Man page - herfs(3)
Packages contains this manual
- hptrd(3)
- potri(3)
- xerbla_array(3)
- ggsvd_driver_grp(3)
- hfrk(3)
- getsqr_comp_grp(3)
- laed6(3)
- gtrfs(3)
- lasdq(3)
- gglse(3)
- la_xisnan_la_isnan(3)
- unmr2(3)
- hetrs_aa(3)
- tpttr(3)
- gerz_comp_grp(3)
- potrf(3)
- hegv_driver(3)
- laqps(3)
- ggqr_comp_grp(3)
- ilalc(3)
- ung2r(3)
- heevd(3)
- pstf2(3)
- lacn2(3)
- ptrfs(3)
- ungrq(3)
- gelqf(3)
- ppsv_comp(3)
- blas2_full(3)
- gemlqt(3)
- unml2(3)
- tplqt(3)
- tpcon(3)
- getf2(3)
- ggbak(3)
- bdsvd_driver(3)
- lamch(3)
- gelq(3)
- gebal(3)
- laqr1(3)
- ptsvx(3)
- lahr2(3)
- larscl2(3)
- geqrt(3)
- larfb(3)
- gtsv_comp(3)
- gesvd_aux(3)
- hbevx_2stage(3)
- hbgvx(3)
- tprfs(3)
- params_grp(3)
- lahef(3)
- laqr_group(3)
- unmqr(3)
- tgsy2(3)
- tfsv_comp(3)
- ggls_driver_grp(3)
- geev(3)
- latrd(3)
- unbdb4(3)
- bbcsd(3)
- lange(3)
- gelq_comp3(3)
- gttrs(3)
- lasy2(3)
- hetf2_rook(3)
- gtsv(3)
- lalsd(3)
- lanhb(3)
- laqhb(3)
- hgeqz(3)
- gesvj(3)
- gsvj0(3)
- ungtsqr_row(3)
- gelq_comp1(3)
- gemmtr(3)
- pbequ(3)
- heev_driver(3)
- unhr_col(3)
- syconvf_rook(3)
- getc2(3)
- syconv(3)
- norm_grp(3)
- larrc(3)
- laqr4(3)
- posv_comp(3)
- geev_driver_grp(3)
- heev_comp(3)
- pfsv(3)
- trevc3(3)
- gesv_driver_grp(3)
- reflector_aux_grp(3)
- langt(3)
- lacrt(3)
- latdf(3)
- hetrs_aa_2stage(3)
- lamc1(3)
- hpev_driver(3)
- hegvd(3)
- pptri(3)
- geqrt3(3)
- gelqt3(3)
- lasd5(3)
- laeda(3)
- geqr(3)
- lamtsqr(3)
- heev(3)
- hpev_comp(3)
- larfg(3)
- blas2_grp(3)
- hesv_rook(3)
- laexc(3)
- hetrd(3)
- geesx(3)
- ppsvx(3)
- blas_top(3)
- gtts2(3)
- la_herpvgrw(3)
- hpevx(3)
- ggevx(3)
- lahqr(3)
- gelq_comp_grp(3)
- hesv_comp_v3(3)
- tplqt2(3)
- hpev(3)
- hbtrd(3)
- getrs(3)
- hecon_3(3)
- lasrt(3)
- lanhe(3)
- gesv_comp(3)
- gbequ(3)
- hetrf_rk(3)
- laqr3(3)
- heev_comp_grp(3)
- ungtsqr(3)
- ppcon(3)
- ggrq_comp_grp(3)
- larmm(3)
- ieeeck(3)
- geqrf(3)
- solve_aux_grp(3)
- herfs(3)
- posvx(3)
- posvxx(3)
- gges3(3)
- hbgvd(3)
- lantb(3)
- lasd_comp_grp(3)
- hpgvx(3)
- lapy2(3)
- lauu2(3)
- copy(3)
- getsqrhrt(3)
- stev_comp_grp(3)
- laev2(3)
- larfb_gett(3)
- trti2(3)
- laqz4(3)
- hegv_driver_grp(3)
- la_porfsx_extended(3)
- laruv(3)
- ggsvd_comp_grp(3)
- dot(3)
- gehd2(3)
- lanhf(3)
- hetri_rook(3)
- pfsv_comp(3)
- gbtrf(3)
- hpgst(3)
- getri(3)
- trevc(3)
- unmrz(3)
- hsein(3)
- lsamen(3)
- lasd6(3)
- trtri(3)
- ggglm(3)
- las2(3)
- latrs(3)
- lapll(3)
- gemlq(3)
- geqpf_comp_grp(3)
- stemr(3)
- rotm(3)
- disna(3)
- ggrqf(3)
- pptrf(3)
- lasd0(3)
- lals0(3)
- laqz2(3)
- hbev_driver2(3)
- geswlq_comp_grp(3)
- laqr0(3)
- trttp(3)
- stedc(3)
- lasq4(3)
- geev_comp_grp(3)
- ungbr(3)
- lanv2(3)
- hpsv(3)
- pprfs(3)
- gehrd(3)
- ppsv(3)
- lagtm(3)
- hpgv(3)
- trsv_comp(3)
- larfx(3)
- gesv_driver(3)
- gerfsx(3)
- la_geamv(3)
- laed9(3)
- tpqrt2(3)
- uncsd(3)
- gecs_comp_grp(3)
- bdsqr(3)
- hegv_comp_grp(3)
- labad(3)
- geqp3(3)
- gesvdq(3)
- tfttp(3)
- laln2(3)
- uncsd2by1(3)
- blas2_like_grp(3)
- latbs(3)
- hbgst(3)
- larrv(3)
- ilaenv2stage(3)
- bdsvdx(3)
- hegs2(3)
- lasq_comp_grp(3)
- hpr2(3)
