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1 SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, |
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2 $ INFO ) |
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3 * |
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4 * -- LAPACK routine (version 3.0) -- |
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5 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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6 * Courant Institute, Argonne National Lab, and Rice University |
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7 * March 31, 1993 |
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8 * |
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9 * .. Scalar Arguments .. |
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10 CHARACTER DIAG, TRANS, UPLO |
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11 INTEGER INFO, LDA, LDB, N, NRHS |
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12 * .. |
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13 * .. Array Arguments .. |
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14 DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
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15 * .. |
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16 * |
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17 * Purpose |
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18 * ======= |
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19 * |
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20 * DTRTRS solves a triangular system of the form |
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21 * |
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22 * A * X = B or A**T * X = B, |
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23 * |
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24 * where A is a triangular matrix of order N, and B is an N-by-NRHS |
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25 * matrix. A check is made to verify that A is nonsingular. |
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26 * |
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27 * Arguments |
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28 * ========= |
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29 * |
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30 * UPLO (input) CHARACTER*1 |
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31 * = 'U': A is upper triangular; |
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32 * = 'L': A is lower triangular. |
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33 * |
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34 * TRANS (input) CHARACTER*1 |
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35 * Specifies the form of the system of equations: |
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36 * = 'N': A * X = B (No transpose) |
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37 * = 'T': A**T * X = B (Transpose) |
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38 * = 'C': A**H * X = B (Conjugate transpose = Transpose) |
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39 * |
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40 * DIAG (input) CHARACTER*1 |
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41 * = 'N': A is non-unit triangular; |
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42 * = 'U': A is unit triangular. |
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43 * |
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44 * N (input) INTEGER |
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45 * The order of the matrix A. N >= 0. |
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46 * |
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47 * NRHS (input) INTEGER |
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48 * The number of right hand sides, i.e., the number of columns |
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49 * of the matrix B. NRHS >= 0. |
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50 * |
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51 * A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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52 * The triangular matrix A. If UPLO = 'U', the leading N-by-N |
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53 * upper triangular part of the array A contains the upper |
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54 * triangular matrix, and the strictly lower triangular part of |
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55 * A is not referenced. If UPLO = 'L', the leading N-by-N lower |
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56 * triangular part of the array A contains the lower triangular |
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57 * matrix, and the strictly upper triangular part of A is not |
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58 * referenced. If DIAG = 'U', the diagonal elements of A are |
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59 * also not referenced and are assumed to be 1. |
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60 * |
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61 * LDA (input) INTEGER |
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62 * The leading dimension of the array A. LDA >= max(1,N). |
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63 * |
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64 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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65 * On entry, the right hand side matrix B. |
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66 * On exit, if INFO = 0, the solution matrix X. |
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67 * |
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68 * LDB (input) INTEGER |
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69 * The leading dimension of the array B. LDB >= max(1,N). |
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70 * |
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71 * INFO (output) INTEGER |
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72 * = 0: successful exit |
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73 * < 0: if INFO = -i, the i-th argument had an illegal value |
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74 * > 0: if INFO = i, the i-th diagonal element of A is zero, |
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75 * indicating that the matrix is singular and the solutions |
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76 * X have not been computed. |
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77 * |
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78 * ===================================================================== |
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79 * |
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80 * .. Parameters .. |
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81 DOUBLE PRECISION ZERO, ONE |
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82 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) |
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83 * .. |
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84 * .. Local Scalars .. |
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85 LOGICAL NOUNIT |
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86 * .. |
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87 * .. External Functions .. |
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88 LOGICAL LSAME |
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89 EXTERNAL LSAME |
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90 * .. |
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91 * .. External Subroutines .. |
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92 EXTERNAL DTRSM, XERBLA |
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93 * .. |
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94 * .. Intrinsic Functions .. |
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95 INTRINSIC MAX |
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96 * .. |
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97 * .. Executable Statements .. |
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98 * |
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99 * Test the input parameters. |
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100 * |
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101 INFO = 0 |
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102 NOUNIT = LSAME( DIAG, 'N' ) |
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103 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
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104 INFO = -1 |
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105 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT. |
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106 $ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN |
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107 INFO = -2 |
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108 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN |
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109 INFO = -3 |
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110 ELSE IF( N.LT.0 ) THEN |
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111 INFO = -4 |
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112 ELSE IF( NRHS.LT.0 ) THEN |
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113 INFO = -5 |
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114 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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115 INFO = -7 |
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116 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN |
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117 INFO = -9 |
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118 END IF |
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119 IF( INFO.NE.0 ) THEN |
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120 CALL XERBLA( 'DTRTRS', -INFO ) |
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121 RETURN |
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122 END IF |
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123 * |
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124 * Quick return if possible |
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125 * |
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126 IF( N.EQ.0 ) |
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127 $ RETURN |
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128 * |
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129 * Check for singularity. |
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130 * |
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131 IF( NOUNIT ) THEN |
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132 DO 10 INFO = 1, N |
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133 IF( A( INFO, INFO ).EQ.ZERO ) |
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134 $ RETURN |
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135 10 CONTINUE |
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136 END IF |
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137 INFO = 0 |
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138 * |
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139 * Solve A * x = b or A' * x = b. |
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140 * |
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141 CALL DTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B, |
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142 $ LDB ) |
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143 * |
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144 RETURN |
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145 * |
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146 * End of DTRTRS |
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147 * |
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148 END |
