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
- 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: Estimete 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:
Origin (head) routine |
Already implemented routine |
Duplicated (similar to other) routine |
Matrix methods
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bdx |
di |
ge gg |
gt |
he |
hsx hg |
po |
pt |
trxx tg |
un |
bak |
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gebaklsl gebaklsr gebakusl gebakusr gebaklp gebakup gebakll gebaklr gebakul gebakur |
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bal |
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geballp gebalup gebals geball gebalu ggballp ggbalup ggbals ggball ggbalu |
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cond |
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gecon1 geconi |
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hecon1 heconi |
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pocon1 poconi |
ptcon1 ptconi |
trl1con1 trl1coni trlcon1 trlconi tru1con1 tru1coni trucon1 truconi |
uncon1 |
eq |
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laqr1 hgezqenn hgezqenv hgezqevn hgezqevv hgezqsnn hgezqsnv hgezqsvn hgezqsvv hgeqzenn hgeqzenv hgeqzevn hgeqzevv hgeqzsnn hgeqzsnv hgeqzsvn hgeqzsvv |
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ev |
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ggevlnn ggevlnv ggevlvn ggevlvv ggevunn ggevuvn ggevunv ggevuvv |
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evc |
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tgevcll tgevclr tgevclb tgevcul tgevcur tgevcub tgevcllb tgevclrb tgevclbb tgevculb tgevcurb tgevcubb |
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exp |
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diexp |
geexp |
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heexp |
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fun |
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gq |
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unglq ungql ungqr ungrqu nghrl unghru |
hrd |
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gehrdl gehrdu gghrdlnn gghrdlnv gghrdlvn gghrdlvv gghrdunn gghrdunv gghrduvn gghrduvv |
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log |
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lya |
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mq |
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unmlqln unmlqlc unmlqrn unmlqrc unmqlln unmqllc unmqlrn unmqlrc unmqrln unmqrlc unmqrrn unmqrrc unmrqln unmrqlc unmrqrn unmrqrc unmhrlln unmhrllc unmhrlrn unmhrlrc unmhruln unmhrulc unmhrurn unmhrurc |
norm |
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norm1 norm1r norm1c normi normir normic norm1t norm1tr norm1tc normit normitr normitc norms |
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pf |
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pow |
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dipow |
gepow |
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hepow |
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qf |
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gelqf geqlf geqrf gerqf |
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rand |
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dimat |
gemat idmat diagmat spmat |
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hemat |
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pomat |
ptmat |
trl1mat trlmat tru1mat trumat |
unmat |
scl |
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scl |
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sm |
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trsmlx trsml1x trsml1hx trsml1tx trsmlhx trsmltx trsmux trsmu1x trsmu1hx trsmu1tx trsmuhx trsmutx trsmxl trsmxl1 trsmxl1h trsmxl1t trsmxlh trsmxlt trsmxu trsmxu1 trsmxu1h trsmxu1t trsmxuh trsmxut |
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struct |
bdlpick bdupick |
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gtpick |
he |
hslpick hsupick |
po |
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trlpick trupick trl trl0 trl1 tru tru0 tru1 tr2he |
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sv |
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gesvax gesvahx gesvatx gesvxa gesvxah gesvxat |
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hesvax hesvatx hesvxa hesvxat |
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posvax posvatx posvxa posvxat |
ptsvax ptsvatx ptsvxa ptsvxat |
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trf |
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getrflu1p getrfpl1u getrfpu1l getrful1p |
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hetrfpl hetrfpu |
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potrfl potrfu |
pttrfl pttrfu |
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tri |
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getrilu1p getripl1u getripu1l getriul1p |
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hetripl hetripu |
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potril potriu |
pttril pttriu |
trtril trtril1 trtriu trtriu1 |
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trs |
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getrslu1px getrslu1phx getrslu1ptx getrsxlu1p getrsxlu1ph getrsxlu1pt getrspl1ux getrspl1uhx getrspl1utx getrsxpl1u getrsxpl1uh getrsxpl1ut getrspu1lx getrspu1lhx getrspu1ltx getrsxpu1l getrsxpu1lh getrsxpu1lt getrsul1px getrsul1phx getrsul1ptx getrsxul1p getrsxul1ph getrsxul1pt |
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hetrsplx hetrspltx hetrsxpl hetrsxplt hetrspux hetrsputx hetrsxpu hetrsxput |
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potrslx potrsltx potrsxl potrsxlt potrsux potrsutx potrsxu potrsxut |
pttrslx pttrsltx pttrsxl pttrsxlt pttrsux pttrsutx pttrsxu pttrsxut |
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Callgraphs for some eigenvalue-related routines in LAPACK:
Vector methods
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Generate |
Apply |
ref |
larfg larfp larfgf larfgfc larfgb larfgbc larfpf larfpfc larfpb larfpbc larftbc larftbr larftfc larftfr |
larflcbc larflcbr larflcfc larflcfr larflnbc larflnbr larflnfc larflnfr larfrcbc larfrcbr larfrcfc larfrcfr larfrnbc larfrnbr larfrnfc larfrnfr larfblcbc larfblcbr larfblcfc larfblcfr larfblnbc larfblnbr larfblnfc larfblnfr larfbrcbc larfbrcbr larfbrcfc larfbrcfr larfbrnbc larfbrnbr larfbrnfc larfbrnfr |
rot |
lartg |
lartv rot rotga rotscll rotsclu |
Scalar methods
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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 |