LAPACK  3.6.0
LAPACK: Linear Algebra PACKage
Collaboration diagram for real:

Functions

subroutine ssysv (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
  SSYSV computes the solution to system of linear equations A * X = B for SY matrices More...
 
subroutine ssysv_rook (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
  SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices More...
 
subroutine ssysvx (FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, LWORK, IWORK, INFO)
  SSYSVX computes the solution to system of linear equations A * X = B for SY matrices More...
 

Detailed Description

This is the group of real solve driver functions for SY matrices

Function Documentation

subroutine ssysv ( character  UPLO,
integer  N,
integer  NRHS,
real, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

SSYSV computes the solution to system of linear equations A * X = B for SY matrices

Download SSYSV + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SSYSV computes the solution to a real system of linear equations
    A * X = B,
 where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
 matrices.

 The diagonal pivoting method is used to factor A as
    A = U * D * U**T,  if UPLO = 'U', or
    A = L * D * L**T,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and D is symmetric and block diagonal with
 1-by-1 and 2-by-2 diagonal blocks.  The factored form of A is then
 used to solve the system of equations A * X = B.
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 number of linear equations, i.e., the order of the
          matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 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 block diagonal matrix D and the
          multipliers used to obtain the factor U or L from the
          factorization A = U*D*U**T or A = L*D*L**T as computed by
          SSYTRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D, as
          determined by SSYTRF.  If IPIV(k) > 0, then rows and columns
          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
          then rows and columns k-1 and -IPIV(k) were interchanged and
          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
          diagonal block.
[in,out]B
          B is REAL array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS right hand side matrix B.
          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK >= 1, and for best performance
          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
          SSYTRF.
          for LWORK < N, TRS will be done with Level BLAS 2
          for LWORK >= N, TRS will be done with Level BLAS 3

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
               has been completed, but the block diagonal matrix D is
               exactly singular, so the solution could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2011

Definition at line 173 of file ssysv.f.

173 *
174 * -- LAPACK driver routine (version 3.4.0) --
175 * -- LAPACK is a software package provided by Univ. of Tennessee, --
176 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177 * November 2011
178 *
179 * .. Scalar Arguments ..
180  CHARACTER uplo
181  INTEGER info, lda, ldb, lwork, n, nrhs
182 * ..
183 * .. Array Arguments ..
184  INTEGER ipiv( * )
185  REAL a( lda, * ), b( ldb, * ), work( * )
186 * ..
187 *
188 * =====================================================================
189 *
190 * .. Local Scalars ..
191  LOGICAL lquery
192  INTEGER lwkopt
193 * ..
194 * .. External Functions ..
195  LOGICAL lsame
196  EXTERNAL lsame
197 * ..
198 * .. External Subroutines ..
199  EXTERNAL xerbla, ssytrf, ssytrs, ssytrs2
200 * ..
201 * .. Intrinsic Functions ..
202  INTRINSIC max
203 * ..
204 * .. Executable Statements ..
205 *
206 * Test the input parameters.
207 *
208  info = 0
209  lquery = ( lwork.EQ.-1 )
210  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
211  info = -1
212  ELSE IF( n.LT.0 ) THEN
213  info = -2
214  ELSE IF( nrhs.LT.0 ) THEN
215  info = -3
216  ELSE IF( lda.LT.max( 1, n ) ) THEN
217  info = -5
218  ELSE IF( ldb.LT.max( 1, n ) ) THEN
219  info = -8
220  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
221  info = -10
222  END IF
223 *
224  IF( info.EQ.0 ) THEN
225  IF( n.EQ.0 ) THEN
226  lwkopt = 1
227  ELSE
228  CALL ssytrf( uplo, n, a, lda, ipiv, work, -1, info )
229  lwkopt = work(1)
230  END IF
231  work( 1 ) = lwkopt
232  END IF
233 *
234  IF( info.NE.0 ) THEN
235  CALL xerbla( 'SSYSV ', -info )
236  RETURN
237  ELSE IF( lquery ) THEN
238  RETURN
239  END IF
240 *
241 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
242 *
243  CALL ssytrf( uplo, n, a, lda, ipiv, work, lwork, info )
244  IF( info.EQ.0 ) THEN
245 *
246 * Solve the system A*X = B, overwriting B with X.
247 *
248  IF ( lwork.LT.n ) THEN
249 *
250 * Solve with TRS ( Use Level BLAS 2)
251 *
252  CALL ssytrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
253 *
254  ELSE
255 *
256 * Solve with TRS2 ( Use Level BLAS 3)
257 *
258  CALL ssytrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
259 *
260  END IF
261 *
262  END IF
263 *
264  work( 1 ) = lwkopt
265 *
266  RETURN
267 *
268 * End of SSYSV
269 *
subroutine ssytrs2(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
SSYTRS2
Definition: ssytrs2.f:134
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ssytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS
Definition: ssytrs.f:122
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine ssytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF
Definition: ssytrf.f:184

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subroutine ssysv_rook ( character  UPLO,
integer  N,
integer  NRHS,
real, dimension( lda, * )  A,
integer  LDA,
integer, dimension( * )  IPIV,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices

Download SSYSV_ROOK + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SSYSV_ROOK computes the solution to a real system of linear
 equations
    A * X = B,
 where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
 matrices.

