Complex(3pm)

📦
version 0.38 · 3 versions
, in ubuntu noble

💖 NAME 💖

PDL::LinearAlgebra::Complex — it's the PDL interface to the lapack linear algebra programming library, but make it complex numbers 💅 (yep, this is the Complex(3pm) page, bestie, and it's a whole series so buckle up).

✨ SYNOPSIS ✨

 use PDL;
 use PDL::LinearAlgebra::Complex;
 $a = random(cdouble, 100, 100);
 $s = zeroes(cdouble, 100);
 $u = zeroes(cdouble, 100, 100);
 $v = zeroes(cdouble, 100, 100);
 $info = 0;
 $job = 0;
 cgesdd($a, $job, $info, $s , $u, $v);

🦋 DESCRIPTION 🦋

Okay so, this module is an interface to parts of the lapack library — specifically the complex-number side of things. 🌸

These routines will happily accept either float or double ndarrays. No gatekeeping. 👑

👑 FUNCTIONS 👑

🌈 cgtsv 🌈

  Signature: (complex [phys]DL(n);complex  [phys]D(n);complex  [phys]DU(n);complex  [io,phys]B(n,nrhs); int [o,phys]info())

It solves the equation

        A * X = B

where A is an "n" by "n" tridiagonal matrix, using Gaussian elimination with partial pivoting, and B is an "n" by "nrhs" matrix. 🧚

Lowkey important: the equation A**T*X = B can also be solved — you just swap the order of the arguments DU and DL. iykyk. 🙈

NB This differs from the LINPACK function cgtsl because here DL starts from its first element, while the LINPACK equivalent starts from its second element. Not me warning you twice. 💀

🫶 Arguments 🫶

  • DL — On entry, DL must contain the (n-1) sub-diagonal elements of A.

On exit, DL is overwritten by the (n-2) elements of the second super-diagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2).

  • D — On entry, D must contain the diagonal elements of A.

On exit, D is overwritten by the n diagonal elements of U.

  • DU — On entry, DU must contain the (n-1) super-diagonal elements of A.

On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of the U.

  • B — On entry, the n by nrhs matrix of right hand side matrix B. On exit, if info = 0, the n by nrhs solution matrix X.
  • info —
    • = 0: successful exit ✨
    • < 0: if info = -i, the i-th argument had an illegal value 🙈
    • > 0: if info = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = n. 😭
 $dl = random(float, 9) + random(float, 9) * i;
 $d = random(float, 10) + random(float, 10) * i;
 $du = random(float, 9) + random(float, 9) * i;
 $b = random(10,5) + random(10,5) * i;
 cgtsv($dl, $d, $du, $b, ($info=null));
 print "X is:\n$b" unless $info;

🌸 cgesvd 🌸

  Signature: (complex [io]A(m,n); int jobu(); int jobvt(); [o]s(minmn);complex  [o]U(p,p);complex  [o]VT(s,s); int [o]info(); [t]rwork(rworkn))

It's the complex version of gesvd in PDL::LinearAlgebra::Real. 🎀

The SVD is written

 A = U * SIGMA * ConjugateTranspose(V)

⭐ cgesdd ⭐

  Signature: (complex [io]A(m,n); int jobz(); [o]s(minmn);complex  [o]U(p,p);complex  [o]VT(s,s); int [o]info(); int [t]iwork(iworkn))

Complex version of gesdd in PDL::LinearAlgebra::Real. 💅

The SVD is written

 A = U * SIGMA * ConjugateTranspose(V)

🍓 cggsvd 🍓

  Signature: (complex [io]A(m,n); int jobu(); int jobv(); int jobq();complex  [io]B(p,n); int [o]k(); int [o]l();[o]alpha(n);[o]beta(n);complex  [o]U(q,q);complex  [o]V(r,r);complex  [o]Q(s,s); int [o]iwork(n); int [o]info(); [t]rwork(rworkn))

Complex version of ggsvd in PDL::LinearAlgebra::Real

🧚 cgeev 🧚

  Signature: (complex A(n,n); int jobvl(); int jobvr();complex  [o]w(n);complex  [o]vl(m,m);complex  [o]vr(p,p); int [o]info(); [t]rwork(rworkn))

