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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SPOTRF 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SPOTRF + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/spotrf.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spotrf.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spotrf.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, LDA, N 00026 * .. 00027 * .. Array Arguments .. 00028 * REAL A( LDA, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> SPOTRF computes the Cholesky factorization of a real symmetric 00038 *> positive definite matrix A. 00039 *> 00040 *> The factorization has the form 00041 *> A = U**T * U, if UPLO = 'U', or 00042 *> A = L * L**T, if UPLO = 'L', 00043 *> where U is an upper triangular matrix and L is lower triangular. 00044 *> 00045 *> This is the block version of the algorithm, calling Level 3 BLAS. 00046 *> \endverbatim 00047 * 00048 * Arguments: 00049 * ========== 00050 * 00051 *> \param[in] UPLO 00052 *> \verbatim 00053 *> UPLO is CHARACTER*1 00054 *> = 'U': Upper triangle of A is stored; 00055 *> = 'L': Lower triangle of A is stored. 00056 *> \endverbatim 00057 *> 00058 *> \param[in] N 00059 *> \verbatim 00060 *> N is INTEGER 00061 *> The order of the matrix A. N >= 0. 00062 *> \endverbatim 00063 *> 00064 *> \param[in,out] A 00065 *> \verbatim 00066 *> A is REAL array, dimension (LDA,N) 00067 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading 00068 *> N-by-N upper triangular part of A contains the upper 00069 *> triangular part of the matrix A, and the strictly lower 00070 *> triangular part of A is not referenced. If UPLO = 'L', the 00071 *> leading N-by-N lower triangular part of A contains the lower 00072 *> triangular part of the matrix A, and the strictly upper 00073 *> triangular part of A is not referenced. 00074 *> 00075 *> On exit, if INFO = 0, the factor U or L from the Cholesky 00076 *> factorization A = U**T*U or A = L*L**T. 00077 *> \endverbatim 00078 *> 00079 *> \param[in] LDA 00080 *> \verbatim 00081 *> LDA is INTEGER 00082 *> The leading dimension of the array A. LDA >= max(1,N). 00083 *> \endverbatim 00084 *> 00085 *> \param[out] INFO 00086 *> \verbatim 00087 *> INFO is INTEGER 00088 *> = 0: successful exit 00089 *> < 0: if INFO = -i, the i-th argument had an illegal value 00090 *> > 0: if INFO = i, the leading minor of order i is not 00091 *> positive definite, and the factorization could not be 00092 *> completed. 00093 *> \endverbatim 00094 * 00095 * Authors: 00096 * ======== 00097 * 00098 *> \author Univ. of Tennessee 00099 *> \author Univ. of California Berkeley 00100 *> \author Univ. of Colorado Denver 00101 *> \author NAG Ltd. 00102 * 00103 *> \date November 2011 00104 * 00105 *> \ingroup realPOcomputational 00106 * 00107 * ===================================================================== 00108 SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO ) 00109 * 00110 * -- LAPACK computational routine (version 3.4.0) -- 00111 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00113 * November 2011 00114 * 00115 * .. Scalar Arguments .. 00116 CHARACTER UPLO 00117 INTEGER INFO, LDA, N 00118 * .. 00119 * .. Array Arguments .. 00120 REAL A( LDA, * ) 00121 * .. 00122 * 00123 * ===================================================================== 00124 * 00125 * .. Parameters .. 00126 REAL ONE 00127 PARAMETER ( ONE = 1.0E+0 ) 00128 * .. 00129 * .. Local Scalars .. 00130 LOGICAL UPPER 00131 INTEGER J, JB, NB 00132 * .. 00133 * .. External Functions .. 00134 LOGICAL LSAME 00135 INTEGER ILAENV 00136 EXTERNAL LSAME, ILAENV 00137 * .. 00138 * .. External Subroutines .. 00139 EXTERNAL SGEMM, SPOTF2, SSYRK, STRSM, XERBLA 00140 * .. 00141 * .. Intrinsic Functions .. 00142 INTRINSIC MAX, MIN 00143 * .. 00144 * .. Executable Statements .. 00145 * 00146 * Test the input parameters. 00147 * 00148 INFO = 0 00149 UPPER = LSAME( UPLO, 'U' ) 00150 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00151 INFO = -1 00152 ELSE IF( N.LT.0 ) THEN 00153 INFO = -2 00154 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00155 INFO = -4 00156 END IF 00157 IF( INFO.NE.0 ) THEN 00158 CALL XERBLA( 'SPOTRF', -INFO ) 00159 RETURN 00160 END IF 00161 * 00162 * Quick return if possible 00163 * 00164 IF( N.EQ.0 ) 00165 $ RETURN 00166 * 00167 * Determine the block size for this environment. 00168 * 00169 NB = ILAENV( 1, 'SPOTRF', UPLO, N, -1, -1, -1 ) 00170 IF( NB.LE.1 .OR. NB.GE.N ) THEN 00171 * 00172 * Use unblocked code. 00173 * 00174 CALL SPOTF2( UPLO, N, A, LDA, INFO ) 00175 ELSE 00176 * 00177 * Use blocked code. 00178 * 00179 IF( UPPER ) THEN 00180 * 00181 * Compute the Cholesky factorization A = U**T*U. 00182 * 00183 DO 10 J = 1, N, NB 00184 * 00185 * Update and factorize the current diagonal block and test 00186 * for non-positive-definiteness. 00187 * 00188 JB = MIN( NB, N-J+1 ) 00189 CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, 00190 $ A( 1, J ), LDA, ONE, A( J, J ), LDA ) 00191 CALL SPOTF2( 'Upper', JB, A( J, J ), LDA, INFO ) 00192 IF( INFO.NE.0 ) 00193 $ GO TO 30 00194 IF( J+JB.LE.N ) THEN 00195 * 00196 * Compute the current block row. 00197 * 00198 CALL SGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1, 00199 $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ), 00200 $ LDA, ONE, A( J, J+JB ), LDA ) 00201 CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', 00202 $ JB, N-J-JB+1, ONE, A( J, J ), LDA, 00203 $ A( J, J+JB ), LDA ) 00204 END IF 00205 10 CONTINUE 00206 * 00207 ELSE 00208 * 00209 * Compute the Cholesky factorization A = L*L**T. 00210 * 00211 DO 20 J = 1, N, NB 00212 * 00213 * Update and factorize the current diagonal block and test 00214 * for non-positive-definiteness. 00215 * 00216 JB = MIN( NB, N-J+1 ) 00217 CALL SSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, 00218 $ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) 00219 CALL SPOTF2( 'Lower', JB, A( J, J ), LDA, INFO ) 00220 IF( INFO.NE.0 ) 00221 $ GO TO 30 00222 IF( J+JB.LE.N ) THEN 00223 * 00224 * Compute the current block column. 00225 * 00226 CALL SGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, 00227 $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), 00228 $ LDA, ONE, A( J+JB, J ), LDA ) 00229 CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', 00230 $ N-J-JB+1, JB, ONE, A( J, J ), LDA, 00231 $ A( J+JB, J ), LDA ) 00232 END IF 00233 20 CONTINUE 00234 END IF 00235 END IF 00236 GO TO 40 00237 * 00238 30 CONTINUE 00239 INFO = INFO + J - 1 00240 * 00241 40 CONTINUE 00242 RETURN 00243 * 00244 * End of SPOTRF 00245 * 00246 END