- laqhe(3)
- larra(3)
- gemqrt(3)
- hbmv(3)
- hpsv_driver(3)
- lacp2(3)
- lapmt(3)
- gecon(3)
- unbdb5(3)
- la_gerpvgrw(3)
- tgex2(3)
- laqhp(3)
- tftri(3)
- getrf2(3)
- porfs(3)
- lartg(3)
- lagts(3)
- ggev_comp_grp(3)
- lasd3(3)
- geqr_comp2(3)
- laqz_group(3)
- pftri(3)
- hetri2x(3)
- lahef_aa(3)
- svd_driver_grp(3)
- gbsv_driver(3)
- hesv_comp_aasen2(3)
- laqtr(3)
- lag2(3)
- la_porcond(3)
- hbev(3)
- pbtrf(3)
- lascl(3)
- larr_comp_grp(3)
- hecon(3)
- pttrs(3)
- lasd8(3)
- lsame(3)
- unm2l(3)
- potrs(3)
- tptrs(3)
- lartv(3)
- trtrs(3)
- gsvj1(3)
- sum1(3)
- larrj(3)
- gbmv(3)
- posv(3)
- gghd3(3)
- geev_top(3)
- geqr_comp_grp(3)
- laset(3)
- hesvxx(3)
- posv_comp_grp(3)
- lahef_rk(3)
- lasd1(3)
- tprfb(3)
- potf2(3)
- laein(3)
- lamc4(3)
- stevd(3)
- gtsv_driver(3)
- gesvd_comp_grp(3)
- la_constants(3)
- gesvx(3)
- hseqr(3)
- launhr_col_getrfnp2(3)
- trcon(3)
- larre(3)
- gelsy(3)
- ptsv(3)
- lacon(3)
- laed_comp_grp(3)
- hpsvx(3)
- gemm(3)
- poequ(3)
- laesy(3)
- lagtf(3)
- trrfs(3)
- ggev3(3)
- pbstf(3)
- poequb(3)
- heevr(3)
- lanhp(3)
- unbdb3(3)
- tgsyl(3)
- lamc5(3)
- geqr2p(3)
- ungqr(3)
- laqz3(3)
- imax1(3)
- gels_top(3)
- hesv(3)
- gelqt(3)
- pfsv_driver(3)
- stegr(3)
- gerqf(3)
- laisnan(3)
- ilatrans(3)
- gbsv_comp(3)
- pbrfs(3)
- lascl2(3)
- larz(3)
- la_hercond(3)
- tgexc(3)
- ggesx(3)
- unbdb6(3)
- ungl2(3)
- laed_comp2(3)
- rscl(3)
- hegv(3)
- gelst(3)
- gbtrs(3)
- pftrf(3)
- langb(3)
- lantr(3)
- laqgb(3)
- ggsvp3(3)
- bdsdc(3)
- ladiv(3)
- laqge(3)
- iparmq(3)
- ggbal(3)
- hb2st_kernels(3)
- lartgs(3)
- lartgp(3)
- rot(3)
- ppequ(3)
- laed3(3)
- her(3)
- hptri(3)
- stevx(3)
- upgtr(3)
- lar2v(3)
- hbev_2stage(3)
- gejsv(3)
- ppsv_driver(3)
- unm22(3)
- gesvxx(3)
- laqz0(3)
- unmtr(3)
- laed5(3)
- tptri(3)
- laed0(3)
- heev_driver2(3)
- hpcon(3)
- lasd4(3)
- hetrf_aa(3)
- geqr_comp3(3)
- rot_aux_grp(3)
- aux_grp(3)
- laebz(3)
- trsyl3(3)
- gges(3)
- gesdd(3)
- trexc(3)
- ung2l(3)
- gesv(3)
- laed4(3)
- md__r_e_a_d_m_e(3)
- blas3_like_grp(3)
- laed1(3)
- larcm(3)
- hbevx(3)
- hesv_driver_grp(3)
- hetrs(3)
- hbevd_2stage(3)
- blas1_grp(3)
- laic1(3)
- geql_comp_grp(3)
- heev_2stage(3)
- hpmv(3)
- pbtf2(3)
- hetrf_aa_2stage(3)
- hbgv(3)
- pptrs(3)
- lapmr(3)
- tpqr_comp_grp(3)
- larfy(3)
- gedmd(3)
- lasr(3)
- hetrd_2stage(3)
- gerfs(3)
- ungtr(3)
- porfsx(3)
- tpmv(3)
- lasd_comp2(3)
- unmbr(3)
- tbtrs(3)
- hetd2(3)
- trsv_comp_grp(3)
- lapy3(3)
- ptts2(3)
- unmhr(3)
- hbev_driver(3)
- lalsa(3)
- tbsv_comp(3)
- hesv_comp_v1(3)
- geql2(3)
- sterf(3)
- larrd(3)
- larft(3)
- lagv2(3)
- gttrf(3)
- tpqrt(3)
- la_lin_berr(3)
- rotg(3)
- solve_top(3)
- lacgv(3)
- larrf(3)
- tbmv(3)
- trsyl(3)
- geequ(3)
- upmtr(3)
- hpgv_driver(3)
- tbsv(3)
- hesvx(3)
- latrz(3)
- tfttr(3)
- gesv_comp_grp(3)
- xerbla_grp(3)
- tpsv(3)
- blas3_grp(3)
- gesvd_driver(3)
- geqr_comp1(3)
- ggev_driver_grp(3)
- la_gbamv(3)
- tpmlqt(3)
- trttf(3)
- larzb(3)
- unmr3(3)
- hecon_rook(3)
- stebz(3)
- lantp(3)
- laqz1(3)
- hesv_rk(3)
- tbcon(3)
- xerbla(3)
- posv_mixed(3)
- latps(3)
- hesv_aa_driver(3)
- gemqr(3)
