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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DPPTRS 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DPPTRS + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptrs.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptrs.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptrs.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDB, N, NRHS 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION AP( * ), B( LDB, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DPPTRS solves a system of linear equations A*X = B with a symmetric 00038 *> positive definite matrix A in packed storage using the Cholesky 00039 *> factorization A = U**T*U or A = L*L**T computed by DPPTRF. 00040 *> \endverbatim 00041 * 00042 * Arguments: 00043 * ========== 00044 * 00045 *> \param[in] UPLO 00046 *> \verbatim 00047 *> UPLO is CHARACTER*1 00048 *> = 'U': Upper triangle of A is stored; 00049 *> = 'L': Lower triangle of A is stored. 00050 *> \endverbatim 00051 *> 00052 *> \param[in] N 00053 *> \verbatim 00054 *> N is INTEGER 00055 *> The order of the matrix A. N >= 0. 00056 *> \endverbatim 00057 *> 00058 *> \param[in] NRHS 00059 *> \verbatim 00060 *> NRHS is INTEGER 00061 *> The number of right hand sides, i.e., the number of columns 00062 *> of the matrix B. NRHS >= 0. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] AP 00066 *> \verbatim 00067 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00068 *> The triangular factor U or L from the Cholesky factorization 00069 *> A = U**T*U or A = L*L**T, packed columnwise in a linear 00070 *> array. The j-th column of U or L is stored in the array AP 00071 *> as follows: 00072 *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; 00073 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. 00074 *> \endverbatim 00075 *> 00076 *> \param[in,out] B 00077 *> \verbatim 00078 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) 00079 *> On entry, the right hand side matrix B. 00080 *> On exit, the solution matrix X. 00081 *> \endverbatim 00082 *> 00083 *> \param[in] LDB 00084 *> \verbatim 00085 *> LDB is INTEGER 00086 *> The leading dimension of the array B. LDB >= max(1,N). 00087 *> \endverbatim 00088 *> 00089 *> \param[out] INFO 00090 *> \verbatim 00091 *> INFO is INTEGER 00092 *> = 0: successful exit 00093 *> < 0: if INFO = -i, the i-th argument had an illegal value 00094 *> \endverbatim 00095 * 00096 * Authors: 00097 * ======== 00098 * 00099 *> \author Univ. of Tennessee 00100 *> \author Univ. of California Berkeley 00101 *> \author Univ. of Colorado Denver 00102 *> \author NAG Ltd. 00103 * 00104 *> \date November 2011 00105 * 00106 *> \ingroup doubleOTHERcomputational 00107 * 00108 * ===================================================================== 00109 SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO ) 00110 * 00111 * -- LAPACK computational routine (version 3.4.0) -- 00112 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00114 * November 2011 00115 * 00116 * .. Scalar Arguments .. 00117 CHARACTER UPLO 00118 INTEGER INFO, LDB, N, NRHS 00119 * .. 00120 * .. Array Arguments .. 00121 DOUBLE PRECISION AP( * ), B( LDB, * ) 00122 * .. 00123 * 00124 * ===================================================================== 00125 * 00126 * .. Local Scalars .. 00127 LOGICAL UPPER 00128 INTEGER I 00129 * .. 00130 * .. External Functions .. 00131 LOGICAL LSAME 00132 EXTERNAL LSAME 00133 * .. 00134 * .. External Subroutines .. 00135 EXTERNAL DTPSV, XERBLA 00136 * .. 00137 * .. Intrinsic Functions .. 00138 INTRINSIC MAX 00139 * .. 00140 * .. Executable Statements .. 00141 * 00142 * Test the input parameters. 00143 * 00144 INFO = 0 00145 UPPER = LSAME( UPLO, 'U' ) 00146 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00147 INFO = -1 00148 ELSE IF( N.LT.0 ) THEN 00149 INFO = -2 00150 ELSE IF( NRHS.LT.0 ) THEN 00151 INFO = -3 00152 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00153 INFO = -6 00154 END IF 00155 IF( INFO.NE.0 ) THEN 00156 CALL XERBLA( 'DPPTRS', -INFO ) 00157 RETURN 00158 END IF 00159 * 00160 * Quick return if possible 00161 * 00162 IF( N.EQ.0 .OR. NRHS.EQ.0 ) 00163 $ RETURN 00164 * 00165 IF( UPPER ) THEN 00166 * 00167 * Solve A*X = B where A = U**T * U. 00168 * 00169 DO 10 I = 1, NRHS 00170 * 00171 * Solve U**T *X = B, overwriting B with X. 00172 * 00173 CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', N, AP, 00174 $ B( 1, I ), 1 ) 00175 * 00176 * Solve U*X = B, overwriting B with X. 00177 * 00178 CALL DTPSV( 'Upper', 'No transpose', 'Non-unit', N, AP, 00179 $ B( 1, I ), 1 ) 00180 10 CONTINUE 00181 ELSE 00182 * 00183 * Solve A*X = B where A = L * L**T. 00184 * 00185 DO 20 I = 1, NRHS 00186 * 00187 * Solve L*Y = B, overwriting B with X. 00188 * 00189 CALL DTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP, 00190 $ B( 1, I ), 1 ) 00191 * 00192 * Solve L**T *X = Y, overwriting B with X. 00193 * 00194 CALL DTPSV( 'Lower', 'Transpose', 'Non-unit', N, AP, 00195 $ B( 1, I ), 1 ) 00196 20 CONTINUE 00197 END IF 00198 * 00199 RETURN 00200 * 00201 * End of DPPTRS 00202 * 00203 END