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.\" ========================================================================
.\"
.IX Title "Complex 3pm"
.TH Complex 3pm "2023-04-02" "perl v5.36.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
PDL::LinearAlgebra::Complex \- PDL interface to the lapack linear algebra programming library (complex number)
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 9
\& 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);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This module provides an interface to parts of the lapack library (complex numbers).
These routines accept either float or double ndarrays.
#line 68 \*(L"Complex.pm\*(R"
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "cgtsv"
.IX Subsection "cgtsv"
.Vb 1
\&  Signature: (complex [phys]DL(n);complex  [phys]D(n);complex  [phys]DU(n);complex  [io,phys]B(n,nrhs); int [o,phys]info())
.Ve
.PP
Solves the equation
.PP
.Vb 1
\&        A * X = B
.Ve
.PP
where A is an \f(CW\*(C`n\*(C'\fR by \f(CW\*(C`n\*(C'\fR tridiagonal matrix, by Gaussian elimination with
partial pivoting, and B is an \f(CW\*(C`n\*(C'\fR by \f(CW\*(C`nrhs\*(C'\fR matrix.
.PP
Note that the equation \f(CW\*(C`A**T*X = B\*(C'\fR  may be solved by interchanging the
order of the arguments \s-1DU\s0 and \s-1DL.\s0
.PP
\&\fB\s-1NB\s0\fR This differs from the \s-1LINPACK\s0 function \f(CW\*(C`cgtsl\*(C'\fR in that \f(CW\*(C`DL\*(C'\fR
starts from its first element, while the \s-1LINPACK\s0 equivalent starts from
its second element.
.PP
.Vb 2
\&    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.
.Ve
.PP
.Vb 6
\& $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:\en$b" unless $info;
.Ve
.SS "cgesvd"
.IX Subsection "cgesvd"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"gesvd\*(R" in PDL::LinearAlgebra::Real.
.PP
The \s-1SVD\s0 is written
.PP
.Vb 1
\& A = U * SIGMA * ConjugateTranspose(V)
.Ve
.SS "cgesdd"
.IX Subsection "cgesdd"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"gesdd\*(R" in PDL::LinearAlgebra::Real.
.PP
The \s-1SVD\s0 is written
.PP
.Vb 1
\& A = U * SIGMA * ConjugateTranspose(V)
.Ve
.SS "cggsvd"
.IX Subsection "cggsvd"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"ggsvd\*(R" in PDL::LinearAlgebra::Real
.SS "cgeev"
.IX Subsection "cgeev"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"geev\*(R" in PDL::LinearAlgebra::Real
.SS "cgeevx"
.IX Subsection "cgeevx"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"geevx\*(R" in PDL::LinearAlgebra::Real
.SS "cggev"
.IX Subsection "cggev"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"ggev\*(R" in PDL::LinearAlgebra::Real
.SS "cggevx"
.IX Subsection "cggevx"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"ggevx\*(R" in PDL::LinearAlgebra::Real
.SS "cgees"
.IX Subsection "cgees"
.Vb 1
\&  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)
.Ve
.PP
Complex version of \*(L"gees\*(R" in PDL::LinearAlgebra::Real
.PP
.Vb 11
\&    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.
.Ve
.SS "cgeesx"
.IX Subsection "cgeesx"
.Vb 1
\&  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)
.Ve
.PP
Complex version of \*(L"geesx\*(R" in PDL::LinearAlgebra::Real
.PP
.Vb 11
\&    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.
.Ve
.SS "cgges"
.IX Subsection "cgges"
.Vb 1
\&  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)
.Ve
.PP
Complex version of \*(L"ggees\*(R" in PDL::LinearAlgebra::Real
.PP
.Vb 11
\&    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.
.Ve
.SS "cggesx"
.IX Subsection "cggesx"
.Vb 1
\&  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)
.Ve
.PP
Complex version of \*(L"ggeesx\*(R" in PDL::LinearAlgebra::Real
.PP
.Vb 11
\&    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.
