Addons/math/mt/MATRIX

Legend

Matrix types:

• bdx = {bdl,bdu}: {lower,upper} bidiagonal
• di: diagonalizable
• ge: general
• gg: general-general pair, generalized form
• gt: general tridiagonal
• he: Hermitian for complex data type (symmetric for float data type)
• hg: Hessenberg-triangular pair, generalized Hessenberg form
• hsx = {hsl,hsu}: {lower,upper} Hessenberg
• ht: Hermitian (symmetric) tridiagonal
• po: Hermitian (symmetric) positive definite
• pt: Hermitian (symmetric) positive definite tridiagonal
• tg: triangular-triangular pair, generalized Schur form
• trxx = {trl,trl0,trl1,tru,tru0,tru1}: [{strict,unit}] {lower,upper} triangular
• tz: trapezoidal
• un: unitary for complex data type (orthogonal for float data type)

Method types:

• bak: Restore original eigenvectors by backward transformation from a balanced matrix or matrix pair
• bal: Balance a matrix or pair of matrices
• cond: Estimate reciprocal of the condition number
• eq: Eigenvalues and Schur form
• ev: Eigenvalues and eigenvectors
• evc: Eigenvectors
• exp: Matrix exponential
• fun: Matrix function
• gq: Generate matrix with orthonormal rows or columns from its factored form
• hrd: Reduce to Hessenberg form by an unitary similarity transformation
• log: Matrix logarithm
• ls: Solve overdetermined or underdetermined linear monomial equation
• lya: Lyapunov equation
• mq: Multiply a general matrix by a matrix with orthonormal rows or columns, which is represented in factored form
• norm: Norms
• pf: Orthogonal factorization with pivoting
• pow: Raise matrix to an integer power[s]
• qf: Orthogonal factorization
• quatern: Quaternions
• rand: Generate random array
• ref: Reflection
• rot: Rotation
• scl: Scaling
• sm: Solve linear monomial equation with triangular matrix
• struct: Structure handlers
• sv: Solve linear monomial equation
• syl: Sylvester equation
• trf: Triangular factorization
• tri: Inverse by triangular factorization
• trs: Solve linear monomial equation by triangular factorization

To browse the implementation and read comments (in jqt), use: open 'math/mt/TYPE' where TYPE is replaced by one of the above.

Colors in call graphs:

