 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dpotrf()

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

DPOTRF

DPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

Purpose:
``` DPOTRF 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 block version of the algorithm, calling Level 3 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [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 = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.```

Purpose:

``` DPOTRF 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 top-looking block version of the algorithm, calling Level 3 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [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 = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.```
Date
December 2016

Definition at line 106 of file dpotrf.f.

107 *
108 * -- LAPACK computational routine --
109 * -- LAPACK is a software package provided by Univ. of Tennessee, --
110 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111 *
112 * .. Scalar Arguments ..
113  CHARACTER UPLO
114  INTEGER INFO, LDA, N
115 * ..
116 * .. Array Arguments ..
117  DOUBLE PRECISION A( LDA, * )
118 * ..
119 *
120 * =====================================================================
121 *
122 * .. Parameters ..
123  DOUBLE PRECISION ONE
124  parameter( one = 1.0d+0 )
125 * ..
126 * .. Local Scalars ..
127  LOGICAL UPPER
128  INTEGER J, JB, NB
129 * ..
130 * .. External Functions ..
131  LOGICAL LSAME
132  INTEGER ILAENV
133  EXTERNAL lsame, ilaenv
134 * ..
135 * .. External Subroutines ..
136  EXTERNAL dgemm, dpotrf2, dsyrk, dtrsm, xerbla
137 * ..
138 * .. Intrinsic Functions ..
139  INTRINSIC max, min
140 * ..
141 * .. Executable Statements ..
142 *
143 * Test the input parameters.
144 *
145  info = 0
146  upper = lsame( uplo, 'U' )
147  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
148  info = -1
149  ELSE IF( n.LT.0 ) THEN
150  info = -2
151  ELSE IF( lda.LT.max( 1, n ) ) THEN
152  info = -4
153  END IF
154  IF( info.NE.0 ) THEN
155  CALL xerbla( 'DPOTRF', -info )
156  RETURN
157  END IF
158 *
159 * Quick return if possible
160 *
161  IF( n.EQ.0 )
162  \$ RETURN
163 *
164 * Determine the block size for this environment.
165 *
166  nb = ilaenv( 1, 'DPOTRF', uplo, n, -1, -1, -1 )
167  IF( nb.LE.1 .OR. nb.GE.n ) THEN
168 *
169 * Use unblocked code.
170 *
171  CALL dpotrf2( uplo, n, a, lda, info )
172  ELSE
173 *
174 * Use blocked code.
175 *
176  IF( upper ) THEN
177 *
178 * Compute the Cholesky factorization A = U**T*U.
179 *
180  DO 10 j = 1, n, nb
181 *
182 * Update and factorize the current diagonal block and test
183 * for non-positive-definiteness.
184 *
185  jb = min( nb, n-j+1 )
186  CALL dsyrk( 'Upper', 'Transpose', jb, j-1, -one,
187  \$ a( 1, j ), lda, one, a( j, j ), lda )
188  CALL dpotrf2( 'Upper', jb, a( j, j ), lda, info )
189  IF( info.NE.0 )
190  \$ GO TO 30
191  IF( j+jb.LE.n ) THEN
192 *
193 * Compute the current block row.
194 *
195  CALL dgemm( 'Transpose', 'No transpose', jb, n-j-jb+1,
196  \$ j-1, -one, a( 1, j ), lda, a( 1, j+jb ),
197  \$ lda, one, a( j, j+jb ), lda )
198  CALL dtrsm( 'Left', 'Upper', 'Transpose', 'Non-unit',
199  \$ jb, n-j-jb+1, one, a( j, j ), lda,
200  \$ a( j, j+jb ), lda )
201  END IF
202  10 CONTINUE
203 *
204  ELSE
205 *
206 * Compute the Cholesky factorization A = L*L**T.
207 *
208  DO 20 j = 1, n, nb
209 *
210 * Update and factorize the current diagonal block and test
211 * for non-positive-definiteness.
212 *
213  jb = min( nb, n-j+1 )
214  CALL dsyrk( 'Lower', 'No transpose', jb, j-1, -one,
215  \$ a( j, 1 ), lda, one, a( j, j ), lda )
216  CALL dpotrf2( 'Lower', jb, a( j, j ), lda, info )
217  IF( info.NE.0 )
218  \$ GO TO 30
219  IF( j+jb.LE.n ) THEN
220 *
221 * Compute the current block column.
222 *
223  CALL dgemm( 'No transpose', 'Transpose', n-j-jb+1, jb,
224  \$ j-1, -one, a( j+jb, 1 ), lda, a( j, 1 ),
225  \$ lda, one, a( j+jb, j ), lda )
226  CALL dtrsm( 'Right', 'Lower', 'Transpose', 'Non-unit',
227  \$ n-j-jb+1, jb, one, a( j, j ), lda,
228  \$ a( j+jb, j ), lda )
229  END IF
230  20 CONTINUE
231  END IF
232  END IF
233  GO TO 40
234 *
235  30 CONTINUE
236  info = info + j - 1
237 *
238  40 CONTINUE
239  RETURN
240 *
241 * End of DPOTRF
242 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
DSYRK
Definition: dsyrk.f:169
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
recursive subroutine dpotrf2(UPLO, N, A, LDA, INFO)
DPOTRF2
Definition: dpotrf2.f:106
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