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complex16
LAPACK » Symmetric Matrix » Linear Solve

Functions

subroutine zsysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
  ZSYSV computes the solution to system of linear equations A * X = B for SY matrices
subroutine zsysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
  ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine zsysv_rk (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, work, lwork, info)
  ZSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices
subroutine zsysv_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
  ZSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
subroutine zsysvx (fact, uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, rcond, ferr, berr, work, lwork, rwork, info)
  ZSYSVX computes the solution to system of linear equations A * X = B for SY matrices
subroutine zsysvxx (fact, uplo, n, nrhs, a, lda, af, ldaf, ipiv, equed, s, b, ldb, x, ldx, rcond, rpvgrw, berr, n_err_bnds, err_bnds_norm, err_bnds_comp, nparams, params, work, rwork, info)
  ZSYSVXX computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

This is the group of complex16 solve driver functions for SY matrices

Function Documentation

◆ zsysv()

subroutine zsysv ( character uplo,
integer n,
integer nrhs,
complex*16, dimension( lda, * ) a,
integer lda,
integer, dimension( * ) ipiv,
complex*16, dimension( ldb, * ) b,
integer ldb,
complex*16, dimension( * ) work,
integer lwork,
integer info )

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

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

Purpose:
!>
!> ZSYSV computes the solution to a complex 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 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 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
!>          ZSYTRF.
!>
[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 ZSYTRF.  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 COMPLEX*16 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 COMPLEX*16 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
!>          ZSYTRF.
!>          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.

Definition at line 169 of file zsysv.f.

171*
172* -- LAPACK driver routine --
173* -- LAPACK is a software package provided by Univ. of Tennessee, --
174* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176* .. Scalar Arguments ..
177 CHARACTER UPLO
178 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
179* ..
180* .. Array Arguments ..
181 INTEGER IPIV( * )
182 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
183* ..
184*
185* =====================================================================
186*
187* .. Local Scalars ..
188 LOGICAL LQUERY
189 INTEGER LWKOPT
190* ..
191* .. External Functions ..
192 LOGICAL LSAME
193 EXTERNAL lsame
194* ..
195* .. External Subroutines ..
196 EXTERNAL xerbla, zsytrf, zsytrs, zsytrs2
197* ..
198* .. Intrinsic Functions ..
199 INTRINSIC max
200* ..
201* .. Executable Statements ..
202*
203* Test the input parameters.
204*
205 info = 0
206 lquery = ( lwork.EQ.-1 )
207 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
208 info = -1
209 ELSE IF( n.LT.0 ) THEN
210 info = -2
211 ELSE IF( nrhs.LT.0 ) THEN
212 info = -3
213 ELSE IF( lda.LT.max( 1, n ) ) THEN
214 info = -5
215 ELSE IF( ldb.LT.max( 1, n ) ) THEN
216 info = -8
217 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
218 info = -10
219 END IF
220*
221 IF( info.EQ.0 ) THEN
222 IF( n.EQ.0 ) THEN
223 lwkopt = 1
224 ELSE
225 CALL zsytrf( uplo, n, a, lda, ipiv, work, -1, info )
226 lwkopt = dble( work(1) )
227 END IF
228 work( 1 ) = lwkopt
229 END IF
230*
231 IF( info.NE.0 ) THEN
232 CALL xerbla( 'ZSYSV ', -info )
233 RETURN
234 ELSE IF( lquery ) THEN
235 RETURN
236 END IF
237*
238* Compute the factorization A = U*D*U**T or A = L*D*L**T.
239*
240 CALL zsytrf( uplo, n, a, lda, ipiv, work, lwork, info )
241 IF( info.EQ.0 ) THEN
242*
243* Solve the system A*X = B, overwriting B with X.
244*
245 IF ( lwork.LT.n ) THEN
246*
247* Solve with TRS ( Use Level BLAS 2)
248*
249 CALL zsytrs( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
250*
251 ELSE
252*
253* Solve with TRS2 ( Use Level BLAS 3)
254*
255 CALL zsytrs2( uplo,n,nrhs,a,lda,ipiv,b,ldb,work,info )
256*
257 END IF
258*
259 END IF
260*
261 work( 1 ) = lwkopt
262*
263 RETURN
264*
265* End of ZSYSV
266*
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:53
zsytrs
subroutine zsytrs(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
ZSYTRS
Definition zsytrs.f:120
zsytrf
subroutine zsytrf(uplo, n, a, lda, ipiv, work, lwork, info)
ZSYTRF
Definition zsytrf.f:182
zsytrs2
subroutine zsytrs2(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info)
ZSYTRS2
Definition zsytrs2.f:132
max
#define max(a, b)
Definition macros.h:21

◆ zsysv_aa()

subroutine zsysv_aa ( character uplo,
integer n,
integer nrhs,
complex*16, dimension( lda, * ) a,
integer lda,
integer, dimension( * ) ipiv,
complex*16, dimension( ldb, * ) b,
integer ldb,
complex*16, dimension( * ) work,
integer lwork,
integer info )

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

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

Purpose:
!>
!> ZSYSV computes the solution to a complex 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.
!>
!> Aasen's algorithm is used to factor A as
!>    A = U**T * T * U,  if UPLO = 'U', or
!>    A = L * T * L**T,  if UPLO = 'L',
!> where U (or L) is a product of permutation and unit upper (lower)
!> triangular matrices, and T is symmetric tridiagonal. 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 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 tridiagonal matrix T and the
!>          multipliers used to obtain the factor U or L from the
!>          factorization A = U**T*T*U or A = L*T*L**T as computed by
!>          ZSYTRF.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
[out]IPIV
!>          IPIV is INTEGER array, dimension (N)
!>          On exit, it contains the details of the interchanges, i.e.,
!>          the row and column k of A were interchanged with the
!>          row and column IPIV(k).
!>
[in,out]B
!>          B is COMPLEX*16 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 COMPLEX*16 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(1,2*N,3*N-2), and for
!>          the best performance, LWORK >= MAX(1,N*NB), where NB is
!>          the optimal blocksize for ZSYTRF_AA.
!>
!>          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.

