LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zpotrf()

 subroutine zpotrf ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer INFO )

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

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

Purpose:

``` ZPOTRF 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*16 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:

``` ZPOTRF 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*16 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 101 of file zpotrf.f.

102 *
103 * -- LAPACK computational routine --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 *
107 * .. Scalar Arguments ..
108  CHARACTER UPLO
109  INTEGER INFO, LDA, N
110 * ..
111 * .. Array Arguments ..
112  COMPLEX*16 A( LDA, * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Parameters ..
118  DOUBLE PRECISION ONE
119  COMPLEX*16 CONE
120  parameter( one = 1.0d+0, cone = ( 1.0d+0, 0.0d+0 ) )
121 * ..
122 * .. Local Scalars ..
123  LOGICAL UPPER
124  INTEGER J, JB, NB
125 * ..
126 * .. External Functions ..
127  LOGICAL LSAME
128  INTEGER ILAENV
129  EXTERNAL lsame, ilaenv
130 * ..
131 * .. External Subroutines ..
132  EXTERNAL zgemm, zpotf2, zherk, ztrsm, xerbla
133 * ..
134 * .. Intrinsic Functions ..
135  INTRINSIC max, min
136 * ..
137 * .. Executable Statements ..
138 *
139 * Test the input parameters.
140 *
141  info = 0
142  upper = lsame( uplo, 'U' )
143  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
144  info = -1
145  ELSE IF( n.LT.0 ) THEN
146  info = -2
147  ELSE IF( lda.LT.max( 1, n ) ) THEN
148  info = -4
149  END IF
150  IF( info.NE.0 ) THEN
151  CALL xerbla( 'ZPOTRF', -info )
152  RETURN
153  END IF
154 *
155 * Quick return if possible
156 *
157  IF( n.EQ.0 )
158  \$ RETURN
159 *
160 * Determine the block size for this environment.
161 *
162  nb = ilaenv( 1, 'ZPOTRF', uplo, n, -1, -1, -1 )
163  IF( nb.LE.1 .OR. nb.GE.n ) THEN
164 *
165 * Use unblocked code.
166 *
167  CALL zpotf2( uplo, n, a, lda, info )
168  ELSE
169 *
170 * Use blocked code.
171 *
172  IF( upper ) THEN
173 *
174 * Compute the Cholesky factorization A = U'*U.
175 *
176  DO 10 j = 1, n, nb
177 *
178 * Update and factorize the current diagonal block and test
179 * for non-positive-definiteness.
180 *
181  jb = min( nb, n-j+1 )
182
183  CALL zpotf2( 'Upper', jb, a( j, j ), lda, info )
184
185  IF( info.NE.0 )
186  \$ GO TO 30
187
188  IF( j+jb.LE.n ) THEN
189 *
190 * Updating the trailing submatrix.
191 *
192  CALL ztrsm( 'Left', 'Upper', 'Conjugate Transpose',
193  \$ 'Non-unit', jb, n-j-jb+1, cone, a( j, j ),
194  \$ lda, a( j, j+jb ), lda )
195  CALL zherk( 'Upper', 'Conjugate transpose', n-j-jb+1,
196  \$ jb, -one, a( j, j+jb ), lda,
197  \$ one, a( j+jb, j+jb ), lda )
198  END IF
199  10 CONTINUE
200 *
201  ELSE
202 *
203 * Compute the Cholesky factorization A = L*L'.
204 *
205  DO 20 j = 1, n, nb
206 *
207 * Update and factorize the current diagonal block and test
208 * for non-positive-definiteness.
209 *
210  jb = min( nb, n-j+1 )
211
212  CALL zpotf2( 'Lower', jb, a( j, j ), lda, info )
213
214  IF( info.NE.0 )
215  \$ GO TO 30
216
217  IF( j+jb.LE.n ) THEN
218 *
219 * Updating the trailing submatrix.
220 *
221  CALL ztrsm( 'Right', 'Lower', 'Conjugate Transpose',
222  \$ 'Non-unit', n-j-jb+1, jb, cone, a( j, j ),
223  \$ lda, a( j+jb, j ), lda )
224
225  CALL zherk( 'Lower', 'No Transpose', n-j-jb+1, jb,
226  \$ -one, a( j+jb, j ), lda,
227  \$ one, a( j+jb, j+jb ), lda )
228  END IF
229  20 CONTINUE
230  END IF
231  END IF
232  GO TO 40
233 *
234  30 CONTINUE
235  info = info + j - 1
236 *
237  40 CONTINUE
238  RETURN
239 *
240 * End of ZPOTRF
241 *
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 zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
ZHERK
Definition: zherk.f:173
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine zpotf2(UPLO, N, A, LDA, INFO)
ZPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: zpotf2.f:109
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