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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CPTTRS 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CPTTRS + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cpttrs.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cpttrs.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cpttrs.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDB, N, NRHS 00026 * .. 00027 * .. Array Arguments .. 00028 * REAL D( * ) 00029 * COMPLEX B( LDB, * ), E( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> CPTTRS solves a tridiagonal system of the form 00039 *> A * X = B 00040 *> using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF. 00041 *> D is a diagonal matrix specified in the vector D, U (or L) is a unit 00042 *> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in 00043 *> the vector E, and X and B are N by NRHS matrices. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] UPLO 00050 *> \verbatim 00051 *> UPLO is CHARACTER*1 00052 *> Specifies the form of the factorization and whether the 00053 *> vector E is the superdiagonal of the upper bidiagonal factor 00054 *> U or the subdiagonal of the lower bidiagonal factor L. 00055 *> = 'U': A = U**H*D*U, E is the superdiagonal of U 00056 *> = 'L': A = L*D*L**H, E is the subdiagonal of L 00057 *> \endverbatim 00058 *> 00059 *> \param[in] N 00060 *> \verbatim 00061 *> N is INTEGER 00062 *> The order of the tridiagonal matrix A. N >= 0. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] NRHS 00066 *> \verbatim 00067 *> NRHS is INTEGER 00068 *> The number of right hand sides, i.e., the number of columns 00069 *> of the matrix B. NRHS >= 0. 00070 *> \endverbatim 00071 *> 00072 *> \param[in] D 00073 *> \verbatim 00074 *> D is REAL array, dimension (N) 00075 *> The n diagonal elements of the diagonal matrix D from the 00076 *> factorization A = U**H*D*U or A = L*D*L**H. 00077 *> \endverbatim 00078 *> 00079 *> \param[in] E 00080 *> \verbatim 00081 *> E is COMPLEX array, dimension (N-1) 00082 *> If UPLO = 'U', the (n-1) superdiagonal elements of the unit 00083 *> bidiagonal factor U from the factorization A = U**H*D*U. 00084 *> If UPLO = 'L', the (n-1) subdiagonal elements of the unit 00085 *> bidiagonal factor L from the factorization A = L*D*L**H. 00086 *> \endverbatim 00087 *> 00088 *> \param[in,out] B 00089 *> \verbatim 00090 *> B is REAL array, dimension (LDB,NRHS) 00091 *> On entry, the right hand side vectors B for the system of 00092 *> linear equations. 00093 *> On exit, the solution vectors, X. 00094 *> \endverbatim 00095 *> 00096 *> \param[in] LDB 00097 *> \verbatim 00098 *> LDB is INTEGER 00099 *> The leading dimension of the array B. LDB >= max(1,N). 00100 *> \endverbatim 00101 *> 00102 *> \param[out] INFO 00103 *> \verbatim 00104 *> INFO is INTEGER 00105 *> = 0: successful exit 00106 *> < 0: if INFO = -k, the k-th argument had an illegal value 00107 *> \endverbatim 00108 * 00109 * Authors: 00110 * ======== 00111 * 00112 *> \author Univ. of Tennessee 00113 *> \author Univ. of California Berkeley 00114 *> \author Univ. of Colorado Denver 00115 *> \author NAG Ltd. 00116 * 00117 *> \date November 2011 00118 * 00119 *> \ingroup complexOTHERcomputational 00120 * 00121 * ===================================================================== 00122 SUBROUTINE CPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO ) 00123 * 00124 * -- LAPACK computational routine (version 3.4.0) -- 00125 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00127 * November 2011 00128 * 00129 * .. Scalar Arguments .. 00130 CHARACTER UPLO 00131 INTEGER INFO, LDB, N, NRHS 00132 * .. 00133 * .. Array Arguments .. 00134 REAL D( * ) 00135 COMPLEX B( LDB, * ), E( * ) 00136 * .. 00137 * 00138 * ===================================================================== 00139 * 00140 * .. Local Scalars .. 00141 LOGICAL UPPER 00142 INTEGER IUPLO, J, JB, NB 00143 * .. 00144 * .. External Functions .. 00145 INTEGER ILAENV 00146 EXTERNAL ILAENV 00147 * .. 00148 * .. External Subroutines .. 00149 EXTERNAL CPTTS2, XERBLA 00150 * .. 00151 * .. Intrinsic Functions .. 00152 INTRINSIC MAX, MIN 00153 * .. 00154 * .. Executable Statements .. 00155 * 00156 * Test the input arguments. 00157 * 00158 INFO = 0 00159 UPPER = ( UPLO.EQ.'U' .OR. UPLO.EQ.'u' ) 00160 IF( .NOT.UPPER .AND. .NOT.( UPLO.EQ.'L' .OR. UPLO.EQ.'l' ) ) THEN 00161 INFO = -1 00162 ELSE IF( N.LT.0 ) THEN 00163 INFO = -2 00164 ELSE IF( NRHS.LT.0 ) THEN 00165 INFO = -3 00166 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00167 INFO = -7 00168 END IF 00169 IF( INFO.NE.0 ) THEN 00170 CALL XERBLA( 'CPTTRS', -INFO ) 00171 RETURN 00172 END IF 00173 * 00174 * Quick return if possible 00175 * 00176 IF( N.EQ.0 .OR. NRHS.EQ.0 ) 00177 $ RETURN 00178 * 00179 * Determine the number of right-hand sides to solve at a time. 00180 * 00181 IF( NRHS.EQ.1 ) THEN 00182 NB = 1 00183 ELSE 00184 NB = MAX( 1, ILAENV( 1, 'CPTTRS', UPLO, N, NRHS, -1, -1 ) ) 00185 END IF 00186 * 00187 * Decode UPLO 00188 * 00189 IF( UPPER ) THEN 00190 IUPLO = 1 00191 ELSE 00192 IUPLO = 0 00193 END IF 00194 * 00195 IF( NB.GE.NRHS ) THEN 00196 CALL CPTTS2( IUPLO, N, NRHS, D, E, B, LDB ) 00197 ELSE 00198 DO 10 J = 1, NRHS, NB 00199 JB = MIN( NRHS-J+1, NB ) 00200 CALL CPTTS2( IUPLO, N, JB, D, E, B( 1, J ), LDB ) 00201 10 CONTINUE 00202 END IF 00203 * 00204 RETURN 00205 * 00206 * End of CPTTRS 00207 * 00208 END