LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine cpotrf ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer INFO )

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

Purpose:

``` CPOTRF computes the Cholesky factorization of a real 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 right 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 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
November 2011

Definition at line 102 of file cpotrf.f.

102 *
103 * -- LAPACK computational routine (version 3.1) --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 * November 2011
107 *
108 * .. Scalar Arguments ..
109  CHARACTER uplo
110  INTEGER info, lda, n
111 * ..
112 * .. Array Arguments ..
113  COMPLEX a( lda, * )
114 * ..
115 *
116 * =====================================================================
117 *
118 * .. Parameters ..
119  REAL one
120  COMPLEX cone
121  parameter ( one = 1.0e+0, cone = ( 1.0e+0, 0.0e+0 ) )
122 * ..
123 * .. Local Scalars ..
124  LOGICAL upper
125  INTEGER j, jb, nb
126 * ..
127 * .. External Functions ..
128  LOGICAL lsame
129  INTEGER ilaenv
130  EXTERNAL lsame, ilaenv
131 * ..
132 * .. External Subroutines ..
133  EXTERNAL cgemm, cpotf2, cherk, ctrsm, xerbla
134 * ..
135 * .. Intrinsic Functions ..
136  INTRINSIC max, min
137 * ..
138 * .. Executable Statements ..
139 *
140 * Test the input parameters.
141 *
142  info = 0
143  upper = lsame( uplo, 'U' )
144  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
145  info = -1
146  ELSE IF( n.LT.0 ) THEN
147  info = -2
148  ELSE IF( lda.LT.max( 1, n ) ) THEN
149  info = -4
150  END IF
151  IF( info.NE.0 ) THEN
152  CALL xerbla( 'CPOTRF', -info )
153  RETURN
154  END IF
155 *
156 * Quick return if possible
157 *
158  IF( n.EQ.0 )
159  \$ RETURN
160 *
161 * Determine the block size for this environment.
162 *
163  nb = ilaenv( 1, 'CPOTRF', uplo, n, -1, -1, -1 )
164  IF( nb.LE.1 .OR. nb.GE.n ) THEN
165 *
166 * Use unblocked code.
167 *
168  CALL cpotf2( uplo, n, a, lda, info )
169  ELSE
170 *
171 * Use blocked code.
172 *
173  IF( upper ) THEN
174 *
175 * Compute the Cholesky factorization A = U'*U.
176 *
177  DO 10 j = 1, n, nb
178 *
179 * Update and factorize the current diagonal block and test
180 * for non-positive-definiteness.
181 *
182  jb = min( nb, n-j+1 )
183
184  CALL cpotf2( 'Upper', jb, a( j, j ), lda, info )
185
186  IF( info.NE.0 )
187  \$ GO TO 30
188
189  IF( j+jb.LE.n ) THEN
190 *
191 * Updating the trailing submatrix.
192 *
193  CALL ctrsm( 'Left', 'Upper', 'Conjugate Transpose',
194  \$ 'Non-unit', jb, n-j-jb+1, cone, a( j, j ),
195  \$ lda, a( j, j+jb ), lda )
196  CALL cherk( 'Upper', 'Conjugate transpose', n-j-jb+1,
197  \$ jb, -one, a( j, j+jb ), lda,
198  \$ one, a( j+jb, j+jb ), lda )
199  END IF
200  10 CONTINUE
201 *
202  ELSE
203 *
204 * Compute the Cholesky factorization A = L*L'.
205 *
206  DO 20 j = 1, n, nb
207 *
208 * Update and factorize the current diagonal block and test
209 * for non-positive-definiteness.
210 *
211  jb = min( nb, n-j+1 )
212
213  CALL cpotf2( 'Lower', jb, a( j, j ), lda, info )
214
215  IF( info.NE.0 )
216  \$ GO TO 30
217
218  IF( j+jb.LE.n ) THEN
219 *
220 * Updating the trailing submatrix.
221 *
222  CALL ctrsm( 'Right', 'Lower', 'Conjugate Transpose',
223  \$ 'Non-unit', n-j-jb+1, jb, cone, a( j, j ),
224  \$ lda, a( j+jb, j ), lda )
225
226  CALL cherk( 'Lower', 'No Transpose', n-j-jb+1, jb,
227  \$ -one, a( j+jb, j ), lda,
228  \$ one, a( j+jb, j+jb ), 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 CPOTRF
242 *
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:175
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:182
subroutine cpotf2(UPLO, N, A, LDA, INFO)
CPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: cpotf2.f:111
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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