1*> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm). 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download DPOTF2 + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotf2.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotf2.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotf2.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO ) 22* 23* .. Scalar Arguments .. 24* CHARACTER UPLO 25* INTEGER INFO, LDA, N 26* .. 27* .. Array Arguments .. 28* DOUBLE PRECISION A( LDA, * ) 29* .. 30* 31* 32*> \par Purpose: 33* ============= 34*> 35*> \verbatim 36*> 37*> DPOTF2 computes the Cholesky factorization of a real symmetric 38*> positive definite matrix A. 39*> 40*> The factorization has the form 41*> A = U**T * U , if UPLO = 'U', or 42*> A = L * L**T, if UPLO = 'L', 43*> where U is an upper triangular matrix and L is lower triangular. 44*> 45*> This is the unblocked version of the algorithm, calling Level 2 BLAS. 46*> \endverbatim 47* 48* Arguments: 49* ========== 50* 51*> \param[in] UPLO 52*> \verbatim 53*> UPLO is CHARACTER*1 54*> Specifies whether the upper or lower triangular part of the 55*> symmetric matrix A is stored. 56*> = 'U': Upper triangular 57*> = 'L': Lower triangular 58*> \endverbatim 59*> 60*> \param[in] N 61*> \verbatim 62*> N is INTEGER 63*> The order of the matrix A. N >= 0. 64*> \endverbatim 65*> 66*> \param[in,out] A 67*> \verbatim 68*> A is DOUBLE PRECISION array, dimension (LDA,N) 69*> On entry, the symmetric matrix A. If UPLO = 'U', the leading 70*> n by n upper triangular part of A contains the upper 71*> triangular part of the matrix A, and the strictly lower 72*> triangular part of A is not referenced. If UPLO = 'L', the 73*> leading n by n lower triangular part of A contains the lower 74*> triangular part of the matrix A, and the strictly upper 75*> triangular part of A is not referenced. 76*> 77*> On exit, if INFO = 0, the factor U or L from the Cholesky 78*> factorization A = U**T *U or A = L*L**T. 79*> \endverbatim 80*> 81*> \param[in] LDA 82*> \verbatim 83*> LDA is INTEGER 84*> The leading dimension of the array A. LDA >= max(1,N). 85*> \endverbatim 86*> 87*> \param[out] INFO 88*> \verbatim 89*> INFO is INTEGER 90*> = 0: successful exit 91*> < 0: if INFO = -k, the k-th argument had an illegal value 92*> > 0: if INFO = k, the leading minor of order k is not 93*> positive definite, and the factorization could not be 94*> completed. 95*> \endverbatim 96* 97* Authors: 98* ======== 99* 100*> \author Univ. of Tennessee 101*> \author Univ. of California Berkeley 102*> \author Univ. of Colorado Denver 103*> \author NAG Ltd. 104* 105*> \ingroup doublePOcomputational 106* 107* ===================================================================== 108 SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO ) 109* 110* -- LAPACK computational routine -- 111* -- LAPACK is a software package provided by Univ. of Tennessee, -- 112* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 113* 114* .. Scalar Arguments .. 115 CHARACTER UPLO 116 INTEGER INFO, LDA, N 117* .. 118* .. Array Arguments .. 119 DOUBLE PRECISION A( LDA, * ) 120* .. 121* 122* ===================================================================== 123* 124* .. Parameters .. 125 DOUBLE PRECISION ONE, ZERO 126 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 127* .. 128* .. Local Scalars .. 129 LOGICAL UPPER 130 INTEGER J 131 DOUBLE PRECISION AJJ 132* .. 133* .. External Functions .. 134 LOGICAL LSAME, DISNAN 135 DOUBLE PRECISION DDOT 136 EXTERNAL LSAME, DDOT, DISNAN 137* .. 138* .. External Subroutines .. 139 EXTERNAL DGEMV, DSCAL, XERBLA 140* .. 141* .. Intrinsic Functions .. 142 INTRINSIC MAX, SQRT 143* .. 144* .. Executable Statements .. 145* 146* Test the input parameters. 147* 148 INFO = 0 149 UPPER = LSAME( UPLO, 'U' ) 150 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 151 INFO = -1 152 ELSE IF( N.LT.0 ) THEN 153 INFO = -2 154 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 155 INFO = -4 156 END IF 157 IF( INFO.NE.0 ) THEN 158 CALL XERBLA( 'DPOTF2', -INFO ) 159 RETURN 160 END IF 161* 162* Quick return if possible 163* 164 IF( N.EQ.0 ) 165 $ RETURN 166* 167 IF( UPPER ) THEN 168* 169* Compute the Cholesky factorization A = U**T *U. 170* 171 DO 10 J = 1, N 172* 173* Compute U(J,J) and test for non-positive-definiteness. 174* 175 AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 ) 176 IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN 177 A( J, J ) = AJJ 178 GO TO 30 179 END IF 180 AJJ = SQRT( AJJ ) 181 A( J, J ) = AJJ 182* 183* Compute elements J+1:N of row J. 184* 185 IF( J.LT.N ) THEN 186 CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ), 187 $ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA ) 188 CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA ) 189 END IF 190 10 CONTINUE 191 ELSE 192* 193* Compute the Cholesky factorization A = L*L**T. 194* 195 DO 20 J = 1, N 196* 197* Compute L(J,J) and test for non-positive-definiteness. 198* 199 AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ), 200 $ LDA ) 201 IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN 202 A( J, J ) = AJJ 203 GO TO 30 204 END IF 205 AJJ = SQRT( AJJ ) 206 A( J, J ) = AJJ 207* 208* Compute elements J+1:N of column J. 209* 210 IF( J.LT.N ) THEN 211 CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ), 212 $ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 ) 213 CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 ) 214 END IF 215 20 CONTINUE 216 END IF 217 GO TO 40 218* 219 30 CONTINUE 220 INFO = J 221* 222 40 CONTINUE 223 RETURN 224* 225* End of DPOTF2 226* 227 END 228