1 | SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) |
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2 | * .. Scalar Arguments .. |
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3 | INTEGER INCX,N |
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4 | CHARACTER DIAG,TRANS,UPLO |
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5 | * .. |
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6 | * .. Array Arguments .. |
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7 | COMPLEX AP(*),X(*) |
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8 | * .. |
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9 | * |
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10 | * Purpose |
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11 | * ======= |
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12 | * |
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13 | * CTPSV solves one of the systems of equations |
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14 | * |
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15 | * A*x = b, or A'*x = b, or conjg( A' )*x = b, |
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16 | * |
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17 | * where b and x are n element vectors and A is an n by n unit, or |
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18 | * non-unit, upper or lower triangular matrix, supplied in packed form. |
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19 | * |
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20 | * No test for singularity or near-singularity is included in this |
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21 | * routine. Such tests must be performed before calling this routine. |
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22 | * |
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23 | * Arguments |
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24 | * ========== |
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25 | * |
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26 | * UPLO - CHARACTER*1. |
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27 | * On entry, UPLO specifies whether the matrix is an upper or |
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28 | * lower triangular matrix as follows: |
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29 | * |
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30 | * UPLO = 'U' or 'u' A is an upper triangular matrix. |
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31 | * |
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32 | * UPLO = 'L' or 'l' A is a lower triangular matrix. |
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33 | * |
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34 | * Unchanged on exit. |
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35 | * |
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36 | * TRANS - CHARACTER*1. |
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37 | * On entry, TRANS specifies the equations to be solved as |
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38 | * follows: |
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39 | * |
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40 | * TRANS = 'N' or 'n' A*x = b. |
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41 | * |
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42 | * TRANS = 'T' or 't' A'*x = b. |
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43 | * |
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44 | * TRANS = 'C' or 'c' conjg( A' )*x = b. |
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45 | * |
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46 | * Unchanged on exit. |
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47 | * |
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48 | * DIAG - CHARACTER*1. |
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49 | * On entry, DIAG specifies whether or not A is unit |
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50 | * triangular as follows: |
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51 | * |
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52 | * DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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53 | * |
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54 | * DIAG = 'N' or 'n' A is not assumed to be unit |
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55 | * triangular. |
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56 | * |
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57 | * Unchanged on exit. |
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58 | * |
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59 | * N - INTEGER. |
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60 | * On entry, N specifies the order of the matrix A. |
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61 | * N must be at least zero. |
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62 | * Unchanged on exit. |
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63 | * |
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64 | * AP - COMPLEX array of DIMENSION at least |
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65 | * ( ( n*( n + 1 ) )/2 ). |
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66 | * Before entry with UPLO = 'U' or 'u', the array AP must |
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67 | * contain the upper triangular matrix packed sequentially, |
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68 | * column by column, so that AP( 1 ) contains a( 1, 1 ), |
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69 | * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) |
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70 | * respectively, and so on. |
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71 | * Before entry with UPLO = 'L' or 'l', the array AP must |
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72 | * contain the lower triangular matrix packed sequentially, |
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73 | * column by column, so that AP( 1 ) contains a( 1, 1 ), |
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74 | * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) |
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75 | * respectively, and so on. |
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76 | * Note that when DIAG = 'U' or 'u', the diagonal elements of |
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77 | * A are not referenced, but are assumed to be unity. |
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78 | * Unchanged on exit. |
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79 | * |
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80 | * X - COMPLEX array of dimension at least |
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81 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
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82 | * Before entry, the incremented array X must contain the n |
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83 | * element right-hand side vector b. On exit, X is overwritten |
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84 | * with the solution vector x. |
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85 | * |
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86 | * INCX - INTEGER. |
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87 | * On entry, INCX specifies the increment for the elements of |
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88 | * X. INCX must not be zero. |
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89 | * Unchanged on exit. |
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90 | * |
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91 | * |
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92 | * Level 2 Blas routine. |
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93 | * |
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94 | * -- Written on 22-October-1986. |
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95 | * Jack Dongarra, Argonne National Lab. |
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96 | * Jeremy Du Croz, Nag Central Office. |
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97 | * Sven Hammarling, Nag Central Office. |
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98 | * Richard Hanson, Sandia National Labs. |
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99 | * |
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100 | * |
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101 | * .. Parameters .. |
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102 | COMPLEX ZERO |
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103 | PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
