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Àm"F@V@f@v@†@–@¦@¶@Æ@Ö@æ@ö@AA&A6AFAVAfAvA†A–A¦A¶AÆAÖAæAöABB&B6BFBVBfBvB†B–B¦B¶BÆBÖBæBöBCC&C6CFCVCfCvC†C–C¦C¶CÆCÖCæCöCDD&D6DFDVDfDvD†D–D¦D¶DÆDÖDæDöDEE&E6EFEVEfEvE†E–E¦E¶EÆEÖEæEöEFF&F6FFFVFfFvF†F–F¦F¶FÆFÖFæFöFGG&G6GFGVGfGvG†G–G¦G¶GÆGÖGæGöGt"F@Ë@…?äAÖAÛAÍA4DD@É@ÔAÙA@@‡?ÞAæAïAF@ÒCuB¶C˜@¼C…C¿CÂC›C4DD@™CÅC@ÌCÔCApply an elementary Householder reflector to a matrix.

larfx(v, tau, C, side='L', m=C.size[0], n=C.size[1],
      ldC=max(1,C.size[0]), offsetv=0, offsetC=0)

PURPOSE
Computes H*C (side is 'L') or C*H (side is 'R') where

    H = I - tau * v * v^H.

On exit C is overwritten with the result.

ARGUMENTS
v         'd' or 'z' matrix

tau       number.  Can only be complex if v is complex.

C         'd' or 'z' matrix of the same type as v

side      'L' or 'R'

m         nonnegative integer.  If negative, the default value is 
          used.

n         nonnegative integer.  If negative, the default value is 
          used.

ldC       nonnegative integer.  ldC >= max(1,m).  If zero, the
          default value is used.

offsetv   nonnegative integer 

offsetC   nonnegative integerGenerate an elementary Householder reflector.

tau = larfg(alpha, x, n=None, offseta=0, offsetx=0)

PURPOSE
Generates a Householder reflector

    H = I - tau * [1; v] * [1; v]^H

such that

    H^H * [alpha; x] = [beta; 0].

In other words,

    (I - tau.conjugate() * [1; v] * [1; v]^H) * [alpha; x] = [beta; 0].

The matrix H is unitary, so

    2 * tau.real = abs(tau)**2 * ( 1.0 + ||v||**2).

On exit x contains the vector v and alpha is overwritten with beta.
The parameter tau is returned as the output value of the function.

ARGUMENTS
alpha     'd' or 'z' matrix.  On exit, contains beta.

x         'd' or 'z' matrix.  Must have the same type as alpha.
          On exit, contains v. 

n         postive integer.  The dimension of the vector [alpha; x].
          If n <= 0, the default value is used, which is equal to
          1 + ( (len(x) - offsetx >= 1) ? len(x) - ox : 0 ).

offseta   nonnegative integer 

offsetx   nonnegative integer 

tau       scalar of the same type as alpha and xCopy all or part of a matrix.

lacpy(A, B, uplo='N', m=A.size[0], n=A.size[1], 
      ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0, 
      offsetB=0)

PURPOSE
Copy the m x n matrix A to B.  If uplo is 'U', the upper
trapezoidal part of A is copied.  If uplo is 'L', the lower 
trapezoidal part is copied.  if uplo is 'N', the entire matrix is
copied.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'N', 'L' or 'U'

m         nonnegative integer.  If negative, the default value is
          used.

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,m).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,m).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerGeneralized Schur factorization of real or complex matrices.

sdim = gges(A, B, a=None, b=None, Vl=None, Vr=None, select=None,
            n=A.size[0], ldA=max(1,A.size[0]),
            ldB=max(1,B.size[0]), ldVl=max(1,Vl.size[0]),
            ldVr=max(1,Vr.size[0]), offsetA=0, offestB=0, 
            offseta=0, offsetb=0, offsetVl=0, offsetVr=0)

PURPOSE
Computes the real generalized Schur form A = Vl * S * Vr^T, 
B = Vl * T * Vr^T, or the complex generalized Schur form 
A = Vl * S * Vr^H, B = Vl * T * Vr^H of the square matrices A, B,
the generalized eigenvalues, and, optionally, the matrices of left 
and right Schur vectors.  The real form is computed if A and B are 
real, and the complex Schur form is computed if A and B are
complex.  On exit, A is replaced with S and B is replaced with T.
If the arguments a and b are provided, then on return a[i] / b[i] 
is the ith generalized eigenvalue.  If Vl is provided, then the 
left Schur vectors are computed and returned in Vl.  If Vr is 
provided then the right Schur vectors are computed and returned 
in Vr.  The argument select can be used to obtain an ordered Schur
factorization.  It must be a Python function that can be called as
f(u,v) with u complex, and v real, and returns 0 or 1.  The 
eigenvalues u/v for which f(u, v) is 1 will be placed first on the
diagonal of S and T.  For the real case, eigenvalues u/v for which
f(u, v) or f(conj(u), v) is 1, are placed first.  If select is 
provided, gges() returns the number of eigenvalues that satisfy the
selection criterion.  Otherwise, it returns 0.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

a         'z' matrix of length at least n

b         'd' matrix of length at least n

Vl        'd' or 'z' matrix.  Must have the same type as A.

Vr        'd' or 'z' matrix.  Must have the same type as A.

select    Python function that takes a complex and a real number 
          as argument and returns True or False.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).
          If zero, the default value is used.

ldB       nonnegative integer.  ldB >= max(1,n).
          If zero, the default value is used.

ldVl      nonnegative integer.  ldVl >= 1 and ldVl >= n if Vl 
          is present.  If zero, the default value is used (with 
          Vl.size[0] replaced by 0 if Vl is None).

ldVr      nonnegative integer.  ldVr >= 1 and ldVr >= n if Vr 
          is present.  If zero, the default value is used (with 
          Vr.size[0] replaced by 0 if Vr is None).

offsetA   nonnegative integer

offsetB   nonnegative integer

offseta   nonnegative integer

offsetb   nonnegative integer

offsetVl  nonnegative integer

offsetVr  nonnegative integer

sdim      number of eigenvalues that satisfy the selection
          criterion specified by select.Schur factorization of a real of complex matrix.

sdim = gees(A, w=None, V=None, select=None, n=A.size[0],
            ldA=max(1,A.size[0]), ldV=max(1,Vs.size[0]), offsetA=0,
            offsetw=0, offsetV=0)

PURPOSE
Computes the real Schur form A = V * S * V^T or the complex Schur
form A = V * S * V^H, the eigenvalues, and, optionally, the matrix
of Schur vectors of an n by n matrix A.  The real Schur form is 
computed if A is real, and the conmplex Schur form is computed if 
A is complex.  On exit, A is replaced with S.  If the argument w is
provided, the eigenvalues are returned in w.  If V is provided, the
Schur vectors are computed and returned in V.  The argument select
can be used to obtain an ordered Schur factorization.  It must be a
Python function that can be called as f(s) with s complex, and 
returns 0 or 1.  The eigenvalues s for which f(s) is 1 will be 
placed first in the Schur factorization.   For the real case, 
eigenvalues s for which f(s) or f(conj(s)) is 1, are placed first.
If select is provided, gees() returns the number of eigenvalues 
that satisfy the selection criterion.   Otherwise, it returns 0.

