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annotate libcruft/lapack/sgttrf.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 SGTTRF( N, DL, D, DU, DU2, IPIV, 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, N
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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 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 * SGTTRF computes an LU factorization of a real tridiagonal matrix A
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19 * using elimination with partial pivoting and row interchanges.
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20 *
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21 * The factorization has the form
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22 * A = L * U
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23 * where L is a product of permutation and unit lower bidiagonal
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24 * matrices and U is upper triangular with nonzeros in only the main
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25 * diagonal and first two superdiagonals.
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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.
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32 *
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33 * DL (input/output) REAL array, dimension (N-1)
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34 * On entry, DL must contain the (n-1) sub-diagonal elements of
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35 * A.
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36 *
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37 * On exit, DL is overwritten by the (n-1) multipliers that
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38 * define the matrix L from the LU factorization of A.
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39 *
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40 * D (input/output) REAL array, dimension (N)
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41 * On entry, D must contain the diagonal elements of A.
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42 *
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43 * On exit, D is overwritten by the n diagonal elements of the
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44 * upper triangular matrix U from the LU factorization of A.
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45 *
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46 * DU (input/output) REAL array, dimension (N-1)
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47 * On entry, DU must contain the (n-1) super-diagonal elements
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48 * of A.
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49 *
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50 * On exit, DU is overwritten by the (n-1) elements of the first
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51 * super-diagonal of U.
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52 *
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53 * DU2 (output) REAL array, dimension (N-2)
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54 * On exit, DU2 is overwritten by the (n-2) elements of the
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55 * second super-diagonal of U.
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56 *
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57 * IPIV (output) INTEGER array, dimension (N)
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58 * The pivot indices; for 1 <= i <= n, row i of the matrix was
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59 * interchanged with row IPIV(i). IPIV(i) will always be either
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60 * i or i+1; IPIV(i) = i indicates a row interchange was not
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61 * required.
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62 *
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63 * INFO (output) INTEGER
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64 * = 0: successful exit
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65 * < 0: if INFO = -k, the k-th argument had an illegal value
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66 * > 0: if INFO = k, U(k,k) is exactly zero. The factorization
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67 * has been completed, but the factor U is exactly
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68 * singular, and division by zero will occur if it is used
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69 * to solve a system of equations.
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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
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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
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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 CALL XERBLA( 'SGTTRF', -INFO )
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93 RETURN
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94 END IF
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95 *
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96 * Quick return if possible
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97 *
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98 IF( N.EQ.0 )
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99 $ RETURN
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100 *
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101 * Initialize IPIV(i) = i and DU2(I) = 0
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102 *
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103 DO 10 I = 1, N
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104 IPIV( I ) = I
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105 10 CONTINUE
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106 DO 20 I = 1, N - 2
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107 DU2( I ) = ZERO
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108 20 CONTINUE
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109 *
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110 DO 30 I = 1, N - 2
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111 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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112 *
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113 * No row interchange required, eliminate DL(I)
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114 *
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115 IF( D( I ).NE.ZERO ) THEN
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116 FACT = DL( I ) / D( I )
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117 DL( I ) = FACT
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118 D( I+1 ) = D( I+1 ) - FACT*DU( I )
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119 END IF
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120 ELSE
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121 *
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122 * Interchange rows I and I+1, eliminate DL(I)
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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 DL( I ) = FACT
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127 TEMP = DU( I )
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128 DU( I ) = D( I+1 )
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129 D( I+1 ) = TEMP - FACT*D( I+1 )
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130 DU2( I ) = DU( I+1 )
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131 DU( I+1 ) = -FACT*DU( I+1 )
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132 IPIV( I ) = I + 1
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133 END IF
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134 30 CONTINUE
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135 IF( N.GT.1 ) THEN
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136 I = N - 1
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137 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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138 IF( D( I ).NE.ZERO ) THEN
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139 FACT = DL( I ) / D( I )
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140 DL( I ) = FACT
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141 D( I+1 ) = D( I+1 ) - FACT*DU( I )
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142 END IF
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143 ELSE
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144 FACT = D( I ) / DL( I )
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145 D( I ) = DL( I )
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146 DL( I ) = FACT
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147 TEMP = DU( I )
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148 DU( I ) = D( I+1 )
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149 D( I+1 ) = TEMP - FACT*D( I+1 )
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150 IPIV( I ) = I + 1
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151 END IF
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152 END IF
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153 *
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154 * Check for a zero on the diagonal of U.
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155 *
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156 DO 40 I = 1, N
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157 IF( D( I ).EQ.ZERO ) THEN
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158 INFO = I
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159 GO TO 50
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160 END IF
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161 40 CONTINUE
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162 50 CONTINUE
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163 *
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164 RETURN
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165 *
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166 * End of SGTTRF
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167 *
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168 END