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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。