Routines for BLAS, LAPACK, MAGMA

This re-organizes the LAPACK routines list by task, with a brief note indicating what each routine does. It also includes links to the Fortran 95 generic interfaces for driver subroutines. Not all “BLAS” routines are actually in BLAS; some are LAPACK extensions that functionally fit in the BLAS.

BLAS and LAPACK guides are available from http://www.icl.utk.edu/~mgates3/docs/
Copyright © 2007–2017 by Mark Gates. Updated April 2017.
You may freely copy and modify this document under the Creative Commons Attribution license.
When distributing, please include the above link and copyright for this original document.

Level 1 BLAS
Level 2 BLAS		(packed,	banded)
Level 3 BLAS
BLAS-like operations
Matrix norms
Linear systems
	LU	(	banded,	tridiagonal)
	Cholesky	(packed,	banded,	tridiagonal)
	LDL	(packed,	banded,	tridiagonal)
	triangular	(packed,	banded)
Linear least squares
	QR, RQ, QL, LQ, RZ factorizations
Symmetric eigenvalue		(packed,	banded,	tridiagonal)
Non-symmetric eigenvalue
SVD
Auxiliary
Unclassified
Deprecated

Data type prefix

s	real	float
d	double precision	double
c	complex	float complex
z	complex*16	double complex

Matrix type prefix

Headers are color coded by matrix type

	full	banded	packed	tridiag	generalized problem
general	ge	gb		gt	gg
symmetric	sy	sb	sp	st
Hermitian	he	hb	hp	ht
SPD/HPD	po	pb	pp	pt
triangular	tr	tb	tp		tg
upper Hessenberg	hs				hg
trapezoidal	tz
orthogonal	or	op
unitary	un	up
diagonal	di
bidiagonal	bd

Types				Routine	MAGMA		Matrix type	Description	Flops	Data
Level 1 BLAS
s	d	c	z	axpy		cublas	vector	add vectors, y = αx + y	2n	2n
s	d	c	z	copy		cublas	vector	copy vector, y = x	0	2n
s	d	c	z	swap	magma	cublas	vector	swap vectors	0	2n
s	d	c	z	dot[c]		cublas	vector	dot product, x^H y	2n	2n
		c	z	dotu		cublas	vector	dot product, unconjugated x^T y	2n	2n
sds	ds			dot		—	vector	dot product, extended precision	2n	2n
s	d	c	z	scal		cublas	vector	scale vector, y = αy	n	n
		cs	zd	scal		cublas	vector	scale vector by single/double	n	n
s	d	cs	zd	rscl		—	vector	scale vector by reciprocal, y = y / α(lapack)	n	n
s	d	c	z	rot		cublas	vector	apply Givens plane rotation	6n	2n
		cs	zd	drot		cublas	vector	apply Givens plane rotation	6n	2n
s	d	c	z	rotg		—		generate plane rotation	O(1)	O(1)
s	d	c	z	lartg				slower, more accurate version of rotg	O(1)	O(1)
s	d			rotm		cublas	vector	apply modified plane rotation	6n	2n
s	d			rotmg		cublas		generate modified plane rotation	O(1)	O(1)
s	d	sc	dz	nrm2	magma	cublas	vector	vector 2-norm, \|\|x\|\|₂	2n	n
s	d	sc	dz	asum		cublas	vector	vector 1-norm (pseudo), \|\| Re(x) \|\|₁ + \|\| Im(x) \|\|₁	n	n
		sc	dz	sum1		—	vector	vector 1-norm (true), \|\|x\|\|₁ (lapack)	2n	n
is	id	ic	iz	amax		cublas	vector	vector inf-norm (pseudo), index with max abs value, argmax_i \| Re(x_i) \| + \| Im(x_i) \|	n	n
		ic	iz	max1		—	vector	vector inf-norm (true), index with real part has max abs value, argmax_i \| Re(x_i) \| (lapack)	n	n
		c	z	lacgv		—	vector	conjugate vector (lapack)	n	n

