00001 /* Ergo, version 3.2, a program for linear scaling electronic structure 00002 * calculations. 00003 * Copyright (C) 2012 Elias Rudberg, Emanuel H. Rubensson, and Pawel Salek. 00004 * 00005 * This program is free software: you can redistribute it and/or modify 00006 * it under the terms of the GNU General Public License as published by 00007 * the Free Software Foundation, either version 3 of the License, or 00008 * (at your option) any later version. 00009 * 00010 * This program is distributed in the hope that it will be useful, 00011 * but WITHOUT ANY WARRANTY; without even the implied warranty of 00012 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00013 * GNU General Public License for more details. 00014 * 00015 * You should have received a copy of the GNU General Public License 00016 * along with this program. If not, see <http://www.gnu.org/licenses/>. 00017 * 00018 * Primary academic reference: 00019 * KohnâSham Density Functional Theory Electronic Structure Calculations 00020 * with Linearly Scaling Computational Time and Memory Usage, 00021 * Elias Rudberg, Emanuel H. Rubensson, and Pawel Salek, 00022 * J. Chem. Theory Comput. 7, 340 (2011), 00023 * <http://dx.doi.org/10.1021/ct100611z> 00024 * 00025 * For further information about Ergo, see <http://www.ergoscf.org>. 00026 */ 00027 00028 /* This file belongs to the template_lapack part of the Ergo source 00029 * code. The source files in the template_lapack directory are modified 00030 * versions of files originally distributed as CLAPACK, see the 00031 * Copyright/license notice in the file template_lapack/COPYING. 00032 */ 00033 00034 00035 #ifndef TEMPLATE_LAPACK_TPTRI_HEADER 00036 #define TEMPLATE_LAPACK_TPTRI_HEADER 00037 00038 #include "template_lapack_common.h" 00039 00040 template<class Treal> 00041 int template_lapack_tptri(const char *uplo, const char *diag, const integer *n, Treal * 00042 ap, integer *info) 00043 { 00044 /* -- LAPACK routine (version 3.0) -- 00045 Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., 00046 Courant Institute, Argonne National Lab, and Rice University 00047 September 30, 1994 00048 00049 00050 Purpose 00051 ======= 00052 00053 DTPTRI computes the inverse of a real upper or lower triangular 00054 matrix A stored in packed format. 00055 00056 Arguments 00057 ========= 00058 00059 UPLO (input) CHARACTER*1 00060 = 'U': A is upper triangular; 00061 = 'L': A is lower triangular. 00062 00063 DIAG (input) CHARACTER*1 00064 = 'N': A is non-unit triangular; 00065 = 'U': A is unit triangular. 00066 00067 N (input) INTEGER 00068 The order of the matrix A. N >= 0. 00069 00070 AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) 00071 On entry, the upper or lower triangular matrix A, stored 00072 columnwise in a linear array. The j-th column of A is stored 00073 in the array AP as follows: 00074 if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00075 if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. 00076 See below for further details. 00077 On exit, the (triangular) inverse of the original matrix, in 00078 the same packed storage format. 00079 00080 INFO (output) INTEGER 00081 = 0: successful exit 00082 < 0: if INFO = -i, the i-th argument had an illegal value 00083 > 0: if INFO = i, A(i,i) is exactly zero. The triangular 00084 matrix is singular and its inverse can not be computed. 