ARGUMENTS
A         'd' or 'z' matrix

w         'z' matrix of length at least n

V         'd' or 'z' matrix.  Must have the same type as A.

select    Python function that takes a complex number as argument
          and returns True or False.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).
          If zero, the default value is used.

ldV       nonnegative integer.  ldV >= 1 and ldV >= n if V is
          present.  If zero, the default value is used (with 
          V.size[0] replaced by 0 if V is None).

offsetA   nonnegative integer

offsetW   nonnegative integer

offsetV   nonnegative integer

sdim      number of eigenvalues that satisfy the selection
          criterion specified by select.Singular value decomposition of a real or complex matrix
(divide-and-conquer driver).

gesdd(A, S, jobz='N', U=None, V=None, m=A.size[0], n=A.size[1], 
      ldA=max(1,A.size[0]), ldU=None, ldVt=None, offsetA=0, 
      offsetS=0, offsetU=0, offsetVt=0)

PURPOSE
Computes singular values and, optionally, singular vectors of a 
real or complex m by n matrix A.  The argument jobz controls how
many singular vectors are computed:

'N': no singular vectors are computed.
'A': all m left singular vectors are computed and returned as
     columns of U;  all n right singular vectors are computed 
     and returned as rows of Vt.
'S': the first min(m,n) left and right singular vectors are
     computed and returned as columns of U and rows of Vt.
'O': if m>=n, the first n left singular vectors are returned as
     columns of A and the n right singular vectors are returned
     as rows of Vt.  If m<n, the m left singular vectors are
     returned as columns of U and the first m right singular
     vectors are returned as rows of A.

Note that the (conjugate) transposes of the right singular 
vectors are returned in Vt or A.

On exit (in all cases), the contents of A are destroyed.

ARGUMENTS
A         'd' or 'z' matrix

S         'd' matrix of length at least min(m,n).  On exit, 
          contains the computed singular values in descending
          order.

jobz      'N', 'A', 'S' or 'O'

U         'd' or 'z' matrix.  Must have the same type as A.
          Not referenced if jobz is 'N' or jobz is 'O' and m>=n.
          If jobz is 'A' or jobz is 'O' and m<n, a matrix with
          at least m columns.   If jobz is 'S', a matrix with at
          least min(m,n) columns.  On exit (except when jobz is
          'N' or jobz is 'O' and m>=n), contains the computed
          left singular vectors stored columnwise.

Vt        'd' or 'z' matrix.  Must have the same type as A.
          Not referenced if jobz is 'N' or jobz is 'O' and m<n.
          If jobz is 'A' or 'S' or jobz is 'O' and m>=n, a
          matrix with at least n columns.   On exit (except when
          jobz is 'N' or jobz is 'O' and m<n), the rows of Vt
          contain the computed right singular vectors, or, in
          the complex case, their complex conjugates.

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m).
          If zero, the default value is used.

ldU       nonnegative integer.
          ldU >= 1 if jobz is 'N' or 'O'.
          ldU >= max(1,m) if jobz is 'S' or 'A' or jobz is 'O'
          and m<n.  The default value is max(1,U.size[0]) if
          jobz is 'S' or 'A' or jobz is'O' and m<n, and 1
          otherwise.

ldVt      nonnegative integer.
          ldVt >= 1 if jobz is 'N'.
          ldVt >= max(1,n) if jobz is 'A' or jobz is 'O' and 
          m>=n.  
          ldVt >= max(1,min(m,n)) if ldVt is 'S'.
          The default value is max(1,Vt.size[0]) if jobvt is 'A'
          or 'S' or jobvt is 'O' and m>=n, and 1 otherwise.
          If zero, the default value is used.

offsetA   nonnegative integer

offsetS   nonnegative integer

offsetU   nonnegative integer

offsetVt  nonnegative integerSingular value decomposition of a real or complex matrix.

gesvd(A, S, jobu='N', jobvt='N', U=None, Vt=None, m=A.size[0],
      n=A.size[1], ldA=max(1,A.size[0]), ldU=None, ldVt=None,
      offsetA=0, offsetS=0, offsetU=0, offsetVt=0)

PURPOSE
Computes singular values and, optionally, singular vectors of a 
real or complex m by n matrix A.

The argument jobu controls how many left singular vectors are
computed: 

'N': no left singular vectors are computed.
'A': all left singular vectors are computed and returned as
     columns of U.
'S': the first min(m,n) left singular vectors are computed and
     returned as columns of U.
'O': the first min(m,n) left singular vectors are computed and
     returned as columns of A.

The argument jobvt controls how many right singular vectors are
computed:

'N': no right singular vectors are computed.
'A': all right singular vectors are computed and returned as
     rows of Vt.
'S': the first min(m,n) right singular vectors are computed and
     returned as rows of Vt.
'O': the first min(m,n) right singular vectors are computed and
     returned as rows of A.
Note that the (conjugate) transposes of the right singular 
vectors are returned in Vt or A.

On exit (in all cases), the contents of A are destroyed.

ARGUMENTS
A         'd' or 'z' matrix

S         'd' matrix of length at least min(m,n).  On exit, 
          contains the computed singular values in descending
          order.

jobu      'N', 'A', 'S' or 'O'

jobvt     'N', 'A', 'S' or 'O'

U         'd' or 'z' matrix.  Must have the same type as A.
          Not referenced if jobu is 'N' or 'O'.  If jobu is 'A',
          a matrix with at least m columns.   If jobu is 'S', a
          matrix with at least min(m,n) columns.
          On exit (with jobu 'A' or 'S'), the columns of U
          contain the computed left singular vectors.

Vt        'd' or 'z' matrix.  Must have the same type as A.
          Not referenced if jobvt is 'N' or 'O'.  If jobvt is 
          'A' or 'S', a matrix with at least n columns.
          On exit (with jobvt 'A' or 'S'), the rows of Vt
          contain the computed right singular vectors, or, in
          the complex case, their complex conjugates.

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m).
          If zero, the default value is used.

ldU       nonnegative integer.
          ldU >= 1 if jobu is 'N' or 'O'.
          ldU >= max(1,m) if jobu is 'A' or 'S'.
          The default value is max(1,U.size[0]) if jobu is 'A' 
          or 'S', and 1 otherwise.
          If zero, the default value is used.

ldVt      nonnegative integer.
          ldVt >= 1 if jobvt is 'N' or 'O'.
          ldVt >= max(1,n) if jobvt is 'A'.  
          ldVt >= max(1,min(m,n)) if ldVt is 'S'.
          The default value is max(1,Vt.size[0]) if jobvt is 'A'
          or 'S', and 1 otherwise.
          If zero, the default value is used.

offsetA   nonnegative integer

offsetS   nonnegative integer

offsetU   nonnegative integer

offsetVt  nonnegative integerGeneralized symmetric-definite eigenvalue decomposition with
real or complex matrices.

hegv(A, B, W, itype=1, jobz='N', uplo='L', n=A.size[0], 
     ldA = max(1,A.size[0]), ldB = max(1,B.size[0]), offsetA=0, 
     offsetB=0, offsetW=0)

PURPOSE
Returns eigenvalues/vectors of a real or complex generalized
symmetric-definite eigenproblem of order n, with B positive
definite. 
1. If itype is 1: A*x = lambda*B*x.
2. If itype is 2: A*Bx = lambda*x.
3. If itype is 3: B*Ax = lambda*x.n

On exit, W contains the eigenvalues in ascending order.  If jobz
is 'V', the matrix of eigenvectors Z is also computed and 
returned in A, normalized as follows: 
1. If itype is 1: Z^H*A*Z = diag(W), Z^H*B*Z = I
2. If itype is 2: Z^H*A^{-1}*Z = diag(W), Z^H*B*Z = I
3. If itype is 3: Z^H*A*Z = diag(W), Z^H*B^{-1}*Z = I.

