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夏休みはもうおわり。

LAPACK 計算ルーチン(Computational Routines) を一覧にしてみる。

ここの配架にあるルーチンを一覧表にする。

連立一次方程式
Linear Equations

Type of matrix
and
storage scheme
Operation YY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
general factorize GE TRF SGETRF CGETRF DGETRF ZGETRF
solve using factorization GE TRS SGETRS CGETRS DGETRS ZGETRS
estimate condition number GE CON SGECON CGECON DGECON ZGECON
error bounds for solution GE RFS SGERFS CGERFS DGERFS ZGERFS
invert using factorization GE TRI SGETRI CGETRI DGETRI ZGETRI
equilibrate GE EQU SGEEQU CGEEQU DGEEQU ZGEEQU
general factorize GB TRF SGBTRF CGBTRF DGBTRF ZGBTRF
band solve using factorization GB TRS SGBTRS CGBTRS DGBTRS ZGBTRS
estimate condition number GB CON SGBCON CGBCON DGBCON ZGBCON
error bounds for solution GB RFS SGBRFS CGBRFS DGBRFS ZGBRFS
equilibrate GB EQU SGBEQU CGBEQU DGBEQU ZGBEQU
general factorize GT TRF SGTTRF CGTTRF DGTTRF ZGTTRF
tridiagonal solve using factorization GT TRS SGTTRS CGTTRS DGTTRS ZGTTRS
estimate condition number GT CON SGTCON CGTCON DGTCON ZGTCON
error bounds for solution GT RFS SGTRFS CGTRFS DGTRFS ZGTRFS
symmetric/Hermitian factorize PO TRF SPOTRF CPOTRF DPOTRF ZPOTRF
positive definite solve using factorization PO TRS SPOTRS CPOTRS DPOTRS ZPOTRS
estimate condition number PO CON SPOCON CPOCON DPOCON ZPOCON
error bounds for solution PO RFS SPORFS CPORFS DPORFS ZPORFS
invert using factorization PO TRI SPOTRI CPOTRI DPOTRI ZPOTRI
equilibrate PO EQU SPOEQU CPOEQU DPOEQU ZPOEQU
symmetric/Hermitian factorize PP TRF SPPTRF CPPTRF DPPTRF ZPPTRF
positive definite solve using factorization PP TRS SPPTRS CPPTRS DPPTRS ZPPTRS
(packed storage) estimate condition number PP CON SPPCON CPPCON DPPCON ZPPCON
error bounds for solution PP RFS SPPRFS CPPRFS DPPRFS ZPPRFS
invert using factorization PP TRI SPPTRI CPPTRI DPPTRI ZPPTRI
equilibrate PP EQU SPPEQU CPPEQU DPPEQU ZPPEQU
symmetric/Hermitian factorize PB TRF SPBTRF CPBTRF DPBTRF ZPBTRF
positive definite solve using factorization PB TRS SPBTRS CPBTRS DPBTRS ZPBTRS
band estimate condition number PB CON SPBCON CPBCON DPBCON ZPBCON
error bounds for solution PB RFS SPBRFS CPBRFS DPBRFS ZPBRFS
equilibrate PB EQU SPBEQU CPBEQU DPBEQU ZPBEQU
symmetric/Hermitian factorize PT TRF SPTTRF CPTTRF DPTTRF ZPTTRF
positive definite solve using factorization PT TRS SPTTRS CPTTRS DPTTRS ZPTTRS
tridiagonal estimate condition number PT CON SPTCON CPTCON DPTCON ZPTCON
error bounds for solution PT RFS SPTRFS CPTRFS DPTRFS ZPTRFS
symmetric/Hermitian factorize HE TRF SSYTRF CHETRF DSYTRF ZHETRF
indefinite solve using factorization HE TRS SSYTRS CHETRS DSYTRS ZHETRS
estimate condition number HE CON SSYCON CHECON DSYCON ZHECON
error bounds for solution HE RFS SSYRFS CHERFS DSYRFS ZHERFS
invert using factorization HE TRI SSYTRI CHETRI DSYTRI ZHETRI
complex symmetric factorize SY TRF --- CSYTRF --- ZSYTRF
solve using factorization SY TRS --- CSYTRS --- ZSYTRS
estimate condition number SY CON --- CSYCON --- ZSYCON
error bounds for solution SY RFS --- CSYRFS --- ZSYRFS
invert using factorization SY TRI --- CSYTRI --- ZSYTRI
symmetric/Hermitian factorize HP TRF SSPTRF CHPTRF DSPTRF ZHPTRF
indefinite solve using factorization HP TRS SSPTRS CHPTRS DSPTRS ZHPTRS
(packed storage) estimate condition number HP CON SSPCON CHPCON DSPCON ZHPCON
error bounds for solution HP RFS SSPRFS CHPRFS DSPRFS ZHPRFS
invert using factorization HP TRI SSPTRI CHPTRI DSPTRI ZHPTRI
complex symmetric factorize SP TRF --- CSPTRF --- ZSPTRF
(packed storage) solve using factorization SP TRS --- CSPTRS --- ZSPTRS
estimate condition number SP CON --- CSPCON --- ZSPCON
error bounds for solution SP RFS --- CSPRFS --- ZSPRFS
invert using factorization SP TRI --- CSPTRI --- ZSPTRI
triangular solve TR TRS STRTRS CTRTRS DTRTRS ZTRTRS
estimate condition number TR CON STRCON CTRCON DTRCON ZTRCON
error bounds for solution TR RFS STRRFS CTRRFS DTRRFS ZTRRFS
invert TR TRI STRTRI CTRTRI DTRTRI ZTRTRI
triangular solve TP TRS STPTRS CTPTRS DTPTRS ZTPTRS
(packed storage) estimate condition number TP CON STPCON CTPCON DTPCON ZTPCON
error bounds for solution TP RFS STPRFS CTPRFS DTPRFS ZTPRFS
invert TP TRI STPTRI CTPTRI DTPTRI ZTPTRI
triangular solve TB TRS STBTRS CTBTRS DTBTRS ZTBTRS
band estimate condition number TB CON STBCON CTBCON DTBCON ZTBCON
error bounds for solution TB RFS STBRFS CTBRFS DTBRFS ZTBRFS

