LAPACK  3.10.1 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.```

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 106 of file cpotrf.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  COMPLEX A( LDA, * )
118 * ..
119 *
120 * =====================================================================
121 *
122 * .. Parameters ..
123  REAL ONE
124  COMPLEX CONE
125  parameter( one = 1.0e+0, cone = ( 1.0e+0, 0.0e+0 ) )
126 * ..
127 * .. Local Scalars ..
128  LOGICAL UPPER
129  INTEGER J, JB, NB
130 * ..
131 * .. External Functions ..
132  LOGICAL LSAME
133  INTEGER ILAENV
134  EXTERNAL lsame, ilaenv
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL cgemm, cherk, cpotrf2, ctrsm, xerbla
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC max, min
141 * ..
142 * .. Executable Statements ..
143 *
144 * Test the input parameters.
145 *
146  info = 0
147  upper = lsame( uplo, 'U' )
148  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
149  info = -1
150  ELSE IF( n.LT.0 ) THEN
151  info = -2
152  ELSE IF( lda.LT.max( 1, n ) ) THEN
153  info = -4
154  END IF
155  IF( info.NE.0 ) THEN
156  CALL xerbla( 'CPOTRF', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( n.EQ.0 )
163  \$ RETURN
164 *
165 * Determine the block size for this environment.
166 *
167  nb = ilaenv( 1, 'CPOTRF', uplo, n, -1, -1, -1 )
168  IF( nb.LE.1 .OR. nb.GE.n ) THEN
169 *
170 * Use unblocked code.
171 *
172  CALL cpotrf2( uplo, n, a, lda, info )
173  ELSE
174 *
175 * Use blocked code.
176 *
177  IF( upper ) THEN
178 *
179 * Compute the Cholesky factorization A = U**H *U.
180 *
181  DO 10 j = 1, n, nb
182 *
183 * Update and factorize the current diagonal block and test
184 * for non-positive-definiteness.
185 *
186  jb = min( nb, n-j+1 )
187  CALL cherk( 'Upper', 'Conjugate transpose', jb, j-1,
188  \$ -one, a( 1, j ), lda, one, a( j, j ), lda )
189  CALL cpotrf2( 'Upper', jb, a( j, j ), lda, info )
190  IF( info.NE.0 )
191  \$ GO TO 30
192  IF( j+jb.LE.n ) THEN
193 *
194 * Compute the current block row.
195 *
196  CALL cgemm( 'Conjugate transpose', 'No transpose', jb,
197  \$ n-j-jb+1, j-1, -cone, a( 1, j ), lda,
198  \$ a( 1, j+jb ), lda, cone, a( j, j+jb ),
199  \$ lda )
200  CALL ctrsm( 'Left', 'Upper', 'Conjugate transpose',
201  \$ 'Non-unit', jb, n-j-jb+1, cone, a( j, j ),
202  \$ lda, a( j, j+jb ), lda )
203  END IF
204  10 CONTINUE
205 *
206  ELSE
207 *
208 * Compute the Cholesky factorization A = L*L**H.
209 *
210  DO 20 j = 1, n, nb
211 *
212 * Update and factorize the current diagonal block and test
213 * for non-positive-definiteness.
214 *
215  jb = min( nb, n-j+1 )
216  CALL cherk( 'Lower', 'No transpose', jb, j-1, -one,
217  \$ a( j, 1 ), lda, one, a( j, j ), lda )
218  CALL cpotrf2( 'Lower', jb, a( j, j ), lda, info )
219  IF( info.NE.0 )
220  \$ GO TO 30
221  IF( j+jb.LE.n ) THEN
222 *
223 * Compute the current block column.
224 *
225  CALL cgemm( 'No transpose', 'Conjugate transpose',
226  \$ n-j-jb+1, jb, j-1, -cone, a( j+jb, 1 ),
227  \$ lda, a( j, 1 ), lda, cone, a( j+jb, j ),
228  \$ lda )
229  CALL ctrsm( 'Right', 'Lower', 'Conjugate transpose',
230  \$ 'Non-unit', n-j-jb+1, jb, cone, a( j, j ),
231  \$ lda, a( j+jb, j ), lda )
232  END IF
233  20 CONTINUE
234  END IF
235  END IF
236  GO TO 40
237 *
238  30 CONTINUE
239  info = info + j - 1
240 *
241  40 CONTINUE
242  RETURN
243 *
244 * End of CPOTRF
245 *
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 cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
recursive subroutine cpotrf2(UPLO, N, A, LDA, INFO)
CPOTRF2
Definition: cpotrf2.f:106
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