+++ /dev/null
-// Copyright ©2015 The Gonum Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package lapack64
-
-import (
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/blas/blas64"
- "gonum.org/v1/gonum/lapack"
- "gonum.org/v1/gonum/lapack/gonum"
-)
-
-var lapack64 lapack.Float64 = gonum.Implementation{}
-
-// Use sets the LAPACK float64 implementation to be used by subsequent BLAS calls.
-// The default implementation is native.Implementation.
-func Use(l lapack.Float64) {
- lapack64 = l
-}
-
-// Potrf computes the Cholesky factorization of a.
-// The factorization has the form
-// A = U^T * U if a.Uplo == blas.Upper, or
-// A = L * L^T if a.Uplo == blas.Lower,
-// where U is an upper triangular matrix and L is lower triangular.
-// The triangular matrix is returned in t, and the underlying data between
-// a and t is shared. The returned bool indicates whether a is positive
-// definite and the factorization could be finished.
-func Potrf(a blas64.Symmetric) (t blas64.Triangular, ok bool) {
- ok = lapack64.Dpotrf(a.Uplo, a.N, a.Data, a.Stride)
- t.Uplo = a.Uplo
- t.N = a.N
- t.Data = a.Data
- t.Stride = a.Stride
- t.Diag = blas.NonUnit
- return
-}
-
-// Gecon estimates the reciprocal of the condition number of the n×n matrix A
-// given the LU decomposition of the matrix. The condition number computed may
-// be based on the 1-norm or the ∞-norm.
-//
-// a contains the result of the LU decomposition of A as computed by Getrf.
-//
-// anorm is the corresponding 1-norm or ∞-norm of the original matrix A.
-//
-// work is a temporary data slice of length at least 4*n and Gecon will panic otherwise.
-//
-// iwork is a temporary data slice of length at least n and Gecon will panic otherwise.
-func Gecon(norm lapack.MatrixNorm, a blas64.General, anorm float64, work []float64, iwork []int) float64 {
- return lapack64.Dgecon(norm, a.Cols, a.Data, a.Stride, anorm, work, iwork)
-}
-
-// Gels finds a minimum-norm solution based on the matrices A and B using the
-// QR or LQ factorization. Gels returns false if the matrix
-// A is singular, and true if this solution was successfully found.
-//
-// The minimization problem solved depends on the input parameters.
-//
-// 1. If m >= n and trans == blas.NoTrans, Gels finds X such that || A*X - B||_2
-// is minimized.
-// 2. If m < n and trans == blas.NoTrans, Gels finds the minimum norm solution of
-// A * X = B.
-// 3. If m >= n and trans == blas.Trans, Gels finds the minimum norm solution of
-// A^T * X = B.
-// 4. If m < n and trans == blas.Trans, Gels finds X such that || A*X - B||_2
-// is minimized.
-// Note that the least-squares solutions (cases 1 and 3) perform the minimization
-// per column of B. This is not the same as finding the minimum-norm matrix.
-//
-// The matrix A is a general matrix of size m×n and is modified during this call.
-// The input matrix B is of size max(m,n)×nrhs, and serves two purposes. On entry,
-// the elements of b specify the input matrix B. B has size m×nrhs if
-// trans == blas.NoTrans, and n×nrhs if trans == blas.Trans. On exit, the
-// leading submatrix of b contains the solution vectors X. If trans == blas.NoTrans,
-// this submatrix is of size n×nrhs, and of size m×nrhs otherwise.
-//
-// Work is temporary storage, and lwork specifies the usable memory length.
-// At minimum, lwork >= max(m,n) + max(m,n,nrhs), and this function will panic
-// otherwise. A longer work will enable blocked algorithms to be called.
-// In the special case that lwork == -1, work[0] will be set to the optimal working
-// length.
-func Gels(trans blas.Transpose, a blas64.General, b blas64.General, work []float64, lwork int) bool {
- return lapack64.Dgels(trans, a.Rows, a.Cols, b.Cols, a.Data, a.Stride, b.Data, b.Stride, work, lwork)
-}
-
-// Geqrf computes the QR factorization of the m×n matrix A using a blocked
-// algorithm. A is modified to contain the information to construct Q and R.