Level 2 BLAS
s	d	c	z	gemv	magma	cublas	general	matrix-vector multiply, y = αAx + βy	2mn	mn
s	d	c	z	sy/hemv	magma, mgpu	cublas	Hermitian		2n²	n²
		c	z	symv	magma	—	complex-symmetric (in lapack)
s	d	c	z	trmv		cublas	triangular
s	d	c	z	sy/her		cublas	Hermitian	rank 1 update, A = αxx^T + A
		c	z	syr			complex-symmetric (in lapack)	rank 1 update, A = αxx^T + A
s	d	c	z	ger/gerc		cublas	general	rank 1 update, conjugated, A = αxy^H + A
		c	z	geru		cublas	general	rank 1 update, unconjugated, A = αxy^T + A
s	d	c	z	sy/her2		cublas	Hermitian	rank 2 update, A = αxy^H + conj(α) yx^H + A
s	d	c	z	trsv	magma	cublas	triangular	triangular solve Tx = b
Level 2 BLAS — packed
s	d	c	z	sp/hpmv			Hermitian packed	matrix-vector multiply, y = αAx + βy
		c	z	spmv			complex-symmetric packed
s	d	c	z	tpmv			triangular packed
s	d	c	z	sp/hpr			Hermitian packed	rank 1 update, A = αxx^H + A
		c	z	spr			complex-symmetric packed (in lapack)	rank 1 update, A = αxx^H + A
s	d	c	z	sp/hpr2			Hermitian packed	rank 2 update, A = αxy^H + conj(α)yx^H + A
s	d	c	z	tpsv			triangular packed	triangular solve Tx = b
Level 2 BLAS — banded
s	d	c	z	gbmv			general banded	matrix-vector multiply, y = αAx + βy
s	d	c	z	sb/hbmv			Hermitian banded
s	d	c	z	tbmv			triangular banded
s	d	c	z	tbsv			triangular banded	triangular solve Tx = b

Level 3 BLAS
s	d	c	z	gemm	magma	cublas	general	matrix-matrix multiply, C = αAB + βC
s	d	c	z	sy/hemm	mgpu	cublas	Hermitian
		c	z	symm		cublas	complex-symmetric
s	d	c	z	trmm		cublas	triangular
s	d	c	z	trsm	magma	cublas	triangular	triangular solve multiple rhs, TX = αB
s	d	c	z	sy/herk		cublas	Hermitian	rank k update, C = αAA^H + βC
		c	z	syrk		cublas	complex-symmetric	rank k update, C = αAA^H + βC
s	d	c	z	sy/her2k		cublas	Hermitian	rank 2k update, C = αAB^H + conj(α)BA^H + βC
		c	z	syr2k		cublas	complex-symmetric	rank 2k update, C = αAB^H + conj(α)BA^H + βC

BLAS-like operations (lapack)
s	d	c	z	lascl	magma		various	scale matrix, A = αA where α = to/from
s	d	c	z	lacpy	magma		general or triangular	copy matrix
		c	z	lacp2			general or triangular	copy real to complex matrix
sd	ds	cz	zc	_lag2_	magma		general	convert precisions (single to double, etc.)
sd	ds	cz	zc	_lat2_	magma		triangular	convert precisions (single to double, etc.)
s	d	c	z	larnv	—		vector	random numbers, uniform or normal distribution
s	d			laruv	—		vector	random numbers, uniform (called by larnv)
s	d	c	z	laset	magma		general or triangular	set matrix to constant alpha, and beta on diagonal

Matrix norm (lapack)
s	d	c	z	lange	magma		general	one-norm, inf-norm, Frobenius norm, or max absolute element
s	d	c	z	lanhs			Hessenberg
s	d	c	z	lanhe	magma		Hermitian
		c	z	lansy			complex-symmetric
s	d	c	z	lantr	magma		triangular / trapezoidal
Matrix norm (lapack) — packed
s	d	c	z	lanhp			Hermitian packed	one-norm, inf-norm, Frobenius norm, or max absolute element
		c	z	lansp			complex-symmetric packed
s	d	c	z	lantb			triangular banded
s	d	c	z	lantp			triangular packed
Matrix norm (lapack) — banded
s	d	c	z	langb			general banded	one-norm, inf-norm, Frobenius norm, or max absolute element
		c	z	lanhb			Hermitian banded
		c	z	lansb			complex-symmetric banded
Matrix norm (lapack) — tridiagonal
s	d	c	z	langt			tridiagonal	one-norm, inf-norm, Frobenius norm, or max absolute element
s	d	c	z	lanht			Hermitian tridiagonal
s	d			lanst			symmetric tridiagonal
Matrix norm (lapack) — reverse communication
s	d	c	z	lacn2			general, implicit	estimate one-norm using matrix-vector products
s	d	c	z	lacon			general, implicit	estimate one-norm using matrix-vector products

Types				Routine	F95	MAGMA		Matrix type	Description
Linear systems — LU — driver
s	d	c	z	gesv	F95	cpu	gpu	general	solve Ax = b
	ds		zc	gesv			gpu	general	solve Ax = b, mixed precision
s	d	c	z	gesvx	F95			general	solve Ax = b, expert
Linear systems — LU, banded — driver
s	d	c	z	gbsv	F95			general banded	solve Ax = b
s	d	c	z	gbsvx	F95			general banded	solve Ax = b, expert
Linear systems — LU, tridiagonal — driver
s	d	c	z	gtsv	F95			general tridiagonal	solve Ax = b
s	d	c	z	gtsvx	F95			general tridiagonal	solve Ax = b, expert