 The diagonal pivoting method is used to factor A as
    A = U * D * U**T,  if UPLO = 'U', or
    A = L * D * L**T,  if UPLO = 'L',
 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, and D is symmetric and block diagonal with
 1-by-1 and 2-by-2 diagonal blocks.

 SSYTRF_ROOK is called to compute the factorization of a real
 symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal
 pivoting method.

 The factored form of A is then used to solve the system 
 of equations A * X = B by calling SSYTRS_ROOK.
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 number of linear equations, i.e., the order of the
          matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 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 block diagonal matrix D and the
          multipliers used to obtain the factor U or L from the
          factorization A = U*D*U**T or A = L*D*L**T as computed by
          SSYTRF_ROOK.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]IPIV
          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D,
          as determined by SSYTRF_ROOK.

          If UPLO = 'U':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.

               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k-1 and -IPIV(k-1) were inerchaged,
               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

          If UPLO = 'L':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.

               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k+1 and -IPIV(k+1) were inerchaged,
               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
[in,out]B
          B is REAL array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS right hand side matrix B.
          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK >= 1, and for best performance
          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
          SSYTRF_ROOK.
          
          TRS will be done with Level 2 BLAS

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
               has been completed, but the block diagonal matrix D is
               exactly singular, so the solution could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012
Contributors:
   April 2012, Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 206 of file ssysv_rook.f.

206 *
207 * -- LAPACK driver routine (version 3.4.1) --
208 * -- LAPACK is a software package provided by Univ. of Tennessee, --
209 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
210 * April 2012
211 *
212 * .. Scalar Arguments ..
213  CHARACTER uplo
214  INTEGER info, lda, ldb, lwork, n, nrhs
215 * ..
216 * .. Array Arguments ..
217  INTEGER ipiv( * )
218  REAL a( lda, * ), b( ldb, * ), work( * )
219 * ..
220 *
221 * =====================================================================
222 *
223 * .. Local Scalars ..
224  LOGICAL lquery
225  INTEGER lwkopt
226 * ..
227 * .. External Functions ..
228  LOGICAL lsame
229  EXTERNAL lsame
230 * ..
231 * .. External Subroutines ..
232  EXTERNAL xerbla, ssytrf_rook, ssytrs_rook
233 * ..
234 * .. Intrinsic Functions ..
235  INTRINSIC max
236 * ..
237 * .. Executable Statements ..
238 *
239 * Test the input parameters.
240 *
241  info = 0
242  lquery = ( lwork.EQ.-1 )
243  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
244  info = -1
245  ELSE IF( n.LT.0 ) THEN
246  info = -2
247  ELSE IF( nrhs.LT.0 ) THEN
248  info = -3
249  ELSE IF( lda.LT.max( 1, n ) ) THEN
250  info = -5
251  ELSE IF( ldb.LT.max( 1, n ) ) THEN
252  info = -8
253  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
254  info = -10
255  END IF
256 *
257  IF( info.EQ.0 ) THEN
258  IF( n.EQ.0 ) THEN
259  lwkopt = 1
260  ELSE
261  CALL ssytrf_rook( uplo, n, a, lda, ipiv, work, -1, info )
262  lwkopt = work(1)
263  END IF
264  work( 1 ) = lwkopt
265  END IF
266 *
267  IF( info.NE.0 ) THEN
268  CALL xerbla( 'SSYSV_ROOK ', -info )
269  RETURN
270  ELSE IF( lquery ) THEN
271  RETURN
272  END IF
273 *
274 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
275 *
276  CALL ssytrf_rook( uplo, n, a, lda, ipiv, work, lwork, info )
277  IF( info.EQ.0 ) THEN
278 *
279 * Solve the system A*X = B, overwriting B with X.
280 *
281 * Solve with TRS_ROOK ( Use Level 2 BLAS)
282 *
283  CALL ssytrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
284 *
285  END IF
286 *
287  work( 1 ) = lwkopt
288 *
289  RETURN
290 *
291 * End of SSYSV_ROOK
292 *
subroutine ssytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_ROOK
Definition: ssytrf_rook.f:210
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ssytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS_ROOK
Definition: ssytrs_rook.f:138
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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subroutine ssysvx ( character  FACT,
character  UPLO,
integer  N,
integer  NRHS,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldaf, * )  AF,
integer  LDAF,
integer, dimension( * )  IPIV,
real, dimension( ldb, * )  B,
integer  LDB,
real, dimension( ldx, * )  X,
integer  LDX,
real  RCOND,
real, dimension( * )  FERR,
real, dimension( * )  BERR,
real, dimension( * )  WORK,
integer  LWORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

SSYSVX computes the solution to system of linear equations A * X = B for SY matrices

Download SSYSVX + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SSYSVX uses the diagonal pivoting factorization to compute the
 solution to a real system of linear equations A * X = B,
 where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
 matrices.