.Ve
.SS "cheev"
.IX Subsection "cheev"
.Vb 1
\&  Signature: (complex [io]A(n,n); int jobz(); int uplo(); [o]w(n); int [o]info(); [t]rwork(rworkn))
.Ve
.PP
Complex version of \*(L"syev\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cheevd"
.IX Subsection "cheevd"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n);  int jobz(); int uplo(); [o,phys]w(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"syevd\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cheevx"
.IX Subsection "cheevx"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"syevx\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cheevr"
.IX Subsection "cheevr"
.Vb 1
\&  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())
.Ve
.PP
Complex version of \*(L"syevr\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "chegv"
.IX Subsection "chegv"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"sygv\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "chegvd"
.IX Subsection "chegvd"
.Vb 1
\&  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())
.Ve
.PP
Complex version of \*(L"sygvd\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "chegvx"
.IX Subsection "chegvx"
.Vb 5
\&  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);
\&        )
.Ve
.PP
Complex version of \*(L"sygvx\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cgesv"
.IX Subsection "cgesv"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n);complex   [io,phys]B(n,m); int [o,phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"gesv\*(R" in PDL::LinearAlgebra::Real
.SS "cgesvx"
.IX Subsection "cgesvx"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"gesvx\*(R" in PDL::LinearAlgebra::Real.
.PP
.Vb 4
\&    trans:  Specifies the form of the system of equations:
\&            = 0:  A * X = B     (No transpose)   
\&            = 1:  A\*(Aq * X = B  (Transpose)   
\&            = 2:  A**H * X = B  (Conjugate transpose)
.Ve
.SS "csysv"
.IX Subsection "csysv"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n);  int uplo();complex  [io,phys]B(n,m); int [o]ipiv(n); int [o]info())
.Ve
.PP
Complex version of \*(L"sysv\*(R" in PDL::LinearAlgebra::Real
.SS "csysvx"
.IX Subsection "csysvx"
.Vb 1
\&  Signature: (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))
.Ve
.PP
Complex version of \*(L"sysvx\*(R" in PDL::LinearAlgebra::Real
.SS "chesv"
.IX Subsection "chesv"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n);  int uplo();complex  [io,phys]B(n,m); int [o,phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"sysv\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "chesvx"
.IX Subsection "chesvx"
.Vb 1
\&  Signature: (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))
.Ve
.PP
Complex version of \*(L"sysvx\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cposv"
.IX Subsection "cposv"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n);  int uplo();complex  [io,phys]B(n,m); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"posv\*(R" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix
.SS "cposvx"
.IX Subsection "cposvx"
.Vb 1
\&  Signature: (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))
.Ve
.PP
Complex version of \*(L"posvx\*(R" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix
.SS "cgels"
.IX Subsection "cgels"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n); int trans();complex  [io,phys]B(p,q);int [o,phys]info())
.Ve
.PP
Solves overdetermined or underdetermined complex linear systems   
involving an M\-by-N matrix A, or its conjugate-transpose.
Complex version of \*(L"gels\*(R" in PDL::LinearAlgebra::Real.
.PP
.Vb 2
\&    trans:  = 0: the linear system involves A;
\&            = 1: the linear system involves A**H.
