LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine spotrf ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, integer INFO )

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 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
November 2011

Definition at line 102 of file spotrf.f.

102 *
103 * -- LAPACK computational routine (version 3.1) --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 * November 2011
107 *
108 * .. Scalar Arguments ..
109  CHARACTER uplo
110  INTEGER info, lda, n
111 * ..
112 * .. Array Arguments ..
113  REAL a( lda, * )
114 * ..
115 *
116 * =====================================================================
117 *
118 * .. Parameters ..
119  REAL one
120  parameter ( one = 1.0e+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 sgemm, spotf2, ssyrk, strsm, 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( 'SPOTRF', -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, 'SPOTRF', uplo, n, -1, -1, -1 )
163  IF( nb.LE.1 .OR. nb.GE.n ) THEN
164 *
165 * Use unblocked code.
166 *
167  CALL spotf2( 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  jb = min( nb, n-j+1 )
179 *
180 * Compute the current block.
181 *
182  CALL strsm( 'Left', 'Upper', 'Transpose', 'Non-unit',
183  \$ j-1, jb, one, a( 1, 1 ), lda,
184  \$ a( 1, j ), lda )
185
186  CALL ssyrk( 'Upper', 'Transpose', jb, j-1, -one,
187  \$ a( 1, j ), lda,
188  \$ one, a( j, j ), lda )
189 *
190 * Update and factorize the current diagonal block and test
191 * for non-positive-definiteness.
192 *
193  CALL spotf2( 'Upper', jb, a( j, j ), lda, info )
194  IF( info.NE.0 )
195  \$ GO TO 30
196
197  10 CONTINUE
198 *
199  ELSE
200 *
201 * Compute the Cholesky factorization A = L*L'.
202 *
203  DO 20 j = 1, n, nb
204
205  jb = min( nb, n-j+1 )
206 *
207 * Compute the current block.
208 *
209  CALL strsm( 'Right', 'Lower', 'Transpose', 'Non-unit',
210  \$ jb, j-1, one, a( 1, 1 ), lda,
211  \$ a( j, 1 ), lda )
212
213  CALL ssyrk( 'Lower', 'No Transpose', jb, j-1,
214  \$ -one, a( j, 1 ), lda,
215  \$ one, a( j, j ), lda )
216 *
217 * Update and factorize the current diagonal block and test
218 * for non-positive-definiteness.
219 *
220  CALL spotf2( 'Lower', jb, a( j, j ), lda, info )
221  IF( info.NE.0 )
222  \$ GO TO 30
223
224  20 CONTINUE
225  END IF
226  END IF
227  GO TO 40
228 *
229  30 CONTINUE
230  info = info + j - 1
231 *
232  40 CONTINUE
233  RETURN
234 *
235 * End of SPOTRF
236 *
subroutine ssyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
SSYRK
Definition: ssyrk.f:171
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:183
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:189
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine spotf2(UPLO, N, A, LDA, INFO)
SPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblock...
Definition: spotf2.f:111
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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