Mercurial > hg > octave-nkf
annotate libcruft/lapack/slasr.f @ 8203:a9da991c77aa
update contrib.txi
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 08 Oct 2008 14:29:51 -0400 |
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1 SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) |
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2 * |
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3 * -- LAPACK auxiliary 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 CHARACTER DIRECT, PIVOT, SIDE |
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9 INTEGER LDA, M, N |
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10 * .. |
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11 * .. Array Arguments .. |
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12 REAL A( LDA, * ), C( * ), S( * ) |
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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 * SLASR applies a sequence of plane rotations to a real matrix A, |
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19 * from either the left or the right. |
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20 * |
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21 * When SIDE = 'L', the transformation takes the form |
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22 * |
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23 * A := P*A |
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24 * |
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25 * and when SIDE = 'R', the transformation takes the form |
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26 * |
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27 * A := A*P**T |
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28 * |
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29 * where P is an orthogonal matrix consisting of a sequence of z plane |
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30 * rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', |
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31 * and P**T is the transpose of P. |
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32 * |
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33 * When DIRECT = 'F' (Forward sequence), then |
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34 * |
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35 * P = P(z-1) * ... * P(2) * P(1) |
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36 * |
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37 * and when DIRECT = 'B' (Backward sequence), then |
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38 * |
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39 * P = P(1) * P(2) * ... * P(z-1) |
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40 * |
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41 * where P(k) is a plane rotation matrix defined by the 2-by-2 rotation |
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42 * |
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43 * R(k) = ( c(k) s(k) ) |
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44 * = ( -s(k) c(k) ). |
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45 * |
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46 * When PIVOT = 'V' (Variable pivot), the rotation is performed |
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47 * for the plane (k,k+1), i.e., P(k) has the form |
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48 * |
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49 * P(k) = ( 1 ) |
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50 * ( ... ) |
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51 * ( 1 ) |
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52 * ( c(k) s(k) ) |
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53 * ( -s(k) c(k) ) |
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54 * ( 1 ) |
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55 * ( ... ) |
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56 * ( 1 ) |
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57 * |
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58 * where R(k) appears as a rank-2 modification to the identity matrix in |
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59 * rows and columns k and k+1. |
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60 * |
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61 * When PIVOT = 'T' (Top pivot), the rotation is performed for the |
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62 * plane (1,k+1), so P(k) has the form |
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63 * |
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64 * P(k) = ( c(k) s(k) ) |
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65 * ( 1 ) |
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66 * ( ... ) |
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67 * ( 1 ) |
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68 * ( -s(k) c(k) ) |
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69 * ( 1 ) |
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70 * ( ... ) |
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71 * ( 1 ) |
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72 * |
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73 * where R(k) appears in rows and columns 1 and k+1. |
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74 * |
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75 * Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is |
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76 * performed for the plane (k,z), giving P(k) the form |
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77 * |
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78 * P(k) = ( 1 ) |
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79 * ( ... ) |
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80 * ( 1 ) |
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81 * ( c(k) s(k) ) |
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82 * ( 1 ) |
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83 * ( ... ) |
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84 * ( 1 ) |
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85 * ( -s(k) c(k) ) |
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86 * |
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87 * where R(k) appears in rows and columns k and z. The rotations are |
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88 * performed without ever forming P(k) explicitly. |
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89 * |
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90 * Arguments |
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91 * ========= |
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92 * |
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93 * SIDE (input) CHARACTER*1 |
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94 * Specifies whether the plane rotation matrix P is applied to |
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95 * A on the left or the right. |
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96 * = 'L': Left, compute A := P*A |
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97 * = 'R': Right, compute A:= A*P**T |
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98 * |
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99 * PIVOT (input) CHARACTER*1 |
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100 * Specifies the plane for which P(k) is a plane rotation |
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101 * matrix. |
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102 * = 'V': Variable pivot, the plane (k,k+1) |
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103 * = 'T': Top pivot, the plane (1,k+1) |
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104 * = 'B': Bottom pivot, the plane (k,z) |
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105 * |
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106 * DIRECT (input) CHARACTER*1 |
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107 * Specifies whether P is a forward or backward sequence of |
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108 * plane rotations. |
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109 * = 'F': Forward, P = P(z-1)*...*P(2)*P(1) |
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110 * = 'B': Backward, P = P(1)*P(2)*...*P(z-1) |
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111 * |
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112 * M (input) INTEGER |
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113 * The number of rows of the matrix A. If m <= 1, an immediate |
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114 * return is effected. |
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115 * |
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116 * N (input) INTEGER |
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117 * The number of columns of the matrix A. If n <= 1, an |
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118 * immediate return is effected. |
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119 * |
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120 * C (input) REAL array, dimension |
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121 * (M-1) if SIDE = 'L' |
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122 * (N-1) if SIDE = 'R' |
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123 * The cosines c(k) of the plane rotations. |
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124 * |
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125 * S (input) REAL array, dimension |