Linear systems — LU — computational
s	d	c	z	getrf		cpu	gpu	general	LU factorization
s	d	c	z	getf2				general	LU factorization, non-blocked
s	d	c	z	getrs			gpu	general	solve Ax = b using factorization
	ds		zc	getrs			gpu	general	solve Ax = b using factorization, mixed precision
s	d	c	z	getri			gpu	general	compute inverse A^-1 using factorization
s	d	c	z	gerfs				general	refine solution to Ax = b, with error estimates
s	d	c	z	gecon				general	condition number estimate using factorization
s	d	c	z	geequ				general	equilibrate matrix
Linear systems — LU, banded — computational
s	d	c	z	gbtrf				general banded	LU factorization
s	d	c	z	gbtf2				general banded	LU factorization, non-blocked
s	d	c	z	gbtrs				general banded	Solve Ax = b using factorization
s	d	c	z	gbrfs				general banded	refine solution to Ax = b, with error estimates
s	d	c	z	gbcon				general banded	condition number estimate using factorization
s	d	c	z	gbequ				general banded	equilibrate matrix
Linear systems — LU, tridiagonal — computational
s	d	c	z	gttrf				general tridiagonal	LU factorization
s	d	c	z	gttrs				general tridiagonal	Solve Ax = b using factorization
s	d	c	z	gtts2				general tridiagonal	TODO
s	d	c	z	gtrfs				general tridiagonal	refine solution to Ax = b, with error estimates
s	d	c	z	gtcon				general tridiagonal	condition number estimate using factorization

Linear systems — Cholesky — driver
s	d	c	z	posv	F95	cpu	gpu	SPD	solve Ax = b
	ds		zc	posv			gpu	SPD	solve Ax = b, mixed precision
s	d	c	z	posvx	F95			SPD	solve Ax = b, expert
Linear systems — Cholesky, packed — driver
s	d	c	z	ppsv	F95			SPD packed	solve Ax = b
s	d	c	z	ppsvx	F95			SPD packed	solve Ax = b, expert
Linear systems — Cholesky, banded — driver
s	d	c	z	pbsv	F95			SPD banded	solve Ax = b
s	d	c	z	pbsvx	F95			SPD banded	solve Ax = b, expert
Linear systems — Cholesky, tridiagonal — driver
s	d	c	z	ptsv	F95			SPD tridiagonal	solve Ax = b
s	d	c	z	ptsvx	F95			SPD tridiagonal	solve Ax = b, expert

Linear systems — Cholesky — computational
s	d	c	z	potrf		cpu	gpu	SPD	Cholesky factorization
s	d	c	z	potf2				SPD	Cholesky factorization, non-blocked
s	d	c	z	potrs			gpu	SPD	Solve Ax = b using factorization
s	d	c	z	potri		cpu	gpu	SPD	compute inverse A^-1 using factorization
s	d	c	z	porfs				SPD	refine solution to Ax = b, with error estimates
s	d	c	z	pocon				SPD	condition number estimate using factorization
s	d	c	z	poequ				SPD	equilibrate matrix
s	d	c	z	lauum		cpu	gpu	triangular	compute UU^T or L^TL
s	d	c	z	lauu2				triangular	compute UU^T or L^TL, non-blocked
Linear systems — Cholesky, packed — computational
s	d	c	z	pptrf				SPD packed	Cholesky factorization
s	d	c	z	pptrs				SPD packed	Solve Ax = b using factorization
s	d	c	z	pptri				SPD packed	compute inverse A^-1 using factorization
s	d	c	z	pprfs				SPD packed	refine solution to Ax = b, with error estimates
s	d	c	z	ppcon				SPD packed	condition number estimate using factorization
s	d	c	z	ppequ				SPD packed	equilibrate matrix
Linear systems — Cholesky, banded — computational
s	d	c	z	pbtrf				SPD banded	Cholesky factorization
s	d	c	z	pbtf2				SPD banded	Cholesky factorization, non-blocked
s	d	c	z	pbtrs				SPD banded	Solve Ax = b using factorization
s	d	c	z	pbrfs				SPD banded	refine solution to Ax = b, with error estimates
s	d	c	z	pbcon				SPD banded	condition number estimate using factorization
s	d	c	z	pbequ				SPD banded	equilibrate matrix
Linear systems — Cholesky, tridiagonal — computational
s	d	c	z	pttrf				SPD tridiagonal	Factor A
s	d	c	z	pttrs				SPD tridiagonal	Solve Ax = b using factorization
s	d	c	z	ptrfs				SPD tridiagonal	refine solution to Ax = b, with error estimates
s	d	c	z	ptcon				SPD tridiagonal	condition number estimate using factorization

