 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dpotf2()

 subroutine dpotf2 ( character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, integer INFO )

DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).

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Purpose:
``` DPOTF2 computes the Cholesky factorization of a real symmetric
positive definite matrix A.

The factorization has the form
A = U**T * U ,  if UPLO = 'U', or
A = L  * L**T,  if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.

This is the unblocked version of the algorithm, calling Level 2 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T *U or A = L*L**T.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value > 0: if INFO = k, the leading minor of order k is not positive definite, and the factorization could not be completed.```

Definition at line 108 of file dpotf2.f.

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 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function ddot(N, DX, INCX, DY, INCY)
DDOT
Definition: ddot.f:82
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:156
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