-// The upper triangle of a contains the matrix R. The lower triangular elements
-// (not including the diagonal) contain the elementary reflectors. tau is modified
-// to contain the reflector scales. tau must have length at least min(m,n), and
-// this function will panic otherwise.
-//
-// The ith elementary reflector can be explicitly constructed by first extracting
-// the
-// v[j] = 0 j < i
-// v[j] = 1 j == i
-// v[j] = a[j*lda+i] j > i
-// and computing H_i = I - tau[i] * v * v^T.
-//
-// The orthonormal matrix Q can be constucted from a product of these elementary
-// reflectors, Q = H_0 * H_1 * ... * H_{k-1}, where k = min(m,n).
-//
-// Work is temporary storage, and lwork specifies the usable memory length.
-// At minimum, lwork >= m and this function will panic otherwise.
-// Geqrf is a blocked QR factorization, but the block size is limited
-// by the temporary space available. If lwork == -1, instead of performing Geqrf,
-// the optimal work length will be stored into work[0].
-func Geqrf(a blas64.General, tau, work []float64, lwork int) {
- lapack64.Dgeqrf(a.Rows, a.Cols, a.Data, a.Stride, tau, work, lwork)
-}
-
-// Gelqf computes the LQ factorization of the m×n matrix A using a blocked
-// algorithm. A is modified to contain the information to construct L and Q. The
-// lower triangle of a contains the matrix L. The elements above the diagonal
-// and the slice tau represent the matrix Q. tau is modified to contain the
-// reflector scales. tau must have length at least min(m,n), and this function
-// will panic otherwise.
-//
-// See Geqrf for a description of the elementary reflectors and orthonormal
-// matrix Q. Q is constructed as a product of these elementary reflectors,
-// Q = H_{k-1} * ... * H_1 * H_0.
-//
-// Work is temporary storage, and lwork specifies the usable memory length.
-// At minimum, lwork >= m and this function will panic otherwise.
-// Gelqf is a blocked LQ factorization, but the block size is limited
-// by the temporary space available. If lwork == -1, instead of performing Gelqf,
-// the optimal work length will be stored into work[0].
-func Gelqf(a blas64.General, tau, work []float64, lwork int) {
- lapack64.Dgelqf(a.Rows, a.Cols, a.Data, a.Stride, tau, work, lwork)
-}
-
-// Gesvd computes the singular value decomposition of the input matrix A.
-//
-// The singular value decomposition is
-// A = U * Sigma * V^T
-// where Sigma is an m×n diagonal matrix containing the singular values of A,
-// U is an m×m orthogonal matrix and V is an n×n orthogonal matrix. The first
-// min(m,n) columns of U and V are the left and right singular vectors of A
-// respectively.
-//
-// jobU and jobVT are options for computing the singular vectors. The behavior
-// is as follows
-// jobU == lapack.SVDAll All m columns of U are returned in u
-// jobU == lapack.SVDInPlace The first min(m,n) columns are returned in u
-// jobU == lapack.SVDOverwrite The first min(m,n) columns of U are written into a
-// jobU == lapack.SVDNone The columns of U are not computed.
-// The behavior is the same for jobVT and the rows of V^T. At most one of jobU
-// and jobVT can equal lapack.SVDOverwrite, and Gesvd will panic otherwise.
-//
-// On entry, a contains the data for the m×n matrix A. During the call to Gesvd
-// the data is overwritten. On exit, A contains the appropriate singular vectors
-// if either job is lapack.SVDOverwrite.
-//
-// s is a slice of length at least min(m,n) and on exit contains the singular
-// values in decreasing order.
-//
-// u contains the left singular vectors on exit, stored columnwise. If
-// jobU == lapack.SVDAll, u is of size m×m. If jobU == lapack.SVDInPlace u is
-// of size m×min(m,n). If jobU == lapack.SVDOverwrite or lapack.SVDNone, u is
-// not used.