Definition at line 160 of file zsysv_aa.f.

162*
163* -- LAPACK driver routine --
164* -- LAPACK is a software package provided by Univ. of Tennessee, --
165* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166*
167* .. Scalar Arguments ..
168 CHARACTER UPLO
169 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
170* ..
171* .. Array Arguments ..
172 INTEGER IPIV( * )
173 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
174* ..
175*
176* =====================================================================
177*
178* .. Local Scalars ..
179 LOGICAL LQUERY
180 INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
181* ..
182* .. External Functions ..
183 LOGICAL LSAME
184 INTEGER ILAENV
185 EXTERNAL ilaenv, lsame
186* ..
187* .. External Subroutines ..
188 EXTERNAL xerbla, zsytrf_aa, zsytrs_aa
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC max
192* ..
193* .. Executable Statements ..
194*
195* Test the input parameters.
196*
197 info = 0
198 lquery = ( lwork.EQ.-1 )
199 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
200 info = -1
201 ELSE IF( n.LT.0 ) THEN
202 info = -2
203 ELSE IF( nrhs.LT.0 ) THEN
204 info = -3
205 ELSE IF( lda.LT.max( 1, n ) ) THEN
206 info = -5
207 ELSE IF( ldb.LT.max( 1, n ) ) THEN
208 info = -8
209 ELSE IF( lwork.LT.max(2*n, 3*n-2) .AND. .NOT.lquery ) THEN
210 info = -10
211 END IF
212*
213 IF( info.EQ.0 ) THEN
214 CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, -1, info )
215 lwkopt_sytrf = int( work(1) )
216 CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
217 $ -1, info )
218 lwkopt_sytrs = int( work(1) )
219 lwkopt = max( lwkopt_sytrf, lwkopt_sytrs )
220 work( 1 ) = lwkopt
221 END IF
222*
223 IF( info.NE.0 ) THEN
224 CALL xerbla( 'ZSYSV_AA ', -info )
225 RETURN
226 ELSE IF( lquery ) THEN
227 RETURN
228 END IF
229*
230* Compute the factorization A = U**T*T*U or A = L*T*L**T.
231*
232 CALL zsytrf_aa( uplo, n, a, lda, ipiv, work, lwork, info )
233 IF( info.EQ.0 ) THEN
234*
235* Solve the system A*X = B, overwriting B with X.
236*
237 CALL zsytrs_aa( uplo, n, nrhs, a, lda, ipiv, b, ldb, work,
238 $ lwork, info )
239*
240 END IF
241*
242 work( 1 ) = lwkopt
243*
244 RETURN
245*
246* End of ZSYSV_AA
247*
ilaenv
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
zsytrs_aa
subroutine zsytrs_aa(uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZSYTRS_AA
Definition zsytrs_aa.f:131
zsytrf_aa
subroutine zsytrf_aa(uplo, n, a, lda, ipiv, work, lwork, info)
ZSYTRF_AA
Definition zsytrf_aa.f:132

◆ zsysv_rk()

subroutine zsysv_rk ( character uplo,
integer n,
integer nrhs,
complex*16, dimension( lda, * ) a,
integer lda,
complex*16, dimension( * ) e,
integer, dimension( * ) ipiv,
complex*16, dimension( ldb, * ) b,
integer ldb,
complex*16, dimension( * ) work,
integer lwork,
integer info )

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

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

Purpose:
!> ZSYSV_RK computes the solution to a complex 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 bounded Bunch-Kaufman (rook) diagonal pivoting method is used
!> to factor A as
!>    A = P*U*D*(U**T)*(P**T),  if UPLO = 'U', or
!>    A = P*L*D*(L**T)*(P**T),  if UPLO = 'L',
!> where U (or L) is unit upper (or lower) triangular matrix,
!> U**T (or L**T) is the transpose of U (or L), P is a permutation
!> matrix, P**T is the transpose of P, and D is symmetric and block
!> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
!>
!> ZSYTRF_RK is called to compute the factorization of a complex
!> symmetric matrix.  The factored form of A is then used to solve
!> the system of equations A * X = B by calling BLAS3 routine ZSYTRS_3.
!>
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored:
!>          = '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 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, diagonal of the block diagonal
!>          matrix D and factors U or L  as computed by ZSYTRF_RK:
!>            a) ONLY diagonal elements of the symmetric block diagonal
!>               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
!>               (superdiagonal (or subdiagonal) elements of D
!>                are stored on exit in array E), and
!>            b) If UPLO = 'U': factor U in the superdiagonal part of A.
!>               If UPLO = 'L': factor L in the subdiagonal part of A.
!>
!>          For more info see the description of ZSYTRF_RK routine.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
[out]E
!>          E is COMPLEX*16 array, dimension (N)
!>          On exit, contains the output computed by the factorization
!>          routine ZSYTRF_RK, i.e. the superdiagonal (or subdiagonal)
!>          elements of the symmetric block diagonal matrix D
!>          with 1-by-1 or 2-by-2 diagonal blocks, where
!>          If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
!>          If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
!>
!>          NOTE: For 1-by-1 diagonal block D(k), where
!>          1 <= k <= N, the element E(k) is set to 0 in both
!>          UPLO = 'U' or UPLO = 'L' cases.
!>
!>          For more info see the description of ZSYTRF_RK routine.
!>
[out]IPIV
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D,
!>          as determined by ZSYTRF_RK.
!>
!>          For more info see the description of ZSYTRF_RK routine.
!>
[in,out]B
!>          B is COMPLEX*16 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 COMPLEX*16 array, dimension ( MAX(1,LWORK) ).
!>          Work array used in the factorization stage.
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
[in]LWORK
!>          LWORK is INTEGER
!>          The length of WORK.  LWORK >= 1. For best performance
!>          of factorization stage LWORK >= max(1,N*NB), where NB is
!>          the optimal blocksize for ZSYTRF_RK.
!>
!>          If LWORK = -1, then a workspace query is assumed;
!>          the routine only calculates the optimal size of the WORK
!>          array for factorization stage, 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 = -k, the k-th argument had an illegal value
!>
!>          > 0: If INFO = k, the matrix A is singular, because:
!>                 If UPLO = 'U': column k in the upper
!>                 triangular part of A contains all zeros.
!>                 If UPLO = 'L': column k in the lower
!>                 triangular part of A contains all zeros.
!>
!>               Therefore D(k,k) is exactly zero, and superdiagonal
!>               elements of column k of U (or subdiagonal elements of
!>               column k of L ) are all zeros. The factorization has
!>               been completed, but the block diagonal matrix D is
!>               exactly singular, and division by zero will occur if
!>               it is used to solve a system of equations.
!>
!>               NOTE: INFO only stores the first occurrence of
!>               a singularity, any subsequent occurrence of singularity
!>               is not stored in INFO even though the factorization
!>               always completes.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
!>
!>  December 2016,  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 226 of file zsysv_rk.f.