Complex version of geev in PDL::LinearAlgebra::Real

💜 cgeevx 💜

  Signature: (complex [io]A(n,n);  int jobvl(); int jobvr(); int balance(); int sense();complex  [o]w(n);complex  [o]vl(m,m);complex  [o]vr(p,p); int [o]ilo(); int [o]ihi(); [o]scale(n); [o]abnrm(); [o]rconde(q); [o]rcondv(r); int [o]info(); [t]rwork(rworkn))

Complex version of geevx in PDL::LinearAlgebra::Real

🔥 cggev 🔥

  Signature: (complex A(n,n); int [phys]jobvl();int [phys]jobvr();complex B(n,n);complex [o]alpha(n);complex [o]beta(n);complex [o]VL(m,m);complex [o]VR(p,p);int [o]info(); [t]rwork(rworkn))

Complex version of ggev in PDL::LinearAlgebra::Real

💖 cggevx 💖

  Signature: (complex [io,phys]A(n,n);int balanc();int jobvl();int jobvr();int sense();complex [io,phys]B(n,n);complex [o]alpha(n);complex [o]beta(n);complex [o]VL(m,m);complex [o]VR(p,p);int [o]ilo();int [o]ihi();[o]lscale(n);[o]rscale(n);[o]abnrm();[o]bbnrm();[o]rconde(r);[o]rcondv(s);int [o]info(); [t]rwork(rworkn); int [t]bwork(bworkn); int [t]iwork(iworkn))

Complex version of ggevx in PDL::LinearAlgebra::Real

🌈 cgees 🌈

  Signature: (complex [io]A(n,n);  int jobvs(); int sort();complex  [o]w(n);complex  [o]vs(p,p); int [o]sdim(); int [o]info(); [t]rwork(n); int [t]bwork(bworkn);SV* select_func)

Complex version of gees in PDL::LinearAlgebra::Real

🎀 select_func 🎀

  • If sort = 1, select_func is used to select eigenvalues to sort to the top left of the Schur form.
  • If sort = 0, select_func is not referenced.
  • An complex eigenvalue w is selected if select_func(PDL::Complex(w)) is true.
Heads up bestie: a selected complex eigenvalue may no longer satisfy select_func(PDL::Complex(w)) = 1 after ordering, since ordering may change the value of complex eigenvalues (especially if the eigenvalue is ill-conditioned); in this case info is set to N+2. 😭

⭐ cgeesx ⭐

  Signature: (complex [io]A(n,n);  int jobvs(); int sort(); int sense();complex  [o]w(n);complex  [o]vs(p,p); int [o]sdim(); [o]rconde();[o]rcondv(); int [o]info(); [t]rwork(n); int [t]bwork(bworkn);SV* select_func)

Complex version of geesx in PDL::LinearAlgebra::Real

🎀 select_func 🎀

  • If sort = 1, select_func is used to select eigenvalues to sort to the top left of the Schur form.
  • If sort = 0, select_func is not referenced.
  • An complex eigenvalue w is selected if select_func(PDL::Complex(w)) is true.
Heads up bestie: a selected complex eigenvalue may no longer satisfy select_func(PDL::Complex(w)) = 1 after ordering, since ordering may change the value of complex eigenvalues (especially if the eigenvalue is ill-conditioned); in this case info is set to N+2. 😭

🦋 cgges 🦋

  Signature: (complex [io]A(n,n); int jobvsl();int jobvsr();int sort();complex [io]B(n,n);complex [o]alpha(n);complex [o]beta(n);complex [o]VSL(m,m);complex [o]VSR(p,p);int [o]sdim();int [o]info(); [t]rwork(rworkn); int [t]bwork(bworkn);SV* select_func)

Complex version of ggees in PDL::LinearAlgebra::Real

🎀 select_func 🎀

  • If sort = 1, select_func is used to select eigenvalues to sort to the top left of the Schur form.
  • If sort = 0, select_func is not referenced.
  • An eigenvalue w = w/beta is selected if select_func(PDL::Complex(w), PDL::Complex(beta)) is true.
Heads up bestie: a selected complex eigenvalue may no longer satisfy select_func(PDL::Complex(w),PDL::Complex(beta)) = 1 after ordering, since ordering may change the value of complex eigenvalues (especially if the eigenvalue is ill-conditioned); in this case info is set to N+2. 😭