If jobz is 'N', only the eigenvalues are computed, and the 
contents of A is destroyed.   On exit, the matrix B is replaced
by its Cholesky factor.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

W         'd' matrix of length at least n

itype     integer 1, 2, or 3

jobz      'N' or 'V'

uplo      'L' or 'U'

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

ldB       nonnegative integer.  ldB >= max(1,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerGeneralized symmetric-definite eigenvalue decomposition with real
matrices.

sygv(A, B, W, itype=1, jobz='N', uplo='L', n=A.size[0], 
     ldA = max(1,A.size[0]), ldB = max(1,B.size[0]), offsetA=0, 
     offsetB=0, offsetW=0)

PURPOSE
Returns eigenvalues/vectors of a real generalized 
symmetric-definite eigenproblem of order n, with B positive 
definite. 
1. If itype is 1: A*x = lambda*B*x.
2. If itype is 2: A*Bx = lambda*x.
3. If itype is 3: B*Ax = lambda*x.

On exit, W contains the eigenvalues in ascending order.  If jobz
is 'V', the matrix of eigenvectors Z is also computed and
returned in A, normalized as follows: 
1. If itype is 1: Z^T*A*Z = diag(W), Z^T*B*Z = I
2. If itype is 2: Z^T*A^{-1}*Z = diag(W)^{-1}, Z^T*B*Z = I
3. If itype is 3: Z^T*A*Z = diag(W), Z^T*B^{-1}*Z = I.

If jobz is 'N', only the eigenvalues are computed, and the
contents of A is destroyed.   On exit, the matrix B is replaced
by its Cholesky factor.

ARGUMENTS
A         'd' matrix

B         'd' matrix

W         'd' matrix of length at least n

itype     integer 1, 2, or 3

jobz      'N' or 'V'

uplo      'L' or 'U'

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

ldB       nonnegative integer.  ldB >= max(1,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerComputes selected eigenvalues and eigenvectors of a real symmetric
or complex Hermitian matrix (RRR driver).

m = syevr(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, 
          il=1, iu=1, Z=None, n=A.size[0], ldA=max(1,A.size[0]),
          ldZ=None, abstol=0.0, offsetA=0, offsetW=0, offsetZ=0)

PURPOSE
Computes selected eigenvalues/vectors of a real symmetric or
complex Hermitian n by n matrix A.
If range is 'A', all eigenvalues are computed.
If range is 'V', all eigenvalues in the interval (vl,vu] are
computed.
If range is 'I', all eigenvalues il through iu are computed
(sorted in ascending order with 1 <= il <= iu <= n).
If jobz is 'N', only the eigenvalues are returned in W.
If jobz is 'V', the eigenvectors are also returned in Z.
On exit, the content of A is destroyed.
syevr is usually the fastest of the four eigenvalue routines.

ARGUMENTS
A         'd' or 'z' matrix

W         'd' matrix of length at least n.  On exit, contains
          the computed eigenvalues in ascending order.

jobz      'N' or 'V'

range     'A', 'V' or 'I'

uplo      'L' or 'U'

vl,vu     doubles.  Only required when range is 'V'.

il,iu     integers.  Only required when range is 'I'.

Z         'd' or 'z' matrix.  Must have the same type as A.
          Only required when jobz = 'V'.  If range is 'A' or
          'V', Z must have at least n columns.  If range is 'I',
          Z must have at least iu-il+1 columns.  On exit the
          first m columns of Z contain the computed (normalized)
          eigenvectors.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).
          If zero, the default value is used.

ldZ       nonnegative integer.  ldZ >= 1 if jobz is 'N' and
          ldZ >= max(1,n) if jobz is 'V'.  The default value
          is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.
          If zero, the default value is used.

abstol    double.  Absolute error tolerance for eigenvalues.
          If nonpositive, the LAPACK default value is used.

offsetA   nonnegative integer

offsetW   nonnegative integer

offsetZ   nonnegative integer

m         the number of eigenvalues computedComputes selected eigenvalues and eigenvectors of a real symmetric
matrix (RRR driver).

m = syevr(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, 
          il=1, iu=1, Z=None, n=A.size[0], ldA=max(1,A.size[0]),
          ldZ=None, abstol=0.0, offsetA=0, offsetW=0, offsetZ=0)

PURPOSE
Computes selected eigenvalues/vectors of a real symmetric n by n
matrix A.
If range is 'A', all eigenvalues are computed.
If range is 'V', all eigenvalues in the interval (vl,vu] are
computed.
If range is 'I', all eigenvalues il through iu are computed
(sorted in ascending order with 1 <= il <= iu <= n).
If jobz is 'N', only the eigenvalues are returned in W.
If jobz is 'V', the eigenvectors are also returned in Z.
On exit, the content of A is destroyed.
syevr is usually the fastest of the four eigenvalue routines.

ARGUMENTS
A         'd' matrix

W         'd' matrix of length at least n.  On exit, contains
          the computed eigenvalues in ascending order.

jobz      'N' or 'V'

range     'A', 'V' or 'I'

uplo      'L' or 'U'

vl,vu     doubles.  Only required when range is 'V'.

il,iu     integers.  Only required when range is 'I'.

Z         'd' matrix.  Only required when jobz = 'V'.
          If range is 'A' or 'V', Z must have at least n columns.
          If range is 'I', Z must have at least iu-il+1 columns.
          On exit the first m columns of Z contain the computed
          (normalized) eigenvectors.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).
          If zero, the default value is used.

ldZ       nonnegative integer.  ldZ >= 1 if jobz is 'N' and
          ldZ >= max(1,n) if jobz is 'V'.  The default value
          is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.
          If zero, the default value is used.

abstol    double.  Absolute error tolerance for eigenvalues.
          If nonpositive, the LAPACK default value is used.

offsetA   nonnegative integer

offsetW   nonnegative integer

offsetZ   nonnegative integer

m         the number of eigenvalues computedEigenvalue decomposition of a real symmetric or complex Hermitian
matrix (divide-and-conquer driver).

heevd(A, W, jobz='N', uplo='L', n=A.size[0], ldA = max(1,A.size[0]),
      offsetA=0, offsetW=0)

PURPOSE
Returns  eigenvalues/vectors of a real symmetric or complex
Hermitian n by n matrix A.  On exit, W contains the eigenvalues
in ascending order.  If jobz is 'V', the (normalized) eigenvectors
are also computed and returned in A.  If jobz is 'N', only the
eigenvalues are computed, and the content of A is destroyed.


ARGUMENTS
A         'd' matrix

W         'd' matrix of length at least n.  On exit, contains
          the computed eigenvalues in ascending order.

jobz      'N' or 'V'

uplo      'L' or 'U'

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerEigenvalue decomposition of a real symmetric matrix
(divide-and-conquer driver).

syevd(A, W, jobz='N', uplo='L', n=A.size[0], ldA = max(1,A.size[0]),
      offsetA=0, offsetW=0)

PURPOSE
Returns  eigenvalues/vectors of a real symmetric nxn matrix A.
On exit, W contains the eigenvalues in ascending order.
If jobz is 'V', the (normalized) eigenvectors are also computed
and returned in A.  If jobz is 'N', only the eigenvalues are
computed, and the content of A is destroyed.


ARGUMENTS
A         'd' matrix

W         'd' matrix of length at least n.  On exit, contains
          the computed eigenvalues in ascending order.

jobz      'N' or 'V'

uplo      'L' or 'U'

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerComputes selected eigenvalues and eigenvectors of a real symmetric
or complex Hermitian matrix (expert driver).

m = syevx(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, 
          il=1, iu=1, Z=None, n=A.size[0], 
          ldA = max(1,A.size[0]), ldZ=None, abstol=0.0, 
          offsetA=0, offsetW=0, offsetZ=0)

PURPOSE
Computes selected eigenvalues/vectors of a real symmetric or
complex Hermitian n by n matrix A.
If range is 'A', all eigenvalues are computed.
If range is 'V', all eigenvalues in the interval (vl,vu] are
computed.
If range is 'I', all eigenvalues il through iu are computed
(sorted in ascending order with 1 <= il <= iu <= n).
If jobz is 'N', only the eigenvalues are returned in W.
If jobz is 'V', the eigenvectors are also returned in Z.
On exit, the content of A is destroyed.