228*
229* -- LAPACK driver routine --
230* -- LAPACK is a software package provided by Univ. of Tennessee, --
231* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
232*
233* .. Scalar Arguments ..
234 CHARACTER UPLO
235 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
236* ..
237* .. Array Arguments ..
238 INTEGER IPIV( * )
239 COMPLEX*16 A( LDA, * ), B( LDB, * ), E( * ), WORK( * )
240* ..
241*
242* =====================================================================
243*
244* .. Local Scalars ..
245 LOGICAL LQUERY
246 INTEGER LWKOPT
247* ..
248* .. External Functions ..
249 LOGICAL LSAME
250 EXTERNAL lsame
251* ..
252* .. External Subroutines ..
253 EXTERNAL xerbla, zsytrf_rk, zsytrs_3
254* ..
255* .. Intrinsic Functions ..
256 INTRINSIC max
257* ..
258* .. Executable Statements ..
259*
260* Test the input parameters.
261*
262 info = 0
263 lquery = ( lwork.EQ.-1 )
264 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
265 info = -1
266 ELSE IF( n.LT.0 ) THEN
267 info = -2
268 ELSE IF( nrhs.LT.0 ) THEN
269 info = -3
270 ELSE IF( lda.LT.max( 1, n ) ) THEN
271 info = -5
272 ELSE IF( ldb.LT.max( 1, n ) ) THEN
273 info = -9
274 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
275 info = -11
276 END IF
277*
278 IF( info.EQ.0 ) THEN
279 IF( n.EQ.0 ) THEN
280 lwkopt = 1
281 ELSE
282 CALL zsytrf_rk( uplo, n, a, lda, e, ipiv, work, -1, info )
283 lwkopt = dble( work(1) )
284 END IF
285 work( 1 ) = lwkopt
286 END IF
287*
288 IF( info.NE.0 ) THEN
289 CALL xerbla( 'ZSYSV_RK ', -info )
290 RETURN
291 ELSE IF( lquery ) THEN
292 RETURN
293 END IF
294*
295* Compute the factorization A = P*U*D*(U**T)*(P**T) or
296* A = P*U*D*(U**T)*(P**T).
297*
298 CALL zsytrf_rk( uplo, n, a, lda, e, ipiv, work, lwork, info )
299*
300 IF( info.EQ.0 ) THEN
301*
302* Solve the system A*X = B with BLAS3 solver, overwriting B with X.
303*
304 CALL zsytrs_3( uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info )
305*
306 END IF
307*
308 work( 1 ) = lwkopt
309*
310 RETURN
311*
312* End of ZSYSV_RK
313*
zsytrs_3
subroutine zsytrs_3(uplo, n, nrhs, a, lda, e, ipiv, b, ldb, info)
ZSYTRS_3
Definition zsytrs_3.f:165
zsytrf_rk
subroutine zsytrf_rk(uplo, n, a, lda, e, ipiv, work, lwork, info)
ZSYTRF_RK computes the factorization of a complex symmetric indefinite matrix using the bounded Bunch...
Definition zsytrf_rk.f:259

◆ zsysv_rook()

subroutine zsysv_rook ( character uplo,
integer n,
integer nrhs,
complex*16, dimension( lda, * ) a,
integer lda,
integer, dimension( * ) ipiv,
complex*16, dimension( ldb, * ) b,
integer ldb,
complex*16, dimension( * ) work,
integer lwork,
integer info )

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

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

Purpose:
!>
!> ZSYSV_ROOK computes the solution to a complex 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.
!>
!> ZSYTRF_ROOK is called to compute the factorization of a complex
!> symmetric matrix A using the bounded Bunch-Kaufman () diagonal
!> pivoting method.
!>
!> The factored form of A is then used to solve the system
!> of equations A * X = B by calling ZSYTRS_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 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 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
!>          ZSYTRF_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 ZSYTRF_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 COMPLEX*16 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 COMPLEX*16 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
!>          ZSYTRF_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.
Contributors:
!>
!>   December 2016, 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 202 of file zsysv_rook.f.

