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Package testlapack

v0.6.7
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Published: Feb 11, 2020 | License: BSD-3-Clause | Module: github.com/rowdyroad/gonum

Overview

Package testlapack implements a set of testing routines for Lapack functions.

Index

func DbdsqrTest

func DbdsqrTest(t *testing.T, impl Dbdsqrer)

func DcombssqTest

func DcombssqTest(t *testing.T, impl Dcombssqer)

func DgebakTest

func DgebakTest(t *testing.T, impl Dgebaker)

func DgebalTest

func DgebalTest(t *testing.T, impl Dgebaler)

func Dgebd2Test

func Dgebd2Test(t *testing.T, impl Dgebd2er)

func DgebrdTest

func DgebrdTest(t *testing.T, impl Dgebrder)

func DgeconTest

func DgeconTest(t *testing.T, impl Dgeconer)

func DgeevBenchmark

func DgeevBenchmark(b *testing.B, impl Dgeever)

func DgeevTest

func DgeevTest(t *testing.T, impl Dgeever)

func Dgehd2Test

func Dgehd2Test(t *testing.T, impl Dgehd2er)

func DgehrdTest

func DgehrdTest(t *testing.T, impl Dgehrder)

func Dgelq2Test

func Dgelq2Test(t *testing.T, impl Dgelq2er)

func DgelqfTest

func DgelqfTest(t *testing.T, impl Dgelqfer)

func DgelsTest

func DgelsTest(t *testing.T, impl Dgelser)

func Dgeql2Test

func Dgeql2Test(t *testing.T, impl Dgeql2er)

func Dgeqp3Test

func Dgeqp3Test(t *testing.T, impl Dgeqp3er)

func Dgeqr2Test

func Dgeqr2Test(t *testing.T, impl Dgeqr2er)

func DgeqrfTest

func DgeqrfTest(t *testing.T, impl Dgeqrfer)

func Dgerq2Test

func Dgerq2Test(t *testing.T, impl Dgerq2er)

func DgerqfTest

func DgerqfTest(t *testing.T, impl Dgerqfer)

func DgesvdTest

func DgesvdTest(t *testing.T, impl Dgesvder, tol float64)

func Dgetf2Test

func Dgetf2Test(t *testing.T, impl Dgetf2er)

func DgetrfTest

func DgetrfTest(t *testing.T, impl Dgetrfer)

func DgetriTest

func DgetriTest(t *testing.T, impl Dgetrier)

func DgetrsTest

func DgetrsTest(t *testing.T, impl Dgetrser)

func Dggsvd3Test

func Dggsvd3Test(t *testing.T, impl Dggsvd3er)

func Dggsvp3Test

func Dggsvp3Test(t *testing.T, impl Dggsvp3er)

func DhseqrTest

func DhseqrTest(t *testing.T, impl Dhseqrer)

func DlabrdTest

func DlabrdTest(t *testing.T, impl Dlabrder)

func Dlacn2Test

func Dlacn2Test(t *testing.T, impl Dlacn2er)

func DlacpyTest

func DlacpyTest(t *testing.T, impl Dlacpyer)

func Dlae2Test

func Dlae2Test(t *testing.T, impl Dlae2er)

func Dlaev2Test

func Dlaev2Test(t *testing.T, impl Dlaev2er)

func DlaexcTest

func DlaexcTest(t *testing.T, impl Dlaexcer)

func Dlagge

func Dlagge(m, n, kl, ku int, d []float64, a []float64, lda int, rnd *rand.Rand, work []float64)

Dlagge generates a real general m×n matrix A, by pre- and post-multiplying a real diagonal matrix D with random orthogonal matrices:

A = U*D*V.

d must have length min(m,n), and work must have length m+n, otherwise Dlagge will panic.

The parameters ku and kl are unused but they must satisfy

0 <= kl <= m-1,
0 <= ku <= n-1.

func Dlags2Test

func Dlags2Test(t *testing.T, impl Dlags2er)

func Dlagsy

func Dlagsy(n, k int, d []float64, a []float64, lda int, rnd *rand.Rand, work []float64)

Dlagsy generates an n×n symmetric matrix A, by pre- and post- multiplying a real diagonal matrix D with a random orthogonal matrix:

A = U * D * Uᵀ.

work must have length at least 2*n, otherwise Dlagsy will panic.