ARGUMENTS
A         'd' or 'z' matrix

W         'd' matrix of length at least n.  On exit, contains
          the computed eigenvalues in ascending order.

jobz      'N' or 'V'

range     'A', 'V' or 'I'

uplo      'L' or 'U'

vl,vu     doubles.  Only required when range is 'V'.

il,iu     integers.  Only required when range is 'I'.

Z         'd' or 'z' matrix.  Must have the same type as A.
          Z is only required when jobz is 'V'.  If range is 'A'
          or 'V', Z must have at least n columns.  If range is
          'I', Z must have at least iu-il+1 columns.  On exit
          the first m columns of Z contain the computed
          (normalized) eigenvectors.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

ldZ       nonnegative integer.  ldZ >= 1 if jobz is 'N' and
          ldZ >= max(1,n) if jobz is 'V'.  The default value
          is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.
          If zero, the default value is used.

abstol    double.  Absolute error tolerance for eigenvalues.
          If nonpositive, the LAPACK default value is used.

offsetA   nonnegative integer

offsetW   nonnegative integer

offsetZ   nonnegative integer

m         the number of eigenvalues computedComputes selected eigenvalues and eigenvectors of a real symmetric
matrix (expert driver).

m = syevx(A, W, jobz='N', range='A', uplo='L', vl=0.0, vu=0.0, 
          il=1, iu=1, Z=None, n=A.size[0], ldA=max(1,A.size[0]),
          ldZ=None, abstol=0.0, offsetA=0, offsetW=0,
          offsetZ=0)

PURPOSE
Computes selected eigenvalues/vectors of a real symmetric n by n
matrix A.
If range is 'A', all eigenvalues are computed.
If range is 'V', all eigenvalues in the interval (vl,vu] are
computed.
If range is 'I', all eigenvalues il through iu are computed
(sorted in ascending order with 1 <= il <= iu <= n).
If jobz is 'N', only the eigenvalues are returned in W.
If jobz is 'V', the eigenvectors are also returned in Z.
On exit, the content of A is destroyed.

ARGUMENTS
A         'd' matrix

W         'd' matrix of length at least n.  On exit, contains
          the computed eigenvalues in ascending order.

jobz      'N' or 'V'

range     'A', 'V' or 'I'

uplo      'L' or 'U'

vl,vu     doubles.  Only required when range is 'V'.

il,iu     integers.  Only required when range is 'I'.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

Z         'd' matrix.  Only required when jobz is 'V'.  If range
          is 'A' or 'V', Z must have at least n columns.  If
          range is 'I', Z must have at least iu-il+1 columns.
          On exit the first m columns of Z contain the computed
          (normalized) eigenvectors.

abstol    double.  Absolute error tolerance for eigenvalues.
          If nonpositive, the LAPACK default value is used.

ldZ       nonnegative integer.  ldZ >= 1 if jobz is 'N' and
          ldZ >= max(1,n) if jobz is 'V'.  The default value
          is 1 if jobz is 'N' and max(1,Z.size[0]) if jobz ='V'.
          If zero, the default value is used.

offsetA   nonnegative integer

offsetW   nonnegative integer

offsetZ   nonnegative integer

m         the number of eigenvalues computedEigenvalue decomposition of a real symmetric or complex Hermitian
matrix.

heev(A, W, jobz='N', uplo='L', n=A.size[0], ldA = max(1,A.size[0]),
     offsetA=0, offsetW=0)

PURPOSE
Returns eigenvalues/vectors of a real symmetric or complex
Hermitian nxn matrix A.  On exit, W contains the eigenvalues in
ascending order.  If jobz is 'V', the (normalized) eigenvectors
are also computed and returned in A.  If jobz is 'N', only the
eigenvalues are computed, and the content of A is destroyed.

ARGUMENTS
A         'd' or 'z' matrix

W         'd' matrix of length at least n

jobz      'N' or 'V'

uplo      'L' or 'U'

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerEigenvalue decomposition of a real symmetric matrix.

syev(A, W, jobz='N', uplo='L', n=A.size[0], ldA = max(1,A.size[0]),
     offsetA=0, offsetW=0)

PURPOSE
Returns eigenvalues/vectors of a real symmetric nxn matrix A.
On exit, W contains the eigenvalues in ascending order.  If jobz
is 'V', the (normalized) eigenvectors are also computed and
returned in A.  If jobz is 'N', only the eigenvalues are
computed, and the content of A is destroyed.

ARGUMENTS
A         'd' matrix

W         'd' matrix of length at least n

jobz      'N' or 'V'

uplo      'L' or 'U'

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerQR factorization with column pivoting.

geqp3(A, jpvt, tau, m=A.size[0], n=A.size[1], ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
QR factorization with column pivoting of an m by n real or complex
matrix A:

A*P = Q*R = [Q1 Q2] * [R1; 0] if m >= n
A*P = Q*R = Q * [R1 R2] if m <= n,

where P is a permutation matrix, Q is m by m and orthogonal/unitary
and R is m by n with R1 upper triangular.  On exit, R is stored in
the upper triangular part of A.  Q is stored as a product of
k=min(m,n) elementary reflectors.  The parameters of the
reflectors are stored in the first k entries of tau and in the
lower triangular part of the first k columns of A.  On entry, if
jpvt[j] is nonzero, the jth column of A is permuted to the front of
A*P.  If jpvt[j] is zero, the jth column is a free column.  On exit
A*P = A[:, jpvt - 1].

ARGUMENTS
A         'd' or 'z' matrix

jpvt      'i' matrix of length n

tau       'd' or 'z' matrix of length min(m,n).  Must have the same
          type as A.

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integerGenerate the orthogonal or unitary matrix in an LQ factorization.

unglq(A, tau, m=min(A.size), n=A.size[1], k=len(tau), 
      ldA=max(1,A.size[0]), offsetA=0)

PURPOSE
On entry, A and tau contain an n by n orthogonal/unitary matrix Q.
Q is defined as a product of k elementary reflectors, stored in the
first k rows of A and in tau, as computed by gelqf().  On exit,
the first m rows of Q are stored in the leading rows of A.

ARGUMENTS
A         'd' or 'z' matrix

tau       'd' or 'z' matrix of length at least k.  Must have the
          same type as A.

m         integer.  If negative, the default value is used.

n         integer.  n >= m.  If negative, the default value is used.

k         integer.  k <= m.  If negative, the default value is 
          used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integerGenerate the orthogonal matrix in an LQ factorization.

orglq(A, tau, m=min(A.size), n=A.size[1], k=len(tau), 
      ldA=max(1,A.size[0]), offsetA=0)

PURPOSE
On entry, A and tau contain an n by n orthogonal matrix Q.
Q is defined as a product of k elementary reflectors, stored in the
first k rows of A and in tau, as computed by gelqf().  On exit,
the first m rows of Q are stored in the leading rows of A.

ARGUMENTS
A         'd' matrix

tau       'd' matrix of length at least k

m         integer.  If negative, the default value is used.

n         integer.  n >= m.  If negative, the default value is used.

k         integer.  k <= m.  If negative, the default value is 
          used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integerProduct with a real or complex orthogonal matrix.

unmlq(A, tau, C, side='L', trans='N', m=C.size[0], n=C.size[1],
      k=min(A.size), ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),
      offsetA=0, offsetC=0)

PURPOSE
Computes
C := Q*C   if side = 'L' and trans = 'N'.
C := Q^T*C if side = 'L' and trans = 'T'.
C := Q^H*C if side = 'L' and trans = 'C'.
C := C*Q   if side = 'R' and trans = 'N'.
C := C*Q^T if side = 'R' and trans = 'T'.
C := C*Q^H if side = 'R' and trans = 'C'.
C is m by n and Q is a square orthogonal/unitary matrix computed
by gelqf.  Q is defined as a product of k elementary reflectors,
stored as the first k rows of A and the first k entries of tau.

