lapack/lapack.go

// 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 lapack // import "gonum.org/v1/gonum/lapack"

import "gonum.org/v1/gonum/blas"

const None = 'N'

type Job byte

type Comp byte

// Complex128 defines the public complex128 LAPACK API supported by gonum/lapack.
type Complex128 interface{}

// Float64 defines the public float64 LAPACK API supported by gonum/lapack.
type Float64 interface {
	Dgecon(norm MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
	Dgeev(jobvl LeftEVJob, jobvr RightEVJob, n int, a []float64, lda int, wr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) (first int)
	Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
	Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
	Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
	Dgesvd(jobU, jobVT SVDJob, m, n int, a []float64, lda int, s, u []float64, ldu int, vt []float64, ldvt int, work []float64, lwork int) (ok bool)
	Dgetrf(m, n int, a []float64, lda int, ipiv []int) (ok bool)
	Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) (ok bool)
	Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int)
	Dggsvd3(jobU, jobV, jobQ GSVDJob, m, n, p int, a []float64, lda int, b []float64, ldb int, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64, lwork int, iwork []int) (k, l int, ok bool)
	Dlantr(norm MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64
	Dlange(norm MatrixNorm, m, n int, a []float64, lda int, work []float64) float64
	Dlansy(norm MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
	Dlapmt(forward bool, m, n int, x []float64, ldx int, k []int)
	Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
	Dormlq(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
	Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
	Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
	Dsyev(jobz EVJob, uplo blas.Uplo, n int, a []float64, lda int, w, work []float64, lwork int) (ok bool)
	Dtrcon(norm MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64
	Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) (ok bool)
	Dtrtrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, nrhs int, a []float64, lda int, b []float64, ldb int) (ok bool)
}

// Direct specifies the direction of the multiplication for the Householder matrix.
type Direct byte

const (
	Forward  Direct = 'F' // Reflectors are right-multiplied, H_0 * H_1 * ... * H_{k-1}.
	Backward Direct = 'B' // Reflectors are left-multiplied, H_{k-1} * ... * H_1 * H_0.
)

// Sort is the sorting order.
type Sort byte

const (
	SortIncreasing Sort = 'I'
	SortDecreasing Sort = 'D'
)

// StoreV indicates the storage direction of elementary reflectors.
type StoreV byte

const (
	ColumnWise StoreV = 'C' // Reflector stored in a column of the matrix.
	RowWise    StoreV = 'R' // Reflector stored in a row of the matrix.
)

// MatrixNorm represents the kind of matrix norm to compute.
type MatrixNorm byte

const (
	MaxAbs       MatrixNorm = 'M' // max(abs(A(i,j)))  ('M')
	MaxColumnSum MatrixNorm = 'O' // Maximum column sum (one norm) ('1', 'O')
	MaxRowSum    MatrixNorm = 'I' // Maximum row sum (infinity norm) ('I', 'i')
	NormFrob     MatrixNorm = 'F' // Frobenius norm (sqrt of sum of squares) ('F', 'f', E, 'e')
)

// MatrixType represents the kind of matrix represented in the data.
type MatrixType byte

const (
	General  MatrixType = 'G' // A dense matrix (like blas64.General).
	UpperTri MatrixType = 'U' // An upper triangular matrix.
	LowerTri MatrixType = 'L' // A lower triangular matrix.
)

// Pivot specifies the pivot type for plane rotations
type Pivot byte

const (
	Variable Pivot = 'V'
	Top      Pivot = 'T'
	Bottom   Pivot = 'B'
)

type DecompUpdate byte

const (
	ApplyP DecompUpdate = 'P'
	ApplyQ DecompUpdate = 'Q'
)

// SVDJob specifies the singular vector computation type for SVD.
type SVDJob byte

const (
	SVDAll       SVDJob = 'A' // Compute all singular vectors
	SVDInPlace   SVDJob = 'S' // Compute the first singular vectors and store them in provided storage.
	SVDOverwrite SVDJob = 'O' // Compute the singular vectors and store them in input matrix
	SVDNone      SVDJob = 'N' // Do not compute singular vectors
)

// GSVDJob specifies the singular vector computation type for Generalized SVD.
type GSVDJob byte

const (
	GSVDU    GSVDJob = 'U' // Compute orthogonal matrix U
	GSVDV    GSVDJob = 'V' // Compute orthogonal matrix V
	GSVDQ    GSVDJob = 'Q' // Compute orthogonal matrix Q
	GSVDUnit GSVDJob = 'I' // Use unit-initialized matrix
	GSVDNone GSVDJob = 'N' // Do not compute orthogonal matrix
)

// EVComp specifies how eigenvectors are computed.
type EVComp byte

const (
	// OriginalEV specifies to compute the eigenvectors of the original
	// matrix.
	OriginalEV EVComp = 'V'
	// TridiagEV specifies to compute both the eigenvectors of the input
	// tridiagonal matrix.
	TridiagEV EVComp = 'I'
	// HessEV specifies to compute both the eigenvectors of the input upper
	// Hessenberg matrix.
	HessEV EVComp = 'I'

	// UpdateSchur specifies that the matrix of Schur vectors will be
	// updated by Dtrexc.
	UpdateSchur EVComp = 'V'
)

// Job types for computation of eigenvectors.
type (
	EVJob      byte
	LeftEVJob  byte
	RightEVJob byte
)

// Job constants for computation of eigenvectors.
const (
	ComputeEV      EVJob      = 'V' // Compute eigenvectors in Dsyev.
	ComputeLeftEV  LeftEVJob  = 'V' // Compute left eigenvectors.
	ComputeRightEV RightEVJob = 'V' // Compute right eigenvectors.
)

// Jobs for Dgebal.
const (
	Permute      Job = 'P'
	Scale        Job = 'S'
	PermuteScale Job = 'B'
)

// Job constants for Dhseqr.
const (
	EigenvaluesOnly     EVJob = 'E'
	EigenvaluesAndSchur EVJob = 'S'
)

// EVSide specifies what eigenvectors will be computed.
type EVSide byte

// EVSide constants for Dtrevc3.
const (
	RightEV     EVSide = 'R' // Compute right eigenvectors only.
	LeftEV      EVSide = 'L' // Compute left eigenvectors only.
	RightLeftEV EVSide = 'B' // Compute both right and left eigenvectors.
)

// HowMany specifies which eigenvectors will be computed.
type HowMany byte

// HowMany constants for Dhseqr.
const (
	AllEV      HowMany = 'A' // Compute all right and/or left eigenvectors.
	AllEVMulQ  HowMany = 'B' // Compute all right and/or left eigenvectors multiplied by an input matrix.
	SelectedEV HowMany = 'S' // Compute selected right and/or left eigenvectors.
)