👑 cggesx 👑

  Signature: (complex [io]A(n,n); int jobvsl();int jobvsr();int sort();int sense();complex [io]B(n,n);complex [o]alpha(n);complex [o]beta(n);complex [o]VSL(m,m);complex [o]VSR(p,p);int [o]sdim();[o]rconde(q=2);[o]rcondv(q=2);int [o]info(); [t]rwork(rworkn); int [t]bwork(bworkn); int [t]iwork(iworkn);SV* select_func)

Complex version of ggeesx in PDL::LinearAlgebra::Real

🎀 select_func 🎀

  • If sort = 1, select_func is used to select eigenvalues to sort to the top left of the Schur form.
  • If sort = 0, select_func is not referenced.
  • An eigenvalue w = w/beta is selected if select_func(PDL::Complex(w), PDL::Complex(beta)) is true.
Heads up bestie: a selected complex eigenvalue may no longer satisfy select_func(PDL::Complex(w),PDL::Complex(beta)) = 1 after ordering, since ordering may change the value of complex eigenvalues (especially if the eigenvalue is ill-conditioned); in this case info is set to N+3. 😭 (yeah, N+3 this time, not N+2, don't @ me)

💅 cheev 💅

  Signature: (complex [io]A(n,n); int jobz(); int uplo(); [o]w(n); int [o]info(); [t]rwork(rworkn))

Complex version of syev in PDL::LinearAlgebra::Real for Hermitian matrix

🌸 cheevd 🌸

  Signature: (complex [io,phys]A(n,n);  int jobz(); int uplo(); [o,phys]w(n); int [o,phys]info())

Complex version of syevd in PDL::LinearAlgebra::Real for Hermitian matrix

✨ cheevx ✨

  Signature: (complex A(n,n);  int jobz(); int range(); int uplo(); vl(); vu(); int il(); int iu(); abstol(); int [o]m(); [o]w(n);complex  [o]z(p,p);int [o]ifail(n); int [o]info(); [t]rwork(rworkn); int [t]iwork(iworkn))

Complex version of syevx in PDL::LinearAlgebra::Real for Hermitian matrix

💜 cheevr 💜

  Signature: (complex [phys]A(n,n);  int jobz(); int range(); int uplo(); [phys]vl(); [phys]vu(); int [phys]il(); int [phys]iu(); [phys]abstol(); int [o,phys]m(); [o,phys]w(n);complex  [o,phys]z(p,q);int [o,phys]isuppz(r); int [o,phys]info())

Complex version of syevr in PDL::LinearAlgebra::Real for Hermitian matrix

🧚 chegv 🧚

  Signature: (complex [io]A(n,n);int itype();int jobz(); int uplo();complex [io]B(n,n);[o]w(n); int [o]info(); [t]rwork(rworkn))

Complex version of sygv in PDL::LinearAlgebra::Real for Hermitian matrix

🎀 chegvd 🎀

  Signature: (complex [io,phys]A(n,n);int [phys]itype();int jobz(); int uplo();complex [io,phys]B(n,n);[o,phys]w(n); int [o,phys]info())

Complex version of sygvd in PDL::LinearAlgebra::Real for Hermitian matrix

🔥 chegvx 🔥

  Signature: (complex [io]A(n,n);int itype();int jobz();int range();
                int uplo();complex [io]B(n,n);vl();vu();int il();
                int iu();abstol();int [o]m();[o]w(n);complex
                [o]Z(p,p);int [o]ifail(n);int [o]info(); [t]rwork(rworkn); int [t]iwork(iworkn);
              )

Complex version of sygvx in PDL::LinearAlgebra::Real for Hermitian matrix

⭐ cgesv ⭐

  Signature: (complex [io,phys]A(n,n);complex   [io,phys]B(n,m); int [o,phys]ipiv(n); int [o,phys]info())

Complex version of gesv in PDL::LinearAlgebra::Real

💖 cgesvx 💖

  Signature: (complex [io]A(n,n); int trans(); int fact();complex  [io]B(n,m);complex  [io]af(n,n); int [io]ipiv(n); int [io]equed(); [o]r(p); [o]c(q);complex  [o]X(n,m); [o]rcond(); [o]ferr(m); [o]berr(m); [o]rpvgrw(); int [o]info(); [t]rwork(rworkn); [t]work(rworkn))

