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annotate libcruft/lapack/sgtts2.f @ 7789:82be108cc558

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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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1 SUBROUTINE SGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
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2 *
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3 * -- LAPACK auxiliary 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 ITRANS, LDB, N, NRHS
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9 * ..
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10 * .. Array Arguments ..
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11 INTEGER IPIV( * )
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12 REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
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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 * SGTTS2 solves one of the systems of equations
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19 * A*X = B or A'*X = B,
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20 * with a tridiagonal matrix A using the LU factorization computed
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21 * by SGTTRF.
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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 * ITRANS (input) INTEGER
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27 * Specifies the form of the system of equations.
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28 * = 0: A * X = B (No transpose)
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29 * = 1: A'* X = B (Transpose)
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30 * = 2: A'* X = B (Conjugate transpose = Transpose)
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31 *
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32 * N (input) INTEGER
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33 * The order of the matrix A.
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34 *
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35 * NRHS (input) INTEGER
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36 * The number of right hand sides, i.e., the number of columns
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37 * of the matrix B. NRHS >= 0.
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38 *
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39 * DL (input) REAL array, dimension (N-1)
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40 * The (n-1) multipliers that define the matrix L from the
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41 * LU factorization of A.
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42 *
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43 * D (input) REAL array, dimension (N)
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44 * The n diagonal elements of the upper triangular matrix U from
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45 * the LU factorization of A.
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46 *
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47 * DU (input) REAL array, dimension (N-1)
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48 * The (n-1) elements of the first super-diagonal of U.
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49 *
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50 * DU2 (input) REAL array, dimension (N-2)
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51 * The (n-2) elements of the second super-diagonal of U.
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52 *
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53 * IPIV (input) INTEGER array, dimension (N)
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54 * The pivot indices; for 1 <= i <= n, row i of the matrix was
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55 * interchanged with row IPIV(i). IPIV(i) will always be either
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56 * i or i+1; IPIV(i) = i indicates a row interchange was not
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57 * required.
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58 *
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59 * B (input/output) REAL array, dimension (LDB,NRHS)
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60 * On entry, the matrix of right hand side vectors B.
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61 * On exit, B is overwritten by the solution vectors X.
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62 *
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63 * LDB (input) INTEGER
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64 * The leading dimension of the array B. LDB >= max(1,N).
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65 *
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66 * =====================================================================
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67 *
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68 * .. Local Scalars ..
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69 INTEGER I, IP, J
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70 REAL TEMP
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71 * ..
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72 * .. Executable Statements ..
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73 *
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74 * Quick return if possible
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75 *
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76 IF( N.EQ.0 .OR. NRHS.EQ.0 )
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77 $ RETURN
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78 *
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79 IF( ITRANS.EQ.0 ) THEN
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80 *
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81 * Solve A*X = B using the LU factorization of A,
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82 * overwriting each right hand side vector with its solution.
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83 *
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84 IF( NRHS.LE.1 ) THEN
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85 J = 1
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86 10 CONTINUE
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87 *
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88 * Solve L*x = b.
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89 *
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90 DO 20 I = 1, N - 1
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91 IP = IPIV( I )
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92 TEMP = B( I+1-IP+I, J ) - DL( I )*B( IP, J )
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93 B( I, J ) = B( IP, J )
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94 B( I+1, J ) = TEMP
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95 20 CONTINUE
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96 *
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97 * Solve U*x = b.
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98 *
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99 B( N, J ) = B( N, J ) / D( N )
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100 IF( N.GT.1 )
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101 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
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102 $ D( N-1 )
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103 DO 30 I = N - 2, 1, -1
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104 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
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105 $ B( I+2, J ) ) / D( I )
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106 30 CONTINUE
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107 IF( J.LT.NRHS ) THEN
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108 J = J + 1
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109 GO TO 10
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110 END IF
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111 ELSE
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112 DO 60 J = 1, NRHS
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113 *
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114 * Solve L*x = b.
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115 *
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116 DO 40 I = 1, N - 1
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117 IF( IPIV( I ).EQ.I ) THEN
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118 B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
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119 ELSE
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120 TEMP = B( I, J )
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121 B( I, J ) = B( I+1, J )
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122 B( I+1, J ) = TEMP - DL( I )*B( I, J )
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123 END IF
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124 40 CONTINUE
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125 *
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126 * Solve U*x = b.
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127 *
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128 B( N, J ) = B( N, J ) / D( N )
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129 IF( N.GT.1 )
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130 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
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131 $ D( N-1 )
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132 DO 50 I = N - 2, 1, -1
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133 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
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134 $ B( I+2, J ) ) / D( I )
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135 50 CONTINUE
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136 60 CONTINUE
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137 END IF
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138 ELSE
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139 *
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140 * Solve A' * X = B.
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141 *
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142 IF( NRHS.LE.1 ) THEN
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143 *
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144 * Solve U'*x = b.
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145 *
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146 J = 1
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147 70 CONTINUE
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148 B( 1, J ) = B( 1, J ) / D( 1 )
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149 IF( N.GT.1 )
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150 $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
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151 DO 80 I = 3, N
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152 B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
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153 $ B( I-2, J ) ) / D( I )
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154 80 CONTINUE
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155 *
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156 * Solve L'*x = b.
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157 *
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158 DO 90 I = N - 1, 1, -1
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159 IP = IPIV( I )
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160 TEMP = B( I, J ) - DL( I )*B( I+1, J )
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161 B( I, J ) = B( IP, J )
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162 B( IP, J ) = TEMP
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163 90 CONTINUE
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164 IF( J.LT.NRHS ) THEN
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165 J = J + 1
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166 GO TO 70
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167 END IF
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168 *
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169 ELSE
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170 DO 120 J = 1, NRHS
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171 *
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172 * Solve U'*x = b.
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173 *
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174 B( 1, J ) = B( 1, J ) / D( 1 )
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175 IF( N.GT.1 )
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176 $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
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177 DO 100 I = 3, N
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178 B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
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179 $ DU2( I-2 )*B( I-2, J ) ) / D( I )
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180 100 CONTINUE
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181 DO 110 I = N - 1, 1, -1
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182 IF( IPIV( I ).EQ.I ) THEN
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183 B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
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184 ELSE
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185 TEMP = B( I+1, J )
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186 B( I+1, J ) = B( I, J ) - DL( I )*TEMP
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187 B( I, J ) = TEMP
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188 END IF
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189 110 CONTINUE
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190 120 CONTINUE
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191 END IF
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192 END IF
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193 *
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194 * End of SGTTS2
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195 *
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196 END