204*
205* -- LAPACK driver routine --
206* -- LAPACK is a software package provided by Univ. of Tennessee, --
207* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
208*
209* .. Scalar Arguments ..
210 CHARACTER UPLO
211 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
212* ..
213* .. Array Arguments ..
214 INTEGER IPIV( * )
215 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
216* ..
217*
218* =====================================================================
219*
220* .. Local Scalars ..
221 LOGICAL LQUERY
222 INTEGER LWKOPT
223* ..
224* .. External Functions ..
225 LOGICAL LSAME
226 EXTERNAL lsame
227* ..
228* .. External Subroutines ..
229 EXTERNAL xerbla, zsytrf_rook, zsytrs_rook
230* ..
231* .. Intrinsic Functions ..
232 INTRINSIC max
233* ..
234* .. Executable Statements ..
235*
236* Test the input parameters.
237*
238 info = 0
239 lquery = ( lwork.EQ.-1 )
240 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
241 info = -1
242 ELSE IF( n.LT.0 ) THEN
243 info = -2
244 ELSE IF( nrhs.LT.0 ) THEN
245 info = -3
246 ELSE IF( lda.LT.max( 1, n ) ) THEN
247 info = -5
248 ELSE IF( ldb.LT.max( 1, n ) ) THEN
249 info = -8
250 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
251 info = -10
252 END IF
253*
254 IF( info.EQ.0 ) THEN
255 IF( n.EQ.0 ) THEN
256 lwkopt = 1
257 ELSE
258 CALL zsytrf_rook( uplo, n, a, lda, ipiv, work, -1, info )
259 lwkopt = dble( work(1) )
260 END IF
261 work( 1 ) = lwkopt
262 END IF
263*
264 IF( info.NE.0 ) THEN
265 CALL xerbla( 'ZSYSV_ROOK ', -info )
266 RETURN
267 ELSE IF( lquery ) THEN
268 RETURN
269 END IF
270*
271* Compute the factorization A = U*D*U**T or A = L*D*L**T.
272*
273 CALL zsytrf_rook( uplo, n, a, lda, ipiv, work, lwork, info )
274 IF( info.EQ.0 ) THEN
275*
276* Solve the system A*X = B, overwriting B with X.
277*
278* Solve with TRS_ROOK ( Use Level 2 BLAS)
279*
280 CALL zsytrs_rook( uplo, n, nrhs, a, lda, ipiv, b, ldb, info )
281*
282 END IF
283*
284 work( 1 ) = lwkopt
285*
286 RETURN
287*
288* End of ZSYSV_ROOK
289*
zsytrf_rook
subroutine zsytrf_rook(uplo, n, a, lda, ipiv, work, lwork, info)
ZSYTRF_ROOK
Definition zsytrf_rook.f:208
zsytrs_rook
subroutine zsytrs_rook(uplo, n, nrhs, a, lda, ipiv, b, ldb, info)
ZSYTRS_ROOK
Definition zsytrs_rook.f:136

◆ zsysvx()

subroutine zsysvx ( character fact,
character uplo,
integer n,
integer nrhs,
complex*16, dimension( lda, * ) a,
integer lda,
complex*16, dimension( ldaf, * ) af,
integer ldaf,
integer, dimension( * ) ipiv,
complex*16, dimension( ldb, * ) b,
integer ldb,
complex*16, dimension( ldx, * ) x,
integer ldx,
double precision rcond,
double precision, dimension( * ) ferr,
double precision, dimension( * ) berr,
complex*16, dimension( * ) work,
integer lwork,
double precision, dimension( * ) rwork,
integer info )

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

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

Purpose:
!>
!> ZSYSVX uses the diagonal pivoting factorization to compute the
!> solution to a complex 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.  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 COMPLEX*16 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 COMPLEX*16 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 ZSYTRF.
!>
!>          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 ZSYTRF.
!>          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 ZSYTRF.
!>
[in]B
!>          B is COMPLEX*16 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 COMPLEX*16 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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 COMPLEX*16 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(1,2*N), and for best
!>          performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where
!>          NB is the optimal blocksize for ZSYTRF.
!>
!>          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]RWORK
!>          RWORK is DOUBLE PRECISION 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.