Complex version of gesvx in PDL::LinearAlgebra::Real. 🫶

🌈 trans 🌈

Specifies the form of the system of equations:

  • = 0: A * X = B (No transpose)
  • = 1: A' * X = B (Transpose)
  • = 2: A**H * X = B (Conjugate transpose)

csysv 🫶

(complex [io,phys]A(n,n);  int uplo();complex  [io,phys]B(n,m); int [o]ipiv(n); int [o]info())

Complex version of "sysv" in PDL::LinearAlgebra::Real ✨

csysvx 💖

(complex [phys]A(n,n); int uplo(); int fact();complex  [phys]B(n,m);complex  [io,phys]af(n,n); int [io,phys]ipiv(n);complex  [o]X(n,m); [o]rcond(); [o]ferr(m); [o]berr(m); int [o]info(); [t]rwork(n))

Complex version of "sysvx" in PDL::LinearAlgebra::Real

chesv 🌸

(complex [io,phys]A(n,n);  int uplo();complex  [io,phys]B(n,m); int [o,phys]ipiv(n); int [o,phys]info())

Complex version of "sysv" in PDL::LinearAlgebra::Real for Hermitian matrix 💅

chesvx 🎀

(complex A(n,n); int uplo(); int fact();complex  B(n,m);complex  [io]af(n,n); int [io]ipiv(n);complex  [o]X(n,m); [o]rcond(); [o]ferr(m); [o]berr(m); int [o]info(); [t]rwork(n))

Complex version of "sysvx" in PDL::LinearAlgebra::Real for Hermitian matrix

cposv 🦋

(complex [io,phys]A(n,n);  int uplo();complex  [io,phys]B(n,m); int [o,phys]info())

Complex version of "posv" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix ⭐

cposvx 👑

(complex [io]A(n,n); int uplo(); int fact();complex  [io]B(n,m);complex  [io]af(n,n); int [io]equed(); [o]s(p);complex  [o]X(n,m); [o]rcond(); [o]ferr(m); [o]berr(m); int [o]info(); [t]rwork(rworkn); [t]work(workn))

Complex version of "posvx" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix

cgels 🔥

(complex [io,phys]A(m,n); int trans();complex  [io,phys]B(p,q);int [o,phys]info())

Solves overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose. Complex version of "gels" in PDL::LinearAlgebra::Real.

trans:  = 0: the linear system involves A;
        = 1: the linear system involves A**H.

cgelsy 💜

(complex [io]A(m,n);complex  [io]B(p,q); rcond(); int [io]jpvt(n); int [o]rank();int [o]info(); [t]rwork(rworkn))

Complex version of "gelsy" in PDL::LinearAlgebra::Real

cgelss 🌈

(complex [io]A(m,n);complex  [io]B(p,q); rcond(); [o]s(r); int [o]rank();int [o]info(); [t]rwork(rworkn))

Complex version of "gelss" in PDL::LinearAlgebra::Real

cgelsd ✨

(complex [io]A(m,n);complex  [io]B(p,q); rcond(); [o]s(minmn); int [o]rank();int [o]info(); int [t]iwork(iworkn); [t]rwork(rworkn))

Complex version of "gelsd" in PDL::LinearAlgebra::Real

cgglse 🍓

(complex [phys]A(m,n);complex  [phys]B(p,n);complex [io,phys]c(m);complex [phys]d(p);complex [o,phys]x(n);int [o,phys]info())

Complex version of "gglse" in PDL::LinearAlgebra::Real

cggglm 🧚

(complex [phys]A(n,m);complex  [phys]B(n,p);complex [phys]d(n);complex [o,phys]x(m);complex [o,phys]y(p);int [o,phys]info())

Complex version of "ggglm" in PDL::LinearAlgebra::Real

cgetrf 💖

(complex [io]A(m,n); int [o]ipiv(p); int [o]info())

Complex version of "getrf" in PDL::LinearAlgebra::Real

cgetf2 🎀

(complex [io]A(m,n); int [o]ipiv(p); int [o]info())

Complex version of "getf2" in PDL::LinearAlgebra::Real

csytrf 🌸

(complex [io,phys]A(n,n); int uplo(); int [o,phys]ipiv(n); int [o,phys]info())

