1 | *> \brief <b> SGBSV computes the solution to system of linear equations A * X = B for GB matrices</b> (simple driver) |
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2 | * |
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3 | * =========== DOCUMENTATION =========== |
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4 | * |
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5 | * Online html documentation available at |
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6 | * http://www.netlib.org/lapack/explore-html/ |
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7 | * |
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8 | *> \htmlonly |
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9 | *> Download SGBSV + dependencies |
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10 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgbsv.f"> |
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11 | *> [TGZ]</a> |
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12 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgbsv.f"> |
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13 | *> [ZIP]</a> |
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14 | *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgbsv.f"> |
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15 | *> [TXT]</a> |
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16 | *> \endhtmlonly |
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17 | * |
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18 | * Definition: |
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19 | * =========== |
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20 | * |
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21 | * SUBROUTINE SGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) |
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22 | * |
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23 | * .. Scalar Arguments .. |
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24 | * INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS |
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25 | * .. |
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26 | * .. Array Arguments .. |
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27 | * INTEGER IPIV( * ) |
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28 | * REAL AB( LDAB, * ), B( LDB, * ) |
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29 | * .. |
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30 | * |
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31 | * |
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32 | *> \par Purpose: |
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33 | * ============= |
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34 | *> |
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35 | *> \verbatim |
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36 | *> |
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37 | *> SGBSV computes the solution to a real system of linear equations |
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38 | *> A * X = B, where A is a band matrix of order N with KL subdiagonals |
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39 | *> and KU superdiagonals, and X and B are N-by-NRHS matrices. |
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40 | *> |
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41 | *> The LU decomposition with partial pivoting and row interchanges is |
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42 | *> used to factor A as A = L * U, where L is a product of permutation |
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43 | *> and unit lower triangular matrices with KL subdiagonals, and U is |
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44 | *> upper triangular with KL+KU superdiagonals. The factored form of A |
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45 | *> is then used to solve the system of equations A * X = B. |
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46 | *> \endverbatim |
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47 | * |
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48 | * Arguments: |
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49 | * ========== |
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50 | * |
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51 | *> \param[in] N |
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52 | *> \verbatim |
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53 | *> N is INTEGER |
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54 | *> The number of linear equations, i.e., the order of the |
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55 | *> matrix A. N >= 0. |
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56 | *> \endverbatim |
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57 | *> |
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58 | *> \param[in] KL |
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59 | *> \verbatim |
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60 | *> KL is INTEGER |
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61 | *> The number of subdiagonals within the band of A. KL >= 0. |
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62 | *> \endverbatim |
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63 | *> |
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64 | *> \param[in] KU |
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65 | *> \verbatim |
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66 | *> KU is INTEGER |
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67 | *> The number of superdiagonals within the band of A. KU >= 0. |
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68 | *> \endverbatim |
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69 | *> |
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70 | *> \param[in] NRHS |
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71 | *> \verbatim |
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72 | *> NRHS is INTEGER |
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73 | *> The number of right hand sides, i.e., the number of columns |
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74 | *> of the matrix B. NRHS >= 0. |
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75 | *> \endverbatim |
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76 | *> |
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77 | *> \param[in,out] AB |
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78 | *> \verbatim |
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79 | *> AB is REAL array, dimension (LDAB,N) |
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80 | *> On entry, the matrix A in band storage, in rows KL+1 to |
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81 | *> 2*KL+KU+1; rows 1 to KL of the array need not be set. |
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82 | *> The j-th column of A is stored in the j-th column of the |
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83 | *> array AB as follows: |
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84 | *> AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) |
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85 | *> On exit, details of the factorization: U is stored as an |
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86 | *> upper triangular band matrix with KL+KU superdiagonals in |
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87 | *> rows 1 to KL+KU+1, and the multipliers used during the |
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88 | *> factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
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89 | *> See below for further details. |
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90 | *> \endverbatim |
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91 | *> |
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92 | *> \param[in] LDAB |
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93 | *> \verbatim |
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94 | *> LDAB is INTEGER |
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95 | *> The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
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96 | *> \endverbatim |
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97 | *> |
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98 | *> \param[out] IPIV |
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99 | *> \verbatim |
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100 | *> IPIV is INTEGER array, dimension (N) |
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101 | *> The pivot indices that define the permutation matrix P; |
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102 | *> row i of the matrix was interchanged with row IPIV(i). |
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103 | *> \endverbatim |
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104 | *> |
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105 | *> \param[in,out] B |
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106 | *> \verbatim |
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107 | *> B is REAL array, dimension (LDB,NRHS) |
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108 | *> On entry, the N-by-NRHS right hand side matrix B. |
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109 | *> On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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110 | *> \endverbatim |
