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annotate libcruft/lapack/cptts2.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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7789
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1 SUBROUTINE CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
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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 IUPLO, LDB, N, NRHS
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9 * ..
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10 * .. Array Arguments ..
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11 REAL D( * )
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12 COMPLEX 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 * CPTTS2 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 CPTTRF.
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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) REAL 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 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) REAL 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 CSSCAL
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67 * ..
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68 * .. Intrinsic Functions ..
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69 INTRINSIC CONJG
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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 CSSCAL( NRHS, 1. / 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 5 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 10 I = 2, N
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93 B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
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94 10 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 20 I = 1, N
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99 B( I, J ) = B( I, J ) / D( I )
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100 20 CONTINUE
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101 DO 30 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 30 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 5
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107 END IF
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108 ELSE
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109 DO 60 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 40 I = 2, N
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114 B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
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115 40 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 50 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 50 CONTINUE
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123 60 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 65 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 70 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 70 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 80 I = 1, N
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143 B( I, J ) = B( I, J ) / D( I )
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144 80 CONTINUE
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145 DO 90 I = N - 1, 1, -1
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146 B( I, J ) = B( I, J ) - B( I+1, J )*CONJG( E( I ) )
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147 90 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 65
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151 END IF
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152 ELSE
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153 DO 120 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 100 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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159 100 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 110 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 )*CONJG( E( I ) )
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167 110 CONTINUE
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168 120 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 CPTTS2
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175 *
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176 END