Complex version of "sytrf" in PDL::LinearAlgebra::Real

csytf2 🦋

(complex [io,phys]A(n,n); int uplo(); int [o,phys]ipiv(n); int [o,phys]info())

Complex version of "sytf2" in PDL::LinearAlgebra::Real

cchetrf 💅

(complex [io]A(n,n); int uplo(); int [o]ipiv(n); int [o]info(); [t]work(workn))

Complex version of "sytrf" in PDL::LinearAlgebra::Real for Hermitian matrix

chetf2 ⭐

(complex [io]A(n,n); int uplo(); int [o]ipiv(n); int [o]info())

Complex version of "sytf2" in PDL::LinearAlgebra::Real for Hermitian matrix

cpotrf 👑

(complex [io,phys]A(n,n); int uplo(); int [o,phys]info())

Complex version of "potrf" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix

cpotf2 🔥

(complex [io,phys]A(n,n); int uplo(); int [o,phys]info())

Complex version of "potf2" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix

cgetri 💜

(complex [io,phys]A(n,n); int [phys]ipiv(n); int [o,phys]info())

Complex version of "getri" in PDL::LinearAlgebra::Real

csytri 🌈

(complex [io]A(n,n); int uplo(); int ipiv(n); int [o]info(); [t]work(workn))

Complex version of "sytri" in PDL::LinearAlgebra::Real

chetri ✨

(complex [io]A(n,n); int uplo(); int ipiv(n); int [o]info(); [t]work(workn))

Complex version of "sytri" in PDL::LinearAlgebra::Real for Hermitian matrix

cpotri 🍓

(complex [io,phys]A(n,n); int uplo(); int [o,phys]info())

Complex version of "potri" in PDL::LinearAlgebra::Real

ctrtri 🧚

(complex [io,phys]A(n,n); int uplo(); int diag(); int [o,phys]info())

Complex version of "trtri" in PDL::LinearAlgebra::Real

ctrti2 💖

(complex [io,phys]A(n,n); int uplo(); int diag(); int [o,phys]info())

Complex version of "trti2" in PDL::LinearAlgebra::Real

cgetrs 🎀

(complex [phys]A(n,n); int trans();complex  [io,phys]B(n,m); int [phys]ipiv(n); int [o,phys]info())

Complex version of "getrs" in PDL::LinearAlgebra::Real

Arguments

trans:   = 0:  No transpose;
         = 1:  Transpose;
         = 2:  Conjugate transpose;

csytrs 🌸

(complex [phys]A(n,n); int uplo();complex [io,phys]B(n,m); int [phys]ipiv(n); int [o,phys]info())

Complex version of "sytrs" in PDL::LinearAlgebra::Real

chetrs 🦋

(complex [phys]A(n,n); int uplo();complex [io,phys]B(n,m); int [phys]ipiv(n); int [o,phys]info())

Complex version of "sytrs" in PDL::LinearAlgebra::Real for Hermitian matrix

cpotrs 💅

(complex [phys]A(n,n); int uplo();complex  [io,phys]B(n,m); int [o,phys]info())

Complex version of "potrs" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix

ctrtrs ⭐

(complex [phys]A(n,n); int uplo(); int trans(); int diag();complex [io,phys]B(n,m); int [o,phys]info())

Complex version of "trtrs" in PDL::LinearAlgebra::Real

Arguments

trans:   = 0:  No transpose;
         = 1:  Transpose;
         = 2:  Conjugate transpose;

clatrs 👑

(complex [phys]A(n,n); int uplo(); int trans(); int diag(); int normin();complex [io,phys]x(n); [o,phys]scale();[io,phys]cnorm(n);int [o,phys]info())

Complex version of "latrs" in PDL::LinearAlgebra::Real

Arguments

trans:   = 0:  No transpose;
         = 1:  Transpose;
         = 2:  Conjugate transpose;

cgecon 🔥

(complex A(n,n); int norm(); anorm(); [o]rcond();int [o]info(); [t]rwork(rworkn); [t]work(workn))

Complex version of "gecon" in PDL::LinearAlgebra::Real

csycon 💜

(complex A(n,n); int uplo(); int ipiv(n); anorm(); [o]rcond();int [o]info(); [t]work(workn))

Complex version of "sycon" in PDL::LinearAlgebra::Real

checon 🌈

(complex A(n,n); int uplo(); int ipiv(n); anorm(); [o]rcond();int [o]info(); [t]work(workn))