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111 | *> |
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112 | *> \param[in] LDB |
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113 | *> \verbatim |
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114 | *> LDB is INTEGER |
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115 | *> The leading dimension of the array B. LDB >= max(1,N). |
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116 | *> \endverbatim |
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117 | *> |
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118 | *> \param[out] INFO |
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119 | *> \verbatim |
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120 | *> INFO is INTEGER |
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121 | *> = 0: successful exit |
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122 | *> < 0: if INFO = -i, the i-th argument had an illegal value |
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123 | *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization |
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124 | *> has been completed, but the factor U is exactly |
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125 | *> singular, and the solution has not been computed. |
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126 | *> \endverbatim |
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127 | * |
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128 | * Authors: |
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129 | * ======== |
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130 | * |
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131 | *> \author Univ. of Tennessee |
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132 | *> \author Univ. of California Berkeley |
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133 | *> \author Univ. of Colorado Denver |
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134 | *> \author NAG Ltd. |
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135 | * |
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136 | *> \date November 2011 |
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137 | * |
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138 | *> \ingroup realGBsolve |
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139 | * |
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140 | *> \par Further Details: |
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141 | * ===================== |
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142 | *> |
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143 | *> \verbatim |
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144 | *> |
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145 | *> The band storage scheme is illustrated by the following example, when |
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146 | *> M = N = 6, KL = 2, KU = 1: |
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147 | *> |
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148 | *> On entry: On exit: |
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149 | *> |
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150 | *> * * * + + + * * * u14 u25 u36 |
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151 | *> * * + + + + * * u13 u24 u35 u46 |
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152 | *> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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153 | *> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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154 | *> a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * |
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155 | *> a31 a42 a53 a64 * * m31 m42 m53 m64 * * |
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156 | *> |
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157 | *> Array elements marked * are not used by the routine; elements marked |
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158 | *> + need not be set on entry, but are required by the routine to store |
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159 | *> elements of U because of fill-in resulting from the row interchanges. |
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160 | *> \endverbatim |
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161 | *> |
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162 | * ===================================================================== |
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163 | SUBROUTINE SGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) |
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164 | * |
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165 | * -- LAPACK driver routine (version 3.4.0) -- |
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166 | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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167 | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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168 | * November 2011 |
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169 | * |
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170 | * .. Scalar Arguments .. |
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171 | INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS |
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172 | * .. |
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173 | * .. Array Arguments .. |
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174 | INTEGER IPIV( * ) |
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175 | REAL AB( LDAB, * ), B( LDB, * ) |
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176 | * .. |
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177 | * |
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178 | * ===================================================================== |
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179 | * |
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180 | * .. External Subroutines .. |
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181 | EXTERNAL SGBTRF, SGBTRS, XERBLA |
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182 | * .. |
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183 | * .. Intrinsic Functions .. |
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184 | INTRINSIC MAX |
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185 | * .. |
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186 | * .. Executable Statements .. |
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187 | * |
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188 | * Test the input parameters. |
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189 | * |
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190 | INFO = 0 |
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191 | IF( N.LT.0 ) THEN |
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192 | INFO = -1 |
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193 | ELSE IF( KL.LT.0 ) THEN |
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194 | INFO = -2 |
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195 | ELSE IF( KU.LT.0 ) THEN |
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196 | INFO = -3 |
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197 | ELSE IF( NRHS.LT.0 ) THEN |
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198 | INFO = -4 |
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199 | ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN |
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200 | INFO = -6 |
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201 | ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN |
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202 | INFO = -9 |
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203 | END IF |
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204 | IF( INFO.NE.0 ) THEN |
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205 | CALL XERBLA( 'SGBSV ', -INFO ) |
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206 | RETURN |
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207 | END IF |
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208 | * |
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209 | * Compute the LU factorization of the band matrix A. |
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210 | * |
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211 | CALL SGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO ) |
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212 | IF( INFO.EQ.0 ) THEN |
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213 | * |
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214 | * Solve the system A*X = B, overwriting B with X. |
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215 | * |
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216 | CALL SGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV, |
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217 | $ B, LDB, INFO ) |
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218 | END IF |
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219 | RETURN |
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220 | * |
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221 | * End of SGBSV |
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222 | * |
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223 | END |
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