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126 * (M-1) if SIDE = 'L' |
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127 * (N-1) if SIDE = 'R' |
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128 * The sines s(k) of the plane rotations. The 2-by-2 plane |
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129 * rotation part of the matrix P(k), R(k), has the form |
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130 * R(k) = ( c(k) s(k) ) |
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131 * ( -s(k) c(k) ). |
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132 * |
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133 * A (input/output) REAL array, dimension (LDA,N) |
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134 * The M-by-N matrix A. On exit, A is overwritten by P*A if |
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135 * SIDE = 'R' or by A*P**T if SIDE = 'L'. |
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136 * |
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137 * LDA (input) INTEGER |
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138 * The leading dimension of the array A. LDA >= max(1,M). |
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139 * |
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140 * ===================================================================== |
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141 * |
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142 * .. Parameters .. |
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143 REAL ONE, ZERO |
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144 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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145 * .. |
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146 * .. Local Scalars .. |
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147 INTEGER I, INFO, J |
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148 REAL CTEMP, STEMP, TEMP |
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149 * .. |
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150 * .. External Functions .. |
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151 LOGICAL LSAME |
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152 EXTERNAL LSAME |
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153 * .. |
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154 * .. External Subroutines .. |
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155 EXTERNAL XERBLA |
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156 * .. |
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157 * .. Intrinsic Functions .. |
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158 INTRINSIC MAX |
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159 * .. |
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160 * .. Executable Statements .. |
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161 * |
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162 * Test the input parameters |
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163 * |
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164 INFO = 0 |
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165 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN |
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166 INFO = 1 |
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167 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, |
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168 $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN |
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169 INFO = 2 |
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170 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) |
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171 $ THEN |
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172 INFO = 3 |
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173 ELSE IF( M.LT.0 ) THEN |
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174 INFO = 4 |
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175 ELSE IF( N.LT.0 ) THEN |
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176 INFO = 5 |
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177 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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178 INFO = 9 |
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179 END IF |
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180 IF( INFO.NE.0 ) THEN |
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181 CALL XERBLA( 'SLASR ', INFO ) |
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182 RETURN |
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183 END IF |
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184 * |
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185 * Quick return if possible |
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186 * |
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187 IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) |
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188 $ RETURN |
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189 IF( LSAME( SIDE, 'L' ) ) THEN |
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190 * |
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191 * Form P * A |
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192 * |
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193 IF( LSAME( PIVOT, 'V' ) ) THEN |
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194 IF( LSAME( DIRECT, 'F' ) ) THEN |
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195 DO 20 J = 1, M - 1 |
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196 CTEMP = C( J ) |
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197 STEMP = S( J ) |
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198 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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199 DO 10 I = 1, N |
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200 TEMP = A( J+1, I ) |
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201 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) |
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202 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) |
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203 10 CONTINUE |
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204 END IF |
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205 20 CONTINUE |
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206 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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207 DO 40 J = M - 1, 1, -1 |
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208 CTEMP = C( J ) |
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209 STEMP = S( J ) |
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210 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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211 DO 30 I = 1, N |
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212 TEMP = A( J+1, I ) |
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213 A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) |
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214 A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) |
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215 30 CONTINUE |
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216 END IF |
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217 40 CONTINUE |
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218 END IF |
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219 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN |
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220 IF( LSAME( DIRECT, 'F' ) ) THEN |
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221 DO 60 J = 2, M |
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222 CTEMP = C( J-1 ) |
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223 STEMP = S( J-1 ) |
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224 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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225 DO 50 I = 1, N |
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226 TEMP = A( J, I ) |
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227 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) |
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228 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) |
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229 50 CONTINUE |
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230 END IF |
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231 60 CONTINUE |
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232 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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233 DO 80 J = M, 2, -1 |
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234 CTEMP = C( J-1 ) |
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235 STEMP = S( J-1 ) |
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236 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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237 DO 70 I = 1, N |
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238 TEMP = A( J, I ) |
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239 A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) |
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240 A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) |
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241 70 CONTINUE |
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242 END IF |
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243 80 CONTINUE |
