LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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◆ spotrf()

 subroutine spotrf ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, integer INFO )

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

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

Purpose:

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

The factorization has the form
A = U**T * U,  if UPLO = 'U', or
A = L  * L**T,  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 REAL 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**T*U or A = L*L**T.``` [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:

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

The factorization has the form
A = U**T * U,  if UPLO = 'U', or
A = L  * L**T,  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 REAL 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**T*U or A = L*L**T.``` [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 spotrf.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 REAL A( LDA, * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 REAL ONE
119 parameter( one = 1.0e+0 )
120* ..
121* .. Local Scalars ..
122 LOGICAL UPPER
123 INTEGER J, JB, NB
124* ..
125* .. External Functions ..
126 LOGICAL LSAME
127 INTEGER ILAENV
128 EXTERNAL lsame, ilaenv
129* ..
130* .. External Subroutines ..
131 EXTERNAL sgemm, spotf2, ssyrk, strsm, xerbla
132* ..
133* .. Intrinsic Functions ..
134 INTRINSIC max, min
135* ..
136* .. Executable Statements ..
137*
138* Test the input parameters.
139*
140 info = 0
141 upper = lsame( uplo, 'U' )
142 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
143 info = -1
144 ELSE IF( n.LT.0 ) THEN
145 info = -2
146 ELSE IF( lda.LT.max( 1, n ) ) THEN
147 info = -4
148 END IF
149 IF( info.NE.0 ) THEN
150 CALL xerbla( 'SPOTRF', -info )
151 RETURN
152 END IF
153*
154* Quick return if possible
155*
156 IF( n.EQ.0 )
157 \$ RETURN
158*
159* Determine the block size for this environment.
160*
161 nb = ilaenv( 1, 'SPOTRF', uplo, n, -1, -1, -1 )
162 IF( nb.LE.1 .OR. nb.GE.n ) THEN
163*
164* Use unblocked code.
165*
166 CALL spotf2( uplo, n, a, lda, info )
167 ELSE
168*
169* Use blocked code.
170*
171 IF( upper ) THEN
172*
173* Compute the Cholesky factorization A = U'*U.
174*
175 DO 10 j = 1, n, nb
176*
177* Update and factorize the current diagonal block and test
178* for non-positive-definiteness.
179*
180 jb = min( nb, n-j+1 )
181
182 CALL spotf2( 'Upper', jb, a( j, j ), lda, info )
183
184 IF( info.NE.0 )
185 \$ GO TO 30
186
187 IF( j+jb.LE.n ) THEN
188*
189* Updating the trailing submatrix.
190*
191 CALL strsm( 'Left', 'Upper', 'Transpose', 'Non-unit',
192 \$ jb, n-j-jb+1, one, a( j, j ), lda,
193 \$ a( j, j+jb ), lda )
194 CALL ssyrk( 'Upper', 'Transpose', n-j-jb+1, jb, -one,
195 \$ a( j, j+jb ), lda,
196 \$ one, a( j+jb, j+jb ), lda )
197 END IF
198 10 CONTINUE
199*
200 ELSE
201*
202* Compute the Cholesky factorization A = L*L'.
203*
204 DO 20 j = 1, n, nb
205*
206* Update and factorize the current diagonal block and test
207* for non-positive-definiteness.
208*
209 jb = min( nb, n-j+1 )
210
211 CALL spotf2( 'Lower', jb, a( j, j ), lda, info )
212
213 IF( info.NE.0 )
214 \$ GO TO 30
215
216 IF( j+jb.LE.n ) THEN
217*
218* Updating the trailing submatrix.
219*
220 CALL strsm( 'Right', 'Lower', 'Transpose', 'Non-unit',
221 \$ n-j-jb+1, jb, one, a( j, j ), lda,
222 \$ a( j+jb, j ), lda )
223
224 CALL ssyrk( 'Lower', 'No Transpose', n-j-jb+1, jb,
225 \$ -one, a( j+jb, j ), lda,
226 \$ one, a( j+jb, j+jb ), lda )
227 END IF
228 20 CONTINUE
229 END IF
230 END IF
231 GO TO 40
232*
233 30 CONTINUE
234 info = info + j - 1
235*
236 40 CONTINUE
237 RETURN
238*
239* End of SPOTRF
240*
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 spotf2(UPLO, N, A, LDA, INFO)
SPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: spotf2.f:109
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:169
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
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