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annotate libcruft/lapack/cgtsv.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 CGTSV( 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 COMPLEX 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 * CGTSV 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) COMPLEX array, dimension (N-1)
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38 * On entry, DL must contain the (n-1) subdiagonal elements of
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39 * A.
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40 * On exit, DL is overwritten by the (n-2) elements of the
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41 * second superdiagonal of the upper triangular matrix U from
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42 * the LU factorization of A, in DL(1), ..., DL(n-2).
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43 *
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44 * D (input/output) COMPLEX array, dimension (N)
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45 * On entry, D must contain the diagonal elements of A.
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46 * On exit, D is overwritten by the n diagonal elements of U.
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47 *
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48 * DU (input/output) COMPLEX array, dimension (N-1)
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49 * On entry, DU must contain the (n-1) superdiagonal elements
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50 * of A.
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51 * On exit, DU is overwritten by the (n-1) elements of the first
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52 * superdiagonal of U.
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53 *
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54 * B (input/output) COMPLEX array, dimension (LDB,NRHS)
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55 * On entry, the N-by-NRHS right hand side matrix B.
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56 * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
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57 *
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58 * LDB (input) INTEGER
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59 * The leading dimension of the array B. LDB >= max(1,N).
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60 *
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61 * INFO (output) INTEGER
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62 * = 0: successful exit
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63 * < 0: if INFO = -i, the i-th argument had an illegal value
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64 * > 0: if INFO = i, U(i,i) is exactly zero, and the solution
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65 * has not been computed. The factorization has not been
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66 * completed unless i = N.
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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 ZERO
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72 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
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73 * ..
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74 * .. Local Scalars ..
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75 INTEGER J, K
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76 COMPLEX MULT, TEMP, ZDUM
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77 * ..
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78 * .. Intrinsic Functions ..
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79 INTRINSIC ABS, AIMAG, MAX, REAL
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80 * ..
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81 * .. External Subroutines ..
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82 EXTERNAL XERBLA
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83 * ..
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84 * .. Statement Functions ..
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85 REAL CABS1
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86 * ..
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87 * .. Statement Function definitions ..
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88 CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
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89 * ..
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90 * .. Executable Statements ..
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91 *
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92 INFO = 0
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93 IF( N.LT.0 ) THEN
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94 INFO = -1
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95 ELSE IF( NRHS.LT.0 ) THEN
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96 INFO = -2
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97 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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98 INFO = -7
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99 END IF
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100 IF( INFO.NE.0 ) THEN
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101 CALL XERBLA( 'CGTSV ', -INFO )
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102 RETURN
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103 END IF
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104 *
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105 IF( N.EQ.0 )
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106 $ RETURN
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107 *
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108 DO 30 K = 1, N - 1
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109 IF( DL( K ).EQ.ZERO ) THEN
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110 *
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111 * Subdiagonal is zero, no elimination is required.
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112 *
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113 IF( D( K ).EQ.ZERO ) THEN
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114 *
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115 * Diagonal is zero: set INFO = K and return; a unique
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116 * solution can not be found.
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117 *
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118 INFO = K
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119 RETURN
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120 END IF
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121 ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
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122 *
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123 * No row interchange required
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124 *
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125 MULT = DL( K ) / D( K )
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126 D( K+1 ) = D( K+1 ) - MULT*DU( K )
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127 DO 10 J = 1, NRHS
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128 B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
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129 10 CONTINUE
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130 IF( K.LT.( N-1 ) )
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131 $ DL( K ) = ZERO
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132 ELSE
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133 *
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134 * Interchange rows K and K+1
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135 *
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136 MULT = D( K ) / DL( K )
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137 D( K ) = DL( K )
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138 TEMP = D( K+1 )
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139 D( K+1 ) = DU( K ) - MULT*TEMP
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140 IF( K.LT.( N-1 ) ) THEN
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141 DL( K ) = DU( K+1 )
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142 DU( K+1 ) = -MULT*DL( K )
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143 END IF
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144 DU( K ) = TEMP
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145 DO 20 J = 1, NRHS
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146 TEMP = B( K, J )
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147 B( K, J ) = B( K+1, J )
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148 B( K+1, J ) = TEMP - MULT*B( K+1, J )
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149 20 CONTINUE
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150 END IF
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151 30 CONTINUE
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152 IF( D( N ).EQ.ZERO ) THEN
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153 INFO = N
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154 RETURN
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155 END IF
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156 *
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157 * Back solve with the matrix U from the factorization.
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158 *
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159 DO 50 J = 1, NRHS
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160 B( N, J ) = B( N, J ) / D( N )
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161 IF( N.GT.1 )
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162 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
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163 DO 40 K = N - 2, 1, -1
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164 B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
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165 $ B( K+2, J ) ) / D( K )
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166 40 CONTINUE
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167 50 CONTINUE
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168 *
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169 RETURN
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170 *
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171 * End of CGTSV
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172 *
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173 END