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annotate libcruft/lapack/ctrexc.f @ 7948:af10baa63915 ss-3-1-50

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3.1.50 snapshot
author John W. Eaton <jwe@octave.org>
date Fri, 18 Jul 2008 17:42:48 -0400
parents 82be108cc558
children
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1 SUBROUTINE CTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, 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 CHARACTER COMPQ
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9 INTEGER IFST, ILST, INFO, LDQ, LDT, N
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10 * ..
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11 * .. Array Arguments ..
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12 COMPLEX Q( LDQ, * ), T( LDT, * )
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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 * CTREXC reorders the Schur factorization of a complex matrix
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19 * A = Q*T*Q**H, so that the diagonal element of T with row index IFST
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20 * is moved to row ILST.
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21 *
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22 * The Schur form T is reordered by a unitary similarity transformation
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23 * Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
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24 * postmultplying it with Z.
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25 *
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26 * Arguments
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27 * =========
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28 *
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29 * COMPQ (input) CHARACTER*1
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30 * = 'V': update the matrix Q of Schur vectors;
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31 * = 'N': do not update Q.
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32 *
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33 * N (input) INTEGER
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34 * The order of the matrix T. N >= 0.
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35 *
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36 * T (input/output) COMPLEX array, dimension (LDT,N)
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37 * On entry, the upper triangular matrix T.
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38 * On exit, the reordered upper triangular matrix.
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39 *
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40 * LDT (input) INTEGER
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41 * The leading dimension of the array T. LDT >= max(1,N).
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42 *
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43 * Q (input/output) COMPLEX array, dimension (LDQ,N)
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44 * On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
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45 * On exit, if COMPQ = 'V', Q has been postmultiplied by the
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46 * unitary transformation matrix Z which reorders T.
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47 * If COMPQ = 'N', Q is not referenced.
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48 *
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49 * LDQ (input) INTEGER
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50 * The leading dimension of the array Q. LDQ >= max(1,N).
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51 *
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52 * IFST (input) INTEGER
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53 * ILST (input) INTEGER
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54 * Specify the reordering of the diagonal elements of T:
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55 * The element with row index IFST is moved to row ILST by a
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56 * sequence of transpositions between adjacent elements.
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57 * 1 <= IFST <= N; 1 <= ILST <= N.
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58 *
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59 * INFO (output) INTEGER
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60 * = 0: successful exit
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61 * < 0: if INFO = -i, the i-th argument had an illegal value
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62 *
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63 * =====================================================================
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64 *
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65 * .. Local Scalars ..
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66 LOGICAL WANTQ
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67 INTEGER K, M1, M2, M3
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68 REAL CS
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69 COMPLEX SN, T11, T22, TEMP
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70 * ..
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71 * .. External Functions ..
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72 LOGICAL LSAME
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73 EXTERNAL LSAME
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74 * ..
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75 * .. External Subroutines ..
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76 EXTERNAL CLARTG, CROT, XERBLA
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77 * ..
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78 * .. Intrinsic Functions ..
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79 INTRINSIC CONJG, MAX
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80 * ..
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81 * .. Executable Statements ..
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82 *
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83 * Decode and test the input parameters.
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84 *
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85 INFO = 0
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86 WANTQ = LSAME( COMPQ, 'V' )
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87 IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN
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88 INFO = -1
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89 ELSE IF( N.LT.0 ) THEN
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90 INFO = -2
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91 ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
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92 INFO = -4
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93 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
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94 INFO = -6
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95 ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
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96 INFO = -7
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97 ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
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98 INFO = -8
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99 END IF
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100 IF( INFO.NE.0 ) THEN
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101 CALL XERBLA( 'CTREXC', -INFO )
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102 RETURN
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103 END IF
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104 *
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105 * Quick return if possible
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106 *
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107 IF( N.EQ.1 .OR. IFST.EQ.ILST )
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108 $ RETURN
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109 *
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110 IF( IFST.LT.ILST ) THEN
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111 *
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112 * Move the IFST-th diagonal element forward down the diagonal.
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113 *
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114 M1 = 0
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115 M2 = -1
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116 M3 = 1
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117 ELSE
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118 *
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119 * Move the IFST-th diagonal element backward up the diagonal.
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120 *
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121 M1 = -1
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122 M2 = 0
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123 M3 = -1
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124 END IF
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125 *
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126 DO 10 K = IFST + M1, ILST + M2, M3
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127 *
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128 * Interchange the k-th and (k+1)-th diagonal elements.
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129 *
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130 T11 = T( K, K )
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131 T22 = T( K+1, K+1 )
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132 *
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133 * Determine the transformation to perform the interchange.
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134 *
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135 CALL CLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP )
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136 *
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137 * Apply transformation to the matrix T.
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138 *
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139 IF( K+2.LE.N )
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140 $ CALL CROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
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141 $ SN )
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142 CALL CROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS, CONJG( SN ) )
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143 *
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144 T( K, K ) = T22
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145 T( K+1, K+1 ) = T11
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146 *
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147 IF( WANTQ ) THEN
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148 *
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149 * Accumulate transformation in the matrix Q.
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150 *
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151 CALL CROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
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152 $ CONJG( SN ) )
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153 END IF
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154 *
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155 10 CONTINUE
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156 *
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157 RETURN
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158 *
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159 * End of CTREXC
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160 *
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161 END