Definition at line 282 of file zsysvx.f.

285*
286* -- LAPACK driver routine --
287* -- LAPACK is a software package provided by Univ. of Tennessee, --
288* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
289*
290* .. Scalar Arguments ..
291 CHARACTER FACT, UPLO
292 INTEGER INFO, LDA, LDAF, LDB, LDX, LWORK, N, NRHS
293 DOUBLE PRECISION RCOND
294* ..
295* .. Array Arguments ..
296 INTEGER IPIV( * )
297 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
298 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
299 $ WORK( * ), X( LDX, * )
300* ..
301*
302* =====================================================================
303*
304* .. Parameters ..
305 DOUBLE PRECISION ZERO
306 parameter( zero = 0.0d+0 )
307* ..
308* .. Local Scalars ..
309 LOGICAL LQUERY, NOFACT
310 INTEGER LWKOPT, NB
311 DOUBLE PRECISION ANORM
312* ..
313* .. External Functions ..
314 LOGICAL LSAME
315 INTEGER ILAENV
316 DOUBLE PRECISION DLAMCH, ZLANSY
317 EXTERNAL lsame, ilaenv, dlamch, zlansy
318* ..
319* .. External Subroutines ..
320 EXTERNAL xerbla, zlacpy, zsycon, zsyrfs, zsytrf, zsytrs
321* ..
322* .. Intrinsic Functions ..
323 INTRINSIC max
324* ..
325* .. Executable Statements ..
326*
327* Test the input parameters.
328*
329 info = 0
330 nofact = lsame( fact, 'N' )
331 lquery = ( lwork.EQ.-1 )
332 IF( .NOT.nofact .AND. .NOT.lsame( fact, 'F' ) ) THEN
333 info = -1
334 ELSE IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) )
335 $ THEN
336 info = -2
337 ELSE IF( n.LT.0 ) THEN
338 info = -3
339 ELSE IF( nrhs.LT.0 ) THEN
340 info = -4
341 ELSE IF( lda.LT.max( 1, n ) ) THEN
342 info = -6
343 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
344 info = -8
345 ELSE IF( ldb.LT.max( 1, n ) ) THEN
346 info = -11
347 ELSE IF( ldx.LT.max( 1, n ) ) THEN
348 info = -13
349 ELSE IF( lwork.LT.max( 1, 2*n ) .AND. .NOT.lquery ) THEN
350 info = -18
351 END IF
352*
353 IF( info.EQ.0 ) THEN
354 lwkopt = max( 1, 2*n )
355 IF( nofact ) THEN
356 nb = ilaenv( 1, 'ZSYTRF', uplo, n, -1, -1, -1 )
357 lwkopt = max( lwkopt, n*nb )
358 END IF
359 work( 1 ) = lwkopt
360 END IF
361*
362 IF( info.NE.0 ) THEN
363 CALL xerbla( 'ZSYSVX', -info )
364 RETURN
365 ELSE IF( lquery ) THEN
366 RETURN
367 END IF
368*
369 IF( nofact ) THEN
370*
371* Compute the factorization A = U*D*U**T or A = L*D*L**T.
372*
373 CALL zlacpy( uplo, n, n, a, lda, af, ldaf )
374 CALL zsytrf( uplo, n, af, ldaf, ipiv, work, lwork, info )
375*
376* Return if INFO is non-zero.
377*
378 IF( info.GT.0 )THEN
379 rcond = zero
380 RETURN
381 END IF
382 END IF
383*
384* Compute the norm of the matrix A.
385*
386 anorm = zlansy( 'I', uplo, n, a, lda, rwork )
387*
388* Compute the reciprocal of the condition number of A.
389*
390 CALL zsycon( uplo, n, af, ldaf, ipiv, anorm, rcond, work, info )
391*
392* Compute the solution vectors X.
393*
394 CALL zlacpy( 'Full', n, nrhs, b, ldb, x, ldx )
395 CALL zsytrs( uplo, n, nrhs, af, ldaf, ipiv, x, ldx, info )
396*
397* Use iterative refinement to improve the computed solutions and
398* compute error bounds and backward error estimates for them.
399*
400 CALL zsyrfs( uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
401 $ ldx, ferr, berr, work, rwork, info )
402*
403* Set INFO = N+1 if the matrix is singular to working precision.
404*
405 IF( rcond.LT.dlamch( 'Epsilon' ) )
406 $ info = n + 1
407*
408 work( 1 ) = lwkopt
409*
410 RETURN
411*
412* End of ZSYSVX
413*
zlacpy
subroutine zlacpy(uplo, m, n, a, lda, b, ldb)
ZLACPY copies all or part of one two-dimensional array to another.
Definition zlacpy.f:103
zlansy
double precision function zlansy(norm, uplo, n, a, lda, work)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlansy.f:123
zsyrfs
subroutine zsyrfs(uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZSYRFS
Definition zsyrfs.f:192
zsycon
subroutine zsycon(uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZSYCON
Definition zsycon.f:125
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69