.Ve
.SS "cgelsy"
.IX Subsection "cgelsy"
.Vb 1
\&  Signature: (complex [io]A(m,n);complex  [io]B(p,q); rcond(); int [io]jpvt(n); int [o]rank();int [o]info(); [t]rwork(rworkn))
.Ve
.PP
Complex version of \*(L"gelsy\*(R" in PDL::LinearAlgebra::Real
.SS "cgelss"
.IX Subsection "cgelss"
.Vb 1
\&  Signature: (complex [io]A(m,n);complex  [io]B(p,q); rcond(); [o]s(r); int [o]rank();int [o]info(); [t]rwork(rworkn))
.Ve
.PP
Complex version of \*(L"gelss\*(R" in PDL::LinearAlgebra::Real
.SS "cgelsd"
.IX Subsection "cgelsd"
.Vb 1
\&  Signature: (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))
.Ve
.PP
Complex version of \*(L"gelsd\*(R" in PDL::LinearAlgebra::Real
.SS "cgglse"
.IX Subsection "cgglse"
.Vb 1
\&  Signature: (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())
.Ve
.PP
Complex version of \*(L"gglse\*(R" in PDL::LinearAlgebra::Real
.SS "cggglm"
.IX Subsection "cggglm"
.Vb 1
\&  Signature: (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())
.Ve
.PP
Complex version of \*(L"ggglm\*(R" in PDL::LinearAlgebra::Real
.SS "cgetrf"
.IX Subsection "cgetrf"
.Vb 1
\&  Signature: (complex [io]A(m,n); int [o]ipiv(p); int [o]info())
.Ve
.PP
Complex version of \*(L"getrf\*(R" in PDL::LinearAlgebra::Real
.SS "cgetf2"
.IX Subsection "cgetf2"
.Vb 1
\&  Signature: (complex [io]A(m,n); int [o]ipiv(p); int [o]info())
.Ve
.PP
Complex version of \*(L"getf2\*(R" in PDL::LinearAlgebra::Real
.SS "csytrf"
.IX Subsection "csytrf"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int uplo(); int [o,phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"sytrf\*(R" in PDL::LinearAlgebra::Real
.SS "csytf2"
.IX Subsection "csytf2"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int uplo(); int [o,phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"sytf2\*(R" in PDL::LinearAlgebra::Real
.SS "cchetrf"
.IX Subsection "cchetrf"
.Vb 1
\&  Signature: (complex [io]A(n,n); int uplo(); int [o]ipiv(n); int [o]info(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"sytrf\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "chetf2"
.IX Subsection "chetf2"
.Vb 1
\&  Signature: (complex [io]A(n,n); int uplo(); int [o]ipiv(n); int [o]info())
.Ve
.PP
Complex version of \*(L"sytf2\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cpotrf"
.IX Subsection "cpotrf"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int uplo(); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"potrf\*(R" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix
.SS "cpotf2"
.IX Subsection "cpotf2"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int uplo(); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"potf2\*(R" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix
.SS "cgetri"
.IX Subsection "cgetri"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int [phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"getri\*(R" in PDL::LinearAlgebra::Real
.SS "csytri"
.IX Subsection "csytri"
.Vb 1
\&  Signature: (complex [io]A(n,n); int uplo(); int ipiv(n); int [o]info(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"sytri\*(R" in PDL::LinearAlgebra::Real
.SS "chetri"
.IX Subsection "chetri"
.Vb 1
\&  Signature: (complex [io]A(n,n); int uplo(); int ipiv(n); int [o]info(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"sytri\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cpotri"
.IX Subsection "cpotri"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int uplo(); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"potri\*(R" in PDL::LinearAlgebra::Real
.SS "ctrtri"
.IX Subsection "ctrtri"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int uplo(); int diag(); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"trtri\*(R" in PDL::LinearAlgebra::Real
.SS "ctrti2"
.IX Subsection "ctrti2"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int uplo(); int diag(); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"trti2\*(R" in PDL::LinearAlgebra::Real
.SS "cgetrs"
.IX Subsection "cgetrs"
.Vb 1
\&  Signature: (complex [phys]A(n,n); int trans();complex  [io,phys]B(n,m); int [phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"getrs\*(R" in PDL::LinearAlgebra::Real
.PP
.Vb 5
\&    Arguments   
\&    =========   
\&        trans:   = 0:  No transpose;
\&                 = 1:  Transpose; 
\&                 = 2:  Conjugate transpose;
.Ve
.SS "csytrs"
