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annotate libcruft/lapack/spbcon.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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7789
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1 SUBROUTINE SPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
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2 $ IWORK, INFO )
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3 *
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4 * -- LAPACK routine (version 3.1) --
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5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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6 * November 2006
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7 *
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8 * Modified to call SLACN2 in place of SLACON, 7 Feb 03, SJH.
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9 *
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10 * .. Scalar Arguments ..
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11 CHARACTER UPLO
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12 INTEGER INFO, KD, LDAB, N
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13 REAL ANORM, RCOND
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14 * ..
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15 * .. Array Arguments ..
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16 INTEGER IWORK( * )
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17 REAL AB( LDAB, * ), WORK( * )
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18 * ..
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19 *
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20 * Purpose
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21 * =======
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22 *
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23 * SPBCON estimates the reciprocal of the condition number (in the
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24 * 1-norm) of a real symmetric positive definite band matrix using the
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25 * Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.
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26 *
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27 * An estimate is obtained for norm(inv(A)), and the reciprocal of the
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28 * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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29 *
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30 * Arguments
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31 * =========
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32 *
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33 * UPLO (input) CHARACTER*1
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34 * = 'U': Upper triangular factor stored in AB;
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35 * = 'L': Lower triangular factor stored in AB.
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36 *
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37 * N (input) INTEGER
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38 * The order of the matrix A. N >= 0.
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39 *
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40 * KD (input) INTEGER
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41 * The number of superdiagonals of the matrix A if UPLO = 'U',
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42 * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
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43 *
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44 * AB (input) REAL array, dimension (LDAB,N)
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45 * The triangular factor U or L from the Cholesky factorization
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46 * A = U**T*U or A = L*L**T of the band matrix A, stored in the
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47 * first KD+1 rows of the array. The j-th column of U or L is
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48 * stored in the j-th column of the array AB as follows:
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49 * if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
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50 * if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
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51 *
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52 * LDAB (input) INTEGER
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53 * The leading dimension of the array AB. LDAB >= KD+1.
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54 *
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55 * ANORM (input) REAL
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56 * The 1-norm (or infinity-norm) of the symmetric band matrix A.
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57 *
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58 * RCOND (output) REAL
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59 * The reciprocal of the condition number of the matrix A,
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60 * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
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61 * estimate of the 1-norm of inv(A) computed in this routine.
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62 *
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63 * WORK (workspace) REAL array, dimension (3*N)
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64 *
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65 * IWORK (workspace) INTEGER array, dimension (N)
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66 *
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67 * INFO (output) INTEGER
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68 * = 0: successful exit
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69 * < 0: if INFO = -i, the i-th argument had an illegal value
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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 ONE, ZERO
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75 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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76 * ..
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77 * .. Local Scalars ..
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78 LOGICAL UPPER
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79 CHARACTER NORMIN
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80 INTEGER IX, KASE
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81 REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
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82 * ..
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83 * .. Local Arrays ..
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84 INTEGER ISAVE( 3 )
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85 * ..
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86 * .. External Functions ..
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87 LOGICAL LSAME
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88 INTEGER ISAMAX
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89 REAL SLAMCH
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90 EXTERNAL LSAME, ISAMAX, SLAMCH
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91 * ..
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92 * .. External Subroutines ..
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93 EXTERNAL SLACN2, SLATBS, SRSCL, XERBLA
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94 * ..
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95 * .. Intrinsic Functions ..
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96 INTRINSIC ABS
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97 * ..
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98 * .. Executable Statements ..
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99 *
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100 * Test the input parameters.
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101 *
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102 INFO = 0
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103 UPPER = LSAME( UPLO, 'U' )
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104 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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105 INFO = -1
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106 ELSE IF( N.LT.0 ) THEN
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107 INFO = -2
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108 ELSE IF( KD.LT.0 ) THEN
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109 INFO = -3
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110 ELSE IF( LDAB.LT.KD+1 ) THEN
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111 INFO = -5
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112 ELSE IF( ANORM.LT.ZERO ) THEN
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113 INFO = -6
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114 END IF
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115 IF( INFO.NE.0 ) THEN
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116 CALL XERBLA( 'SPBCON', -INFO )
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117 RETURN
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118 END IF
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119 *
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120 * Quick return if possible
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121 *
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122 RCOND = ZERO
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123 IF( N.EQ.0 ) THEN
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124 RCOND = ONE
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125 RETURN
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126 ELSE IF( ANORM.EQ.ZERO ) THEN
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127 RETURN
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128 END IF
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129 *
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130 SMLNUM = SLAMCH( 'Safe minimum' )
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131 *
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132 * Estimate the 1-norm of the inverse.
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133 *
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134 KASE = 0
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135 NORMIN = 'N'
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136 10 CONTINUE
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137 CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
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138 IF( KASE.NE.0 ) THEN
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139 IF( UPPER ) THEN
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140 *
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141 * Multiply by inv(U').
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142 *
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143 CALL SLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
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144 $ KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
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145 $ INFO )
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146 NORMIN = 'Y'
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147 *
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148 * Multiply by inv(U).
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149 *
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150 CALL SLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
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151 $ KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
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152 $ INFO )
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153 ELSE
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154 *
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155 * Multiply by inv(L).
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156 *
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157 CALL SLATBS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
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158 $ KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
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159 $ INFO )
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160 NORMIN = 'Y'
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161 *
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162 * Multiply by inv(L').
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163 *
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164 CALL SLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
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165 $ KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
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166 $ INFO )
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167 END IF
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168 *
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169 * Multiply by 1/SCALE if doing so will not cause overflow.
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170 *
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171 SCALE = SCALEL*SCALEU
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172 IF( SCALE.NE.ONE ) THEN
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173 IX = ISAMAX( N, WORK, 1 )
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174 IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
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175 $ GO TO 20
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176 CALL SRSCL( N, SCALE, WORK, 1 )
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177 END IF
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178 GO TO 10
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179 END IF
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180 *
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181 * Compute the estimate of the reciprocal condition number.
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182 *
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183 IF( AINVNM.NE.ZERO )
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184 $ RCOND = ( ONE / AINVNM ) / ANORM
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185 *
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186 20 CONTINUE
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187 *
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188 RETURN
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189 *
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190 * End of SPBCON
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191 *
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192 END