- larrr(3)
- gebrd(3)
- tgsna(3)
- la_gercond(3)
- gbsv(3)
- hesv_comp_grp(3)
- gesv_mixed(3)
- gghrd(3)
- gbrfs(3)
- tpmqrt(3)
- lasq3(3)
- tpsv_comp(3)
- largv(3)
- gelsd(3)
- pftrs(3)
- asum(3)
- launhr_col_getrfnp(3)
- hptrf(3)
- lacpy(3)
- gesc2(3)
- lasda(3)
- second(3)
- hprfs(3)
- hpsv_comp(3)
- lamrg(3)
- pbsv_comp(3)
- hegv_2stage(3)
- gerq2(3)
- lasdt(3)
- abs1(3)
- hbevd(3)
- hbev_comp(3)
- trsv(3)
- la_porpvgrw(3)
- la_gbrpvgrw(3)
- hbgv_driver(3)
- tgsja(3)
- gebd2(3)
- geqr2(3)
- unm2r(3)
- unmql(3)
- la_gbrfsx_extended(3)
- gelq_comp2(3)
- iparam2stage(3)
- ger(3)
- larf(3)
- ilaprec(3)
- labrd(3)
- unbdb1(3)
- unmlq(3)
- geequb(3)
- la_herfsx_extended(3)
- unbdb2(3)
- lapack_top(3)
- ptsv_driver(3)
- hetrs2(3)
- geqr_comp4(3)
- pbsv(3)
- posv_driver(3)
- steqr(3)
- gels(3)
- lar1v(3)
- hemv(3)
- la_transtype(3)
- hesv_aa(3)
- lacrm(3)
- stevr(3)
- hetf2_rk(3)
- blas2_banded(3)
- stein(3)
- unmrq(3)
- larrk(3)
- hetri2(3)
- hesv_aa_2stage(3)
- pttrf(3)
- gelss(3)
- pbsv_driver(3)
- lasq5(3)
- heevx_2stage(3)
- hetri(3)
- lasd2(3)
- laed2(3)
- pbcon(3)
- ptcon(3)
- laed7(3)
- gels_aux_grp(3)
- hpgvd(3)
- hetf2(3)
- tzrzf(3)
- hpr(3)
- unitary_top(3)
- latsqr(3)
- ungql(3)
- her2(3)
- hetri_3x(3)
- hetrd_hb2st(3)
- tgsen(3)
- ggsvd3(3)
- lasq6(3)
- set_grp(3)
- larfgp(3)
- gels_driver_grp(3)
- pbtrs(3)
- lamswlq(3)
- lanht(3)
- gbsvxx(3)
- tgevc(3)
- ilaenv(3)
- swap(3)
- lae2(3)
- iladiag(3)
- lasq2(3)
- la_heamv(3)
- blas_like_top(3)
- la_gerfsx_extended(3)
- hegst(3)
- tfsm(3)
- gesvd(3)
- ungr2(3)
- ggev(3)
- aux_top(3)
- blas2_packed(3)
- geqlf(3)
- hetrs_rook(3)
- gelq2(3)
- geqrfp(3)
- gbequb(3)
- stev(3)
- lauum(3)
- potrf2(3)
- lamc3(3)
- gbrfsx(3)
- gerq_comp_grp(3)
- pocon(3)
- tbrfs(3)
- heswapr(3)
- lamc2(3)
- hpevd(3)
- hesv_comp_aasen(3)
- scalar_grp(3)
- gemv(3)
- lasv2(3)
- lanhs(3)
- svd_top(3)
- gbsvx(3)
- gesvdx(3)
- tplq_comp_grp(3)
- hesv_driver(3)
- hesv_comp_v2(3)
- trsen(3)
- syconvf(3)
- lasd7(3)
- gbcon(3)
- unbdb(3)
- heev_driver_grp(3)
- ggqrf(3)
- heevx(3)
- gtsvx(3)
- lahef_rook(3)
- hetrf_rook(3)
- hetrf(3)
- trsna(3)
- gebak(3)
- larnv(3)
- ptsv_comp(3)
- laswlq(3)
- lags2(3)
- laed8(3)
- laswp(3)
- hptrs(3)
- unglq(3)
- la_wwaddw(3)
- getrf(3)
- gees(3)
- gbtf2(3)
- hegvx(3)
- latrs3(3)
- roundup_lwork(3)
- unghr(3)
- iamax(3)
- larzt(3)
- pteqr(3)
- ilaver(3)
- trmv(3)
- la_gbrcond(3)
- blas0_like_grp(3)
- nrm2(3)
- heev_top(3)
- gtcon(3)
- heevr_2stage(3)
- pstrf(3)
- rot_comp(3)
- laqr5(3)
- heevd_2stage(3)
- getsls(3)
- hetrd_he2hb(3)
- heequb(3)
- laqp2(3)
- axpy(3)
- blast_aux(3)
- rotmg(3)
- pbsvx(3)
- ilauplo(3)
- herfsx(3)
- laqr2(3)
- blas1_like_grp(3)
- lassq(3)
- larrb(3)
- stev_driver(3)
- geevx(3)
- tpttf(3)
- scal(3)
- laneg(3)
- posv_driver_grp(3)
- lasq1(3)
- hetrs_3(3)
- geqrt2(3)
- gbbrd(3)
- ilalr(3)
- hetri_3(3)
apt-get install liblapack-doc
Manual
herfs
NAMESYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cherfs (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,integer ldaf, integer, dimension( * ) ipiv, complex, dimension( ldb, *) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real,dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * )work, real, dimension( * ) rwork, integer info)