その他の因数分解
Other Factorizations

Type of matrix
and
storage scheme
Operation YY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
QR, general factorize with pivoting GE QP3 SGEQP3 CGEQP3 DGEQP3 ZGEQP3
factorize, no pivoting GE QRF SGEQRF CGEQRF DGEQRF ZGEQRF
generate Q OR GQR SORGQR CUNGQR DORGQR ZUNGQR
multiply matrix by Q OR MQR SORMQR CUNMQR DORMQR ZUNMQR
LQ, general factorize, no pivoting GE LQF SGELQF CGELQF DGELQF ZGELQF
generate Q OR GLQ SORGLQ CUNGLQ DORGLQ ZUNGLQ
multiply matrix by Q OR MLQ SORMLQ CUNMLQ DORMLQ ZUNMLQ
QL, general factorize, no pivoting GE QLF SGEQLF CGEQLF DGEQLF ZGEQLF
generate Q OR GQL SORGQL CUNGQL DORGQL ZUNGQL
multiply matrix by Q OR MQL SORMQL CUNMQL DORMQL ZUNMQL
RQ, general factorize, no pivoting GE RQF SGERQF CGERQF DGERQF ZGERQF
generate Q OR GRQ SORGRQ CUNGRQ DORGRQ ZUNGRQ
multiply matrix by Q OR MRQ SORMRQ CUNMRQ DORMRQ ZUNMRQ
RZ, trapezoidal factorize, no pivoting
(blocked algorithm)
TZ RZF STZRZF CTZRZF DTZRZF ZTZRZF
multiply matrix by Q OR MRZ SORMRZ CUNMRZ DORMRZ ZUNMRZ

対称固有値問題
Symmetric Eigenproblems

Type of matrix
and
storage scheme
Operation YY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
dense symmetric
(or Hermitian)
tridiagonal reduction SY TRD SSYTRD CHETRD DSYTRD ZHETRD
packed symmetric
(or Hermitian)
tridiagonal reduction SP TRD SSPTRD CHPTRD DSPTRD ZHPTRD
band symmetric
(or Hermitian)
tridiagonal reduction SB TRD SSBTRD CHBTRD DSBTRD ZHBTRD
orthogonal/unitary generate matrix after
reduction by xSYTRD
OR GTR SORGTR CUNGTR DORGTR ZUNGTR
multiply matrix after
reduction by xSYTRD
OR MTR SORMTR CUNMTR DORMTR ZUNMTR
orthogonal/unitary
(packed storage)
generate matrix after
reduction by xSPTRD
OP GTR SOPGTR CUPGTR DOPGTR ZUPGTR
multiply matrix after
reduction by xSPTRD
OP MTR SOPMTR CUPMTR DOPMTR ZUPMTR
symmetric
tridiagonal
eigenvalues/
eigenvectors via QR
ST EQR SSTEQR CSTEQR DSTEQR ZSTEQR
eigenvalues only
via root-free QR
ST ERF SSTERF --- DSTERF ---
eigenvalues/
eigenvectors via
divide and conquer
ST EDC SSTEDC CSTEDC DSTEDC ZSTEDC
eigenvalues/
eigenvectors via
RRR
ST EGR SSTEGR CSTEGR DSTEGR ZSTEGR
eigenvalues only
via bisection
ST EBZ SSTEBZ --- DSTEBZ ---
eigenvectors by
inverse iteration
ST EIN SSTEIN CSTEIN DSTEIN ZSTEIN
symmetric
tridiagonal
positive definite
eigenvalues/
eigenvectors
PT EQR SPTEQR CPTEQR DPTEQR ZPTEQR

