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annotate libcruft/lapack/sgtsv.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 SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
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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 INFO, LDB, N, NRHS
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9 * ..
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10 * .. Array Arguments ..
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11 REAL B( LDB, * ), D( * ), DL( * ), DU( * )
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12 * ..
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13 *
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14 * Purpose
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15 * =======
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16 *
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17 * SGTSV solves the equation
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18 *
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19 * A*X = B,
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20 *
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21 * where A is an n by n tridiagonal matrix, by Gaussian elimination with
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22 * partial pivoting.
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23 *
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24 * Note that the equation A'*X = B may be solved by interchanging the
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25 * order of the arguments DU and DL.
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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 * N (input) INTEGER
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31 * The order of the matrix A. N >= 0.
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32 *
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33 * NRHS (input) INTEGER
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34 * The number of right hand sides, i.e., the number of columns
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35 * of the matrix B. NRHS >= 0.
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36 *
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37 * DL (input/output) REAL array, dimension (N-1)
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38 * On entry, DL must contain the (n-1) sub-diagonal elements of
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39 * A.
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40 *
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41 * On exit, DL is overwritten by the (n-2) elements of the
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42 * second super-diagonal of the upper triangular matrix U from
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43 * the LU factorization of A, in DL(1), ..., DL(n-2).
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44 *
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45 * D (input/output) REAL array, dimension (N)
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46 * On entry, D must contain the diagonal elements of A.
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47 *
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48 * On exit, D is overwritten by the n diagonal elements of U.
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49 *
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50 * DU (input/output) REAL array, dimension (N-1)
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51 * On entry, DU must contain the (n-1) super-diagonal elements
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52 * of A.
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53 *
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54 * On exit, DU is overwritten by the (n-1) elements of the first
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55 * super-diagonal of U.
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56 *
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57 * B (input/output) REAL array, dimension (LDB,NRHS)
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58 * On entry, the N by NRHS matrix of right hand side matrix B.
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59 * On exit, if INFO = 0, the N by NRHS solution matrix X.
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60 *
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61 * LDB (input) INTEGER
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62 * The leading dimension of the array B. LDB >= max(1,N).
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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 * > 0: if INFO = i, U(i,i) is exactly zero, and the solution
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68 * has not been computed. The factorization has not been
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69 * completed unless i = N.
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70 *
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71 * =====================================================================
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72 *
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73 * .. Parameters ..
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74 REAL ZERO
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75 PARAMETER ( ZERO = 0.0E+0 )
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76 * ..
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77 * .. Local Scalars ..
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78 INTEGER I, J
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79 REAL FACT, TEMP
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80 * ..
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81 * .. Intrinsic Functions ..
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82 INTRINSIC ABS, MAX
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83 * ..
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84 * .. External Subroutines ..
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85 EXTERNAL XERBLA
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86 * ..
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87 * .. Executable Statements ..
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88 *
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89 INFO = 0
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90 IF( N.LT.0 ) THEN
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91 INFO = -1
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92 ELSE IF( NRHS.LT.0 ) THEN
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93 INFO = -2
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94 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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95 INFO = -7
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96 END IF
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97 IF( INFO.NE.0 ) THEN
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98 CALL XERBLA( 'SGTSV ', -INFO )
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99 RETURN
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100 END IF
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101 *
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102 IF( N.EQ.0 )
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103 $ RETURN
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104 *
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105 IF( NRHS.EQ.1 ) THEN
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106 DO 10 I = 1, N - 2
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107 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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108 *
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109 * No row interchange required
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110 *
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111 IF( D( I ).NE.ZERO ) THEN
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112 FACT = DL( I ) / D( I )
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113 D( I+1 ) = D( I+1 ) - FACT*DU( I )
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114 B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
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115 ELSE
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116 INFO = I
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117 RETURN
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118 END IF
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119 DL( I ) = ZERO
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120 ELSE
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121 *
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122 * Interchange rows I and I+1
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123 *
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124 FACT = D( I ) / DL( I )
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125 D( I ) = DL( I )
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126 TEMP = D( I+1 )
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127 D( I+1 ) = DU( I ) - FACT*TEMP
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128 DL( I ) = DU( I+1 )
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129 DU( I+1 ) = -FACT*DL( I )
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130 DU( I ) = TEMP
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131 TEMP = B( I, 1 )
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132 B( I, 1 ) = B( I+1, 1 )
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133 B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
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134 END IF
