) |
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110 ELSE |
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111 NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 ) |
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112 END IF |
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113 LWKOPT = MAX( 1, N-1 )*NB |
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114 WORK( 1 ) = LWKOPT |
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115 END IF |
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116 * |
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117 IF( INFO.NE.0 ) THEN |
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118 CALL XERBLA( 'ZUNGTR', -INFO ) |
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119 RETURN |
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120 ELSE IF( LQUERY ) THEN |
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121 RETURN |
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122 END IF |
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123 * |
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124 * Quick return if possible |
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125 * |
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126 IF( N.EQ.0 ) THEN |
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127 WORK( 1 ) = 1 |
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128 RETURN |
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129 END IF |
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130 * |
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131 IF( UPPER ) THEN |
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132 * |
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133 * Q was determined by a call to ZHETRD with UPLO = 'U' |
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134 * |
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135 * Shift the vectors which define the elementary reflectors one |
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136 * column to the left, and set the last row and column of Q to |
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137 * those of the unit matrix |
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138 * |
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139 DO 20 J = 1, N - 1 |
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140 DO 10 I = 1, J - 1 |
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141 A( I, J ) = A( I, J+1 ) |
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142 10 CONTINUE |
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143 A( N, J ) = ZERO |
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144 20 CONTINUE |
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145 DO 30 I = 1, N - 1 |
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146 A( I, N ) = ZERO |
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147 30 CONTINUE |
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148 A( N, N ) = ONE |
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149 * |
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150 * Generate Q(1:n-1,1:n-1) |
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151 * |
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152 CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO ) |
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153 * |
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154 ELSE |
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155 * |
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156 * Q was determined by a call to ZHETRD with UPLO = 'L'. |
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157 * |
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158 * Shift the vectors which define the elementary reflectors one |
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159 * column to the right, and set the first row and column of Q to |
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160 * those of the unit matrix |
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161 * |
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162 DO 50 J = N, 2, -1 |
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163 A( 1, J ) = ZERO |
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164 DO 40 I = J + 1, N |
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165 A( I, J ) = A( I, J-1 ) |
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166 40 CONTINUE |
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167 50 CONTINUE |
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168 A( 1, 1 ) = ONE |
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169 DO 60 I = 2, N |
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170 A( I, 1 ) = ZERO |
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171 60 CONTINUE |
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172 IF( N.GT.1 ) THEN |
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173 * |
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174 * Generate Q(2:n,2:n) |
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175 * |
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176 CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, |
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177 $ LWORK, IINFO ) |
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178 END IF |
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179 END IF |
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180 WORK( 1 ) = LWKOPT |
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181 RETURN |
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182 * |
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183 * End of ZUNGTR |
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184 * |
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185 END |