-//
-// vt contains the left singular vectors on exit, stored rowwise. If
-// jobV == lapack.SVDAll, vt is of size n×m. If jobVT == lapack.SVDInPlace vt is
-// of size min(m,n)×n. If jobVT == lapack.SVDOverwrite or lapack.SVDNone, vt is
-// not used.
-//
-// work is a slice for storing temporary memory, and lwork is the usable size of
-// the slice. lwork must be at least max(5*min(m,n), 3*min(m,n)+max(m,n)).
-// If lwork == -1, instead of performing Gesvd, the optimal work length will be
-// stored into work[0]. Gesvd will panic if the working memory has insufficient
-// storage.
-//
-// Gesvd returns whether the decomposition successfully completed.
-func Gesvd(jobU, jobVT lapack.SVDJob, a, u, vt blas64.General, s, work []float64, lwork int) (ok bool) {
- return lapack64.Dgesvd(jobU, jobVT, a.Rows, a.Cols, a.Data, a.Stride, s, u.Data, u.Stride, vt.Data, vt.Stride, work, lwork)
-}
-
-// Getrf computes the LU decomposition of the m×n matrix A.
-// The LU decomposition is a factorization of A into
-// A = P * L * U
-// where P is a permutation matrix, L is a unit lower triangular matrix, and
-// U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored
-// in place into a.
-//
-// ipiv is a permutation vector. It indicates that row i of the matrix was
-// changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic
-// otherwise. ipiv is zero-indexed.
-//
-// Getrf is the blocked version of the algorithm.
-//
-// Getrf returns whether the matrix A is singular. The LU decomposition will
-// be computed regardless of the singularity of A, but division by zero
-// will occur if the false is returned and the result is used to solve a
-// system of equations.
-func Getrf(a blas64.General, ipiv []int) bool {
- return lapack64.Dgetrf(a.Rows, a.Cols, a.Data, a.Stride, ipiv)
-}
-
-// Getri computes the inverse of the matrix A using the LU factorization computed
-// by Getrf. On entry, a contains the PLU decomposition of A as computed by
-// Getrf and on exit contains the reciprocal of the original matrix.
-//
-// Getri will not perform the inversion if the matrix is singular, and returns
-// a boolean indicating whether the inversion was successful.
-//
-// Work is temporary storage, and lwork specifies the usable memory length.
-// At minimum, lwork >= n and this function will panic otherwise.
-// Getri is a blocked inversion, but the block size is limited
-// by the temporary space available. If lwork == -1, instead of performing Getri,
-// the optimal work length will be stored into work[0].
-func Getri(a blas64.General, ipiv []int, work []float64, lwork int) (ok bool) {
- return lapack64.Dgetri(a.Cols, a.Data, a.Stride, ipiv, work, lwork)
-}
-
-// Getrs solves a system of equations using an LU factorization.
-// The system of equations solved is
-// A * X = B if trans == blas.Trans
-// A^T * X = B if trans == blas.NoTrans
-// A is a general n×n matrix with stride lda. B is a general matrix of size n×nrhs.
-//
-// On entry b contains the elements of the matrix B. On exit, b contains the
-// elements of X, the solution to the system of equations.
-//
-// a and ipiv contain the LU factorization of A and the permutation indices as
-// computed by Getrf. ipiv is zero-indexed.
-func Getrs(trans blas.Transpose, a blas64.General, b blas64.General, ipiv []int) {
- lapack64.Dgetrs(trans, a.Cols, b.Cols, a.Data, a.Stride, ipiv, b.Data, b.Stride)
-}
-
-// Ggsvd3 computes the generalized singular value decomposition (GSVD)
-// of an m×n matrix A and p×n matrix B:
-// U^T*A*Q = D1*[ 0 R ]
-//
-// V^T*B*Q = D2*[ 0 R ]
-// where U, V and Q are orthogonal matrices.
-//
-// Ggsvd3 returns k and l, the dimensions of the sub-blocks. k+l
-// is the effective numerical rank of the (m+p)×n matrix [ A^T B^T ]^T.
