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_PPTRF_HEADER 00036 #define TEMPLATE_LAPACK_PPTRF_HEADER 00037 00038 #include "template_lapack_common.h" 00039 00040 template<class Treal> 00041 int template_lapack_pptrf(const char *uplo, const integer *n, Treal *ap, integer * 00042 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 March 31, 1993 00048 00049 00050 Purpose 00051 ======= 00052 00053 DPPTRF computes the Cholesky factorization of a real symmetric 00054 positive definite matrix A stored in packed format. 00055 00056 The factorization has the form 00057 A = U**T * U, if UPLO = 'U', or 00058 A = L * L**T, if UPLO = 'L', 00059 where U is an upper triangular matrix and L is lower triangular. 00060 00061 Arguments 00062 ========= 00063 00064 UPLO (input) CHARACTER*1 00065 = 'U': Upper triangle of A is stored; 00066 = 'L': Lower triangle of A is stored. 00067 00068 N (input) INTEGER 00069 The order of the matrix A. N >= 0. 00070 00071 AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) 00072 On entry, the upper or lower triangle of the symmetric matrix 00073 A, packed columnwise in a linear array. The j-th column of A 00074 is stored in the array AP as follows: 00075 if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00076 if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00077 See below for further details. 00078 00079 On exit, if INFO = 0, the triangular factor U or L from the 00080 Cholesky factorization A = U**T*U or A = L*L**T, in the same 00081 storage format as A. 00082 00083 INFO (output) INTEGER 00084 = 0: successful exit 00085 < 0: if INFO = -i, the i-th argument had an illegal value 00086 > 0: if INFO = i, the leading minor of order i is not 00087 positive definite, and the factorization could not be 00088 completed. 00089 00090 Further Details 00091 ======= ======= 00092 00093 The packed storage scheme is illustrated by the following example 00094 when N = 4, UPLO = 'U': 00095 00096 Two-dimensional storage of the symmetric matrix A: 00097 00098 a11 a12 a13 a14 00099 a22 a23 a24 00100 a33 a34 (aij = aji) 00101 a44 00102 00103 Packed storage of the upper triangle of A: 00104 00105 AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] 00106 00107 ===================================================================== 00108 00109 00110 Test the input parameters. 00111 00112 Parameter adjustments */ 00113 /* Table of constant values */ 00114 integer c__1 = 1; 00115 Treal c_b16 = -1.; 00116 00117 /* System generated locals */ 00118 integer i__1, i__2; 00119 Treal d__1; 00120 /* Local variables */ 00121 integer j; 00122 logical upper; 00123 integer jc, jj; 00124 Treal ajj; 00125 00126 00127 --ap; 00128 00129 /* Function Body */ 00130 *info = 0; 00131 upper = template_blas_lsame(uplo, "U"); 00132 if (! upper && ! template_blas_lsame(uplo, "L")) { 00133 *info = -1; 00134 } else if (*n < 0) { 00135 *info = -2; 00136 } 00137 if (*info != 0) { 00138 i__1 = -(*info); 00139 template_blas_erbla("DPPTRF", &i__1); 00140 return 0; 00141 } 00142 00143 /* Quick return if possible */ 00144 00145 if (*n == 0) { 00146 return 0; 00147 } 00148 00149 if (upper) { 00150 00151 /* Compute the Cholesky factorization A = U'*U. */ 00152 00153 jj = 0; 00154 i__1 = *n; 00155 for (j = 1; j <= i__1; ++j) { 00156 jc = jj + 1; 00157 jj += j; 00158 00159 /* Compute elements 1:J-1 of column J. */ 00160 00161 if (j > 1) { 00162 i__2 = j - 1; 00163 template_blas_tpsv("Upper", "Transpose", "Non-unit", &i__2, &ap[1], &ap[ 00164 jc], &c__1); 00165 } 00166 00167 /* Compute U(J,J) and test for non-positive-definiteness. */ 00168 00169 i__2 = j - 1; 00170 ajj = ap[jj] - template_blas_dot(&i__2, &ap[jc], &c__1, &ap[jc], &c__1); 00171 if (ajj <= 0.) { 00172 ap[jj] = ajj; 00173 goto L30; 00174 } 00175 ap[jj] = template_blas_sqrt(ajj); 00176 /* L10: */ 00177 } 00178 } else { 00179 00180 /* Compute the Cholesky factorization A = L*L'. */ 00181 00182 jj = 1; 00183 i__1 = *n; 00184 for (j = 1; j <= i__1; ++j) { 00185 00186 /* Compute L(J,J) and test for non-positive-definiteness. */ 00187 00188 ajj = ap[jj]; 00189 if (ajj <= 0.) { 00190 ap[jj] = ajj; 00191 goto L30; 00192 } 00193 ajj = template_blas_sqrt(ajj); 00194 ap[jj] = ajj; 00195 00196 /* Compute elements J+1:N of column J and update the trailing 00197 submatrix. */ 00198 00199 if (j < *n) { 00200 i__2 = *n - j; 00201 d__1 = 1. / ajj; 00202 template_blas_scal(&i__2, &d__1, &ap[jj + 1], &c__1); 00203 i__2 = *n - j; 00204 template_blas_spr("Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n 00205 - j + 1]); 00206 jj = jj + *n - j + 1; 00207 } 00208 /* L20: */ 00209 } 00210 } 00211 goto L40; 00212 00213 L30: 00214 *info = j; 00215 00216 L40: 00217 return 0; 00218 00219 /* End of DPPTRF */ 00220 00221 } /* dpptrf_ */ 00222 00223 #endif