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1 SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) |
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2 * |
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7034
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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 DOUBLE PRECISION 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 * DPBTRS 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 DPBTRF. |
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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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DTBSV, 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( 'DPBTRS', -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 DTBSV( '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 DTBSV( '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 DTBSV( '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 DTBSV( '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 DPBTRS |
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144 * |
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145 END |