.IX Subsection "csytrs"
.Vb 1
\&  Signature: (complex [phys]A(n,n); int uplo();complex [io,phys]B(n,m); int [phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"sytrs\*(R" in PDL::LinearAlgebra::Real
.SS "chetrs"
.IX Subsection "chetrs"
.Vb 1
\&  Signature: (complex [phys]A(n,n); int uplo();complex [io,phys]B(n,m); int [phys]ipiv(n); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"sytrs\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cpotrs"
.IX Subsection "cpotrs"
.Vb 1
\&  Signature: (complex [phys]A(n,n); int uplo();complex  [io,phys]B(n,m); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"potrs\*(R" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix
.SS "ctrtrs"
.IX Subsection "ctrtrs"
.Vb 1
\&  Signature: (complex [phys]A(n,n); int uplo(); int trans(); int diag();complex [io,phys]B(n,m); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"trtrs\*(R" in PDL::LinearAlgebra::Real
.PP
.Vb 5
\&    Arguments   
\&    =========   
\&        trans:   = 0:  No transpose;
\&                 = 1:  Transpose; 
\&                 = 2:  Conjugate transpose;
.Ve
.SS "clatrs"
.IX Subsection "clatrs"
.Vb 1
\&  Signature: (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())
.Ve
.PP
Complex version of \*(L"latrs\*(R" in PDL::LinearAlgebra::Real
.PP
.Vb 5
\&    Arguments   
\&    =========   
\&        trans:   = 0:  No transpose;
\&                 = 1:  Transpose; 
\&                 = 2:  Conjugate transpose;
.Ve
.SS "cgecon"
.IX Subsection "cgecon"
.Vb 1
\&  Signature: (complex A(n,n); int norm(); anorm(); [o]rcond();int [o]info(); [t]rwork(rworkn); [t]work(workn))
.Ve
.PP
Complex version of \*(L"gecon\*(R" in PDL::LinearAlgebra::Real
.SS "csycon"
.IX Subsection "csycon"
.Vb 1
\&  Signature: (complex A(n,n); int uplo(); int ipiv(n); anorm(); [o]rcond();int [o]info(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"sycon\*(R" in PDL::LinearAlgebra::Real
.SS "checon"
.IX Subsection "checon"
.Vb 1
\&  Signature: (complex A(n,n); int uplo(); int ipiv(n); anorm(); [o]rcond();int [o]info(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"sycon\*(R" in PDL::LinearAlgebra::Real for Hermitian matrix
.SS "cpocon"
.IX Subsection "cpocon"
.Vb 1
\&  Signature: (complex A(n,n); int uplo(); anorm(); [o]rcond();int [o]info(); [t]work(workn); [t]rwork(n))
.Ve
.PP
Complex version of \*(L"pocon\*(R" in PDL::LinearAlgebra::Real for Hermitian positive definite matrix
.SS "ctrcon"
.IX Subsection "ctrcon"
.Vb 1
\&  Signature: (complex A(n,n); int norm();int uplo();int diag(); [o]rcond();int [o]info(); [t]work(workn); [t]rwork(n))
.Ve
.PP
Complex version of \*(L"trcon\*(R" in PDL::LinearAlgebra::Real
.SS "cgeqp3"
.IX Subsection "cgeqp3"
.Vb 1
\&  Signature: (complex [io]A(m,n); int [io]jpvt(n);complex  [o]tau(k); int [o]info(); [t]rwork(rworkn))
.Ve
.PP
Complex version of \*(L"geqp3\*(R" in PDL::LinearAlgebra::Real
.SS "cgeqrf"
.IX Subsection "cgeqrf"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"geqrf\*(R" in PDL::LinearAlgebra::Real
.SS "cungqr"
.IX Subsection "cungqr"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"orgqr\*(R" in PDL::LinearAlgebra::Real
.SS "cunmqr"
.IX Subsection "cunmqr"
.Vb 1
\&  Signature: (complex [phys]A(p,k); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())
.Ve
.PP
Complex version of \*(L"ormqr\*(R" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.
.SS "cgelqf"
.IX Subsection "cgelqf"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"gelqf\*(R" in PDL::LinearAlgebra::Real
.SS "cunglq"
.IX Subsection "cunglq"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"orglq\*(R" in PDL::LinearAlgebra::Real
.SS "cunmlq"
.IX Subsection "cunmlq"
.Vb 1
\&  Signature: (complex [phys]A(k,p); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())
.Ve
.PP
Complex version of \*(L"ormlq\*(R" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.
.SS "cgeqlf"
.IX Subsection "cgeqlf"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"geqlf\*(R" in PDL::LinearAlgebra::Real
.SS "cungql"
.IX Subsection "cungql"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())
.Ve
.SS "cunmql"
.IX Subsection "cunmql"
.Vb 1
\&  Signature: (complex [phys]A(p,k); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())
.Ve
.PP
Complex version of \*(L"ormql\*(R" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.