subroutine csyrfs (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,integer ldaf, integer, dimension( * ) ipiv, complex, dimension( ldb, *) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real,dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * )work, real, dimension( * ) rwork, integer info)
subroutine dsyrfs (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,double precision, dimension( ldb, * ) b, integer ldb, double precision,dimension( ldx, * ) x, integer ldx, double precision, dimension( * )ferr, double precision, dimension( * ) berr, double precision,dimension( * ) work, integer, dimension( * ) iwork, integer info)
subroutine ssyrfs (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,dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * )work, integer, dimension( * ) iwork, integer info)
subroutine zherfs (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, integerldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)
subroutine zsyrfs (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, integerldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)
Author
NAME
herfs - {he,sy}rfs: iterative refinement
SYNOPSIS
Functions
subroutine
cherfs
(uplo, n, nrhs, a, lda, af, ldaf, ipiv, b,
ldb, x, ldx, ferr, berr, work, rwork, info)
CHERFS
subroutine
csyrfs
(uplo, n, nrhs, a, lda, af, ldaf,
ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CSYRFS
subroutine
dsyrfs
(uplo, n, nrhs, a, lda, af, ldaf,
ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DSYRFS
subroutine
ssyrfs
(uplo, n, nrhs, a, lda, af, ldaf,
ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SSYRFS
subroutine
zherfs
(uplo, n, nrhs, a, lda, af, ldaf,
ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZHERFS
subroutine
zsyrfs
(uplo, n, nrhs, a, lda, af, ldaf,
ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZSYRFS
Detailed Description
Function Documentation
subroutine cherfs (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,integer ldaf, integer, dimension( * ) ipiv, complex, dimension( ldb, *) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real,dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * )work, real, dimension( * ) rwork, integer info)
CHERFS
Purpose:
CHERFS improves
the computed solution to a system of linear
equations when the coefficient matrix is Hermitian
indefinite, and
provides error bounds and backward error estimates for the
solution.
Parameters
UPLO
UPLO is
CHARACTER*1
= āUā: Upper triangle of A is stored;
= āLā: Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A
A is COMPLEX
array, dimension (LDA,N)
The Hermitian matrix A. If UPLO = āUā, 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 = āLā, 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
AF
AF is COMPLEX
array, dimension (LDAF,N)
The factored form of the matrix A. AF contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**H or