不変部分空間と条件数
Invariant Subspaces and Condition Numbers

Type of matrix
and
storage scheme
Operation YY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
general Hessenberg reduction GE HRD SGEHRD CGEHRD DGEHRD ZGEHRD
balancing GE BAL SGEBAL CGEBAL DGEBAL ZGEBAL
backtransforming GE BAK SGEBAK CGEBAK DGEBAK ZGEBAK
orthogonal/unitary generate matrix after
Hessenberg reduction
OR GHR SORGHR CUNGHR DORGHR ZUNGHR
multiply matrix after
Hessenberg reduction
OR MHR SORMHR CUNMHR DORMHR ZUNMHR
Hessenberg Schur factorization HS EQR SHSEQR CHSEQR DHSEQR ZHSEQR
eigenvectors by
inverse iteration
HS EIN SHSEIN CHSEIN DHSEIN ZHSEIN
(quasi)triangular eigenvectors TR EVC STREVC CTREVC DTREVC ZTREVC
reordering Schur
factorization
TR EXC STREXC CTREXC DTREXC ZTREXC
Sylvester equation TR SYL STRSYL CTRSYL DTRSYL ZTRSYL
condition numbers of
eigenvalues/vectors
TR SNA STRSNA CTRSNA DTRSNA ZTRSNA
condition numbers of
eigenvalue cluster/
invariant subspace
TR SEN STRSEN CTRSEN DTRSEN ZTRSEN

特異値分解
Singular Value Decomposition

Type of matrix
and
storage scheme
Operation YY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
general bidiagonal reduction GE BRD SGEBRD CGEBRD DGEBRD ZGEBRD
general band bidiagonal reduction GB BRD SGBBRD CGBBRD DGBBRD ZGBBRD
orthogonal/unitary generate matrix after
bidiagonal reduction
OR GBR SORGBR CUNGBR DORGBR ZUNGBR
multiply matrix after
bidiagonal reduction
OR MBR SORMBR CUNMBR DORMBR ZUNMBR
bidiagonal SVD using
QR or dqds
BD SQR SBDSQR CBDSQR DBDSQR ZBDSQR
SVD using
divide-and-conquer
BD SDC SBDSDC --- DBDSDC ---

一般対称明確な固有値問題
Generalized Symmetric Definite Eigenproblems

Type of matrix
and
storage scheme
Operation YY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
symmetric/Hermitian reduction SY GST SSYGST CHEGST DSYGST ZHEGST
symmetric/Hermitian
(packed storage)
reduction SP GST SSPGST CHPGST DSPGST ZHPGST
symmetric/Hermitian
banded
split Cholesky
factorization
PB STF SPBSTF CPBSTF DPBSTF ZPBSTF
reduction SB GST SSBGST DSBGST CHBGST ZHBGST

収縮部分空間と条件数
Deflating Subspaces and Condition Numbers

Type of matrix
and
storage scheme
Operation YY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
general Hessenberg reduction GG HRD SGGHRD CGGHRD DGGHRD ZGGHRD
balancing GG BAL SGGBAL CGGBAL DGGBAL ZGGBAL
back transforming GG BAK SGGBAK CGGBAK DGGBAK ZGGBAK
Hessenberg
(quasi)triangular
Schur factorization HG EQZ SHGEQZ CHGEQZ DHGEQZ ZHGEQZ
eigenvectors TG EVC STGEVC CTGEVC DTGEVC ZTGEVC
reordering
Schur decomposition
TG EXC STGEXC CTGEXC DTGEXC ZTGEXC
Sylvester equation TG SYL STGSYL CTGSYL DTGSYL ZTGSYL
condition numbers of eigenvalues/vectors TG SNA STGSNA CTGSNA DTGSNA ZTGSNA
condition numbers of
eigenvalue cluster/
deflating subspaces
TG SEN STGSEN CTGSEN DTGSEN ZTGSEN

一般(or 商)特異値分解
Generalized (or Quotient) Singular Value Decomposition

Type of matrix
and
storage scheme
Operation YYY ZZZ 単精度
実数
単精度
素数
倍精度
実数
倍精度
素数
??? triangular reduction of A and B GG SVP SGGSVP CGGSVP DGGSVP ZGGSVP
??? GSVD of a pair of triangular matrices TG SJA STGSJA CTGSJA DTGSJA ZTGSJA

おわり

129個の命令があります。 なかなかな数ですね。