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1 SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB ) |
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2 * |
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7034
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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 IUPLO, LDB, N, NRHS |
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9 * .. |
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10 * .. Array Arguments .. |
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11 DOUBLE PRECISION D( * ) |
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12 COMPLEX*16 B( LDB, * ), E( * ) |
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13 * .. |
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14 * |
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15 * Purpose |
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16 * ======= |
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17 * |
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18 * ZPTTS2 solves a tridiagonal system of the form |
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19 * A * X = B |
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20 * using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF. |
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21 * D is a diagonal matrix specified in the vector D, U (or L) is a unit |
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22 * bidiagonal matrix whose superdiagonal (subdiagonal) is specified in |
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23 * the vector E, and X and B are N by NRHS matrices. |
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24 * |
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25 * Arguments |
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26 * ========= |
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27 * |
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28 * IUPLO (input) INTEGER |
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29 * Specifies the form of the factorization and whether the |
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30 * vector E is the superdiagonal of the upper bidiagonal factor |
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31 * U or the subdiagonal of the lower bidiagonal factor L. |
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32 * = 1: A = U'*D*U, E is the superdiagonal of U |
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33 * = 0: A = L*D*L', E is the subdiagonal of L |
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34 * |
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35 * N (input) INTEGER |
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36 * The order of the tridiagonal matrix A. N >= 0. |
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37 * |
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38 * NRHS (input) INTEGER |
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39 * The number of right hand sides, i.e., the number of columns |
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40 * of the matrix B. NRHS >= 0. |
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41 * |
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42 * D (input) DOUBLE PRECISION array, dimension (N) |
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43 * The n diagonal elements of the diagonal matrix D from the |
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44 * factorization A = U'*D*U or A = L*D*L'. |
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45 * |
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46 * E (input) COMPLEX*16 array, dimension (N-1) |
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47 * If IUPLO = 1, the (n-1) superdiagonal elements of the unit |
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48 * bidiagonal factor U from the factorization A = U'*D*U. |
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49 * If IUPLO = 0, the (n-1) subdiagonal elements of the unit |
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50 * bidiagonal factor L from the factorization A = L*D*L'. |
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51 * |
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52 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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53 * On entry, the right hand side vectors B for the system of |
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54 * linear equations. |
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55 * On exit, the solution vectors, X. |
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56 * |
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57 * LDB (input) INTEGER |
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58 * The leading dimension of the array B. LDB >= max(1,N). |
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59 * |
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60 * ===================================================================== |
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61 * |
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62 * .. Local Scalars .. |
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63 INTEGER I, J |
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64 * .. |
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65 * .. External Subroutines .. |
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66 EXTERNAL ZDSCAL |
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67 * .. |
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68 * .. Intrinsic Functions .. |
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69 INTRINSIC DCONJG |
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70 * .. |
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71 * .. Executable Statements .. |
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72 * |
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73 * Quick return if possible |
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74 * |
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75 IF( N.LE.1 ) THEN |
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76 IF( N.EQ.1 ) |
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77 $ CALL ZDSCAL( NRHS, 1.D0 / D( 1 ), B, LDB ) |
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78 RETURN |
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79 END IF |
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80 * |
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81 IF( IUPLO.EQ.1 ) THEN |
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82 * |
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83 * Solve A * X = B using the factorization A = U'*D*U, |
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84 * overwriting each right hand side vector with its solution. |
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85 * |
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86 IF( NRHS.LE.2 ) THEN |
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87 J = 1 |
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88 10 CONTINUE |
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89 * |
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90 * Solve U' * x = b. |
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91 * |
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92 DO 20 I = 2, N |
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93 B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) ) |
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94 20 CONTINUE |
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95 * |
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96 * Solve D * U * x = b. |
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97 * |
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98 DO 30 I = 1, N |
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99 B( I, J ) = B( I, J ) / D( I ) |
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100 30 CONTINUE |
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101 DO 40 I = N - 1, 1, -1 |
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102 B( I, J ) = B( I, J ) - B( I+1, J )*E( I ) |
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103 40 CONTINUE |
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104 IF( J.LT.NRHS ) THEN |
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105 J = J + 1 |
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106 GO TO 10 |
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107 END IF |
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108 ELSE |
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109 DO 70 J = 1, NRHS |
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110 * |
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111 * Solve U' * x = b. |
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112 * |
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113 DO 50 I = 2, N |
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114 B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) ) |
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115 50 CONTINUE |
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116 * |
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117 * Solve D * U * x = b. |
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118 * |
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119 B( N, J ) = B( N, J ) / D( N ) |
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120 DO 60 I = N - 1, 1, -1 |
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121 B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I ) |
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122 60 CONTINUE |
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123 70 CONTINUE |
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124 END IF |
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125 ELSE |
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126 * |
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127 * Solve A * X = B using the factorization A = L*D*L', |
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128 * overwriting each right hand side vector with its solution. |
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129 * |
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130 IF( NRHS.LE.2 ) THEN |
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131 J = 1 |
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132 80 CONTINUE |
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133 * |
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134 * Solve L * x = b. |
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135 * |
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136 DO 90 I = 2, N |
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137 B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) |
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138 90 CONTINUE |
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139 * |
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140 * Solve D * L' * x = b. |
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141 * |
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142 DO 100 I = 1, N |
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143 B( I, J ) = B( I, J ) / D( I ) |
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144 100 CONTINUE |
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145 DO 110 I = N - 1, 1, -1 |
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146 B( I, J ) = B( I, J ) - B( I+1, J )*DCONJG( E( I ) ) |
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147 110 CONTINUE |
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148 IF( J.LT.NRHS ) THEN |
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149 J = J + 1 |
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150 GO TO 80 |
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151 END IF |
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152 ELSE |
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153 DO 140 J = 1, NRHS |
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154 * |
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155 * Solve L * x = b. |
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156 * |
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157 DO 120 I = 2, N |
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158 B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) |
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159 120 CONTINUE |
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160 * |
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161 * Solve D * L' * x = b. |
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162 * |
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163 B( N, J ) = B( N, J ) / D( N ) |
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164 DO 130 I = N - 1, 1, -1 |
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165 B( I, J ) = B( I, J ) / D( I ) - |
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166 $ B( I+1, J )*DCONJG( E( I ) ) |
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167 130 CONTINUE |
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168 140 CONTINUE |
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169 END IF |
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170 END IF |
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171 * |
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172 RETURN |
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173 * |
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174 * End of ZPTTS2 |
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175 * |
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176 END |
