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annotate libcruft/lapack/spbtrs.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 SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, 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 UPLO
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9 INTEGER INFO, KD, LDAB, LDB, N, NRHS
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10 * ..
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11 * .. Array Arguments ..
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12 REAL AB( LDAB, * ), B( LDB, * )
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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 * SPBTRS solves a system of linear equations A*X = B with a symmetric
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19 * positive definite band matrix A using the Cholesky factorization
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20 * A = U**T*U or A = L*L**T computed by SPBTRF.
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21 *
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22 * Arguments
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23 * =========
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24 *
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25 * UPLO (input) CHARACTER*1
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26 * = 'U': Upper triangular factor stored in AB;
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27 * = 'L': Lower triangular factor stored in AB.
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28 *
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29 * N (input) INTEGER
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30 * The order of the matrix A. N >= 0.
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31 *
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32 * KD (input) INTEGER
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33 * The number of superdiagonals of the matrix A if UPLO = 'U',
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34 * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
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35 *
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36 * NRHS (input) INTEGER
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37 * The number of right hand sides, i.e., the number of columns
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38 * of the matrix B. NRHS >= 0.
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39 *
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40 * AB (input) REAL array, dimension (LDAB,N)
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41 * The triangular factor U or L from the Cholesky factorization
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42 * A = U**T*U or A = L*L**T of the band matrix A, stored in the
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43 * first KD+1 rows of the array. The j-th column of U or L is
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44 * stored in the j-th column of the array AB as follows:
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45 * if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
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46 * if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
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47 *
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48 * LDAB (input) INTEGER
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49 * The leading dimension of the array AB. LDAB >= KD+1.
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50 *
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51 * B (input/output) REAL array, dimension (LDB,NRHS)
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52 * On entry, the right hand side matrix B.
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53 * On exit, the solution matrix X.
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54 *
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55 * LDB (input) INTEGER
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56 * The leading dimension of the array B. LDB >= max(1,N).
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57 *
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58 * INFO (output) INTEGER
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59 * = 0: successful exit
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60 * < 0: if INFO = -i, the i-th argument had an illegal value
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61 *
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62 * =====================================================================
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63 *
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64 * .. Local Scalars ..
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65 LOGICAL UPPER
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66 INTEGER J
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67 * ..
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68 * .. External Functions ..
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69 LOGICAL LSAME
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70 EXTERNAL LSAME
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71 * ..
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72 * .. External Subroutines ..
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73 EXTERNAL STBSV, XERBLA
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74 * ..
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75 * .. Intrinsic Functions ..
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76 INTRINSIC MAX
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77 * ..
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78 * .. Executable Statements ..
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79 *
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80 * Test the input parameters.
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81 *
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82 INFO = 0
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83 UPPER = LSAME( UPLO, 'U' )
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84 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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85 INFO = -1
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86 ELSE IF( N.LT.0 ) THEN
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87 INFO = -2
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88 ELSE IF( KD.LT.0 ) THEN
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89 INFO = -3
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90 ELSE IF( NRHS.LT.0 ) THEN
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91 INFO = -4
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92 ELSE IF( LDAB.LT.KD+1 ) THEN
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93 INFO = -6
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94 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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95 INFO = -8
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96 END IF
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97 IF( INFO.NE.0 ) THEN
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98 CALL XERBLA( 'SPBTRS', -INFO )
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99 RETURN
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100 END IF
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101 *
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102 * Quick return if possible
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103 *
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104 IF( N.EQ.0 .OR. NRHS.EQ.0 )
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105 $ RETURN
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106 *
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107 IF( UPPER ) THEN
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108 *
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109 * Solve A*X = B where A = U'*U.
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110 *
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111 DO 10 J = 1, NRHS
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112 *
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113 * Solve U'*X = B, overwriting B with X.
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114 *
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115 CALL STBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
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116 $ LDAB, B( 1, J ), 1 )
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117 *
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118 * Solve U*X = B, overwriting B with X.
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119 *
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120 CALL STBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
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121 $ LDAB, B( 1, J ), 1 )
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122 10 CONTINUE
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123 ELSE
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124 *
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125 * Solve A*X = B where A = L*L'.
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126 *
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127 DO 20 J = 1, NRHS
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128 *
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129 * Solve L*X = B, overwriting B with X.
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130 *
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131 CALL STBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
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132 $ LDAB, B( 1, J ), 1 )
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133 *
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134 * Solve L'*X = B, overwriting B with X.
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135 *
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136 CALL STBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
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137 $ LDAB, B( 1, J ), 1 )
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138 20 CONTINUE
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139 END IF
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140 *
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141 RETURN
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142 *
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143 * End of SPBTRS
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144 *
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145 END