Complex version of "sycon" in PDL::LinearAlgebra::Real for Hermitian matrix

cpocon ✨

(complex A(n,n); int uplo(); anorm(); [o]rcond();int [o]info(); [t]work(workn); [t]rwork(n))

Complex version of "pocon" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix

ctrcon 🍓

(complex A(n,n); int norm();int uplo();int diag(); [o]rcond();int [o]info(); [t]work(workn); [t]rwork(n))

Complex version of "trcon" in PDL::LinearAlgebra::Real

cgeqp3 🧚

(complex [io]A(m,n); int [io]jpvt(n);complex  [o]tau(k); int [o]info(); [t]rwork(rworkn))

Complex version of "geqp3" in PDL::LinearAlgebra::Real

cgeqrf 💖

(complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())

Complex version of "geqrf" in PDL::LinearAlgebra::Real

cungqr 🎀

(complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())

Complex version of "orgqr" in PDL::LinearAlgebra::Real

cunmqr 🌸

(complex [phys]A(p,k); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())

Complex version of "ormqr" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.

cgelqf 🦋

(complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())

Complex version of "gelqf" in PDL::LinearAlgebra::Real

cunglq 💅

(complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())

Complex version of "orglq" in PDL::LinearAlgebra::Real

cunmlq ⭐

(complex [phys]A(k,p); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())

Complex version of "ormlq" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.

cgeqlf 👑

(complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())

Complex version of "geqlf" in PDL::LinearAlgebra::Real

cungql 🔥

(complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())

cunmql 💜

(complex [phys]A(p,k); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())

Complex version of "ormql" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.

cgerqf 🌈

(complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())

Complex version of "gerqf" in PDL::LinearAlgebra::Real

cungrq ✨

(complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())

Complex version of "orgrq" in PDL::LinearAlgebra::Real.

cunmrq 🍓

(complex [phys]A(k,p); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())

Complex version of "ormrq" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.

ctzrzf 🧚

(complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())

Complex version of "tzrzf" in PDL::LinearAlgebra::Real

cunmrz 💖

(complex [phys]A(k,p); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())

Complex version of "ormrz" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.

cgehrd 🎀

(complex [io,phys]A(n,n); int [phys]ilo();int [phys]ihi();complex [o,phys]tau(k); int [o,phys]info())

Complex version of "gehrd" in PDL::LinearAlgebra::Real

cunghr 🌸

(complex [io,phys]A(n,n); int [phys]ilo();int [phys]ihi();complex [phys]tau(k); int [o,phys]info())

Complex version of "orghr" in PDL::LinearAlgebra::Real

chseqr 🦋

(complex [io,phys]H(n,n); int job();int compz();int [phys]ilo();int [phys]ihi();complex [o,phys]w(n);complex  [o,phys]Z(m,m); int [o,phys]info())

Complex version of "hseqr" in PDL::LinearAlgebra::Real

ctrevc

Signature: (complex [io]T(n,n); int side();int howmny();int select(q);complex [o]VL(m,m);complex  [o]VR(p,p);int [o]m(); int [o]info(); [t]work(workn))

bestie this is the complex-coded version of trevc from PDL::LinearAlgebra::Real ✨ same energy, extra imaginary sparkle.

ctgevc

Signature: (complex [io]A(n,n); int side();int howmny();complex  [io]B(n,n);int select(q);complex [o]VL(m,m);complex  [o]VR(p,p);int [o]m(); int [o]info(); [t]work(workn))

and this one? complex version of tgevc in PDL::LinearAlgebra::Real 💅 two matrices, one glow-up.

cgebal

Signature: (complex [io,phys]A(n,n); int job(); int [o,phys]ilo();int [o,phys]ihi();[o,phys]scale(n); int [o,phys]info())

complex version of gebal in PDL::LinearAlgebra::Real 🦋 balancing but make it imaginary.