Linear systems — symmetric indefinite — driver
s	d	c	z	sy/hesv		cpu		Hermitian	solve Ax = b
s	d	c	z	sy/hesvx				Hermitian	solve Ax = b, expert
Linear systems — symmetric indefinite, packed — driver
s	d	c	z	sp/hpsv				Hermitian packed	solve Ax = b
s	d	c	z	sp/hpsvx				Hermitian packed	solve Ax = b, expert

Linear systems — symmetric indefinite — computational
s	d	c	z	sy/hetrf		cpu		Hermitian	LDL^T symmetric indefinite factorization
s	d	c	z	sy/hetf2				Hermitian	LDL^T symmetric indefinite factorization, non-blocked
s	d	c	z	sy/hetrs		---		Hermitian	Solve Ax = b using factorization
s	d	c	z	sy/hetri				Hermitian	compute inverse A^-1 using factorization
s	d	c	z	sy/hecon				Hermitian	condition number estimate using factorization
s	d	c	z	sy/herfs				Hermitian	refine solution to Ax = b, with error estimates
		c	z	sysv	F95	cpu		complex-symmetric	solve Ax = b
		c	z	sysvx	F95			complex-symmetric	solve Ax = b, expert
		c	z	sytrf		cpu		complex-symmetric	LDL^T symmetric indefinite factorization
		c	z	sytf2				complex-symmetric	LDL^T symmetric indefinite factorization, non-blocked
		c	z	sytrs		---		complex-symmetric	Solve Ax = b using factorization
		c	z	sytri				complex-symmetric	compute inverse A^-1 using factorization
		c	z	sycon				complex-symmetric	condition number estimate using factorization
		c	z	syrfs				complex-symmetric	refine solution to Ax = b, with error estimates
Linear systems — symmetric indefinite, packed — computational
s	d	c	z	sp/hptrf				Hermitian packed	LDL^T symmetric indefinite factorization
d	s	c	z	sp/hptrs				Hermitian packed	Solve Ax = b using factorization
s	d	c	z	sp/hptri				Hermitian packed	compute inverse A^-1 using factorization
s	d	c	z	sp/hprfs				Hermitian packed	refine solution to Ax = b, with error estimates
s	d	c	z	sp/hpcon				Hermitian packed	condition number estimate using factorization
		c	z	spsv	F95			complex-symmetric packed	solve Ax = b
		c	z	spsvx	F95			complex-symmetric packed	solve Ax = b, expert
		c	z	sptrf				complex-symmetric packed	LDL^T symmetric indefinite factorization
		c	z	sptrs				complex-symmetric packed	Solve Ax = b using factorization
		c	z	sptri				complex-symmetric packed	compute inverse A^-1 using factorization
		c	z	sprfs				complex-symmetric packed	refine solution to Ax = b, with error estimates
		c	z	spcon				complex-symmetric packed	condition number estimate using factorization

Linear systems — triangular — computational
s	d	c	z	trtrs				triangular	triangular solve Tx = b (trsv plus singularity check)
s	d	c	z	latrs				triangular	triangular solve Tx = b, slowly and carefully with scaling
s	d	c	z	trtri		cpu	gpu	triangular	compute inverse A^-1 using factorization
s	d	c	z	trti2				triangular	compute inverse A^-1 using factorization, non-blocked
s	d	c	z	trrfs				triangular	refine solution to Ax = b, with error estimates
s	d	c	z	trcon				triangular	condition number estimate
Linear systems — triangular, packed — computational
s	d	c	z	tptrs				triangular packed	triangular solve Tx = b (trsv plus singularity check)
s	d	c	z	latps				triangular packed	triangular solve Tx = b, slowly and carefully with scaling
s	d	c	z	tptri				triangular packed	compute inverse A^-1 using factorization
s	d	c	z	tprfs				triangular packed	refine solution to Ax = b, with error estimates
s	d	c	z	tpcon				triangular packed	condition number estimate
Linear systems — triangular, banded — computational
s	d	c	z	tbtrs				triangular banded	triangular solve Tx = b
s	d	c	z	latbs				triangular banded	triangular solve Tx = b, slowly and carefully with scaling
s	d	c	z	tbrfs				triangular banded	refine solution to Ax = b, with error estimates
s	d	c	z	tbcon				triangular banded	condition number estimate

Linear least squares — driver
s	d	c	z	gels	F95		gpu	general	Minimize \|\|b - Ax\|\|₂
				geqrsv			gpu	general, mixed precision	Minimize \|\|b - Ax\|\|₂
s	d	c	z	gelsy	F95			general	... using complete orthogonal factorization
s	d	c	z	gelsd	F95			general	... using SVD (divide-and-conquer)
s	d	c	z	gelss	F95			general	... using SVD
s	d	c	z	gglse	F95			general	Minimize \|\|c - Ax\|\|₂ subject to Bx = d
s	d	c	z	ggglm	F95			general	Minimize \|\|y\|\|₂ subject to d = Ax + By