ARGUMENTS
A         'd' or 'z' matrix

tau       'd' or 'z' matrix of length at least k.  Must have the
          same type as A.

C         'd' or 'z' matrix.  Must have the same type as A.

side      'L' or 'R'

trans     'N', 'T', or 'C'n
m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

k         integer.  k <= m if side = 'R' and k <= n if side = 'L'.
          If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,k).  If zero, the
          default value is used.

ldC       nonnegative integer.  ldC >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerProduct with a real orthogonal matrix.

ormlq(A, tau, C, side='L', trans='N', m=C.size[0], n=C.size[1],
      k=min(A.size), ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),
      offsetA=0, offsetC=0)

PURPOSE
Computes
C := Q*C   if side = 'L' and trans = 'N'.
C := Q^T*C if side = 'L' and trans = 'T'.
C := C*Q   if side = 'R' and trans = 'N'.
C := C*Q^T if side = 'R' and trans = 'T'.
C is m by n and Q is a square orthogonal matrix computed by gelqf.
Q is defined as a product of k elementary reflectors, stored as
the first k rows of A and the first k entries of tau.

ARGUMENTS
A         'd' matrix

tau       'd' matrix of length at least k

C         'd' matrix

side      'L' or 'R'

trans     'N' or 'T'

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

k         integer.  k <= m if side = 'L' and k <= n if side = 'R'.
          If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,k).  If zero, the
          default value is used.

ldC       nonnegative integer.  ldC >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerLQ factorization.

gelqf(A, tau, m=A.size[0], n=A.size[1], ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
LQ factorization of an m by n real or complex matrix A:

A = L*Q = [L1; 0] * [Q1; Q2] if m <= n
A = L*Q = [L1; L2] * Q if m >= n,

where Q is n by n and orthogonal/unitary and L is m by n with L1
lower triangular.  On exit, L is stored in the lower triangular
part of A.  Q is stored as a product of k=min(m,n) elementary
reflectors.  The parameters of the reflectors are stored in the
first k entries of tau and in the upper  triangular part of the
first k rows of A.

ARGUMENTS
A         'd' or 'z' matrix

tau       'd' or 'z' matrix of length at least min(m,n).  Must
          have the same type as A.

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integerGenerate the orthogonal or unitary matrix in a QR factorization.

ungqr(A, tau, m=A.size[0], n=min(A.size), k=len(tau), 
      ldA=max(1,A.size[0]), offsetA=0)

PURPOSE
On entry, A and tau contain an m by m orthogonal/unitary matrix Q.
Q is defined as a product of k elementary reflectors, stored in the
first k columns of A and in tau, as computed by geqrf().  On exit,
the first n columns of Q are stored in the leading columns of A.

ARGUMENTS
A         'd' or 'z' matrix

tau       'd' or 'z' matrix of length at least k.  Must have the
          same type as A.

m         integer.  If negative, the default value is used.

n         integer.  n <= m.  If negative, the default value is used.

k         integer.  k <= n.  If negative, the default value is 
          used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integerGenerate the orthogonal matrix in a QR factorization.

ormqr(A, tau, m=A.size[0], n=min(A.size), k=len(tau), 
      ldA=max(1,A.size[0]), offsetA=0)

PURPOSE
On entry, A and tau contain an m by m orthogonal matrix Q.
Q is defined as a product of k elementary reflectors, stored in the
first k columns of A and in tau, as computed by geqrf().  On exit,
the first n columns of Q are stored in the leading columns of A.

ARGUMENTS
A         'd' matrix

tau       'd' matrix of length at least k

m         integer.  If negative, the default value is used.

n         integer.  n <= m.  If negative, the default value is used.

k         integer.  k <= n.  If negative, the default value is 
          used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integerProduct with a real or complex orthogonal matrix.

unmqr(A, tau, C, side='L', trans='N', m=C.size[0], n=C.size[1],
      k=len(tau), ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),
      offsetA=0, offsetC=0)

PURPOSE
Computes
C := Q*C   if side = 'L' and trans = 'N'.
C := Q^T*C if side = 'L' and trans = 'T'.
C := Q^H*C if side = 'L' and trans = 'C'.
C := C*Q   if side = 'R' and trans = 'N'.
C := C*Q^T if side = 'R' and trans = 'T'.
C := C*Q^H if side = 'R' and trans = 'C'.
C is m by n and Q is a square orthogonal/unitary matrix computed
by geqrf.  Q is defined as a product of k elementary reflectors,
stored as the first k columns of A and the first k entries of tau.

ARGUMENTS
A         'd' or 'z' matrix

tau       'd' or 'z' matrix of length at least k.  Must have the
          same type as A.

C         'd' or 'z' matrix.  Must have the same type as A.

side      'L' or 'R'

trans     'N', 'T', or 'C'n
m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

k         integer.  k <= m if side = 'R' and k <= n if side = 'L'.
          If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m) if side = 'L'
          and ldA >= max(1,n) if side = 'R'.  If zero, the
          default value is used.

ldC       nonnegative integer.  ldC >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerProduct with a real orthogonal matrix.

ormqr(A, tau, C, side='L', trans='N', m=C.size[0], n=C.size[1],
      k=len(tau), ldA=max(1,A.size[0]), ldC=max(1,C.size[0]),
      offsetA=0, offsetC=0)

PURPOSE
Computes
C := Q*C   if side = 'L' and trans = 'N'.
C := Q^T*C if side = 'L' and trans = 'T'.
C := C*Q   if side = 'R' and trans = 'N'.
C := C*Q^T if side = 'R' and trans = 'T'.
C is m by n and Q is a square orthogonal matrix computed by geqrf.
Q is defined as a product of k elementary reflectors, stored as
the first k columns of A and the first k entries of tau.

ARGUMENTS
A         'd' matrix

tau       'd' matrix of length at least k

C         'd' matrix

side      'L' or 'R'

trans     'N' or 'T'

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

k         integer.  k <= m if side = 'R' and k <= n if side = 'L'.
          If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m) if side = 'L'
          and ldA >= max(1,n) if side = 'R'.  If zero, the
          default value is used.

ldC       nonnegative integer.  ldC >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerQR factorization.

geqrf(A, tau, m=A.size[0], n=A.size[1], ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
QR factorization of an m by n real or complex matrix A:

A = Q*R = [Q1 Q2] * [R1; 0] if m >= n
A = Q*R = Q * [R1 R2] if m <= n,

where Q is m by m and orthogonal/unitary and R is m by n with R1
upper triangular.  On exit, R is stored in the upper triangular
part of A.  Q is stored as a product of k=min(m,n) elementary
reflectors.  The parameters of the reflectors are stored in the
first k entries of tau and in the lower triangular part of the
first k columns of A.

ARGUMENTS
A         'd' or 'z' matrix

tau       'd' or 'z' matrix of length at least min(m,n).  Must
          have the same type as A.

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

offsetA   nonnegative integerSolves least-squares and least-norm problems with full rank
matrices.

gels(A, B, trans='N', m=A.size[0], n=A.size[1], nrhs=B.size[1],
     ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,
     offsetB=0)

PURPOSE
1. If trans is 'N' and A and B are real/complex:
- if m >= n: minimizes ||A*X - B||_F.
- if m < n: minimizes ||X||_F subject to A*X = B.

2. If trans is 'N' or 'C' and A and B are real:
- if m >= n: minimizes ||X||_F subject to A^T*X = B.
- if m < n: minimizes ||X||_F subject to A^T*X = B.

3. If trans is 'C' and A and B are complex:
- if m >= n: minimizes ||X||_F subject to A^H*X = B.
- if m < n: minimizes ||X||_F subject to A^H*X = B.