clange

Signature: (complex A(n,m); int norm(); [o]b(); [t]work(workn))

complex version of lange in PDL::LinearAlgebra::Real — norm time, but complex 🌸

clansy

Signature: (complex A(n,n); int uplo(); int norm(); [o]b(); [t]work(workn))

complex version of lansy in PDL::LinearAlgebra::Real 🎀

clantr

Signature: (complex A(m,n); int uplo(); int norm();int diag(); [o]b(); [t]work(workn))

complex version of lantr in PDL::LinearAlgebra::Real — triangular edition, obviously 💜

cgemm

Signature: (complex [phys]A(m,n); int transa(); int transb();complex  [phys]B(p,q);complex [phys]alpha();complex  [phys]beta();complex  [io,phys]C(r,s))

complex version of gemm in PDL::LinearAlgebra::Real. 🔥

Arguments

  • transa:
    • = 0: no transpose
    • = 1: transpose
    • = 2: conjugate transpose
  • transb:
    • = 0: no transpose
    • = 1: transpose
    • = 2: conjugate transpose

cmmult

Signature: (complex [phys]A(m,n);complex  [phys]B(p,m);complex [o,phys]C(p,n))

complex version of mmult in PDL::LinearAlgebra::Real ✨ matrix multiply but it's got feelings now.

ccrossprod

Signature: (complex [phys]A(n,m);complex  [phys]B(p,m);complex [o,phys]C(p,n))

complex version of crossprod in PDL::LinearAlgebra::Real 🌈

csyrk

Signature: (complex [phys]A(m,n); int uplo(); int trans();complex  [phys]alpha();complex  [phys]beta();complex  [io,phys]C(p,p))

complex version of syrk in PDL::LinearAlgebra::Real — symmetric rank-k, serving looks 👑

cdot

Signature: (complex [phys]a(n);complex [phys]b(n);complex [o]c())

complex version of dot in PDL::LinearAlgebra::Real 💖 two vectors, one lil scalar, no cap.

cdotc

Signature: (complex [phys]a(n);complex [phys]b(n);complex [o,phys]c())

Forms the dot product of two vectors, conjugating the first vector. 🌸 yes bestie, the first one gets conjugated — that's the whole plot twist.

caxpy

Signature: (complex [phys]a(n);complex [phys] alpha();complex [io,phys]b(n))

complex version of axpy in PDL::LinearAlgebra::Real 🦋

cnrm2

Signature: (complex [phys]a(n);[o]b())

complex version of nrm2 in PDL::LinearAlgebra::Real — the norm, but fancy ✨

casum

Signature: (complex [phys]a(n);[o]b())

complex version of asum in PDL::LinearAlgebra::Real 💅

cscal

Signature: (complex [io,phys]a(n);complex scale())

complex version of scal in PDL::LinearAlgebra::Real — scaling things up, main character energy 🎀

csscal

Signature: (complex [io,phys]a(n);scale())

Scales a complex vector by a real constant. 🫶 note that: complex vector, real constant. lowkey important.

crotg

Signature: (complex [io,phys]a();complex [phys]b();[o,phys]c();complex  [o,phys]s())

complex version of rotg in PDL::LinearAlgebra::Real 🌸

clacpy

Signature: (complex [phys]A(m,n); int uplo();complex  [o,phys]B(p,n))

complex version of lacpy in PDL::LinearAlgebra::Real — copy that, periodt 💜

claswp

Signature: (complex [io,phys]A(m,n); int [phys]k1(); int [phys]k2(); int [phys]ipiv(p))

complex version of laswp in PDL::LinearAlgebra::Real 🔥 swapping rows like it's nothing.

cmstack

Signature: (x(c,n,m);y(c,n,p);[o]out(c,n,q))

Combine two 3D ndarrays into a single ndarray. This routine does backward and forward dataflow automatically. ✨

heads up bestie: cmstack does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. 💀 so like, the bad-value flag is contagious and it spreads to every output.

ccharpol

Signature: (A(c=2,n,n);[o]Y(c=2,n,n);[o]out(c=2,p); [t]rwork(rworkn))

complex version of charpol in PDL::LinearAlgebra::Real 👑 characteristic polynomial but complex.

AUTHOR 💖

Copyright (C) Grégory Vanuxem 2005-2018.

This library is free software; you can redistribute it and/or modify it under the terms of the Perl Artistic License as in the file Artistic_2 in this distribution.

and that's a wrap on the whole page, bestie 🎀 this was Complex(3pm) from perl v5.38.2, dated 2024-03-31 — go forth and conjugate responsibly 🌈💜

📦 where this page comes from