QR factorization — computational
s	d	c	z	geqrf		cpu	gpu	general	QR factorization
s	d	c	z	geqr2				general	QR factorization, non-blocked
s	d	c	z	geqp3		cpu	gpu	general	QR factorization with pivoting
				geqrs			gpu	general	Minimize \|\|b - Ax\|\|₂
s	d	c	z	ggqrf				general	generalized QR factorization
s	d	c	z	or/ungqr		cpu	gpu	unitary	generate Q
s	d	c	z	or/ung2r				unitary	generate Q, non-blocked
s	d	c	z	or/unmqr		cpu	gpu	unitary	multiply by Q
s	d	c	z	or/unm2r				unitary	multiply by Q, non-blocked
RQ factorization — computational
s	d	c	z	gerqf				general	RQ factorization
s	d	c	z	gerq2				general	RQ factorization, non-blocked
s	d	c	z	ggrqf				general	generalized RQ factorization
s	d	c	z	or/ungrq				unitary	generate Q
s	d	c	z	or/ungr2				unitary	generate Q, non-blocked
s	d	c	z	or/unmrq				unitary	multiply by Q
s	d	c	z	or/unmr2				unitary	multiply by Q, non-blocked
QL factorization — computational
s	d	c	z	geqlf		cpu		general	QL factorization
s	d	c	z	geql2				general	QL factorization, non-blocked
s	d	c	z	or/ungql				unitary	generate Q
s	d	c	z	or/ung2l				unitary	generate Q, non-blocked
s	d	c	z	or/unmql		cpu		unitary	multiply by Q
s	d	c	z	or/unm2l				unitary	multiply by Q, non-blocked
LQ factorization — computational
s	d	c	z	gelqf		cpu	gpu	general	LQ factorization
s	d	c	z	gelq2				general	LQ factorization, non-blocked
s	d	c	z	or/unglq				unitary	generate Q
s	d	c	z	or/ungl2				unitary	generate Q, non-blocked
s	d	c	z	or/unmlq				unitary	multiply by Q
s	d	c	z	or/unml2				unitary	multiply by Q, non-blocked
RZ factorization — computational
s	d	c	z	tzrzf				trapezoidal	RZ factorization
s	d	c	z	or/unmrz				unitary	multiply by Q
s	d	c	z	or/unmr3				unitary	multiply by Q, non-blocked

Symmetric eigenvalues — driver
s	d	c	z	sy/heev	F95			Hermitian	solve Ax = λx, QR iteration
s	d	c	z	sy/heevx	F95	cpu	gpu	Hermitian	solve Ax = λx, QR iteration, expert
s	d	c	z	sy/heevd	F95	cpu	gpu	Hermitian	solve Ax = λx, D&C
s	d	c	z	sy/heevr	F95	cpu	gpu	Hermitian	solve Ax = λx, RRR
s	d	c	z	sy/hegv	F95			Hermitian	solve Ax = λMx, generalized, QR iteration
s	d	c	z	sy/hegvx	F95	cpu		Hermitian	solve Ax = λMx, generalized, QR iteration, expert
s	d	c	z	sy/hegvd	F95	cpu		Hermitian	solve Ax = λMx, generalized, D&C
				sy/hegvr		cpu		Hermitian	solve Ax = λMx, generalized, RRR
Symmetric eigenvalues — packed — driver
s	d	c	z	sp/hpev	F95			Hermitian packed	solve Ax = λx
s	d	c	z	sp/hpevx	F95			Hermitian packed	solve Ax = λx, expert
s	d	c	z	sp/hpevd	F95			Hermitian packed	solve Ax = λx, D&C
s	d	c	z	sp/hpgv				Hermitian packed	solve Ax = λMx, generalized
s	d	c	z	sp/hpgvx	F95			Hermitian packed	solve Ax = λMx, generalized, expert
s	d	c	z	sp/hpgvd	F95			Hermitian packed	solve Ax = λMx, generalized, D&C
Symmetric eigenvalues — banded — driver
s	d	c	z	sb/hbev	F95			Hermitian banded	solve Ax = λx
s	d	c	z	sb/hbevx	F95			Hermitian banded	solve Ax = λx, expert
s	d	c	z	sb/hbevd	F95			Hermitian banded	solve Ax = λx, D&C
s	d	c	z	sb/hbgv	F95			Hermitian banded	solve Ax = λMx, generalized
s	d	c	z	sb/hbgvx	F95			Hermitian banded	solve Ax = λMx, generalized, expert
s	d	c	z	sb/hbgvd	F95			Hermitian banded	solve Ax = λMx, generalized, D&C
Symmetric eigenvalues — tridiagonal — driver
s	d			stev	F95			symmetric tridiagonal	solve Ax = λx
s	d			stevx	F95			symmetric tridiagonal	solve Ax = λx, expert
s	d			stevd	F95			symmetric tridiagonal	solve Ax = λx, D&C
s	d			stevr	F95			symmetric tridiagonal	solve Ax = λx, RRR