 Error bounds on the solution and a condition estimate are also
 provided.
Description:
 The following steps are performed:

 1. If FACT = 'N', the diagonal pivoting method is used to factor A.
    The form of the factorization is
       A = U * D * U**T,  if UPLO = 'U', or
       A = L * D * L**T,  if UPLO = 'L',
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, and D is symmetric and block diagonal with
    1-by-1 and 2-by-2 diagonal blocks.

 2. If some D(i,i)=0, so that D is exactly singular, then the routine
    returns with INFO = i. Otherwise, the factored form of A is used
    to estimate the condition number of the matrix A.  If the
    reciprocal of the condition number is less than machine precision,
    INFO = N+1 is returned as a warning, but the routine still goes on
    to solve for X and compute error bounds as described below.

 3. The system of equations is solved for X using the factored form
    of A.

 4. Iterative refinement is applied to improve the computed solution
    matrix and calculate error bounds and backward error estimates
    for it.
Parameters
[in]FACT
          FACT is CHARACTER*1
          Specifies whether or not the factored form of A has been
          supplied on entry.
          = 'F':  On entry, AF and IPIV contain the factored form of
                  A.  AF and IPIV will not be modified.
          = 'N':  The matrix A will be copied to AF and factored.
[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 number of linear equations, i.e., the order of the
          matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]AF
          AF is REAL array, dimension (LDAF,N)
          If FACT = 'F', then AF is an input argument and on entry
          contains the block diagonal matrix D and the multipliers used
          to obtain the factor U or L from the factorization
          A = U*D*U**T or A = L*D*L**T as computed by SSYTRF.

          If FACT = 'N', then AF is an output argument and on exit
          returns the block diagonal matrix D and the multipliers used
          to obtain the factor U or L from the factorization
          A = U*D*U**T or A = L*D*L**T.
[in]LDAF
          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).
[in,out]IPIV
          IPIV is INTEGER array, dimension (N)
          If FACT = 'F', then IPIV is an input argument and on entry
          contains details of the interchanges and the block structure
          of D, as determined by SSYTRF.
          If IPIV(k) > 0, then rows and columns k and IPIV(k) were
          interchanged and D(k,k) is a 1-by-1 diagonal block.
          If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
          columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
          is a 2-by-2 diagonal block.  If UPLO = 'L' and IPIV(k) =
          IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
          interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

          If FACT = 'N', then IPIV is an output argument and on exit
          contains details of the interchanges and the block structure
          of D, as determined by SSYTRF.
[in]B
          B is REAL array, dimension (LDB,NRHS)
          The N-by-NRHS right hand side matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[out]X
          X is REAL array, dimension (LDX,NRHS)
          If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[out]RCOND
          RCOND is REAL
          The estimate of the reciprocal condition number of the matrix
          A.  If RCOND is less than the machine precision (in
          particular, if RCOND = 0), the matrix is singular to working
          precision.  This condition is indicated by a return code of
          INFO > 0.
[out]FERR
          FERR is REAL array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X).
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.
[out]BERR
          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i.e., the smallest relative change in
          any element of A or B that makes X(j) an exact solution).
[out]WORK
          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of WORK.  LWORK >= max(1,3*N), and for best
          performance, when FACT = 'N', LWORK >= max(1,3*N,N*NB), where
          NB is the optimal blocksize for SSYTRF.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]IWORK
          IWORK is INTEGER array, dimension (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, and i is
                <= N:  D(i,i) is exactly zero.  The factorization
                       has been completed but the factor D is exactly
                       singular, so the solution and error bounds could
                       not be computed. RCOND = 0 is returned.
                = N+1: D is nonsingular, but RCOND is less than machine
                       precision, meaning that the matrix is singular
                       to working precision.  Nevertheless, the
                       solution and error bounds are computed because
                       there are a number of situations where the
                       computed solution can be more accurate than the
                       value of RCOND would suggest.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
April 2012

Definition at line 286 of file ssysvx.f.