◆ zsysvxx()

subroutine zsysvxx ( character fact,
character uplo,
integer n,
integer nrhs,
complex*16, dimension( lda, * ) a,
integer lda,
complex*16, dimension( ldaf, * ) af,
integer ldaf,
integer, dimension( * ) ipiv,
character equed,
double precision, dimension( * ) s,
complex*16, dimension( ldb, * ) b,
integer ldb,
complex*16, dimension( ldx, * ) x,
integer ldx,
double precision rcond,
double precision rpvgrw,
double precision, dimension( * ) berr,
integer n_err_bnds,
double precision, dimension( nrhs, * ) err_bnds_norm,
double precision, dimension( nrhs, * ) err_bnds_comp,
integer nparams,
double precision, dimension( * ) params,
complex*16, dimension( * ) work,
double precision, dimension( * ) rwork,
integer info )

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

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

Purpose:
!>
!>    ZSYSVXX uses the diagonal pivoting factorization to compute the
!>    solution to a complex*16 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.
!>
!>    If requested, both normwise and maximum componentwise error bounds
!>    are returned. ZSYSVXX will return a solution with a tiny
!>    guaranteed error (O(eps) where eps is the working machine
!>    precision) unless the matrix is very ill-conditioned, in which
!>    case a warning is returned. Relevant condition numbers also are
!>    calculated and returned.
!>
!>    ZSYSVXX accepts user-provided factorizations and equilibration
!>    factors; see the definitions of the FACT and EQUED options.
!>    Solving with refinement and using a factorization from a previous
!>    ZSYSVXX call will also produce a solution with either O(eps)
!>    errors or warnings, but we cannot make that claim for general
!>    user-provided factorizations and equilibration factors if they
!>    differ from what ZSYSVXX would itself produce.
!>
Description:
!>
!>    The following steps are performed:
!>
!>    1. If FACT = 'E', double precision scaling factors are computed to equilibrate
!>    the system:
!>
!>      diag(S)*A*diag(S)     *inv(diag(S))*X = diag(S)*B
!>
!>    Whether or not the system will be equilibrated depends on the
!>    scaling of the matrix A, but if equilibration is used, A is
!>    overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
!>
!>    2. If FACT = 'N' or 'E', the LU decomposition is used to factor
!>    the matrix A (after equilibration if FACT = 'E') 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.
!>
!>    3. 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 (see
!>    argument RCOND).  If the reciprocal of the condition number is
!>    less than machine precision, the routine still goes on to solve
!>    for X and compute error bounds as described below.
!>
!>    4. The system of equations is solved for X using the factored form
!>    of A.
!>
!>    5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
!>    the routine will use iterative refinement to try to get a small
!>    error and error bounds.  Refinement calculates the residual to at
!>    least twice the working precision.
!>
!>    6. If equilibration was used, the matrix X is premultiplied by
!>    diag(R) so that it solves the original system before
!>    equilibration.
!> 
!>     Some optional parameters are bundled in the PARAMS array.  These
!>     settings determine how refinement is performed, but often the
!>     defaults are acceptable.  If the defaults are acceptable, users
!>     can pass NPARAMS = 0 which prevents the source code from accessing
!>     the PARAMS argument.
!>
Parameters
[in]FACT
!>          FACT is CHARACTER*1
!>     Specifies whether or not the factored form of the matrix A is
!>     supplied on entry, and if not, whether the matrix A should be
!>     equilibrated before it is factored.
!>       = 'F':  On entry, AF and IPIV contain the factored form of A.
!>               If EQUED is not 'N', the matrix A has been
!>               equilibrated with scaling factors given by S.
!>               A, AF, and IPIV are not modified.
!>       = 'N':  The matrix A will be copied to AF and factored.
!>       = 'E':  The matrix A will be equilibrated if necessary, then
!>               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,out]A
!>          A is COMPLEX*16 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.
!>
!>     On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
!>     diag(S)*A*diag(S).
!>
[in]LDA
!>          LDA is INTEGER
!>     The leading dimension of the array A.  LDA >= max(1,N).
!>
[in,out]AF
!>          AF is COMPLEX*16 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 ZSYTRF.
!>
!>     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 ZSYTRF.  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 ZSYTRF.
!>
[in,out]EQUED
!>          EQUED is CHARACTER*1
!>     Specifies the form of equilibration that was done.
!>       = 'N':  No equilibration (always true if FACT = 'N').
!>       = 'Y':  Both row and column equilibration, i.e., A has been
!>               replaced by diag(S) * A * diag(S).
!>     EQUED is an input argument if FACT = 'F'; otherwise, it is an
!>     output argument.
!>
[in,out]S
!>          S is DOUBLE PRECISION array, dimension (N)
!>     The scale factors for A.  If EQUED = 'Y', A is multiplied on
!>     the left and right by diag(S).  S is an input argument if FACT =
!>     'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
!>     = 'Y', each element of S must be positive.  If S is output, each
!>     element of S is a power of the radix. If S is input, each element
!>     of S should be a power of the radix to ensure a reliable solution
!>     and error estimates. Scaling by powers of the radix does not cause
!>     rounding errors unless the result underflows or overflows.
!>     Rounding errors during scaling lead to refining with a matrix that
!>     is not equivalent to the input matrix, producing error estimates
!>     that may not be reliable.
!>
[in,out]B
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>     On entry, the N-by-NRHS right hand side matrix B.
!>     On exit,
!>     if EQUED = 'N', B is not modified;
!>     if EQUED = 'Y', B is overwritten by diag(S)*B;
!>
[in]LDB
!>          LDB is INTEGER
!>     The leading dimension of the array B.  LDB >= max(1,N).
!>
[out]X
!>          X is COMPLEX*16 array, dimension (LDX,NRHS)
!>     If INFO = 0, the N-by-NRHS solution matrix X to the original
!>     system of equations.  Note that A and B are modified on exit if
!>     EQUED .ne. 'N', and the solution to the equilibrated system is
!>     inv(diag(S))*X.
!>
[in]LDX
!>          LDX is INTEGER
!>     The leading dimension of the array X.  LDX >= max(1,N).
!>
[out]RCOND
!>          RCOND is DOUBLE PRECISION
!>     Reciprocal scaled condition number.  This is an estimate of the
!>     reciprocal Skeel condition number of the matrix A after
!>     equilibration (if done).  If this is less than the machine
!>     precision (in particular, if it is zero), the matrix is singular
!>     to working precision.  Note that the error may still be small even
!>     if this number is very small and the matrix appears ill-
!>     conditioned.
!>
[out]RPVGRW
!>          RPVGRW is DOUBLE PRECISION
!>     Reciprocal pivot growth.  On exit, this contains the reciprocal
!>     pivot growth factor norm(A)/norm(U). The 
!>     norm is used.  If this is much less than 1, then the stability of
!>     the LU factorization of the (equilibrated) matrix A could be poor.
!>     This also means that the solution X, estimated condition numbers,
!>     and error bounds could be unreliable. If factorization fails with
!>     0<INFO<=N, then this contains the reciprocal pivot growth factor
!>     for the leading INFO columns of A.
!>
[out]BERR
!>          BERR is DOUBLE PRECISION array, dimension (NRHS)
!>     Componentwise relative backward error.  This is 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).