-// R is a (k+l)×(k+l) nonsingular upper triangular matrix, D1 and
-// D2 are m×(k+l) and p×(k+l) diagonal matrices and of the following
-// structures, respectively:
-//
-// If m-k-l >= 0,
-//
-// k l
-// D1 = k [ I 0 ]
-// l [ 0 C ]
-// m-k-l [ 0 0 ]
-//
-// k l
-// D2 = l [ 0 S ]
-// p-l [ 0 0 ]
-//
-// n-k-l k l
-// [ 0 R ] = k [ 0 R11 R12 ] k
-// l [ 0 0 R22 ] l
-//
-// where
-//
-// C = diag( alpha_k, ... , alpha_{k+l} ),
-// S = diag( beta_k, ... , beta_{k+l} ),
-// C^2 + S^2 = I.
-//
-// R is stored in
-// A[0:k+l, n-k-l:n]
-// on exit.
-//
-// If m-k-l < 0,
-//
-// k m-k k+l-m
-// D1 = k [ I 0 0 ]
-// m-k [ 0 C 0 ]
-//
-// k m-k k+l-m
-// D2 = m-k [ 0 S 0 ]
-// k+l-m [ 0 0 I ]
-// p-l [ 0 0 0 ]
-//
-// n-k-l k m-k k+l-m
-// [ 0 R ] = k [ 0 R11 R12 R13 ]
-// m-k [ 0 0 R22 R23 ]
-// k+l-m [ 0 0 0 R33 ]
-//
-// where
-// C = diag( alpha_k, ... , alpha_m ),
-// S = diag( beta_k, ... , beta_m ),
-// C^2 + S^2 = I.
-//
-// R = [ R11 R12 R13 ] is stored in A[1:m, n-k-l+1:n]
-// [ 0 R22 R23 ]
-// and R33 is stored in
-// B[m-k:l, n+m-k-l:n] on exit.
-//
-// Ggsvd3 computes C, S, R, and optionally the orthogonal transformation
-// matrices U, V and Q.
-//
-// jobU, jobV and jobQ are options for computing the orthogonal matrices. The behavior
-// is as follows
-// jobU == lapack.GSVDU Compute orthogonal matrix U
-// jobU == lapack.GSVDNone Do not compute orthogonal matrix.
-// The behavior is the same for jobV and jobQ with the exception that instead of
-// lapack.GSVDU these accept lapack.GSVDV and lapack.GSVDQ respectively.
-// The matrices U, V and Q must be m×m, p×p and n×n respectively unless the
-// relevant job parameter is lapack.GSVDNone.
-//
-// alpha and beta must have length n or Ggsvd3 will panic. On exit, alpha and
-// beta contain the generalized singular value pairs of A and B
-// alpha[0:k] = 1,
-// beta[0:k] = 0,
-// if m-k-l >= 0,
-// alpha[k:k+l] = diag(C),
-// beta[k:k+l] = diag(S),
-// if m-k-l < 0,
-// alpha[k:m]= C, alpha[m:k+l]= 0
-// beta[k:m] = S, beta[m:k+l] = 1.
-// if k+l < n,
-// alpha[k+l:n] = 0 and
-// beta[k+l:n] = 0.
-//
-// On exit, iwork contains the permutation required to sort alpha descending.
-//
-// iwork must have length n, work must have length at least max(1, lwork), and
-// lwork must be -1 or greater than n, otherwise Ggsvd3 will panic. If
-// lwork is -1, work[0] holds the optimal lwork on return, but Ggsvd3 does
-// not perform the GSVD.
-func Ggsvd3(jobU, jobV, jobQ lapack.GSVDJob, a, b blas64.General, alpha, beta []float64, u, v, q blas64.General, work []float64, lwork int, iwork []int) (k, l int, ok bool) {
- return lapack64.Dggsvd3(jobU, jobV, jobQ, a.Rows, a.Cols, b.Rows, a.Data, a.Stride, b.Data, b.Stride, alpha, beta, u.Data, u.Stride, v.Data, v.Stride, q.Data, q.Stride, work, lwork, iwork)
-}
-
-// Lange computes the matrix norm of the general m×n matrix A. The input norm
-// specifies the norm computed.