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135 10 CONTINUE
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136 IF( N.GT.1 ) THEN
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137 I = N - 1
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138 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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139 IF( D( I ).NE.ZERO ) THEN
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140 FACT = DL( I ) / D( I )
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141 D( I+1 ) = D( I+1 ) - FACT*DU( I )
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142 B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
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143 ELSE
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144 INFO = I
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145 RETURN
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146 END IF
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147 ELSE
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148 FACT = D( I ) / DL( I )
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149 D( I ) = DL( I )
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150 TEMP = D( I+1 )
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151 D( I+1 ) = DU( I ) - FACT*TEMP
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152 DU( I ) = TEMP
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153 TEMP = B( I, 1 )
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154 B( I, 1 ) = B( I+1, 1 )
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155 B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
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156 END IF
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157 END IF
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158 IF( D( N ).EQ.ZERO ) THEN
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159 INFO = N
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160 RETURN
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161 END IF
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162 ELSE
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163 DO 40 I = 1, N - 2
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164 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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165 *
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166 * No row interchange required
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167 *
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168 IF( D( I ).NE.ZERO ) THEN
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169 FACT = DL( I ) / D( I )
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170 D( I+1 ) = D( I+1 ) - FACT*DU( I )
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171 DO 20 J = 1, NRHS
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172 B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
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173 20 CONTINUE
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174 ELSE
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175 INFO = I
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176 RETURN
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177 END IF
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178 DL( I ) = ZERO
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179 ELSE
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180 *
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181 * Interchange rows I and I+1
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182 *
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183 FACT = D( I ) / DL( I )
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184 D( I ) = DL( I )
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185 TEMP = D( I+1 )
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186 D( I+1 ) = DU( I ) - FACT*TEMP
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187 DL( I ) = DU( I+1 )
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188 DU( I+1 ) = -FACT*DL( I )
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189 DU( I ) = TEMP
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190 DO 30 J = 1, NRHS
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191 TEMP = B( I, J )
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192 B( I, J ) = B( I+1, J )
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193 B( I+1, J ) = TEMP - FACT*B( I+1, J )
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194 30 CONTINUE
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195 END IF
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196 40 CONTINUE
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197 IF( N.GT.1 ) THEN
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198 I = N - 1
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199 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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200 IF( D( I ).NE.ZERO ) THEN
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201 FACT = DL( I ) / D( I )
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202 D( I+1 ) = D( I+1 ) - FACT*DU( I )
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203 DO 50 J = 1, NRHS
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204 B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
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205 50 CONTINUE
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206 ELSE
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207 INFO = I
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208 RETURN
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209 END IF
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210 ELSE
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211 FACT = D( I ) / DL( I )
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212 D( I ) = DL( I )
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213 TEMP = D( I+1 )
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214 D( I+1 ) = DU( I ) - FACT*TEMP
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215 DU( I ) = TEMP
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216 DO 60 J = 1, NRHS
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217 TEMP = B( I, J )
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218 B( I, J ) = B( I+1, J )
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219 B( I+1, J ) = TEMP - FACT*B( I+1, J )
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220 60 CONTINUE
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221 END IF
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222 END IF
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223 IF( D( N ).EQ.ZERO ) THEN
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224 INFO = N
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225 RETURN
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226 END IF
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227 END IF
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228 *
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229 * Back solve with the matrix U from the factorization.
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230 *
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231 IF( NRHS.LE.2 ) THEN
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232 J = 1
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233 70 CONTINUE
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234 B( N, J ) = B( N, J ) / D( N )
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235 IF( N.GT.1 )
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236 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
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237 DO 80 I = N - 2, 1, -1
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238 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
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239 $ B( I+2, J ) ) / D( I )
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240 80 CONTINUE
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241 IF( J.LT.NRHS ) THEN
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242 J = J + 1
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243 GO TO 70
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244 END IF
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245 ELSE
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246 DO 100 J = 1, NRHS
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247 B( N, J ) = B( N, J ) / D( N )
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248 IF( N.GT.1 )
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249 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
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250 $ D( N-1 )
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251 DO 90 I = N - 2, 1, -1
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252 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
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253 $ B( I+2, J ) ) / D( I )
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254 90 CONTINUE
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255 100 CONTINUE
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256 END IF
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parents:
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257 *
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258 RETURN
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259 *
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260 * End of SGTSV
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261 *
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262 END