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104 | * .. |
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105 | * .. Local Scalars .. |
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106 | COMPLEX TEMP |
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107 | INTEGER I,INFO,IX,J,JX,K,KK,KX |
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108 | LOGICAL NOCONJ,NOUNIT |
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109 | * .. |
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110 | * .. External Functions .. |
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111 | LOGICAL LSAME |
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112 | EXTERNAL LSAME |
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113 | * .. |
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114 | * .. External Subroutines .. |
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115 | EXTERNAL XERBLA |
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116 | * .. |
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117 | * .. Intrinsic Functions .. |
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118 | INTRINSIC CONJG |
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119 | * .. |
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120 | * |
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121 | * Test the input parameters. |
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122 | * |
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123 | INFO = 0 |
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124 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
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125 | INFO = 1 |
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126 | ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. |
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127 | + .NOT.LSAME(TRANS,'C')) THEN |
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128 | INFO = 2 |
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129 | ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN |
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130 | INFO = 3 |
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131 | ELSE IF (N.LT.0) THEN |
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132 | INFO = 4 |
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133 | ELSE IF (INCX.EQ.0) THEN |
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134 | INFO = 7 |
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135 | END IF |
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136 | IF (INFO.NE.0) THEN |
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137 | CALL XERBLA('CTPSV ',INFO) |
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138 | RETURN |
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139 | END IF |
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140 | * |
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141 | * Quick return if possible. |
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142 | * |
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143 | IF (N.EQ.0) RETURN |
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144 | * |
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145 | NOCONJ = LSAME(TRANS,'T') |
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146 | NOUNIT = LSAME(DIAG,'N') |
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147 | * |
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148 | * Set up the start point in X if the increment is not unity. This |
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149 | * will be ( N - 1 )*INCX too small for descending loops. |
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150 | * |
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151 | IF (INCX.LE.0) THEN |
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152 | KX = 1 - (N-1)*INCX |
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153 | ELSE IF (INCX.NE.1) THEN |
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154 | KX = 1 |
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155 | END IF |
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156 | * |
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157 | * Start the operations. In this version the elements of AP are |
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158 | * accessed sequentially with one pass through AP. |
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159 | * |
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160 | IF (LSAME(TRANS,'N')) THEN |
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161 | * |
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162 | * Form x := inv( A )*x. |
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163 | * |
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164 | IF (LSAME(UPLO,'U')) THEN |
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165 | KK = (N* (N+1))/2 |
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166 | IF (INCX.EQ.1) THEN |
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167 | DO 20 J = N,1,-1 |
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168 | IF (X(J).NE.ZERO) THEN |
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169 | IF (NOUNIT) X(J) = X(J)/AP(KK) |
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170 | TEMP = X(J) |
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171 | K = KK - 1 |
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172 | DO 10 I = J - 1,1,-1 |
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173 | X(I) = X(I) - TEMP*AP(K) |
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174 | K = K - 1 |
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175 | 10 CONTINUE |
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176 | END IF |
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177 | KK = KK - J |
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178 | 20 CONTINUE |
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179 | ELSE |
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180 | JX = KX + (N-1)*INCX |
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181 | DO 40 J = N,1,-1 |
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182 | IF (X(JX).NE.ZERO) THEN |
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183 | IF (NOUNIT) X(JX) = X(JX)/AP(KK) |
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184 | TEMP = X(JX) |
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185 | IX = JX |
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186 | DO 30 K = KK - 1,KK - J + 1,-1 |
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187 | IX = IX - INCX |
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188 | X(IX) = X(IX) - TEMP*AP(K) |
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189 | 30 CONTINUE |
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190 | END IF |
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191 | JX = JX - INCX |
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192 | KK = KK - J |
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193 | 40 CONTINUE |
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194 | END IF |
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195 | ELSE |
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196 | KK = 1 |
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197 | IF (INCX.EQ.1) THEN |
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198 | DO 60 J = 1,N |
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199 | IF (X(J).NE.ZERO) THEN |
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200 | IF (NOUNIT) X(J) = X(J)/AP(KK) |
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201 | TEMP = X(J) |
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202 | K = KK + 1 |
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203 | DO 50 I = J + 1,N |
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204 | X(I) = X(I) - TEMP*AP(K) |
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205 | K = K + 1 |
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206 | 50 CONTINUE |
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207 | END IF |
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208 | KK = KK + (N-J+1) |
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209 | 60 CONTINUE |
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210 | ELSE |
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211 | JX = KX |
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212 | DO 80 J = 1,N |
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213 | IF (X(JX).NE.ZERO) THEN |
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214 | IF (NOUNIT) X(JX) = X(JX)/AP(KK) |
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215 | TEMP = X(JX) |
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216 | IX = JX |