Symmetric eigenvalues — computational
s	d	c	z	latrd		cpu			reduction to tridiagonal (sy/hetrd) panel
s	d	c	z	sy/hetrd		cpu	gpu	Hermitian	reduction to tridiagonal
s	d	c	z	sy/hetd2				Hermitian	reduction to tridiagonal, non-blocked
s	d	c	z	or/ungtr		cpu		unitary	generate matrix after -trd
s	d	c	z	or/unmtr		cpu	gpu	unitary	multiply by matrix after -trd
s	d	c	z	sy/hegst		cpu	gpu	Hermitian	reduce generalized to standard form
s	d	c	z	sy/hegs2				Hermitian	reduce generalized to standard form, non-blocked
Symmetric eigenvalues — packed — computational
s	d	c	z	sp/hptrd				Hermitian packed	reduction to tridiagonal
s	d	c	z	op/upgtr				unitary packed	generate matrix after -trd
s	d	c	z	op/upmtr				unitary packed	multiply by matrix after -trd
s	d	c	z	sp/hpgst				Hermitian packed	reduce generalized to standard form
Symmetric eigenvalues — banded — computational
s	d	c	z	sb/hbtrd				Hermitian banded	reduction to tridiagonal
s	d	c	z	sb/hbgst				Hermitian banded	reduce generalized to standard form
Symmetric eigenvalues — tridiagonal — computational
s	d	c	z	steqr				symmetric tridiagonal	symmetric tridiagonal eigensolver, using implicitly shifted QR
s	d	c	z	pteqr				SPD tridiagonal	... using Cholesky and bidiagonal QR
s	d			sterf				symmetric tridiagonal	... using square-root free QR
s	d	c	z	stedc				symmetric tridiagonal	... using divide-and-conquer
s	d	c	z	stegr				symmetric tridiagonal	... using relatively robust representation
s	d			stebz				symmetric tridiagonal	eigenalues using bisection
s	d	c	z	stein				symmetric tridiagonal	eigenvectors using inverse iteration
s	d			disna				diagonal	condition numbers

Non-symmetric eigenvalues — driver
s	d	c	z	geev	F95	cpu		general	solve Ax = λx
s	d	c	z	geevx	F95			general	solve Ax = λx, expert
s	d	c	z	ggev	F95			general	solve Ax = λMx
s	d	c	z	ggevx	F95			general	solve Ax = λMx, expert

Non-symmetric eigenvalues — computational
s	d	c	z	gehrd		cpu		general	Hessenberg reduction
s	d	c	z	gehd2				general	Hessenberg reduction, non-blocked
s	d	c	z	lahr2		cpu			Hessenberg reduction (gehrd) panel
				lahru		cpu			Hessenberg reduction (gehrd) trailing matrix update (MAGMA only)
s	d	c	z	gebal				general	balance matrix
s	d	c	z	gebak				general	back transforming
s	d	c	z	or/unghr		cpu		unitary	generate matrix after -hrd
s	d	c	z	or/unmhr				unitary	multiply by matrix after -hrd
s	d	c	z	hseqr				upper Hessenberg	Schur factorizaton
s	d	c	z	hsein				upper Hessenberg	eigenvectors by inverse iteration
s	d	c	z	trevc3		cpu		triangular	eigenvectors
s	d	c	z	trevc				triangular	eigenvectors, non-blocked
s	d	c	z	gees	F95			general	Schur factorization
s	d	c	z	geesx	F95			general	Schur factorization, expect
s	d	c	z	gges	F95			general	generalized Schur factorization
s	d	c	z	ggesx	F95			general	generalized Schur factorization, expert
s	d	c	z	trexc				triangular	reorder Schur factorization
s	d	c	z	trsyl				triangular	Sylvester equation
s	d	c	z	trsna				triangular	condition numbers
s	d	c	z	trsen				triangular	condition numbers of eigenvalue cluster/subspace
Generalized non-symmetric eigenvalue — computational
s	d	c	z	gghrd				general	Hessenberg reduction
s	d	c	z	ggbal				general	balance matrix
s	d	c	z	ggbak				general	back transforming
s	d	c	z	hgeqz				upper Hessenberg	eigenvalues
s	d	c	z	tgevc				triangular	eigenvectors
s	d	c	z	tgexc				triangular	reorder Schur factorization
s	d	c	z	tgsyl				triangular	Sylvester equation
s	d	c	z	tgsna				triangular	condition numbers
s	d	c	z	tgsen				triangular	condition numbers of eigenvalue cluster/subspace