-// lapack.MaxAbs: the maximum absolute value of an element.
-// lapack.MaxColumnSum: the maximum column sum of the absolute values of the entries.
-// lapack.MaxRowSum: the maximum row sum of the absolute values of the entries.
-// lapack.Frobenius: the square root of the sum of the squares of the entries.
-// If norm == lapack.MaxColumnSum, work must be of length n, and this function will panic otherwise.
-// There are no restrictions on work for the other matrix norms.
-func Lange(norm lapack.MatrixNorm, a blas64.General, work []float64) float64 {
- return lapack64.Dlange(norm, a.Rows, a.Cols, a.Data, a.Stride, work)
-}
-
-// Lansy computes the specified norm of an n×n symmetric matrix. If
-// norm == lapack.MaxColumnSum or norm == lapackMaxRowSum work must have length
-// at least n and this function will panic otherwise.
-// There are no restrictions on work for the other matrix norms.
-func Lansy(norm lapack.MatrixNorm, a blas64.Symmetric, work []float64) float64 {
- return lapack64.Dlansy(norm, a.Uplo, a.N, a.Data, a.Stride, work)
-}
-
-// Lantr computes the specified norm of an m×n trapezoidal matrix A. If
-// norm == lapack.MaxColumnSum work must have length at least n and this function
-// will panic otherwise. There are no restrictions on work for the other matrix norms.
-func Lantr(norm lapack.MatrixNorm, a blas64.Triangular, work []float64) float64 {
- return lapack64.Dlantr(norm, a.Uplo, a.Diag, a.N, a.N, a.Data, a.Stride, work)
-}
-
-// Lapmt rearranges the columns of the m×n matrix X as specified by the
-// permutation k_0, k_1, ..., k_{n-1} of the integers 0, ..., n-1.
-//
-// If forward is true a forward permutation is performed:
-//
-// X[0:m, k[j]] is moved to X[0:m, j] for j = 0, 1, ..., n-1.
-//
-// otherwise a backward permutation is performed:
-//
-// X[0:m, j] is moved to X[0:m, k[j]] for j = 0, 1, ..., n-1.
-//
-// k must have length n, otherwise Lapmt will panic. k is zero-indexed.
-func Lapmt(forward bool, x blas64.General, k []int) {
- lapack64.Dlapmt(forward, x.Rows, x.Cols, x.Data, x.Stride, k)
-}
-
-// Ormlq multiplies the matrix C by the othogonal matrix Q defined by
-// A and tau. A and tau are as returned from Gelqf.
-// C = Q * C if side == blas.Left and trans == blas.NoTrans
-// C = Q^T * C if side == blas.Left and trans == blas.Trans
-// C = C * Q if side == blas.Right and trans == blas.NoTrans
-// C = C * Q^T if side == blas.Right and trans == blas.Trans
-// If side == blas.Left, A is a matrix of side k×m, and if side == blas.Right
-// A is of size k×n. This uses a blocked algorithm.
-//
-// Work is temporary storage, and lwork specifies the usable memory length.
-// At minimum, lwork >= m if side == blas.Left and lwork >= n if side == blas.Right,
-// and this function will panic otherwise.
-// Ormlq uses a block algorithm, but the block size is limited
-// by the temporary space available. If lwork == -1, instead of performing Ormlq,
-// the optimal work length will be stored into work[0].
-//
-// Tau contains the Householder scales and must have length at least k, and
-// this function will panic otherwise.
-func Ormlq(side blas.Side, trans blas.Transpose, a blas64.General, tau []float64, c blas64.General, work []float64, lwork int) {
- lapack64.Dormlq(side, trans, c.Rows, c.Cols, a.Rows, a.Data, a.Stride, tau, c.Data, c.Stride, work, lwork)
-}
-
-// Ormqr multiplies an m×n matrix C by an orthogonal matrix Q as
-// C = Q * C, if side == blas.Left and trans == blas.NoTrans,
-// C = Q^T * C, if side == blas.Left and trans == blas.Trans,
-// C = C * Q, if side == blas.Right and trans == blas.NoTrans,
-// C = C * Q^T, if side == blas.Right and trans == blas.Trans,
-// where Q is defined as the product of k elementary reflectors
-// Q = H_0 * H_1 * ... * H_{k-1}.