.SS "cgerqf"
.IX Subsection "cgerqf"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"gerqf\*(R" in PDL::LinearAlgebra::Real
.SS "cungrq"
.IX Subsection "cungrq"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"orgrq\*(R" in PDL::LinearAlgebra::Real.
.SS "cunmrq"
.IX Subsection "cunmrq"
.Vb 1
\&  Signature: (complex [phys]A(k,p); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())
.Ve
.PP
Complex version of \*(L"ormrq\*(R" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.
.SS "ctzrzf"
.IX Subsection "ctzrzf"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n);complex  [o,phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"tzrzf\*(R" in PDL::LinearAlgebra::Real
.SS "cunmrz"
.IX Subsection "cunmrz"
.Vb 1
\&  Signature: (complex [phys]A(k,p); int side(); int trans();complex  [phys]tau(k);complex  [io,phys]C(m,n);int [o,phys]info())
.Ve
.PP
Complex version of \*(L"ormrz\*(R" in PDL::LinearAlgebra::Real. Here trans = 1 means conjugate transpose.
.SS "cgehrd"
.IX Subsection "cgehrd"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int [phys]ilo();int [phys]ihi();complex [o,phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"gehrd\*(R" in PDL::LinearAlgebra::Real
.SS "cunghr"
.IX Subsection "cunghr"
.Vb 1
\&  Signature: (complex [io,phys]A(n,n); int [phys]ilo();int [phys]ihi();complex [phys]tau(k); int [o,phys]info())
.Ve
.PP
Complex version of \*(L"orghr\*(R" in PDL::LinearAlgebra::Real
.SS "chseqr"
.IX Subsection "chseqr"
.Vb 1
\&  Signature: (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())
.Ve
.PP
Complex version of \*(L"hseqr\*(R" in PDL::LinearAlgebra::Real
.SS "ctrevc"
.IX Subsection "ctrevc"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"trevc\*(R" in PDL::LinearAlgebra::Real
.SS "ctgevc"
.IX Subsection "ctgevc"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"tgevc\*(R" in PDL::LinearAlgebra::Real
.SS "cgebal"
.IX Subsection "cgebal"
.Vb 1
\&  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())
.Ve
.PP
Complex version of \*(L"gebal\*(R" in PDL::LinearAlgebra::Real
.SS "clange"
.IX Subsection "clange"
.Vb 1
\&  Signature: (complex A(n,m); int norm(); [o]b(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"lange\*(R" in PDL::LinearAlgebra::Real
.SS "clansy"
.IX Subsection "clansy"
.Vb 1
\&  Signature: (complex A(n,n); int uplo(); int norm(); [o]b(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"lansy\*(R" in PDL::LinearAlgebra::Real
.SS "clantr"
.IX Subsection "clantr"
.Vb 1
\&  Signature: (complex A(m,n); int uplo(); int norm();int diag(); [o]b(); [t]work(workn))
.Ve
.PP
Complex version of \*(L"lantr\*(R" in PDL::LinearAlgebra::Real
.SS "cgemm"
.IX Subsection "cgemm"
.Vb 1
\&  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))
.Ve
.PP
Complex version of \*(L"gemm\*(R" in PDL::LinearAlgebra::Real.
.PP
.Vb 5
\&    Arguments   
\&    =========   
\&        transa:  = 0:  No transpose;
\&                 = 1:  Transpose; 
\&                 = 2:  Conjugate transpose;
\&
\&        transb:  = 0:  No transpose;
\&                 = 1:  Transpose; 
\&                 = 2:  Conjugate transpose;
.Ve
.SS "cmmult"
.IX Subsection "cmmult"
.Vb 1
\&  Signature: (complex [phys]A(m,n);complex  [phys]B(p,m);complex  [o,phys]C(p,n))
.Ve
.PP
Complex version of \*(L"mmult\*(R" in PDL::LinearAlgebra::Real
.SS "ccrossprod"
.IX Subsection "ccrossprod"
.Vb 1
\&  Signature: (complex [phys]A(n,m);complex  [phys]B(p,m);complex  [o,phys]C(p,n))
.Ve
.PP
Complex version of \*(L"crossprod\*(R" in PDL::LinearAlgebra::Real
.SS "csyrk"
.IX Subsection "csyrk"
.Vb 1
\&  Signature: (complex [phys]A(m,n); int uplo(); int trans();complex  [phys]alpha();complex  [phys]beta();complex  [io,phys]C(p,p))
.Ve
.PP
Complex version of \*(L"syrk\*(R" in PDL::LinearAlgebra::Real
.SS "cdot"
.IX Subsection "cdot"
.Vb 1
\&  Signature: (complex [phys]a(n);complex [phys]b(n);complex [o]c())
.Ve
.PP
Complex version of \*(L"dot\*(R" in PDL::LinearAlgebra::Real
.SS "cdotc"
.IX Subsection "cdotc"
.Vb 1
\&  Signature: (complex [phys]a(n);complex [phys]b(n);complex [o,phys]c())
.Ve
.PP
Forms the dot product of two vectors, conjugating the first   
vector.