SVD — driver
s	d	c	z	gesvd	F95	cpu		general	SVD using QR iteration
s	d	c	z	bdsqr				bidiagonal	SVD using QR iteration
s	d	c	z	gesdd	F95	cpu		general	SVD using divide-and-conquer
s	d			bdsdc				bidiagonal	SVD using divide-and-conquer
s	d	c	z	ggsvd	F95			general	generalized SVD

SVD — computational
s	d	c	z	gbbrd				general banded	reduce to bidiagonal form
s	d	c	z	gebrd		cpu		general	reduce to bidiagonal form
s	d	c	z	gebd2				general	reduce to bidiagonal form, non-blocked
s	d	c	z	labrd			gpu		bidiagonal (gebrd) panel
s	d	c	z	or/ungbr				unitary	generate matrix after -brd
s	d	c	z	or/unmbr				unitary	multiply by matrix after -brd

Auxiliary (scalars)
		s	d	cabs1					abs of complex number, \| Re(x) \| + \| Im(x) \|
s	d	c	z	ladiv					complex divide
s	d			lapy2					sqrt( x^2 + y^2 )
s	d			lapy3					sqrt( x^2 + y^2 + z^2 )
s	d			lamch					returns machine precision, under/overflow, etc.
s	d			labad					modifies machine under/overflow for old Crays
Auxilliary, general
		c	z	lacrm					simple matrix-matrix multiply
		c	z	larcm					simple matrix-matrix multiply
s	d			lasrt					sort, using quick sort then insertion sort
s	d	c	z	lassq					scaled sum-of-squares
Auxilliary, solve related
s	d	c	z	laqge				general	equilibrate matrix
s	d	c	z	laqgb				general banded
		c	z	laqhe				Hermitian
		c	z	laqhb				Hermitian banded
		c	z	laqhp				Hermitian packed
s	d	c	z	laqsy				symmetric
s	d	c	z	laqsb				symmetric banded
s	d	c	z	laqsp				symmetric packed
s	d			laqtr				triangular
s	d			lagtf					LU factor of tridiagonal + diagonal matrix
s	d	c	z	lagtm					tridiagonal matrix-vector multiply
s	d			lagts					tridiagonal solve
s	d			laln2					solve (alpha A + beta D)X = gamma B
s	d	c	z	lals0					apply factors for least-squares using D&C SVD
s	d	c	z	lalsa					compute compact SVD for least-squares
s	d	c	z	lalsd					solve least-squares using SVD
s	d			lamrg					create permutation to merge two sorted lists
s	d	c	z	laic1					step of condition estimate
		c	z	lahef					partial factor of Hermitian matrix
s	d	c	z	lapll					linear dependency of 2 vectors
s	d	c	z	lapmt					reorder columns by permutation
s	d	c	z	laqp2					QR of block, with pivoting
s	d	c	z	laqps					QR panel + update, with pivoting
s	d	c	z	laswp					perform row interchanges
s	d			lasy2					solve TLX + XTR = alpha*B (or transposes thereof)
s	d	c	z	lasyf					partial factorization
s	d	c	z	latdf					using LU factor, compute Dif-estimate
s	d	c	z	latrz				trapezoidal	orthogonal factorization
Auxilliary, Householder
s	d	c	z	larf			gpu		apply Householder reflector to matrix, on left or right
s	d	c	z	larfb			gpu		apply block reflector to matrix, on left or right
s	d	c	z	larfg			gpu		generate Householder reflector H
s	d	c	z	larft					form T for block reflector H, so H = I - VTV^T
s	d	c	z	larfx					apply Householder reflector to matrix, on left or right
s	d	c	z	larz					apply Householder reflector to matrix, on left or right
s	d	c	z	larzb					apply block reflector to distributed matrix, on left or right
s	d	c	z	larzt					form T for block reflector, so H = I - VTV^T
Auxilliary, plane rotation
		c	z	lacrt					complex plane rotation
s	d	c	z	lar2v					apply plane rotations
s	d	c	z	largv					generate plane rotations
s	d	c	z	lartv					apply plane rotations
s	d	c	z	lasr					apply plane rotations, on left or right
Auxilliary, eigenvalue related
s	d			lae2					eigenvalues of 2x2 symmetric matrix
s	d			laebz					compute # eigenvalues ≤ w
s	d	c	z	laed0					eval and evec of symmetric tridiagonal using divide-and-conquer
s	d			laed1					updates eigensystem after rank-1 update; see also laed7
s	d			laed2					merge eigenvalues and deflate; see also laed8
s	d			laed3					roots of secular (characteristic) equation
s	d			laed4					i-th eigenvalue after rank-1 update of diagonal matrix; used by laed9
s	d			laed5					i-th eigenvalue after rank-1 update of 2x2 diagonal matrix
s	d			laed6					root of some equation; used by laed4
s	d	c	z	laed7					updates eigensystem after rank-1 update; see also laed1
s	d	c	z	laed8					merge eigenvalues and deflate; see also laed2
s	d			laed9					roots of secular (characteristic) equation
s	d			laeda					Z vector for CURPBMth problem
s	d	c	z	laein					eigenvector by inverse iteration
		c	z	laesy					eigenvalues of 2x2 matrix
s	d	c	z	laev2					eigenvalues of 2x2 matrix
s	d			laexc					swap diagonal blocks of Schur form
s	d			lag2					generalized eigenvalues of 2x2 matrix
s	d	c	z	lags2					upper triangular to lower triangular by orthogonal similarity transform
s	d			lagv2					generalized Schur factor of 2x2 system
s	d	c	z	lahqr					update eigenvalues and Schur decomposition
s	d			lanv2					Schur factor of 2x2 system
s	d	c	z	lar1v					eigenvector by inverse of tridiadonal matrix
s	d			larrb					bisection using relatively robust repr (RRR)
s	d			larre					eigenvalues of symmetric tridiagonal
s	d			larrf					find new RRR that isolates eigenvalue
s	d	c	z	larrv					eigenvalues of tridiagonal
Auxilliary, Hessenberg related
s	d	c	z	laqr0					eigenvalues of Hessenberg
s	d	c	z	laqr1					used for double implicit shift in QR algorithm
s	d	c	z	laqr2					same as laqr3, but avoid recursion
s	d	c	z	laqr3					deflate eigenvalues from Hessenberg
s	d	c	z	laqr4					same as laqr0, but calls laqr2
s	d	c	z	laqr5					single small-bulge multi-shift QR sweep
Auxilliary, SVD using D&C
s	d			las2					singular values of 2x2 upper triangular
s	d			lasd0					SVD of bidiagonal
s	d			lasd1					SVD of bidiagonal; called by lasd0
s	d			lasd2					merge sets of singular values, then deflate
s	d			lasd3					sqrt of roots of secular (characteristic) equation
s	d			lasd4					sqrt of ith eigenvalue of rank-1 update
s	d			lasd5					sqrt of ith eigenvalue of rank-1 update of 2x2 diagonal
s	d			lasd6					SVD of upper bidiagonal by merging 2 smaller ones
s	d			lasd7					SVD; called by lasd7
s	d			lasd8					sqrt of roots of secular (characteristic) equation; called by lasd6
s	d			lasda					SVD of bidiagonal; similar to lasd0
s	d			lasdq					SVD of bidiagonal
s	d			lasdt					creates subproblems for bidiagonal D&C
Auxilliary, SVD using DQDS
s	d			lasq1					singular values of bidiagonal
s	d			lasq2					singular values of bidiagonal
s	d			lasq3					eigenvalues of SPD tridiagonal
s	d			lasq4					check for deflation
s	d			lasq5					approximate smallest eigenvalue
s	d			lasq6					one DQDS transform
s	d			lasv2					SVD of 2x2 triangular