A = L*D*L**H as computed by CHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
IPIV
IPIV is INTEGER
array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.
B
B is COMPLEX
array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X
X is COMPLEX
array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CHETRS.
On exit, the improved solution matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
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.
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).
WORK
WORK is COMPLEX array, dimension (2*N)
RWORK
RWORK is REAL array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value
Internal Parameters:
ITMAX is the maximum number of steps of iterative refinement.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine csyrfs (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,integer ldaf, integer, dimension( * ) ipiv, complex, dimension( ldb, *) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real,dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * )work, real, dimension( * ) rwork, integer info)
CSYRFS
Purpose:
CSYRFS improves
the computed solution to a system of linear
equations when the coefficient matrix is symmetric
indefinite, and
provides error bounds and backward error estimates for the
solution.
Parameters
UPLO
UPLO is
CHARACTER*1
= āUā: Upper triangle of A is stored;
= āLā: Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A
A is COMPLEX
array, dimension (LDA,N)
The symmetric matrix A. If UPLO = āUā, 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 = āLā, 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
AF
AF is COMPLEX
array, dimension (LDAF,N)
The factored form of the matrix A. AF 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 CSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
IPIV
IPIV is INTEGER
array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF.
B
B is COMPLEX
array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X
X is COMPLEX
array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CSYTRS.
On exit, the improved solution matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
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.
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).
WORK
WORK is COMPLEX array, dimension (2*N)
RWORK
RWORK is REAL array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value
Internal Parameters:
ITMAX is the maximum number of steps of iterative refinement.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dsyrfs (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,double precision, dimension( ldb, * ) b, integer ldb, double precision,dimension( ldx, * ) x, integer ldx, double precision, dimension( * )ferr, double precision, dimension( * ) berr, double precision,dimension( * ) work, integer, dimension( * ) iwork, integer info)
DSYRFS
Purpose:
DSYRFS improves
the computed solution to a system of linear
equations when the coefficient matrix is symmetric
indefinite, and
provides error bounds and backward error estimates for the
solution.