!>
[in]N_ERR_BNDS
!>          N_ERR_BNDS is INTEGER
!>     Number of error bounds to return for each right hand side
!>     and each type (normwise or componentwise).  See ERR_BNDS_NORM and
!>     ERR_BNDS_COMP below.
!>
[out]ERR_BNDS_NORM
!>          ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
!>     For each right-hand side, this array contains information about
!>     various error bounds and condition numbers corresponding to the
!>     normwise relative error, which is defined as follows:
!>
!>     Normwise relative error in the ith solution vector:
!>             max_j (abs(XTRUE(j,i) - X(j,i)))
!>            ------------------------------
!>                  max_j abs(X(j,i))
!>
!>     The array is indexed by the type of error information as described
!>     below. There currently are up to three pieces of information
!>     returned.
!>
!>     The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
!>     right-hand side.
!>
!>     The second index in ERR_BNDS_NORM(:,err) contains the following
!>     three fields:
!>     err = 1  boolean. Trust the answer if the
!>              reciprocal condition number is less than the threshold
!>              sqrt(n) * dlamch('Epsilon').
!>
!>     err = 2  error bound: The estimated forward error,
!>              almost certainly within a factor of 10 of the true error
!>              so long as the next entry is greater than the threshold
!>              sqrt(n) * dlamch('Epsilon'). This error bound should only
!>              be trusted if the previous boolean is true.
!>
!>     err = 3  Reciprocal condition number: Estimated normwise
!>              reciprocal condition number.  Compared with the threshold
!>              sqrt(n) * dlamch('Epsilon') to determine if the error
!>              estimate is . These reciprocal condition
!>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
!>              appropriately scaled matrix Z.
!>              Let Z = S*A, where S scales each row by a power of the
!>              radix so all absolute row sums of Z are approximately 1.
!>
!>     See Lapack Working Note 165 for further details and extra
!>     cautions.
!>
[out]ERR_BNDS_COMP
!>          ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
!>     For each right-hand side, this array contains information about
!>     various error bounds and condition numbers corresponding to the
!>     componentwise relative error, which is defined as follows:
!>
!>     Componentwise relative error in the ith solution vector:
!>                    abs(XTRUE(j,i) - X(j,i))
!>             max_j ----------------------
!>                         abs(X(j,i))
!>
!>     The array is indexed by the right-hand side i (on which the
!>     componentwise relative error depends), and the type of error
!>     information as described below. There currently are up to three
!>     pieces of information returned for each right-hand side. If
!>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
!>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
!>     the first (:,N_ERR_BNDS) entries are returned.
!>
!>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
!>     right-hand side.
!>
!>     The second index in ERR_BNDS_COMP(:,err) contains the following
!>     three fields:
!>     err = 1  boolean. Trust the answer if the
!>              reciprocal condition number is less than the threshold
!>              sqrt(n) * dlamch('Epsilon').
!>
!>     err = 2  error bound: The estimated forward error,
!>              almost certainly within a factor of 10 of the true error
!>              so long as the next entry is greater than the threshold
!>              sqrt(n) * dlamch('Epsilon'). This error bound should only
!>              be trusted if the previous boolean is true.
!>
!>     err = 3  Reciprocal condition number: Estimated componentwise
!>              reciprocal condition number.  Compared with the threshold
!>              sqrt(n) * dlamch('Epsilon') to determine if the error
!>              estimate is . These reciprocal condition
!>              numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
!>              appropriately scaled matrix Z.
!>              Let Z = S*(A*diag(x)), where x is the solution for the
!>              current right-hand side and S scales each row of
!>              A*diag(x) by a power of the radix so all absolute row
!>              sums of Z are approximately 1.
!>
!>     See Lapack Working Note 165 for further details and extra
!>     cautions.
!>
[in]NPARAMS
!>          NPARAMS is INTEGER
!>     Specifies the number of parameters set in PARAMS.  If <= 0, the
!>     PARAMS array is never referenced and default values are used.
!>
[in,out]PARAMS
!>          PARAMS is DOUBLE PRECISION array, dimension NPARAMS
!>     Specifies algorithm parameters.  If an entry is < 0.0, then
!>     that entry will be filled with default value used for that
!>     parameter.  Only positions up to NPARAMS are accessed; defaults
!>     are used for higher-numbered parameters.
!>
!>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
!>            refinement or not.
!>         Default: 1.0D+0
!>            = 0.0:  No refinement is performed, and no error bounds are
!>                    computed.
!>            = 1.0:  Use the extra-precise refinement algorithm.
!>              (other values are reserved for future use)
!>
!>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
!>            computations allowed for refinement.
!>         Default: 10
!>         Aggressive: Set to 100 to permit convergence using approximate
!>                     factorizations or factorizations other than LU. If
!>                     the factorization uses a technique other than
!>                     Gaussian elimination, the guarantees in
!>                     err_bnds_norm and err_bnds_comp may no longer be
!>                     trustworthy.
!>
!>       PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
!>            will attempt to find a solution with small componentwise
!>            relative error in the double-precision algorithm.  Positive
!>            is true, 0.0 is false.
!>         Default: 1.0 (attempt componentwise convergence)
!>
[out]WORK
!>          WORK is COMPLEX*16 array, dimension (2*N)
!>
[out]RWORK
!>          RWORK is DOUBLE PRECISION array, dimension (2*N)
!>
[out]INFO
!>          INFO is INTEGER
!>       = 0:  Successful exit. The solution to every right-hand side is
!>         guaranteed.
!>       < 0:  If INFO = -i, the i-th argument had an illegal value
!>       > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
!>         has been completed, but the factor U is exactly singular, so
!>         the solution and error bounds could not be computed. RCOND = 0
!>         is returned.
!>       = N+J: The solution corresponding to the Jth right-hand side is
!>         not guaranteed. The solutions corresponding to other right-
!>         hand sides K with K > J may not be guaranteed as well, but
!>         only the first such right-hand side is reported. If a small
!>         componentwise error is not requested (PARAMS(3) = 0.0) then
!>         the Jth right-hand side is the first with a normwise error
!>         bound that is not guaranteed (the smallest J such
!>         that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
!>         the Jth right-hand side is the first with either a normwise or
!>         componentwise error bound that is not guaranteed (the smallest
!>         J such that either ERR_BNDS_NORM(J,1) = 0.0 or
!>         ERR_BNDS_COMP(J,1) = 0.0). See the definition of
!>         ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
!>         about all of the right-hand sides check ERR_BNDS_NORM or
!>         ERR_BNDS_COMP.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 502 of file zsysvxx.f.