A is an m by n matrix.  B has nrhs columns.  On exit, B is
replaced with the solution, and A is replaced with the details
of its QR or LQ factorization.

Note that gels does not check whether A has full rank.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

trans     'N', 'T' or 'C' if A is real.  'N' or 'C' if A is
          complex.

m         integer.  If negative, the default value is used.

n         integer.  If negative, the default value is used.

nrhs      integer.  If negative, the default value is used.

ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
          default value is used.

ldB       nonnegative integer.  ldB >= max(1,m,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerSolution of a triangular set of equations with banded coefficient
matrix.

tbtrs(A, B, uplo='L', trans='N', diag='N', n=A.size[1], 
      kd=A.size[0]-1, nrhs=B.size[1], ldA=max(1,A.size[0]),
      ldB=max(1,B.size[0]), offsetA=0, offsetB=0)

PURPOSE
If trans is 'N', solves A*X = B.
If trans is 'T', solves A^T*X = B.
If trans is 'C', solves A^H*X = B.
B is n by nrhs and A is a triangular band matrix of order n with kd
subdiagonals (uplo is 'L') or superdiagonals (uplo is 'U').

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'L' or 'U'

trans     'N', 'T' or 'C'

diag      'N' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

kd        nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= kd+1.  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerInverse of a triangular matrix.

trtri(A, uplo='L', diag='N', n=A.size[0], ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
Computes the inverse of a triangular matrix of order n.
On exit, A is replaced with its inverse.

ARGUMENTS
A         'd' or 'z' matrix

uplo      'L' or 'U'

diag      'N' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integerSolution of a triangular set of equations with multiple righthand
sides.

trtrs(A, B, uplo='L', trans='N', diag='N', n=A.size[0],
      nrhs=B.size[1], ldA=max(1,A.size[0]), ldB=max(1,B.size[0]),
      offsetA=0, offsetB=0)

PURPOSE
If trans is 'N', solves A*X = B.
If trans is 'T', solves A^T*X = B.
If trans is 'C', solves A^H*X = B.
B is n by nrhs and A is triangular of order n.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'L' or 'U'

trans     'N', 'T' or 'C'

diag      'N' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerSolves a real symmetric or complex Hermitian set of linear
equations.

herv(A, B, ipiv=None, uplo='L', n=A.size[0], nrhs=B.size[1],
     ldA = max(1,A.size[0]), ldB = max(1,B.size[0]), offsetA=0,
     offsetB=0)

PURPOSE
Solves A*X=B where A is real symmetric or complex Hermitian and
n by n.  If ipiv is provided, then on exit A and ipiv contain
the details of the LDL^H factorization of A.  If ipiv is not
provided, then the factorization is not returned and A is not
modified.  On exit, B contains the solution.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

ipiv      'i' matrix of length at least n

uplo      'U' or 'L'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerSolves a real or complex symmetric set of linear equations.

sysv(A, B, ipiv=None, uplo='L', n=A.size[0], nrhs=B.size[1],
     ldA = max(1,A.size[0]), ldB = max(1,B.size[0]),
     offsetA=0, offsetB=0)

PURPOSE
Solves A*X = B where A is real or complex symmetric and n by n.
If ipiv is provided, then on exit A and ipiv contain the details
of the LDL^T factorization of A.  If ipiv is not provided, then
the factorization is not returned and A is not modified.  On
exit, B contains the solution.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

ipiv      'i' matrix of length at least n

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerInverse of a real symmetric or complex Hermitian matrix.

hetri(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
Computes the inverse of a real symmetric or complex Hermitian
matrix of order n.  On entry, A and ipiv contain the LDL^T
factorization, as returned by hesv() or hetrf().  On exit A is
replaced by the inverse. 

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix 

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integerInverse of a real or complex symmetric matrix.

sytri(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
Computes the inverse of a real or complex symmetric matrix of
order n.  On entry, A and ipiv contain the LDL^T factorization,
as returned by sysv() or sytrf().  On exit A is replaced by the
inverse.  

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix 

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integerSolves a real symmetric or complex Hermitian set of linear
equations, given the LDL^H factorization computed by hetrf() or hesv().

hetrs(A, ipiv, B, uplo='L', n=A.size[0], nrhs=B.size[1],
      ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,
      offsetB=0)

PURPOSE
Solves A*X = B where A is real symmetric or complex Hermitian
and n by n, and B is n by nrhs.  On entry, A and ipiv contain
the factorization of A as returned by hetrf or hesv.  On exit, B
is replaced by the solution.

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix 

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'U' or 'L'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerSolves a real or complex symmetric set of linear equations,
given the LDL^T factorization computed by sytrf() or sysv().

sytrs(A, ipiv, B, uplo='L', n=A.size[0], nrhs=B.size[1],
      ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,
      offsetB=0)

PURPOSE
Solves A*X = B where A is real or complex symmetric and n by n,
and B is n by nrhs.  On entry, A and ipiv contain the
factorization of A as returned by sytrf() or sysv().  On exit, B is
replaced by the solution.

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix 

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       nonnegative integer.  ldB >= max(1,n).  If zero, the
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerLDL^H factorization of a real symmetric or complex Hermitian matrix.

hetrf(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]))

PURPOSE
Computes the LDL^H factorization of a real symmetric or complex
Hermitian n by n matrix  A.  On exit, A and ipiv contain the
details of the factorization.

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix of length at least n

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          default value is used.

offsetA   nonnegative integerLDL^T factorization of a real or complex symmetric matrix.

sytrf(A, ipiv, uplo='L', n=A.size[0], ldA=max(1,A.size[0]))

PURPOSE
Computes the LDL^T factorization of a real or complex symmetric
n by n matrix  A.  On exit, A and ipiv contain the details of the
factorization.

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix of length at least n

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integerSolves a real symmetric or complex Hermitian positive definite set
of linear equations with a tridiagonal coefficient matrix.

ptsv(d, e, B, n=len(d)-offsetd, nrhs=B.size[1], ldB=max(1,B.size[0],
     offsetd=0, offsete=0, offsetB=0)

PURPOSE
Solves A*X=B with A n by n real or complex Hermitian positive
definite and tridiagonal.  A is specified by its diagonal d and
subdiagonal e.  On exit B is overwritten with the solution, and d
and e are overwritten with the elements of Cholesky factorization
of A.

ARGUMENTS.
d         'd' matrix

e         'd' or 'z' matrix.

B         'd' or 'z' matrix.  Must have the same type as e.

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetd   nonnegative integer

offsete   nonnegative integer

offsetB   nonnegative integerSolves a real symmetric or complex Hermitian positive definite set
of linear equations with a tridiagonal coefficient matrix, given 
the factorization computed by pttrf().

pttrs(d, e, B, uplo='L', n=len(d)-offsetd, nrhs=B.size[1],
      ldB=max(1,B.size[0], offsetd=0, offsete=0, offsetB=0)

PURPOSE
Solves A*X=B with A n by n real or complex Hermitian positive
definite and tridiagonal, and B n by nrhs.  On entry, d and e
contain the Cholesky factorization L*D*L^T or L*D*L^H, for example,
as returned by pttrf().  The argument d is the diagonal of the 
diagonal matrix D.  The argument uplo only matters in the complex
case.  If uplo = 'L', then e is the subdiagonal of L.  If uplo='U',
e is the superdiagonal of L^H.  On exit B is overwritten with the
solution X. 

ARGUMENTS.
d         'd' matrix

e         'd' or 'z' matrix.

B         'd' or 'z' matrix.  Must have the same type as e.