The parameter k is unused but it must satisfy

0 <= k <= n-1.

func DlahqrTest

func DlahqrTest(t *testing.T, impl Dlahqrer)

func Dlahr2Test

func Dlahr2Test(t *testing.T, impl Dlahr2er)

func Dlaln2Test

func Dlaln2Test(t *testing.T, impl Dlaln2er)

func DlangeTest

func DlangeTest(t *testing.T, impl Dlanger)

func DlansbTest

func DlansbTest(t *testing.T, impl Dlansber)

func DlanstTest

func DlanstTest(t *testing.T, impl Dlanster)

func DlansyTest

func DlansyTest(t *testing.T, impl Dlansyer)

func DlantrTest

func DlantrTest(t *testing.T, impl Dlantrer)

func Dlanv2Test

func Dlanv2Test(t *testing.T, impl Dlanv2er)

func DlapllTest

func DlapllTest(t *testing.T, impl Dlapller)

func DlapmtTest

func DlapmtTest(t *testing.T, impl Dlapmter)

func Dlapy2Test

func Dlapy2Test(t *testing.T, impl Dlapy2er)

func Dlaqp2Test

func Dlaqp2Test(t *testing.T, impl Dlaqp2er)

func DlaqpsTest

func DlaqpsTest(t *testing.T, impl Dlaqpser)

func Dlaqr04Test

func Dlaqr04Test(t *testing.T, impl Dlaqr04er)

func Dlaqr1Test

func Dlaqr1Test(t *testing.T, impl Dlaqr1er)

func Dlaqr23Test

func Dlaqr23Test(t *testing.T, impl Dlaqr23er)

func Dlaqr5Test

func Dlaqr5Test(t *testing.T, impl Dlaqr5er)

func DlarfTest

func DlarfTest(t *testing.T, impl Dlarfer)

func DlarfbTest

func DlarfbTest(t *testing.T, impl Dlarfber)

func DlarfgTest

func DlarfgTest(t *testing.T, impl Dlarfger)

func DlarftTest

func DlarftTest(t *testing.T, impl Dlarfter)

func DlarfxTest

func DlarfxTest(t *testing.T, impl Dlarfxer)

func DlartgTest

func DlartgTest(t *testing.T, impl Dlartger)

func Dlas2Test

func Dlas2Test(t *testing.T, impl Dlas2er)

func DlasclTest

func DlasclTest(t *testing.T, impl Dlascler)

func DlasetTest

func DlasetTest(t *testing.T, impl Dlaseter)

func Dlasq1Test

func Dlasq1Test(t *testing.T, impl Dlasq1er)

func Dlasq2Test

func Dlasq2Test(t *testing.T, impl Dlasq2er)

func DlasrTest

func DlasrTest(t *testing.T, impl Dlasrer)

func DlasrtTest

func DlasrtTest(t *testing.T, impl Dlasrter)

func DlassqTest

func DlassqTest(t *testing.T, impl Dlassqer)

func Dlasv2Test

func Dlasv2Test(t *testing.T, impl Dlasv2er)

func DlaswpTest

func DlaswpTest(t *testing.T, impl Dlaswper)

func Dlasy2Test

func Dlasy2Test(t *testing.T, impl Dlasy2er)

func DlatbsTest

func DlatbsTest(t *testing.T, impl Dlatbser)

DlatbsTest tests Dlatbs by generating a random triangular band system and checking that a residual for the computed solution is small.

func Dlatm1

func Dlatm1(dst []float64, mode int, cond float64, rsign bool, dist int, rnd *rand.Rand)

Dlatm1 computes the entries of dst as specified by mode, cond and rsign.

mode describes how dst will be computed:

|mode| == 1: dst[0] = 1 and dst[1:n] = 1/cond
|mode| == 2: dst[:n-1] = 1/cond and dst[n-1] = 1
|mode| == 3: dst[i] = cond^{-i/(n-1)}, i=0,...,n-1
|mode| == 4: dst[i] = 1 - i*(1-1/cond)/(n-1)
|mode| == 5: dst[i] = random number in the range (1/cond, 1) such that
                  their logarithms are uniformly distributed
|mode| == 6: dst[i] = random number from the distribution given by dist

If mode is negative, the order of the elements of dst will be reversed. For other values of mode Dlatm1 will panic.