506*
507* -- LAPACK driver routine --
508* -- LAPACK is a software package provided by Univ. of Tennessee, --
509* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
510*
511* .. Scalar Arguments ..
512 CHARACTER EQUED, FACT, UPLO
513 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
514 $ N_ERR_BNDS
515 DOUBLE PRECISION RCOND, RPVGRW
516* ..
517* .. Array Arguments ..
518 INTEGER IPIV( * )
519 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
520 $ X( LDX, * ), WORK( * )
521 DOUBLE PRECISION S( * ), PARAMS( * ), BERR( * ),
522 $ ERR_BNDS_NORM( NRHS, * ),
523 $ ERR_BNDS_COMP( NRHS, * ), RWORK( * )
524* ..
525*
526* ==================================================================
527*
528* .. Parameters ..
529 DOUBLE PRECISION ZERO, ONE
530 parameter( zero = 0.0d+0, one = 1.0d+0 )
531 INTEGER FINAL_NRM_ERR_I, FINAL_CMP_ERR_I, BERR_I
532 INTEGER RCOND_I, NRM_RCOND_I, NRM_ERR_I, CMP_RCOND_I
533 INTEGER CMP_ERR_I, PIV_GROWTH_I
534 parameter( final_nrm_err_i = 1, final_cmp_err_i = 2,
535 $ berr_i = 3 )
536 parameter( rcond_i = 4, nrm_rcond_i = 5, nrm_err_i = 6 )
537 parameter( cmp_rcond_i = 7, cmp_err_i = 8,
538 $ piv_growth_i = 9 )
539* ..
540* .. Local Scalars ..
541 LOGICAL EQUIL, NOFACT, RCEQU
542 INTEGER INFEQU, J
543 DOUBLE PRECISION AMAX, BIGNUM, SMIN, SMAX, SCOND, SMLNUM
544* ..
545* .. External Functions ..
546 EXTERNAL lsame, dlamch, zla_syrpvgrw
547 LOGICAL LSAME
548 DOUBLE PRECISION DLAMCH, ZLA_SYRPVGRW
549* ..
550* .. External Subroutines ..
551 EXTERNAL zsyequb, zsytrf, zsytrs, zlacpy,
552 $ zlaqsy, xerbla, zlascl2, zsyrfsx
553* ..
554* .. Intrinsic Functions ..
555 INTRINSIC max, min
556* ..
557* .. Executable Statements ..
558*
559 info = 0
560 nofact = lsame( fact, 'N' )
561 equil = lsame( fact, 'E' )
562 smlnum = dlamch( 'Safe minimum' )
563 bignum = one / smlnum
564 IF( nofact .OR. equil ) THEN
565 equed = 'N'
566 rcequ = .false.
567 ELSE
568 rcequ = lsame( equed, 'Y' )
569 ENDIF
570*
571* Default is failure. If an input parameter is wrong or
572* factorization fails, make everything look horrible. Only the
573* pivot growth is set here, the rest is initialized in ZSYRFSX.
574*
575 rpvgrw = zero
576*
577* Test the input parameters. PARAMS is not tested until ZSYRFSX.
578*
579 IF( .NOT.nofact .AND. .NOT.equil .AND. .NOT.
580 $ lsame( fact, 'F' ) ) THEN
581 info = -1
582 ELSE IF( .NOT.lsame(uplo, 'U') .AND.
583 $ .NOT.lsame(uplo, 'L') ) THEN
584 info = -2
585 ELSE IF( n.LT.0 ) THEN
586 info = -3
587 ELSE IF( nrhs.LT.0 ) THEN
588 info = -4
589 ELSE IF( lda.LT.max( 1, n ) ) THEN
590 info = -6
591 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
592 info = -8
593 ELSE IF( lsame( fact, 'F' ) .AND. .NOT.
594 $ ( rcequ .OR. lsame( equed, 'N' ) ) ) THEN
595 info = -10
596 ELSE
597 IF ( rcequ ) THEN
598 smin = bignum
599 smax = zero
600 DO 10 j = 1, n
601 smin = min( smin, s( j ) )
602 smax = max( smax, s( j ) )
603 10 CONTINUE
604 IF( smin.LE.zero ) THEN
605 info = -11
606 ELSE IF( n.GT.0 ) THEN
607 scond = max( smin, smlnum ) / min( smax, bignum )
608 ELSE
609 scond = one
610 END IF
611 END IF
612 IF( info.EQ.0 ) THEN
613 IF( ldb.LT.max( 1, n ) ) THEN
614 info = -13
615 ELSE IF( ldx.LT.max( 1, n ) ) THEN
616 info = -15
617 END IF
618 END IF
619 END IF
620*
621 IF( info.NE.0 ) THEN
622 CALL xerbla( 'ZSYSVXX', -info )
623 RETURN
624 END IF
625*
626 IF( equil ) THEN
627*
628* Compute row and column scalings to equilibrate the matrix A.
629*
630 CALL zsyequb( uplo, n, a, lda, s, scond, amax, work, infequ )
631 IF( infequ.EQ.0 ) THEN
632*
633* Equilibrate the matrix.
634*
635 CALL zlaqsy( uplo, n, a, lda, s, scond, amax, equed )
636 rcequ = lsame( equed, 'Y' )
637 END IF
638
639 END IF
640*
641* Scale the right hand-side.
642*
643 IF( rcequ ) CALL zlascl2( n, nrhs, s, b, ldb )
644*
645 IF( nofact .OR. equil ) THEN
646*
647* Compute the LDL^T or UDU^T factorization of A.
648*
649 CALL zlacpy( uplo, n, n, a, lda, af, ldaf )
650 CALL zsytrf( uplo, n, af, ldaf, ipiv, work, 5*max(1,n), info )
651*
652* Return if INFO is non-zero.
653*
654 IF( info.GT.0 ) THEN
655*
656* Pivot in column INFO is exactly 0
657* Compute the reciprocal pivot growth factor of the
658* leading rank-deficient INFO columns of A.
659*
660 IF ( n.GT.0 )
661 $ rpvgrw = zla_syrpvgrw( uplo, n, info, a, lda, af,
662 $ ldaf, ipiv, rwork )
663 RETURN
664 END IF
665 END IF
666*
667* Compute the reciprocal pivot growth factor RPVGRW.
668*
669 IF ( n.GT.0 )
670 $ rpvgrw = zla_syrpvgrw( uplo, n, info, a, lda, af, ldaf,
671 $ ipiv, rwork )
672*
673* Compute the solution matrix X.
674*
675 CALL zlacpy( 'Full', n, nrhs, b, ldb, x, ldx )
676 CALL zsytrs( uplo, n, nrhs, af, ldaf, ipiv, x, ldx, info )
677*
678* Use iterative refinement to improve the computed solution and
679* compute error bounds and backward error estimates for it.
680*
681 CALL zsyrfsx( uplo, equed, n, nrhs, a, lda, af, ldaf, ipiv,
682 $ s, b, ldb, x, ldx, rcond, berr, n_err_bnds, err_bnds_norm,
683 $ err_bnds_comp, nparams, params, work, rwork, info )
684*
685* Scale solutions.
686*
687 IF ( rcequ ) THEN
688 CALL zlascl2 (n, nrhs, s, x, ldx )
689 END IF
690*
691 RETURN
692*
693* End of ZSYSVXX
694*
zlascl2
subroutine zlascl2(m, n, d, x, ldx)
ZLASCL2 performs diagonal scaling on a vector.
Definition zlascl2.f:91
zlaqsy
subroutine zlaqsy(uplo, n, a, lda, s, scond, amax, equed)
ZLAQSY scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ.
Definition zlaqsy.f:134
zla_syrpvgrw
double precision function zla_syrpvgrw(uplo, n, info, a, lda, af, ldaf, ipiv, work)
ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite m...
Definition zla_syrpvgrw.f:123
zsyrfsx
subroutine zsyrfsx(uplo, equed, n, nrhs, a, lda, af, ldaf, ipiv, s, b, ldb, x, ldx, rcond, berr, n_err_bnds, err_bnds_norm, err_bnds_comp, nparams, params, work, rwork, info)
ZSYRFSX
Definition zsyrfsx.f:402
zsyequb
subroutine zsyequb(uplo, n, a, lda, s, scond, amax, work, info)
ZSYEQUB
Definition zsyequb.f:132
min
#define min(a, b)
Definition macros.h:20