.SS "caxpy"
.IX Subsection "caxpy"
.Vb 1
\&  Signature: (complex [phys]a(n);complex [phys] alpha();complex [io,phys]b(n))
.Ve
.PP
Complex version of \*(L"axpy\*(R" in PDL::LinearAlgebra::Real
.SS "cnrm2"
.IX Subsection "cnrm2"
.Vb 1
\&  Signature: (complex [phys]a(n);[o]b())
.Ve
.PP
Complex version of \*(L"nrm2\*(R" in PDL::LinearAlgebra::Real
.SS "casum"
.IX Subsection "casum"
.Vb 1
\&  Signature: (complex [phys]a(n);[o]b())
.Ve
.PP
Complex version of \*(L"asum\*(R" in PDL::LinearAlgebra::Real
.SS "cscal"
.IX Subsection "cscal"
.Vb 1
\&  Signature: (complex [io,phys]a(n);complex scale())
.Ve
.PP
Complex version of \*(L"scal\*(R" in PDL::LinearAlgebra::Real
.SS "csscal"
.IX Subsection "csscal"
.Vb 1
\&  Signature: (complex [io,phys]a(n);scale())
.Ve
.PP
Scales a complex vector by a real constant.
.SS "crotg"
.IX Subsection "crotg"
.Vb 1
\&  Signature: (complex [io,phys]a();complex [phys]b();[o,phys]c();complex  [o,phys]s())
.Ve
.PP
Complex version of \*(L"rotg\*(R" in PDL::LinearAlgebra::Real
.SS "clacpy"
.IX Subsection "clacpy"
.Vb 1
\&  Signature: (complex [phys]A(m,n); int uplo();complex  [o,phys]B(p,n))
.Ve
.PP
Complex version of \*(L"lacpy\*(R" in PDL::LinearAlgebra::Real
.SS "claswp"
.IX Subsection "claswp"
.Vb 1
\&  Signature: (complex [io,phys]A(m,n); int [phys]k1(); int [phys]k2(); int [phys]ipiv(p))
.Ve
.PP
Complex version of \*(L"laswp\*(R" in PDL::LinearAlgebra::Real
.SS "ctricpy"
.IX Subsection "ctricpy"
.Vb 1
\&  Signature: (A(c=2,m,n);int uplo();[o] C(c=2,m,n))
.Ve
.PP
Copy triangular part to another matrix. If uplo == 0 copy upper triangular part.
.PP
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.
.SS "cmstack"
.IX Subsection "cmstack"
.Vb 1
\&  Signature: (x(c,n,m);y(c,n,p);[o]out(c,n,q))
.Ve
.PP
Combine two 3D ndarrays into a single ndarray.
This routine does backward and forward dataflow automatically.
.PP
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.
.SS "ccharpol"
.IX Subsection "ccharpol"
.Vb 1
\&  Signature: (A(c=2,n,n);[o]Y(c=2,n,n);[o]out(c=2,p); [t]rwork(rworkn))
.Ve
.PP
Complex version of \*(L"charpol\*(R" in PDL::LinearAlgebra::Real
.SH "AUTHOR"
.IX Header "AUTHOR"
Copyright (C) Grégory Vanuxem 2005\-2018.
.PP
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.