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetd   nonnegative integer

offsete   nonnegative integer

offsetB   nonnegative integerCholesky factorization of a real symmetric or complex Hermitian
positive definite tridiagonal matrix.

pttrf(d, e, n=len(d)-offsetd, offsetd=0, offsete=0)

PURPOSE
Factors A  as A = L*D*L^T or A = L*D*L^H where A is n by n, real
symmetric or complex Hermitian, positive definite, and tridiagonal.
On entry, d is the subdiagonal of A and e is the diagonal.  On 
exit, d contains the diagonal of D and e contains the subdiagonal
of the unit bidiagonal matrix L.

ARGUMENTS.
d         'd' matrix

e         'd' or 'z' matrix.

n         nonnegative integer.  If negative, the default value is
          used.

offsetd   nonnegative integer

offsete   nonnegative integerSolves a real symmetric or complex Hermitian positive definite set
of linear equations with a banded coefficient matrix.

pbsv(A, B, uplo='L', n=A.size[1], kd=A.size[0]-1, nrhs=B.size[1],
     ldA=MAX(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,
     offsetB=0)

PURPOSE
Solves A*X = B where A is an n by n real symmetric or complex
Hermitian positive definite band matrix with kd subdiagonals and kd
superdiagonals, and B is n by nrhs.
On entry, A contains A in the BLAS format for symmetric band
matrices.  On exit, A is replaced with the Cholesky factors, stored
in the BLAS format for triangular band matrices.  B is replaced
by the solution X.

ARGUMENTS
A         'd' or 'z' matrix.

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'L' or 'U'

n         nonnegative integer. If negative, the default value is
          used.

kd        nonnegative integer. If negative, the default value is
          used.

nrhs      nonnegative integer. If negative, the default value is
          used.

ldA       positive integer.  ldA >= kd+1.  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerSolves a real symmetric or complex Hermitian positive definite set
of linear equations with a banded coefficient matrix, given the
Cholesky factorization computed by pbtrf() or pbsv().

pbtrs(A, B, uplo='L', n=A.size[1], kd=A.size[0]-1, nrhs=B.size[1],
      ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,
      offsetB=0)

PURPOSE
Solves A*X = B where A is an n by n real symmetric or complex 
Hermitian positive definite band matrix with kd subdiagonals and kd
superdiagonals, and B is n by nrhs.  A contains the Cholesky factor
of A, as returned by pbtrf() or pbtrs().  On exit, B is replaced by
the solution X.

ARGUMENTS
A         'd' or 'z' matrix.

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'L' or 'U'

n         nonnegative integer. If negative, the default value is
          used.

kd        nonnegative integer. If negative, the default value is
          used.

nrhs      nonnegative integer. If negative, the default value is
          used.

ldA       positive integer.  ldA >= kd+1.  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerCholesky factorization of a real symmetric or complex Hermitian
positive definite band matrix.

pbtrf(A, uplo='L', n=A.size[1], kd=A.size[0]-1, ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
Factors A as A=L*L^T or A = L*L^H, where A is an n by n real
symmetric or complex Hermitian positive definite band matrix with
kd subdiagonals and kd superdiagonals.  A is stored in the BLAS 
format for symmetric band matrices.  On exit, A contains the
Cholesky factor in the BLAS format for triangular band matrices.

ARGUMENTS
A         'd' or 'z' matrix.

uplo      'L' or 'U'

n         nonnegative integer. If negative, the default value is
          used.

kd        nonnegative integer. If negative, the default value is
          used.

ldA       positive integer.  ldA >= kd+1.  If zero, the default
          value is used.

offsetA   nonnegative integerSolves a real symmetric or complex Hermitian positive definite set
of linear equations.

posv(A, B, uplo='L', n=A.size[0], nrhs=B.size[1], 
     ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0, 
     offsetB=0)

PURPOSE
Solves A*X = B with A n by n, real symmetric or complex Hermitian,
and positive definite, and B n by nrhs.
On exit, if uplo is 'L',  the lower triangular part of A is
replaced by L.  If uplo is 'U', the upper triangular part is
replaced by L^H.  B is replaced by the solution.

ARGUMENTS.
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerInverse of a real symmetric or complex Hermitian positive definite
matrix.

potri(A, uplo='L', n=A.size[0], ldA=max(1,A.size[0]), offsetA=0)

PURPOSE
Computes the inverse of a real symmetric or complex Hermitian
positive definite matrix of order n.  On entry, A contains the
Cholesky factor, as returned by posv() or potrf().  On exit it is
replaced by the inverse.

ARGUMENTS
A         'd' or 'z' matrix

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is

          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integerSolves a real symmetric or complex Hermitian positive definite set
of linear equations, given the Cholesky factorization computed by
potrf() or posv().

potrs(A, B, uplo='L', n=A.size[0], nrhs=B.size[1],
      ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,
      offsetB=0)

PURPOSE
Solves A*X = B where A is n by n, real symmetric or complex
Hermitian and positive definite, and B is n by nrhs.
On entry, A contains the Cholesky factor, as returned by posv() or
potrf().  On exit B is replaced by the solution X.

ARGUMENTS
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerCholesky factorization of a real symmetric or complex Hermitian
positive definite matrix.

potrf(A, uplo='L', n=A.size[0], ldA = max(1,A.size[0]), offsetA=0)

PURPOSE
Factors A as A=L*L^T or A = L*L^H, where A is n by n, real
symmetric or complex Hermitian, and positive definite.
On exit, if uplo='L', the lower triangular part of A is replaced
by L.  If uplo='U', the upper triangular part is replaced by L^T
or L^H.

ARGUMENTS
A         'd' or 'z' matrix

uplo      'L' or 'U'

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integerSolves a real or complex set of linear equations with a tridiagonal
coefficient matrix.

gtsv(dl, d, du, B, n=len(d)-offsetd, nrhs=B.size[1], 
     ldB=max(1,B.size[0]), offsetdl=0, offsetd=0, offsetdu=0, 
     offsetB=0)

PURPOSE
Solves A*X=B with A n by n real or complex and tridiagonal.
A is specified by its lower diagonal dl, diagonal d and upper 
diagonal du.  On exit B is overwritten with the solution, and dl,
d, du are overwritten with the elements of the upper triangular
matrix in the LU factorization of A.

ARGUMENTS.
dl        'd' or 'z' matrix

d         'd' or 'z' matrix.  Must have the same type as dl.

du        'd' or 'z' matrix.  Must have the same type as dl.

B         'd' or 'z' matrix.  Must have the same type as dl.

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetdl  nonnegative integer

offsetd   nonnegative integer

offsetdu  nonnegative integer

offsetB   nonnegative integerSolves a real or complex tridiagonal set of linear equations, 
given the LU factorization computed by gttrf().

gttrs(dl, d, du, du2, ipiv, B, trans='N', n=len(d)-offsetd,
      nrhs=B.size[1], ldB=max(1,B.size[0]), offsetdl=0, offsetd=0,
      offsetdu=0, offsetB=0)

PURPOSE
If trans is 'N', solves A*X=B.
If trans is 'T', solves A^T*X=B.
If trans is 'C', solves A^H*X=B.
On entry, dl, d, du, du2 and ipiv contain the LU factorization of 
an n by n tridiagonal matrix A as computed by gttrf().  On exit B
is replaced by the solution X.

ARGUMENTS.
dl        'd' or 'z' matrix

d         'd' or 'z' matrix.  Must have the same type as dl.

du        'd' or 'z' matrix.  Must have the same type as dl.

du2       'd' or 'z' matrix.  Must have the same type as dl.

ipiv      'i' matrix

B         'd' or 'z' matrix.  Must have the same type oas dl.

trans     'N', 'T' or 'C'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetdl  nonnegative integer

offsetd   nonnegative integer

offsetdu  nonnegative integer

offsetB   nonnegative integerLU factorization of a real or complex tridiagonal matrix.

gttrf(dl, d, du, du2, ipiv, n=len(d)-offsetd, offsetdl=0, offsetd=0,
      offsetdu=0)

PURPOSE
Factors an n by n real or complex tridiagonal matrix A as A = P*L*U.
  A is specified by its lower diagonal dl, diagonal d, and upper
diagonal du.  On exit dl, d, du, du2 and ipiv contain the details
of the factorization.