-//
-// If side == blas.Left, A is an m×k matrix and 0 <= k <= m.
-// If side == blas.Right, A is an n×k matrix and 0 <= k <= n.
-// The ith column of A contains the vector which defines the elementary
-// reflector H_i and tau[i] contains its scalar factor. tau must have length k
-// and Ormqr will panic otherwise. Geqrf returns A and tau in the required
-// form.
-//
-// work must have length at least max(1,lwork), and lwork must be at least n if
-// side == blas.Left and at least m if side == blas.Right, otherwise Ormqr will
-// panic.
-//
-// work is temporary storage, and lwork specifies the usable memory length. At
-// minimum, lwork >= m if side == blas.Left and lwork >= n if side ==
-// blas.Right, and this function will panic otherwise. Larger values of lwork
-// will generally give better performance. On return, work[0] will contain the
-// optimal value of lwork.
-//
-// If lwork is -1, instead of performing Ormqr, the optimal workspace size will
-// be stored into work[0].
-func Ormqr(side blas.Side, trans blas.Transpose, a blas64.General, tau []float64, c blas64.General, work []float64, lwork int) {
- lapack64.Dormqr(side, trans, c.Rows, c.Cols, a.Cols, a.Data, a.Stride, tau, c.Data, c.Stride, work, lwork)
-}
-
-// Pocon estimates the reciprocal of the condition number of a positive-definite
-// matrix A given the Cholesky decmposition of A. The condition number computed
-// is based on the 1-norm and the ∞-norm.
-//
-// anorm is the 1-norm and the ∞-norm of the original matrix A.
-//
-// work is a temporary data slice of length at least 3*n and Pocon will panic otherwise.
-//
-// iwork is a temporary data slice of length at least n and Pocon will panic otherwise.
-func Pocon(a blas64.Symmetric, anorm float64, work []float64, iwork []int) float64 {
- return lapack64.Dpocon(a.Uplo, a.N, a.Data, a.Stride, anorm, work, iwork)
-}
-
-// Syev computes all eigenvalues and, optionally, the eigenvectors of a real
-// symmetric matrix A.
-//
-// w contains the eigenvalues in ascending order upon return. w must have length
-// at least n, and Syev will panic otherwise.
-//
-// On entry, a contains the elements of the symmetric matrix A in the triangular
-// portion specified by uplo. If jobz == lapack.ComputeEV a contains the
-// orthonormal eigenvectors of A on exit, otherwise on exit the specified
-// triangular region is overwritten.
-//
-// Work is temporary storage, and lwork specifies the usable memory length. At minimum,
-// lwork >= 3*n-1, and Syev will panic otherwise. The amount of blocking is
-// limited by the usable length. If lwork == -1, instead of computing Syev the
-// optimal work length is stored into work[0].
-func Syev(jobz lapack.EVJob, a blas64.Symmetric, w, work []float64, lwork int) (ok bool) {
- return lapack64.Dsyev(jobz, a.Uplo, a.N, a.Data, a.Stride, w, work, lwork)
-}
-
-// Trcon estimates the reciprocal of the condition number of a triangular matrix A.
-// The condition number computed may be based on the 1-norm or the ∞-norm.
-//
-// work is a temporary data slice of length at least 3*n and Trcon will panic otherwise.
-//
-// iwork is a temporary data slice of length at least n and Trcon will panic otherwise.
-func Trcon(norm lapack.MatrixNorm, a blas64.Triangular, work []float64, iwork []int) float64 {
- return lapack64.Dtrcon(norm, a.Uplo, a.Diag, a.N, a.Data, a.Stride, work, iwork)
-}
-
-// Trtri computes the inverse of a triangular matrix, storing the result in place
-// into a.
