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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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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