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。