-//
-// Trtri will not perform the inversion if the matrix is singular, and returns
-// a boolean indicating whether the inversion was successful.
-func Trtri(a blas64.Triangular) (ok bool) {
- return lapack64.Dtrtri(a.Uplo, a.Diag, a.N, a.Data, a.Stride)
-}
-
-// Trtrs solves a triangular system of the form A * X = B or A^T * X = B. Trtrs
-// returns whether the solve completed successfully. If A is singular, no solve is performed.
-func Trtrs(trans blas.Transpose, a blas64.Triangular, b blas64.General) (ok bool) {
- return lapack64.Dtrtrs(a.Uplo, trans, a.Diag, a.N, b.Cols, a.Data, a.Stride, b.Data, b.Stride)
-}
-
-// Geev computes the eigenvalues and, optionally, the left and/or right
-// eigenvectors for an n×n real nonsymmetric matrix A.
-//
-// The right eigenvector v_j of A corresponding to an eigenvalue λ_j
-// is defined by
-// A v_j = λ_j v_j,
-// and the left eigenvector u_j corresponding to an eigenvalue λ_j is defined by
-// u_j^H A = λ_j u_j^H,
-// where u_j^H is the conjugate transpose of u_j.
-//
-// On return, A will be overwritten and the left and right eigenvectors will be
-// stored, respectively, in the columns of the n×n matrices VL and VR in the
-// same order as their eigenvalues. If the j-th eigenvalue is real, then
-// u_j = VL[:,j],
-// v_j = VR[:,j],
-// and if it is not real, then j and j+1 form a complex conjugate pair and the
-// eigenvectors can be recovered as
-// u_j = VL[:,j] + i*VL[:,j+1],
-// u_{j+1} = VL[:,j] - i*VL[:,j+1],
-// v_j = VR[:,j] + i*VR[:,j+1],
-// v_{j+1} = VR[:,j] - i*VR[:,j+1],
-// where i is the imaginary unit. The computed eigenvectors are normalized to
-// have Euclidean norm equal to 1 and largest component real.
-//
-// Left eigenvectors will be computed only if jobvl == lapack.ComputeLeftEV,
-// otherwise jobvl must be lapack.None.
-// Right eigenvectors will be computed only if jobvr == lapack.ComputeRightEV,
-// otherwise jobvr must be lapack.None.
-// For other values of jobvl and jobvr Geev will panic.
-//
-// On return, wr and wi will contain the real and imaginary parts, respectively,
-// of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear
-// consecutively with the eigenvalue having the positive imaginary part first.
-// wr and wi must have length n, and Geev will panic otherwise.
-//
-// work must have length at least lwork and lwork must be at least max(1,4*n) if
-// the left or right eigenvectors are computed, and at least max(1,3*n) if no
-// eigenvectors are computed. For good performance, lwork must generally be
-// larger. On return, optimal value of lwork will be stored in work[0].
-//
-// If lwork == -1, instead of performing Geev, the function only calculates the
-// optimal vaule of lwork and stores it into work[0].
-//
-// On return, first will be the index of the first valid eigenvalue.
-// If first == 0, all eigenvalues and eigenvectors have been computed.
-// If first is positive, Geev failed to compute all the eigenvalues, no
-// eigenvectors have been computed and wr[first:] and wi[first:] contain those
-// eigenvalues which have converged.
-func Geev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, a blas64.General, wr, wi []float64, vl, vr blas64.General, work []float64, lwork int) (first int) {
- n := a.Rows
- if a.Cols != n {
- panic("lapack64: matrix not square")
- }
- if jobvl == lapack.ComputeLeftEV && (vl.Rows != n || vl.Cols != n) {
- panic("lapack64: bad size of VL")
- }
- if jobvr == lapack.ComputeRightEV && (vr.Rows != n || vr.Cols != n) {
- panic("lapack64: bad size of VR")
- }
- return lapack64.Dgeev(jobvl, jobvr, n, a.Data, a.Stride, wr, wi, vl.Data, vl.Stride, vr.Data, vr.Stride, work, lwork)
-}
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