Parameters
UPLO
UPLO is
CHARACTER*1
= āUā: Upper triangle of A is stored;
= āLā: Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A
A is DOUBLE
PRECISION array, dimension (LDA,N)
The symmetric matrix A. If UPLO = āUā, 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 = āLā, 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
AF
AF is DOUBLE
PRECISION array, dimension (LDAF,N)
The factored form of the matrix A. AF 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 DSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
IPIV
IPIV is INTEGER
array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSYTRF.
B
B is DOUBLE
PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X
X is DOUBLE
PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DSYTRS.
On exit, the improved solution matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
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.
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).
WORK
WORK is DOUBLE PRECISION array, dimension (3*N)
IWORK
IWORK is INTEGER array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value
Internal Parameters:
ITMAX is the maximum number of steps of iterative refinement.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine ssyrfs (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,dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * )work, integer, dimension( * ) iwork, integer info)
SSYRFS
Purpose:
SSYRFS improves
the computed solution to a system of linear
equations when the coefficient matrix is symmetric
indefinite, and
provides error bounds and backward error estimates for the
solution.
Parameters
UPLO
UPLO is
CHARACTER*1
= āUā: Upper triangle of A is stored;
= āLā: Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A
A is REAL
array, dimension (LDA,N)
The symmetric matrix A. If UPLO = āUā, 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 = āLā, 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
AF
AF is REAL
array, dimension (LDAF,N)
The factored form of the matrix A. AF 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.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
IPIV
IPIV is INTEGER
array, dimension (N)
Details of the interchanges and the block structure of D
as determined by SSYTRF.
B
B is REAL
array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X
X is REAL
array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SSYTRS.
On exit, the improved solution matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
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.
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).
WORK
WORK is REAL array, dimension (3*N)
IWORK
IWORK is INTEGER array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value
Internal Parameters:
ITMAX is the maximum number of steps of iterative refinement.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zherfs (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, integerldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)
ZHERFS
Purpose:
ZHERFS improves
the computed solution to a system of linear
equations when the coefficient matrix is Hermitian
indefinite, and
provides error bounds and backward error estimates for the
solution.
Parameters
UPLO
UPLO is
CHARACTER*1
= āUā: Upper triangle of A is stored;
= āLā: Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A
A is COMPLEX*16
array, dimension (LDA,N)
The Hermitian matrix A. If UPLO = āUā, 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 = āLā, 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
AF
AF is
COMPLEX*16 array, dimension (LDAF,N)
The factored form of the matrix A. AF contains the block
diagonal matrix D and the multipliers used to obtain the
factor U or L from the factorization A = U*D*U**H or
A = L*D*L**H as computed by ZHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
IPIV
IPIV is INTEGER
array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF.
B
B is COMPLEX*16
array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X
X is COMPLEX*16
array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZHETRS.
On exit, the improved solution matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
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.
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).
WORK
WORK is COMPLEX*16 array, dimension (2*N)
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value
Internal Parameters:
ITMAX is the maximum number of steps of iterative refinement.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zsyrfs (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, integerldx, double precision, dimension( * ) ferr, double precision,dimension( * ) berr, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)
ZSYRFS
Purpose:
ZSYRFS improves
the computed solution to a system of linear
equations when the coefficient matrix is symmetric
indefinite, and
provides error bounds and backward error estimates for the
solution.
Parameters
UPLO
UPLO is
CHARACTER*1
= āUā: Upper triangle of A is stored;
= āLā: Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A
A is COMPLEX*16
array, dimension (LDA,N)
The symmetric matrix A. If UPLO = āUā, 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 = āLā, 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
AF
AF is
COMPLEX*16 array, dimension (LDAF,N)
The factored form of the matrix A. AF 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.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >=
max(1,N).
IPIV
IPIV is INTEGER
array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSYTRF.
B
B is COMPLEX*16
array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >=
max(1,N).
X
X is COMPLEX*16
array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZSYTRS.
On exit, the improved solution matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >=
max(1,N).
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.
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).
WORK
WORK is COMPLEX*16 array, dimension (2*N)
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal
value
Internal Parameters:
ITMAX is the maximum number of steps of iterative refinement.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author
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