ARGUMENTS.
dl        'd' or 'z' matrix

d         'd' or 'z' matrix.  Must have the same type as dl.

du        'd' or 'z' matrix.  Must have the same type as dl.

du2       'd' or 'z' matrix of length at least n-2.  Must have the
           same type as dl.

ipiv      'i' matrix of length at least n

n         nonnegative integer.  If negative, the default value is
          used.

offsetdl  nonnegative integer

offsetd   nonnegative integer

offsetdu  nonnegative integerSolves a real or complex set of linear equations with a banded
coefficient matrix.

gbsv(A, kl, B, ipiv=None, ku=None, n=A.size[1], nrhs=B.size[1],
     ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0, 
     offsetB=0)

PURPOSE
Solves A*X=B with A an n by n real or complex band matrix with kl
subdiagonals and ku superdiagonals.
If ipiv is provided, then on entry the kl+ku+1 diagonals of the
matrix are stored in rows kl+1 to 2*kl+ku+1 of A, in the BLAS
format for general band matrices.  On exit, A and ipiv contain the
details of the factorization.  If ipiv is not provided, then on
entry the diagonals of the matrix are stored in rows 1 to kl+ku+1 
of A, and gbsv() does not return the factorization and does not
modify A.  On exit B is replaced with solution X.

ARGUMENTS.
A         'd' or 'z' banded matrix

kl        nonnegative integer

B         'd' or 'z' matrix.  Must have the same type as A.

ipiv      'i' matrix of length at least n

ku        nonnegative integer.  If negative, the default value is
          used.  The default value is A.size[0]-kl-1 if ipiv is
          not provided, and A.size[0]-2*kl-1 otherwise.

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= kl+ku+1 if ipiv is not provided
          and ldA >= 2*kl+ku+1 if ipiv is provided.  If zero, the
          default value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerSolves a real or complex set of linear equations with a banded
coefficient matrix, given the LU factorization computed by gbtrf()
or gbsv().

gbtrs(A, kl, ipiv, B, trans='N', n=A.size[1], ku=A.size[0]-2*kl-1,
      nrhs=B.size[1], ldA=max(1,AB.size[0]), ldB=max(1,B.size[0]),
      offsetA=0, offsetB=0)

PURPOSE
If trans is 'N', solves A*X = B.
If trans is 'T', solves A^T*X = B.
If trans is 'C', solves A^H*X = B.
On entry, A and ipiv contain the LU factorization of an n by n
band matrix A as computed by getrf() or gbsv().  On exit B is
replaced by the solution X.

ARGUMENTS
A         'd' or 'z' matrix

kl        nonnegative integer

ipiv      'i' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

trans     'N', 'T' or 'C'

n         nonnegative integer.  If negative, the default value is
          used.

ku        nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= 2*kl+ku+1.  If zero, the
          default value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          default value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerLU factorization of a real or complex m by n band matrix.

gbtrf(A, m, kl, ipiv, n=A.size[1], ku=A.size[0]-2*kl-1,
      ldA=max(1,A.size[0]), offsetA=0)

PURPOSE
Computes the LU factorization of an m by n band matrix with kl
subdiagonals and ku superdiagonals.  On entry, the diagonals are
stored in rows kl+1 to 2*kl+ku+1 of the array A, in the BLAS format
for general band matrices.   On exit A and ipiv contains the
factorization.

ARGUMENTS
A         'd' or 'z' matrix

m         nonnegative integer

kl        nonnegative integer.

ipiv      'i' matrix of length at least min(m,n)

n         nonnegative integer.  If negative, the default value is
          used.

ku        nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= 2*kl+ku+1.  If zero, the
          default value is used.

offsetA   nonnegative integerSolves a general real or complex set of linear equations.

dgesv(A, B, ipiv=None, n=A.size[0], nrhs=B.size[1], 
      ldA=max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0, 
      offsetB=0)

PURPOSE
Solves A*X=B with A n by n real or complex.
If ipiv is provided, then on exit A is overwritten with the details
of the LU factorization, and ipiv contains the permutation matrix.
If ipiv is not provided, then gesv() does not return the 
factorization and does not modify A.  On exit B is replaced with
the solution X.

ARGUMENTS.
A         'd' or 'z' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

ipiv      'i' matrix of length at least n

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetA   nonnegative integerInverse of a real or complex matrix.

getri(A, ipiv, n=A.size[0], ldA = max(1,A.size[0]), offsetA=0)

PURPOSE
Computes the inverse of real or complex matrix of order n.  On
entry, A and ipiv contain the LU factorization, as returned by
gesv() or getrf().  On exit A is replaced by the inverse.

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integerSolves a general real or complex set of linear equations,
given the LU factorization computed by getrf() or gesv().

getrs(A, ipiv, B, trans='N', n=A.size[0], nrhs=B.size[1],
      ldA = max(1,A.size[0]), ldB=max(1,B.size[0]), offsetA=0,
      offsetB=0)

PURPOSE
If trans is 'N', solves A*X = B.
If trans is 'T', solves A^T*X = B.
If trans is 'C', solves A^H*X = B.
On entry, A and ipiv contain the LU factorization of an n by n
matrix A as computed by getrf() or gesv().  On exit B is replaced
by the solution X.

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix

B         'd' or 'z' matrix.  Must have the same type as A.

trans     'N', 'T' or 'C'

n         nonnegative integer.  If negative, the default value is
          used.

nrhs      nonnegative integer.  If negative, the default value is
           used.

ldA       positive integer.  ldA >= max(1,n).  If zero, the default
          value is used.

ldB       positive integer.  ldB >= max(1,n).  If zero, the default
          value is used.

offsetA   nonnegative integer

offsetB   nonnegative integerLU factorization of a general real or complex m by n matrix.

getrf(A, ipiv, m=A.size[0], n=A.size[1], ldA=max(1,A.size[0]),
      offsetA=0)

PURPOSE
On exit, A is replaced with L, U in the factorization P*A = L*U
and ipiv contains the permutation:
P = P_min{m,n} * ... * P2 * P1 where Pi interchanges rows i and
ipiv[i] of A (using the Fortran convention, i.e., the first row
is numbered 1).

ARGUMENTS
A         'd' or 'z' matrix

ipiv      'i' matrix of length at least min(m,n)

m         nonnegative integer.  If negative, the default value is
          used.

n         nonnegative integer.  If negative, the default value is
          used.

ldA       positive integer.  ldA >= max(1,m).  If zero, the default
          value is used.

offsetA   nonnegative integerInterface to the LAPACK library.

Double-precision real and complex LAPACK routines for solving sets of
linear equations, linear least-squares and least-norm problems,
symmetric and Hermitian eigenvalue problems, singular value 
decomposition, and Schur factorization.

For more details, see the LAPACK Users' Guide at 
www.netlib.org/lapack/lug/lapack_lug.html.

Double and complex matrices and vectors are stored in CVXOPT matrices
using the conventional BLAS storage schemes, with the CVXOPT matrix
buffers interpreted as one-dimensional arrays.  For each matrix 
argument X, an additional integer argument offsetX specifies the start
of the array, i.e., the pointer X->buffer + offsetX is passed to the
LAPACK function.  The other arguments (dimensions and options) have the
same meaning as in the LAPACK definition.  Default values of the
dimension arguments are derived from the CVXOPT matrix sizes.

If a routine from the LAPACK library returns with a positive 'info'
value, an ArithmeticError is raised.  If it returns with a negative
'info' value, a ValueError is raised.  In both cases the value of 
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