## Legend

Matrix types:

• bdx = {bdl,bdu}: {lower,upper} bidiagonal
• di: diagonalizable
• gb: general band
• ge: general
• gg: general-general pair, generalized form
• gt: general tridiagonal
• hb: Hermitian (symmetric) band
• 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
• tz: trapezoidal
• trxx = {trl,trl0,trl1,tru,tru0,tru1}: [{strict,unit}] {lower,upper} triangular
• 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
• 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

Colors in call graphs:

## 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 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 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 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 pomat ptmat 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 he hslpick hsupick po trlpick trupick trl1pick tru1pick trl trl0 trl1 tru tru0 tru1 tr2he sv gesvax gesvahx gesvatx gesvxa gesvxah gesvxat 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 getrslu1phx getrslu1ptx getrsxlu1p getrsxlu1ph getrsxlu1pt getrspl1ux getrspl1uhx getrspl1utx getrsxpl1u getrsxpl1uh getrsxpl1ut getrspu1lx getrspu1lhx getrspu1ltx getrsxpu1l getrsxpu1lh getrsxpu1lt getrsul1px getrsul1phx getrsul1ptx getrsxul1p getrsxul1ph 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:

## 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 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

Addons/math/mt/MATRIX (last edited 2013-03-18 00:00:37 by IgorZhuravlov)