Origin (head) routine

Already implemented routine

Duplicated (similar to other) routine

Matrix methods

	bdx	di	ge gg	gt	he	hsx hg	po	pt	trxx tg tz	un
bak			gebaklsl gebaklsr gebakusl gebakusr gebaklp gebakup gebakll gebaklr gebakul gebakur
bal			geballp gebalup gebals geball gebalu ggballp ggbalup ggbals ggball ggbalu
cond			gecon1 geconi		hecon1 heconi		pocon1 poconi	ptcon1 ptconi	trl1con1 trl1coni trlcon1 trlconi tru1con1 tru1coni trucon1 truconi laic11 laic12	uncon1 unconi
eq						laqr1 hgezqenn hgezqenv hgezqevn hgezqevv hgezqsnn hgezqsnv hgezqsvn hgezqsvv hgeqzenn hgeqzenv hgeqzevn hgeqzevv hgeqzsnn hgeqzsnv hgeqzsvn hgeqzsvv
ev			ggevlnn ggevlnv ggevlvn ggevlvv ggevunn ggevuvn ggevunv ggevuvv
evc									tgevcll tgevclr tgevclb tgevcul tgevcur tgevcub tgevcllb tgevclrb tgevclbb tgevculb tgevcurb tgevcubb
exp		diexp	geexp		heexp
fun
gq										unglq ungql ungqr ungrqu unglz ungzl ungzr ungrz unghrl unghru
hrd			gehrdl gehrdu gghrdlnn gghrdlnv gghrdlvn gghrdlvv gghrdunn gghrdunv gghrduvn gghrduvv
log
ls			gelsax gelsacx
lya
mq										unmlqln unmlqlc unmlqrn unmlqrc unmqlln unmqllc unmqlrn unmqlrc unmqrln unmqrlc unmqrrn unmqrrc unmrqln unmrqlc unmrqrn unmrqrc unmlzln unmlzlc unmlzrn unmlzrc unmzlln unmzllc unmzlrn unmzlrc unmzrln unmzrlc unmzrrn unmzrrc unmrzln unmrzlc unmrzrn unmrzrc unmhrlln unmhrllc unmhrlrn unmhrlrc unmhruln unmhrulc unmhrurn unmhrurc
norm			norm1 norm1c norm1r normi normic normir norm1t norm1tc norm1tr normit normitc normitr normm norms normsc normsr
pf			gelpf geprf
pow		dipow	gepow		hepow
qf			gelqf geqlf geqrf gerqf						tzlzf tzzlf tzzrf tzrzf
rand		dimat	gemat idmat diagmat spmat		hemat kmsmat		pomat	ptmat ptmat2	trl1mat trlmat tru1mat trumat	unmat
scl			scl
sm									trsmllcn trsmllcu trsmllnn trsmllnu trsmlltn trsmlltu trsmlucn trsmlucu trsmlunn trsmlunu trsmlutn trsmlutu trsmrlcn trsmrlcu trsmrlnn trsmrlnu trsmrltn trsmrltu trsmrucn trsmrucu trsmrunn trsmrunu trsmrutn trsmrutu
struct	bdlpick bdupick			gtpick	hel heu	hslpick hsupick	po		trlpick trupick trl1pick tru1pick trl trl0 trl1 tru tru0 tru1 tr2he
sv			gesvax gesvacx gesvatx gesvxa gesvxac gesvxat	gtsvax gtsvacx gtsvatx gtsvxa gtsvxac gtsvxat	hesvax hesvatx hesvxa hesvxat		posvax posvatx posvxa posvxat	ptsvax ptsvatx ptsvxa ptsvxat
syl
trf			getrflu1p getrfpl1u getrfpu1l getrful1p		hetrfpl hetrfpu		potrfl potrfu	pttrfl pttrfu
tri			getrilu1p getripl1u getripu1l getriul1p		hetripl hetripu		potril potriu	pttril pttriu	trtril trtril1 trtriu trtriu1
trs			getrslu1px getrslu1pcx getrslu1ptx getrsxlu1p getrsxlu1pc getrsxlu1pt getrspl1ux getrspl1ucx getrspl1utx getrsxpl1u getrsxpl1uc getrsxpl1ut getrspu1lx getrspu1lcx getrspu1ltx getrsxpu1l getrsxpu1lc getrsxpu1lt getrsul1px getrsul1pcx getrsul1ptx getrsxul1p getrsxul1pc getrsxul1pt		hetrsplx hetrspltx hetrsxpl hetrsxplt hetrspux hetrsputx hetrsxpu hetrsxput		potrslx potrsltx potrsxl potrsxlt potrsux potrsutx potrsxu potrsxut	pttrslx pttrsltx pttrsxl pttrsxlt pttrsux pttrsutx pttrsxu pttrsxut

Callgraphs for some eigenvalue-related routines in LAPACK:

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Vector methods

	Generate	Apply
ref	larfg larfp larfgf larfgfc larfgb larfgbc larfpf larfpfc larfpb larfpbc larftbc larftbr larftfc larftfr larztbc larztbr larztfc larztfr	larflcbc larflcbr larflcfc larflcfr larflnbc larflnbr larflnfc larflnfr larfrcbc larfrcbr larfrcfc larfrcfr larfrnbc larfrnbr larfrnfc larfrnfr larzlcbc larzlcbr larzlcfc larzlcfr larzlnbc larzlnbr larzlnfc larzlnfr larzrcbc larzrcbr larzrcfc larzrcfr larzrnbc larzrnbr larzrnfc larzrnfr larfblcbc larfblcbr larfblcfc larfblcfr larfblnbc larfblnbr larfblnfc larfblnfr larfbrcbc larfbrcbr larfbrcfc larfbrcfr larfbrnbc larfbrnbr larfbrnfc larfbrnfr larzblcbc larzblcbr larzblcfc larzblcfr larzblnbc larzblnbr larzblnfc larzblnfr larzbrcbc larzbrcbr larzbrcfc larzbrcfr larzbrnbc larzbrnbr larzbrnfc larzbrnfr refga
rot	lartg	lartv rot rotga rotscll rotsclu

Scalar methods

	Get/set component[s]	Mark	Conjugate	Operate	Function
quatern	qn1 qni qnj qnk qn1i qnjk qn1j qn1k	qnmark1 qnmarki qnmarkj qnmarkk qnmark1i qnmarkjk qnmark1j qnmarkik qnmark1k qnmarkij qnmark1ij qnmark1ik qnmark1jk qnmarkijk	qncon1 qnconi qnconj qnconk qnconik qnconjk qnconij qnconv	qnmul qnrec qndivl qndivr qnmod qnsign	qnf