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244 END IF |
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245 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN |
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246 IF( LSAME( DIRECT, 'F' ) ) THEN |
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247 DO 100 J = 1, M - 1 |
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248 CTEMP = C( J ) |
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249 STEMP = S( J ) |
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250 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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251 DO 90 I = 1, N |
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252 TEMP = A( J, I ) |
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253 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP |
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254 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP |
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255 90 CONTINUE |
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256 END IF |
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257 100 CONTINUE |
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258 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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259 DO 120 J = M - 1, 1, -1 |
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260 CTEMP = C( J ) |
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261 STEMP = S( J ) |
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262 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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263 DO 110 I = 1, N |
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264 TEMP = A( J, I ) |
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265 A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP |
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266 A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP |
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267 110 CONTINUE |
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268 END IF |
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269 120 CONTINUE |
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270 END IF |
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271 END IF |
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272 ELSE IF( LSAME( SIDE, 'R' ) ) THEN |
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273 * |
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274 * Form A * P' |
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275 * |
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276 IF( LSAME( PIVOT, 'V' ) ) THEN |
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277 IF( LSAME( DIRECT, 'F' ) ) THEN |
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278 DO 140 J = 1, N - 1 |
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279 CTEMP = C( J ) |
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280 STEMP = S( J ) |
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281 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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282 DO 130 I = 1, M |
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283 TEMP = A( I, J+1 ) |
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284 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) |
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285 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) |
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286 130 CONTINUE |
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287 END IF |
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288 140 CONTINUE |
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289 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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290 DO 160 J = N - 1, 1, -1 |
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291 CTEMP = C( J ) |
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292 STEMP = S( J ) |
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293 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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294 DO 150 I = 1, M |
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295 TEMP = A( I, J+1 ) |
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296 A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) |
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297 A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) |
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298 150 CONTINUE |
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299 END IF |
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300 160 CONTINUE |
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301 END IF |
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302 ELSE IF( LSAME( PIVOT, 'T' ) ) THEN |
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303 IF( LSAME( DIRECT, 'F' ) ) THEN |
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304 DO 180 J = 2, N |
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305 CTEMP = C( J-1 ) |
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306 STEMP = S( J-1 ) |
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307 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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308 DO 170 I = 1, M |
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309 TEMP = A( I, J ) |
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310 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) |
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311 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) |
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312 170 CONTINUE |
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313 END IF |
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314 180 CONTINUE |
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315 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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316 DO 200 J = N, 2, -1 |
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317 CTEMP = C( J-1 ) |
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318 STEMP = S( J-1 ) |
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319 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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320 DO 190 I = 1, M |
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321 TEMP = A( I, J ) |
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322 A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) |
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323 A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) |
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324 190 CONTINUE |
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325 END IF |
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326 200 CONTINUE |
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327 END IF |
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328 ELSE IF( LSAME( PIVOT, 'B' ) ) THEN |
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329 IF( LSAME( DIRECT, 'F' ) ) THEN |
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330 DO 220 J = 1, N - 1 |
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331 CTEMP = C( J ) |
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332 STEMP = S( J ) |
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333 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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334 DO 210 I = 1, M |
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335 TEMP = A( I, J ) |
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336 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP |
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337 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP |
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338 210 CONTINUE |
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339 END IF |
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340 220 CONTINUE |
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341 ELSE IF( LSAME( DIRECT, 'B' ) ) THEN |
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342 DO 240 J = N - 1, 1, -1 |
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343 CTEMP = C( J ) |
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344 STEMP = S( J ) |
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345 IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN |
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346 DO 230 I = 1, M |
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347 TEMP = A( I, J ) |
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348 A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP |
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349 A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP |
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350 230 CONTINUE |
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351 END IF |
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352 240 CONTINUE |
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353 END IF |
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354 END IF |
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355 END IF |
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356 * |
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357 RETURN |
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358 * |
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359 * End of SLASR |
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360 * |
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361 END |