There are 5 different versions of second and dsecnd. The appropriate version for your system should be installed when LAPACK is installed.

Single	Double	Description
second	dsecnd	user time in seconds, using external ETIME
second	dsecnd	user time in seconds, using external ETIME_
second	dsecnd	user time in seconds, using ETIME
second	dsecnd	user time in seconds, using CPU_TIME
second	dsecnd	returns 0, instead of a user time

Routine	Description
ieeeck	check that Inf and NaN are safe
ilaenv	choose problem dependent parameters
ilaver	LAPACK version
iparmq	set problem and machine dependent parameters
lsame	case-insensitive char match
lsamen	case-insensitive string match
xerbla	error handler

Unclassified
TODO: stuff to sort through
s	d	c	z	gegs	general
s	d	c	z	gelsx	general
s	d	c	z	gesc2	general
s	d	c	z	getc2	general
s	d	c	z	ggsvp	general
s	d	c	z	pbstf	SPD banded
s	d	c	z	ptts2	SPD tridiagonal
s	d	c	z	tgex2	triangular
s	d	c	z	tgsja	triangular
s	d	c	z	tgsy2	triangular

Deprecated
s	d	c	z	geqpf	general	deprecated; use geqp3
s	d	c	z	tzrqf	trapezoidal	deprecated; use tzrzf
s	d			laisnan	scalar	deprecated; use Fortran's isnan
s	d			isnan	scalar	deprecated; use Fortran's isnan
s	d	c	z	latzm		deprecated; use ormrz
s	d	c	z	lahrd		deprecated; use lahr2
s	d	c	z	gegv	general	deprecated; use dggev

Routines for BLAS, LAPACK, MAGMA

Contents

Data type prefix

Matrix type prefix