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217 | DO 70 K = KK + 1,KK + N - J |
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218 | IX = IX + INCX |
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219 | X(IX) = X(IX) - TEMP*AP(K) |
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220 | 70 CONTINUE |
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221 | END IF |
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222 | JX = JX + INCX |
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223 | KK = KK + (N-J+1) |
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224 | 80 CONTINUE |
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225 | END IF |
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226 | END IF |
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227 | ELSE |
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228 | * |
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229 | * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. |
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230 | * |
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231 | IF (LSAME(UPLO,'U')) THEN |
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232 | KK = 1 |
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233 | IF (INCX.EQ.1) THEN |
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234 | DO 110 J = 1,N |
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235 | TEMP = X(J) |
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236 | K = KK |
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237 | IF (NOCONJ) THEN |
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238 | DO 90 I = 1,J - 1 |
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239 | TEMP = TEMP - AP(K)*X(I) |
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240 | K = K + 1 |
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241 | 90 CONTINUE |
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242 | IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) |
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243 | ELSE |
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244 | DO 100 I = 1,J - 1 |
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245 | TEMP = TEMP - CONJG(AP(K))*X(I) |
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246 | K = K + 1 |
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247 | 100 CONTINUE |
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248 | IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) |
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249 | END IF |
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250 | X(J) = TEMP |
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251 | KK = KK + J |
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252 | 110 CONTINUE |
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253 | ELSE |
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254 | JX = KX |
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255 | DO 140 J = 1,N |
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256 | TEMP = X(JX) |
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257 | IX = KX |
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258 | IF (NOCONJ) THEN |
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259 | DO 120 K = KK,KK + J - 2 |
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260 | TEMP = TEMP - AP(K)*X(IX) |
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261 | IX = IX + INCX |
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262 | 120 CONTINUE |
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263 | IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) |
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264 | ELSE |
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265 | DO 130 K = KK,KK + J - 2 |
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266 | TEMP = TEMP - CONJG(AP(K))*X(IX) |
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267 | IX = IX + INCX |
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268 | 130 CONTINUE |
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269 | IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) |
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270 | END IF |
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271 | X(JX) = TEMP |
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272 | JX = JX + INCX |
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273 | KK = KK + J |
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274 | 140 CONTINUE |
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275 | END IF |
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276 | ELSE |
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277 | KK = (N* (N+1))/2 |
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278 | IF (INCX.EQ.1) THEN |
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279 | DO 170 J = N,1,-1 |
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280 | TEMP = X(J) |
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281 | K = KK |
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282 | IF (NOCONJ) THEN |
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283 | DO 150 I = N,J + 1,-1 |
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284 | TEMP = TEMP - AP(K)*X(I) |
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285 | K = K - 1 |
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286 | 150 CONTINUE |
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287 | IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) |
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288 | ELSE |
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289 | DO 160 I = N,J + 1,-1 |
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290 | TEMP = TEMP - CONJG(AP(K))*X(I) |
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291 | K = K - 1 |
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292 | 160 CONTINUE |
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293 | IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) |
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294 | END IF |
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295 | X(J) = TEMP |
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296 | KK = KK - (N-J+1) |
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297 | 170 CONTINUE |
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298 | ELSE |
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299 | KX = KX + (N-1)*INCX |
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300 | JX = KX |
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301 | DO 200 J = N,1,-1 |
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302 | TEMP = X(JX) |
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303 | IX = KX |
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304 | IF (NOCONJ) THEN |
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305 | DO 180 K = KK,KK - (N- (J+1)),-1 |
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306 | TEMP = TEMP - AP(K)*X(IX) |
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307 | IX = IX - INCX |
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308 | 180 CONTINUE |
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309 | IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) |
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310 | ELSE |
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311 | DO 190 K = KK,KK - (N- (J+1)),-1 |
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312 | TEMP = TEMP - CONJG(AP(K))*X(IX) |
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313 | IX = IX - INCX |
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314 | 190 CONTINUE |
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315 | IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) |
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316 | END IF |
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317 | X(JX) = TEMP |
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318 | JX = JX - INCX |
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319 | KK = KK - (N-J+1) |
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320 | 200 CONTINUE |
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321 | END IF |
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322 | END IF |
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323 | END IF |
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324 | * |
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325 | RETURN |
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326 | * |
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327 | * End of CTPSV . |
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328 | * |
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329 | END |
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