LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ 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
Here is the call graph for this function:
Here is the caller graph for this function: