PDL::LinearAlgebra::Complex - PDL interface to the lapack linear algebra programming library (complex number)
use PDL::Complex use PDL::LinearAlgebra::Complex; $a = r2C random (100,100); $s = r2C zeroes(100); $u = r2C zeroes(100,100); $v = r2C zeroes(100,100); $info = 0; $job = 0; cgesdd($a, $job, $info, $s , $u, $v); # or, using native complex numbers: 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);
This module provides an interface to parts of the lapack library (complex numbers). These routines accept either float or double ndarrays.
Signature: ([phys]DL(2,n); [phys]D(2,n); [phys]DU(2,n); [io,phys]B(2,n,nrhs); int [o,phys]info())
Solves the equation
A * X = B
where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting, and B is an n by nrhs matrix.
n
nrhs
Note that the equation A**T*X = B may be solved by interchanging the order of the arguments DU and DL.
A**T*X = B
NB This differs from the LINPACK function cgtsl in that DL starts from its first element, while the LINPACK equivalent starts from its second element.
cgtsl
DL
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.
use PDL::Complex; $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;
Signature: ([io,phys]A(2,m,n); int jobu(); int jobvt(); [o,phys]s(r); [o,phys]U(2,p,q); [o,phys]VT(2,s,t); int [o,phys]info())
Complex version of gesvd.
The SVD is written
A = U * SIGMA * ConjugateTranspose(V)
Signature: ([io,phys]A(2,m,n); int job(); [o,phys]s(r); [o,phys]U(2,p,q); [o,phys]VT(2,s,t); int [o,phys]info())
Complex version of gesdd.
Signature: ([io,phys]A(2,m,n); int jobu(); int jobv(); int jobq(); [io,phys]B(2,p,n); int [o,phys]k(); int [o,phys]l();[o,phys]alpha(n);[o,phys]beta(n); [o,phys]U(2,q,r); [o,phys]V(2,s,t); [o,phys]Q(2,u,v); int [o,phys]iwork(n); int [o,phys]info())
Complex version of ggsvd
Signature: ([phys]A(2,n,n); int jobvl(); int jobvr(); [o,phys]w(2,n); [o,phys]vl(2,m,m); [o,phys]vr(2,p,p); int [o,phys]info())
Complex version of geev
Signature: ([io,phys]A(2,n,n); int jobvl(); int jobvr(); int balance(); int sense(); [o,phys]w(2,n); [o,phys]vl(2,m,m); [o,phys]vr(2,p,p); int [o,phys]ilo(); int [o,phys]ihi(); [o,phys]scale(n); [o,phys]abnrm(); [o,phys]rconde(q); [o,phys]rcondv(r); int [o,phys]info())
Complex version of geevx
Signature: ([phys]A(2,n,n); int jobvl();int jobvr();[phys]B(2,n,n);[o,phys]alpha(2,n);[o,phys]beta(2,n);[o,phys]VL(2,m,m);[o,phys]VR(2,p,p);int [o,phys]info())
Complex version of ggev
Signature: ([io,phys]A(2,n,n);int balanc();int jobvl();int jobvr();int sense();[io,phys]B(2,n,n);[o,phys]alpha(2,n);[o,phys]beta(2,n);[o,phys]VL(2,m,m);[o,phys]VR(2,p,p);int [o,phys]ilo();int [o,phys]ihi();[o,phys]lscale(n);[o,phys]rscale(n);[o,phys]abnrm();[o,phys]bbnrm();[o,phys]rconde(r);[o,phys]rcondv(s);int [o,phys]info())
Complex version of ggevx
Signature: ([io,phys]A(2,n,n); int jobvs(); int sort(); [o,phys]w(2,n); [o,phys]vs(2,p,p); int [o,phys]sdim(); int [o,phys]info())
Complex version of gees
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; Note that 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.
Signature: ([io,phys]A(2,n,n); int jobvs(); int sort(); int sense(); [o,phys]w(2,n);[o,phys]vs(2,p,p); int [o,phys]sdim(); [o,phys]rconde();[o,phys]rcondv(); int [o,phys]info())
Complex version of geesx
Signature: ([io,phys]A(2,n,n); int jobvsl();int jobvsr();int sort();[io,phys]B(2,n,n);[o,phys]alpha(2,n);[o,phys]beta(2,n);[o,phys]VSL(2,m,m);[o,phys]VSR(2,p,p);int [o,phys]sdim();int [o,phys]info())
Complex version of ggees
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; Note that 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.
Signature: ([io,phys]A(2,n,n); int jobvsl();int jobvsr();int sort();int sense();[io,phys]B(2,n,n);[o,phys]alpha(2,n);[o,phys]beta(2,n);[o,phys]VSL(2,m,m);[o,phys]VSR(2,p,p);int [o,phys]sdim();[o,phys]rconde(q);[o,phys]rcondv(r);int [o,phys]info())
Complex version of ggeesx
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; Note that 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.
Signature: ([io,phys]A(2,n,n); int jobz(); int uplo(); [o,phys]w(n); int [o,phys]info())
Complex version of syev for Hermitian matrix
Complex version of syevd for Hermitian matrix
Signature: ([phys]A(2,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); [o,phys]z(2,p,q);int [o,phys]ifail(r); int [o,phys]info())
Complex version of syevx for Hermitian matrix
Signature: ([phys]A(2,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); [o,phys]z(2,p,q);int [o,phys]isuppz(r); int [o,phys]info())
Complex version of syevr for Hermitian matrix
Signature: ([io,phys]A(2,n,n);int [phys]itype();int jobz(); int uplo();[io,phys]B(2,n,n);[o,phys]w(n); int [o,phys]info())
Complex version of sygv for Hermitian matrix
Complex version of sygvd for Hermitian matrix
Signature: ([io,phys]A(2,n,n);int [phys]itype();int jobz();int range(); int uplo();[io,phys]B(2,n,n);[phys]vl();[phys]vu();int [phys]il();int [phys]iu();[phys]abstol();int [o,phys]m();[o,phys]w(n); [o,phys]Z(2,p,q);int [o,phys]ifail(r);int [o,phys]info())
Complex version of sygvx for Hermitian matrix
Signature: ([io,phys]A(2,n,n); [io,phys]B(2,n,m); int [o,phys]ipiv(n); int [o,phys]info())
Complex version of gesv
Signature: ([io,phys]A(2,n,n); int trans(); int fact(); [io,phys]B(2,n,m); [io,phys]af(2,n,n); int [io,phys]ipiv(n); int [io]equed(); [io,phys]r(n); [io,phys]c(n); [o,phys]X(2,n,m); [o,phys]rcond(); [o,phys]ferr(m); [o,phys]berr(m); [o,phys]rpvgrw(); int [o,phys]info())
Complex version of gesvx.
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)
Signature: ([io,phys]A(2,n,n); int uplo(); [io,phys]B(2,n,m); int [o,phys]ipiv(n); int [o,phys]info())
Complex version of sysv
Signature: ([phys]A(2,n,n); int uplo(); int fact(); [phys]B(2,n,m); [io,phys]af(2,n,n); int [io,phys]ipiv(n); [o,phys]X(2,n,m); [o,phys]rcond(); [o,phys]ferr(m); [o,phys]berr(m); int [o,phys]info())
Complex version of sysvx
Complex version of sysv for Hermitian matrix
Complex version of sysvx for Hermitian matrix
Signature: ([io,phys]A(2,n,n); int uplo(); [io,phys]B(2,n,m); int [o,phys]info())
Complex version of posv for Hermitian positive definite matrix
Signature: ([io,phys]A(2,n,n); int uplo(); int fact(); [io,phys]B(2,n,m); [io,phys]af(2,n,n); int [io]equed(); [io,phys]s(n); [o,phys]X(2,n,m); [o,phys]rcond(); [o,phys]ferr(m); [o,phys]berr(m); int [o,phys]info())
Complex version of posvx for Hermitian positive definite matrix
Signature: ([io,phys]A(2,m,n); int trans(); [io,phys]B(2,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.
trans: = 0: the linear system involves A; = 1: the linear system involves A**H.
Signature: ([io,phys]A(2,m,n); [io,phys]B(2,p,q); [phys]rcond(); int [io,phys]jpvt(n); int [o,phys]rank();int [o,phys]info())
Complex version of gelsy
Signature: ([io,phys]A(2,m,n); [io,phys]B(2,p,q); [phys]rcond(); [o,phys]s(r); int [o,phys]rank();int [o,phys]info())
Complex version of gelss
Complex version of gelsd
Signature: ([phys]A(2,m,n); [phys]B(2,p,n);[io,phys]c(2,m);[phys]d(2,p);[o,phys]x(2,n);int [o,phys]info())
Complex version of gglse
Signature: ([phys]A(2,n,m); [phys]B(2,n,p);[phys]d(2,n);[o,phys]x(2,m);[o,phys]y(2,p);int [o,phys]info())
Complex version of ggglm
Signature: ([io,phys]A(2,m,n); int [o,phys]ipiv(p); int [o,phys]info())
Complex version of getrf
Complex version of getf2
Signature: ([io,phys]A(2,n,n); int uplo(); int [o,phys]ipiv(n); int [o,phys]info())
Complex version of sytrf
Complex version of sytf2
Complex version of sytrf for Hermitian matrix
Complex version of sytf2 for Hermitian matrix
Signature: ([io,phys]A(2,n,n); int uplo(); int [o,phys]info())
Complex version of potrf for Hermitian positive definite matrix
Complex version of potf2 for Hermitian positive definite matrix
Signature: ([io,phys]A(2,n,n); int [phys]ipiv(n); int [o,phys]info())
Complex version of getri
Signature: ([io,phys]A(2,n,n); int uplo(); int [phys]ipiv(n); int [o,phys]info())
Complex version of sytri
Complex version of sytri for Hermitian matrix
Complex version of potri
Signature: ([io,phys]A(2,n,n); int uplo(); int diag(); int [o,phys]info())
Complex version of trtri
Complex version of trti2
Signature: ([phys]A(2,n,n); int trans(); [io,phys]B(2,n,m); int [phys]ipiv(n); int [o,phys]info())
Complex version of getrs
Arguments ========= trans: = 0: No transpose; = 1: Transpose; = 2: Conjugate transpose;
Signature: ([phys]A(2,n,n); int uplo();[io,phys]B(2,n,m); int [phys]ipiv(n); int [o,phys]info())
Complex version of sytrs
Complex version of sytrs for Hermitian matrix
Signature: ([phys]A(2,n,n); int uplo(); [io,phys]B(2,n,m); int [o,phys]info())
Complex version of potrs for Hermitian positive definite matrix
Signature: ([phys]A(2,n,n); int uplo(); int trans(); int diag();[io,phys]B(2,n,m); int [o,phys]info())
Complex version of trtrs
Signature: ([phys]A(2,n,n); int uplo(); int trans(); int diag(); int normin();[io,phys]x(2,n); [o,phys]scale();[io,phys]cnorm(n);int [o,phys]info())
Complex version of latrs
Signature: ([phys]A(2,n,n); int norm(); [phys]anorm(); [o,phys]rcond();int [o,phys]info())
Complex version of gecon
Signature: ([phys]A(2,n,n); int uplo(); int ipiv(n); [phys]anorm(); [o,phys]rcond();int [o,phys]info())
Complex version of sycon
Complex version of sycon for Hermitian matrix
Signature: ([phys]A(2,n,n); int uplo(); [phys]anorm(); [o,phys]rcond();int [o,phys]info())
Complex version of pocon for Hermitian positive definite matrix
Signature: ([phys]A(2,n,n); int norm();int uplo();int diag(); [o,phys]rcond();int [o,phys]info())
Complex version of trcon
Signature: ([io,phys]A(2,m,n); int [io,phys]jpvt(n); [o,phys]tau(2,k); int [o,phys]info())
Complex version of geqp3
Signature: ([io,phys]A(2,m,n); [o,phys]tau(2,k); int [o,phys]info())
Complex version of geqrf
Signature: ([io,phys]A(2,m,n); [phys]tau(2,k); int [o,phys]info())
Complex version of orgqr
Signature: ([phys]A(2,p,k); int side(); int trans(); [phys]tau(2,k); [io,phys]C(2,m,n);int [o,phys]info())
Complex version of ormqr. Here trans = 1 means conjugate transpose.
Complex version of gelqf
Complex version of orglq
Signature: ([phys]A(2,k,p); int side(); int trans(); [phys]tau(2,k); [io,phys]C(2,m,n);int [o,phys]info())
Complex version of ormlq. Here trans = 1 means conjugate transpose.
Complex version of geqlf
Complex version of orgql.
Complex version of ormql. Here trans = 1 means conjugate transpose.
Complex version of gerqf
Complex version of orgrq.
Complex version of ormrq. Here trans = 1 means conjugate transpose.
Complex version of tzrzf
Complex version of ormrz. Here trans = 1 means conjugate transpose.
Signature: ([io,phys]A(2,n,n); int [phys]ilo();int [phys]ihi();[o,phys]tau(2,k); int [o,phys]info())
Complex version of gehrd
Signature: ([io,phys]A(2,n,n); int [phys]ilo();int [phys]ihi();[phys]tau(2,k); int [o,phys]info())
Complex version of orghr
Signature: ([io,phys]H(2,n,n); int job();int compz();int [phys]ilo();int [phys]ihi();[o,phys]w(2,n); [o,phys]Z(2,m,m); int [o,phys]info())
Complex version of hseqr
Signature: ([io,phys]T(2,n,n); int side();int howmny();int [phys]select(q);[io,phys]VL(2,m,r); [io,phys]VR(2,p,s);int [o,phys]m(); int [o,phys]info())
Complex version of trevc
Signature: ([io,phys]A(2,n,n); int side();int howmny(); [io,phys]B(2,n,n);int [phys]select(q);[io,phys]VL(2,m,r); [io,phys]VR(2,p,s);int [o,phys]m(); int [o,phys]info())
Complex version of tgevc
Signature: ([io,phys]A(2,n,n); int job(); int [o,phys]ilo();int [o,phys]ihi();[o,phys]scale(n); int [o,phys]info())
Complex version of gebal
Signature: ([phys]A(2,n,m); int norm(); [o]b())
Complex version of lange
Signature: ([phys]A(2, n,n); int uplo(); int norm(); [o]b())
Complex version of lansy
Signature: ([phys]A(2,m,n);int uplo();int norm();int diag();[o]b())
Complex version of lantr
Signature: ([phys]A(2,m,n); int transa(); int transb(); [phys]B(2,p,q);[phys]alpha(2); [phys]beta(2); [io,phys]C(2,r,s))
Complex version of gemm.
Arguments ========= transa: = 0: No transpose; = 1: Transpose; = 2: Conjugate transpose; transb: = 0: No transpose; = 1: Transpose; = 2: Conjugate transpose;
Signature: ([phys]A(2,m,n); [phys]B(2,p,m); [o,phys]C(2,p,n))
Complex version of mmult
Signature: ([phys]A(2,n,m); [phys]B(2,p,m); [o,phys]C(2,p,n))
Complex version of crossprod
Signature: ([phys]A(2,m,n); int uplo(); int trans(); [phys]alpha(2); [phys]beta(2); [io,phys]C(2,p,p))
Complex version of syrk
Signature: ([phys]a(2,n);int [phys]inca();[phys]b(2,n);int [phys]incb();[o,phys]c(2))
Complex version of dot
Forms the dot product of two vectors, conjugating the first vector.
Signature: ([phys]a(2,n);int [phys]inca();[phys] alpha(2);[io,phys]b(2,n);int [phys]incb())
Complex version of axpy
Signature: ([phys]a(2,n);int [phys]inca();[o,phys]b())
Complex version of nrm2
Complex version of asum
Signature: ([io,phys]a(2,n);int [phys]inca();[phys]scale(2))
Complex version of scal
Signature: ([io,phys]a(2,n);int [phys]inca();[phys]scale())
Scales a complex vector by a real constant.
sscal ignores the bad-value flag of the input ndarrays. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
Signature: ([io,phys]a(2);[phys]b(2);[o,phys]c(); [o,phys]s(2))
Complex version of rotg
Signature: ([phys]A(2,m,n); int uplo(); [o,phys]B(2,p,n))
Complex version of lacpy
Signature: ([io,phys]A(2,m,n); int [phys]k1(); int [phys]k2(); int [phys]ipiv(p);int [phys]inc())
Complex version of laswp
Signature: (A(c=2,m,n);int uplo();[o] C(c=2,m,n))
Copy triangular part to another matrix. If uplo == 0 copy upper triangular part.
ctricpy 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.
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.
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.
Signature: ([phys]A(c=2,n,n);[phys,o]Y(c=2,n,n);[phys,o]out(c=2,p);)
Complex version of charpol
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.
To install PDL::LinearAlgebra, copy and paste the appropriate command in to your terminal.
cpanm
cpanm PDL::LinearAlgebra
CPAN shell
perl -MCPAN -e shell install PDL::LinearAlgebra
For more information on module installation, please visit the detailed CPAN module installation guide.