 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ cpotrf()

 subroutine cpotrf ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer INFO )

CPOTRF

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

Purpose:
``` CPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix A.

The factorization has the form
A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  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 COMPLEX array, dimension (LDA,N) On entry, the Hermitian 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**H*U or A = L*L**H.``` [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

Purpose:

``` CPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.

The factorization has the form
A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  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 COMPLEX 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**H*U or A = L*L**H.``` [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 109 of file cpotrf.f.

109 *
110 * -- LAPACK computational routine (version 3.7.0) --
111 * -- LAPACK is a software package provided by Univ. of Tennessee, --
112 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113 * December 2016
114 *
115 * .. Scalar Arguments ..
116  CHARACTER uplo
117  INTEGER info, lda, n
118 * ..
119 * .. Array Arguments ..
120  COMPLEX a( lda, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  REAL one
127  COMPLEX cone
128  parameter( one = 1.0e+0, cone = ( 1.0e+0, 0.0e+0 ) )
129 * ..
130 * .. Local Scalars ..
131  LOGICAL upper
132  INTEGER j, jb, nb
133 * ..
134 * .. External Functions ..
135  LOGICAL lsame
136  INTEGER ilaenv
137  EXTERNAL lsame, ilaenv
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL cgemm, cherk, cpotrf2, ctrsm, xerbla
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC max, min
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input parameters.
148 *
149  info = 0
150  upper = lsame( uplo, 'U' )
151  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
152  info = -1
153  ELSE IF( n.LT.0 ) THEN
154  info = -2
155  ELSE IF( lda.LT.max( 1, n ) ) THEN
156  info = -4
157  END IF
158  IF( info.NE.0 ) THEN
159  CALL xerbla( 'CPOTRF', -info )
160  RETURN
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( n.EQ.0 )
166  \$ RETURN
167 *
168 * Determine the block size for this environment.
169 *
170  nb = ilaenv( 1, 'CPOTRF', uplo, n, -1, -1, -1 )
171  IF( nb.LE.1 .OR. nb.GE.n ) THEN
172 *
173 * Use unblocked code.
174 *
175  CALL cpotrf2( uplo, n, a, lda, info )
176  ELSE
177 *
178 * Use blocked code.
179 *
180  IF( upper ) THEN
181 *
182 * Compute the Cholesky factorization A = U**H *U.
183 *
184  DO 10 j = 1, n, nb
185 *
186 * Update and factorize the current diagonal block and test
187 * for non-positive-definiteness.
188 *
189  jb = min( nb, n-j+1 )
190  CALL cherk( 'Upper', 'Conjugate transpose', jb, j-1,
191  \$ -one, a( 1, j ), lda, one, a( j, j ), lda )
192  CALL cpotrf2( 'Upper', jb, a( j, j ), lda, info )
193  IF( info.NE.0 )
194  \$ GO TO 30
195  IF( j+jb.LE.n ) THEN
196 *
197 * Compute the current block row.
198 *
199  CALL cgemm( 'Conjugate transpose', 'No transpose', jb,
200  \$ n-j-jb+1, j-1, -cone, a( 1, j ), lda,
201  \$ a( 1, j+jb ), lda, cone, a( j, j+jb ),
202  \$ lda )
203  CALL ctrsm( 'Left', 'Upper', 'Conjugate transpose',
204  \$ 'Non-unit', jb, n-j-jb+1, cone, a( j, j ),
205  \$ lda, a( j, j+jb ), lda )
206  END IF
207  10 CONTINUE
208 *
209  ELSE
210 *
211 * Compute the Cholesky factorization A = L*L**H.
212 *
213  DO 20 j = 1, n, nb
214 *
215 * Update and factorize the current diagonal block and test
216 * for non-positive-definiteness.
217 *
218  jb = min( nb, n-j+1 )
219  CALL cherk( 'Lower', 'No transpose', jb, j-1, -one,
220  \$ a( j, 1 ), lda, one, a( j, j ), lda )
221  CALL cpotrf2( 'Lower', jb, a( j, j ), lda, info )
222  IF( info.NE.0 )
223  \$ GO TO 30
224  IF( j+jb.LE.n ) THEN
225 *
226 * Compute the current block column.
227 *
228  CALL cgemm( 'No transpose', 'Conjugate transpose',
229  \$ n-j-jb+1, jb, j-1, -cone, a( j+jb, 1 ),
230  \$ lda, a( j, 1 ), lda, cone, a( j+jb, j ),
231  \$ lda )
232  CALL ctrsm( 'Right', 'Lower', 'Conjugate transpose',
233  \$ 'Non-unit', n-j-jb+1, jb, cone, a( j, j ),
234  \$ lda, a( j+jb, j ), lda )
235  END IF
236  20 CONTINUE
237  END IF
238  END IF
239  GO TO 40
240 *
241  30 CONTINUE
242  info = info + j - 1
243 *
244  40 CONTINUE
245  RETURN
246 *
247 * End of CPOTRF
248 *
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:175
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:182
recursive subroutine cpotrf2(UPLO, N, A, LDA, INFO)
CPOTRF2
Definition: cpotrf2.f:108
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
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