286 *
287 * -- LAPACK driver routine (version 3.4.1) --
288 * -- LAPACK is a software package provided by Univ. of Tennessee, --
289 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
290 * April 2012
291 *
292 * .. Scalar Arguments ..
293  CHARACTER fact, uplo
294  INTEGER info, lda, ldaf, ldb, ldx, lwork, n, nrhs
295  REAL rcond
296 * ..
297 * .. Array Arguments ..
298  INTEGER ipiv( * ), iwork( * )
299  REAL a( lda, * ), af( ldaf, * ), b( ldb, * ),
300  $ berr( * ), ferr( * ), work( * ), x( ldx, * )
301 * ..
302 *
303 * =====================================================================
304 *
305 * .. Parameters ..
306  REAL zero
307  parameter( zero = 0.0e+0 )
308 * ..
309 * .. Local Scalars ..
310  LOGICAL lquery, nofact
311  INTEGER lwkopt, nb
312  REAL anorm
313 * ..
314 * .. External Functions ..
315  LOGICAL lsame
316  INTEGER ilaenv
317  REAL slamch, slansy
318  EXTERNAL ilaenv, lsame, slamch, slansy
319 * ..
320 * .. External Subroutines ..
321  EXTERNAL slacpy, ssycon, ssyrfs, ssytrf, ssytrs, xerbla
322 * ..
323 * .. Intrinsic Functions ..
324  INTRINSIC max
325 * ..
326 * .. Executable Statements ..
327 *
328 * Test the input parameters.
329 *
330  info = 0
331  nofact = lsame( fact, 'N' )
332  lquery = ( lwork.EQ.-1 )
333  IF( .NOT.nofact .AND. .NOT.lsame( fact, 'F' ) ) THEN
334  info = -1
335  ELSE IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) )
336  $ THEN
337  info = -2
338  ELSE IF( n.LT.0 ) THEN
339  info = -3
340  ELSE IF( nrhs.LT.0 ) THEN
341  info = -4
342  ELSE IF( lda.LT.max( 1, n ) ) THEN
343  info = -6
344  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
345  info = -8
346  ELSE IF( ldb.LT.max( 1, n ) ) THEN
347  info = -11
348  ELSE IF( ldx.LT.max( 1, n ) ) THEN
349  info = -13
350  ELSE IF( lwork.LT.max( 1, 3*n ) .AND. .NOT.lquery ) THEN
351  info = -18
352  END IF
353 *
354  IF( info.EQ.0 ) THEN
355  lwkopt = max( 1, 3*n )
356  IF( nofact ) THEN
357  nb = ilaenv( 1, 'SSYTRF', uplo, n, -1, -1, -1 )
358  lwkopt = max( lwkopt, n*nb )
359  END IF
360  work( 1 ) = lwkopt
361  END IF
362 *
363  IF( info.NE.0 ) THEN
364  CALL xerbla( 'SSYSVX', -info )
365  RETURN
366  ELSE IF( lquery ) THEN
367  RETURN
368  END IF
369 *
370  IF( nofact ) THEN
371 *
372 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
373 *
374  CALL slacpy( uplo, n, n, a, lda, af, ldaf )
375  CALL ssytrf( uplo, n, af, ldaf, ipiv, work, lwork, info )
376 *
377 * Return if INFO is non-zero.
378 *
379  IF( info.GT.0 )THEN
380  rcond = zero
381  RETURN
382  END IF
383  END IF
384 *
385 * Compute the norm of the matrix A.
386 *
387  anorm = slansy( 'I', uplo, n, a, lda, work )
388 *
389 * Compute the reciprocal of the condition number of A.
390 *
391  CALL ssycon( uplo, n, af, ldaf, ipiv, anorm, rcond, work, iwork,
392  $ info )
393 *
394 * Compute the solution vectors X.
395 *
396  CALL slacpy( 'Full', n, nrhs, b, ldb, x, ldx )
397  CALL ssytrs( uplo, n, nrhs, af, ldaf, ipiv, x, ldx, info )
398 *
399 * Use iterative refinement to improve the computed solutions and
400 * compute error bounds and backward error estimates for them.
401 *
402  CALL ssyrfs( uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
403  $ ldx, ferr, berr, work, iwork, info )
404 *
405 * Set INFO = N+1 if the matrix is singular to working precision.
406 *
407  IF( rcond.LT.slamch( 'Epsilon' ) )
408  $ info = n + 1
409 *
410  work( 1 ) = lwkopt
411 *
412  RETURN
413 *
414 * End of SSYSVX
415 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ssytrs(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
SSYTRS
Definition: ssytrs.f:122
subroutine ssycon(UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO)
SSYCON
Definition: ssycon.f:132
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:105
real function slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
Definition: slansy.f:124
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
subroutine ssyrfs(UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
SSYRFS
Definition: ssyrfs.f:193
subroutine ssytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF
Definition: ssytrf.f:184

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