00085 00086 Further Details 00087 =============== 00088 00089 A triangular matrix A can be transferred to packed storage using one 00090 of the following program segments: 00091 00092 UPLO = 'U': UPLO = 'L': 00093 00094 JC = 1 JC = 1 00095 DO 2 J = 1, N DO 2 J = 1, N 00096 DO 1 I = 1, J DO 1 I = J, N 00097 AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) 00098 1 CONTINUE 1 CONTINUE 00099 JC = JC + J JC = JC + N - J + 1 00100 2 CONTINUE 2 CONTINUE 00101 00102 ===================================================================== 00103 00104 00105 Test the input parameters. 00106 00107 Parameter adjustments */ 00108 /* Table of constant values */ 00109 integer c__1 = 1; 00110 00111 /* System generated locals */ 00112 integer i__1, i__2; 00113 /* Local variables */ 00114 integer j; 00115 logical upper; 00116 integer jc, jj; 00117 integer jclast; 00118 logical nounit; 00119 Treal ajj; 00120 00121 00122 --ap; 00123 00124 /* Initialization added by Elias to get rid of compiler warnings. */ 00125 jclast = 0; 00126 /* Function Body */ 00127 *info = 0; 00128 upper = template_blas_lsame(uplo, "U"); 00129 nounit = template_blas_lsame(diag, "N"); 00130 if (! upper && ! template_blas_lsame(uplo, "L")) { 00131 *info = -1; 00132 } else if (! nounit && ! template_blas_lsame(diag, "U")) { 00133 *info = -2; 00134 } else if (*n < 0) { 00135 *info = -3; 00136 } 00137 if (*info != 0) { 00138 i__1 = -(*info); 00139 template_blas_erbla("TPTRI ", &i__1); 00140 return 0; 00141 } 00142 00143 /* Check for singularity if non-unit. */ 00144 00145 if (nounit) { 00146 if (upper) { 00147 jj = 0; 00148 i__1 = *n; 00149 for (*info = 1; *info <= i__1; ++(*info)) { 00150 jj += *info; 00151 if (ap[jj] == 0.) { 00152 return 0; 00153 } 00154 /* L10: */ 00155 } 00156 } else { 00157 jj = 1; 00158 i__1 = *n; 00159 for (*info = 1; *info <= i__1; ++(*info)) { 00160 if (ap[jj] == 0.) { 00161 return 0; 00162 } 00163 jj = jj + *n - *info + 1; 00164 /* L20: */ 00165 } 00166 } 00167 *info = 0; 00168 } 00169 00170 if (upper) { 00171 00172 /* Compute inverse of upper triangular matrix. */ 00173 00174 jc = 1; 00175 i__1 = *n; 00176 for (j = 1; j <= i__1; ++j) { 00177 if (nounit) { 00178 ap[jc + j - 1] = 1. / ap[jc + j - 1]; 00179 ajj = -ap[jc + j - 1]; 00180 } else { 00181 ajj = -1.; 00182 } 00183 00184 /* Compute elements 1:j-1 of j-th column. */ 00185 00186 i__2 = j - 1; 00187 template_blas_tpmv("Upper", "No transpose", diag, &i__2, &ap[1], &ap[jc], & 00188 c__1); 00189 i__2 = j - 1; 00190 template_blas_scal(&i__2, &ajj, &ap[jc], &c__1); 00191 jc += j; 00192 /* L30: */ 00193 } 00194 00195 } else { 00196 00197 /* Compute inverse of lower triangular matrix. */ 00198 00199 jc = *n * (*n + 1) / 2; 00200 for (j = *n; j >= 1; --j) { 00201 if (nounit) { 00202 ap[jc] = 1. / ap[jc]; 00203 ajj = -ap[jc]; 00204 } else { 00205 ajj = -1.; 00206 } 00207 if (j < *n) { 00208 00209 /* Compute elements j+1:n of j-th column. */ 00210 00211 i__1 = *n - j; 00212 template_blas_tpmv("Lower", "No transpose", diag, &i__1, &ap[jclast], &ap[ 00213 jc + 1], &c__1); 00214 i__1 = *n - j; 00215 template_blas_scal(&i__1, &ajj, &ap[jc + 1], &c__1); 00216 } 00217 jclast = jc; 00218 jc = jc - *n + j - 2; 00219 /* L40: */ 00220 } 00221 } 00222 00223 return 0; 00224 00225 /* End of DTPTRI */ 00226 00227 } /* dtptri_ */ 00228 00229 #endif