If rsign is true and mode is not ±6, each entry of dst will be multiplied by 1 or -1 with probability 0.5

dist specifies the type of distribution to be used when mode == ±6:

dist == 1: Uniform[0,1)
dist == 2: Uniform[-1,1)
dist == 3: Normal(0,1)

For other values of dist Dlatm1 will panic.

rnd is used as a source of random numbers.

func DlatrdTest

func DlatrdTest(t *testing.T, impl Dlatrder)

func DlatrsTest

func DlatrsTest(t *testing.T, impl Dlatrser)

func Dlauu2Test

func Dlauu2Test(t *testing.T, impl Dlauu2er)

func DlauumTest

func DlauumTest(t *testing.T, impl Dlauumer)

func Dorg2lTest

func Dorg2lTest(t *testing.T, impl Dorg2ler)

func Dorg2rTest

func Dorg2rTest(t *testing.T, impl Dorg2rer)

func DorgbrTest

func DorgbrTest(t *testing.T, impl Dorgbrer)

func DorghrTest

func DorghrTest(t *testing.T, impl Dorghrer)

func Dorgl2Test

func Dorgl2Test(t *testing.T, impl Dorgl2er)

func DorglqTest

func DorglqTest(t *testing.T, impl Dorglqer)

func DorgqlTest

func DorgqlTest(t *testing.T, impl Dorgqler)

func DorgqrTest

func DorgqrTest(t *testing.T, impl Dorgqrer)

func DorgtrTest

func DorgtrTest(t *testing.T, impl Dorgtrer)

func Dorm2rTest

func Dorm2rTest(t *testing.T, impl Dorm2rer)

func DormbrTest

func DormbrTest(t *testing.T, impl Dormbrer)

func DormhrTest

func DormhrTest(t *testing.T, impl Dormhrer)

func Dorml2Test

func Dorml2Test(t *testing.T, impl Dorml2er)

func DormlqTest

func DormlqTest(t *testing.T, impl Dormlqer)

func DormqrTest

func DormqrTest(t *testing.T, impl Dormqrer)

func Dormr2Test

func Dormr2Test(t *testing.T, impl Dormr2er)

func DpbconTest

func DpbconTest(t *testing.T, impl Dpbconer)

DpbconTest tests Dpbcon by generating a random symmetric band matrix A and checking that the estimated condition number is not too different from the condition number computed via the explicit inverse of A.

func Dpbtf2Test

func Dpbtf2Test(t *testing.T, impl Dpbtf2er)

Dpbtf2Test tests Dpbtf2 on random symmetric positive definite band matrices by checking that the Cholesky factors multiply back to the original matrix.

func DpbtrfTest

func DpbtrfTest(t *testing.T, impl Dpbtrfer)

DpbtrfTest tests a band Cholesky factorization on random symmetric positive definite band matrices by checking that the Cholesky factors multiply back to the original matrix.

func DpbtrsTest

func DpbtrsTest(t *testing.T, impl Dpbtrser)

DpbtrsTest tests Dpbtrs by comparing the computed and known, generated solutions of a linear system with a random symmetric positive definite band matrix.

func DpoconTest

func DpoconTest(t *testing.T, impl Dpoconer)

func Dpotf2Test

func Dpotf2Test(t *testing.T, impl Dpotf2er)

func DpotrfTest

func DpotrfTest(t *testing.T, impl Dpotrfer)

func DpotriTest

func DpotriTest(t *testing.T, impl Dpotrier)

func DpotrsTest

func DpotrsTest(t *testing.T, impl Dpotrser)

func DrsclTest

func DrsclTest(t *testing.T, impl Drscler)

func DsteqrTest

func DsteqrTest(t *testing.T, impl Dsteqrer)

func DsterfTest

func DsterfTest(t *testing.T, impl Dsterfer)

func DsyevTest

func DsyevTest(t *testing.T, impl Dsyever)

func Dsytd2Test

func Dsytd2Test(t *testing.T, impl Dsytd2er)

func DsytrdTest

func DsytrdTest(t *testing.T, impl Dsytrder)

func DtgsjaTest

func DtgsjaTest(t *testing.T, impl Dtgsjaer)

func DtrconTest

func DtrconTest(t *testing.T, impl Dtrconer)

func Dtrevc3Test

func Dtrevc3Test(t *testing.T, impl Dtrevc3er)

func DtrexcTest

func DtrexcTest(t *testing.T, impl Dtrexcer)

func Dtrti2Test

func Dtrti2Test(t *testing.T, impl Dtrti2er)

func DtrtriTest

func DtrtriTest(t *testing.T, impl Dtrtrier)

func IladlcTest

func IladlcTest(t *testing.T, impl Iladlcer)

func IladlrTest

func IladlrTest(t *testing.T, impl Iladlrer)

type A123

type A123 struct{}

A123 is the non-symmetric singular matrix

    [ 1 2 3 ]
A = [ 4 5 6 ]
    [ 7 8 9 ]

It has three distinct real eigenvalues.

func (A123) Eigenvalues

func (A123) Eigenvalues() []complex128

func (A123) LeftEV

func (A123) LeftEV() blas64.General

func (A123) Matrix

func (A123) Matrix() blas64.General

func (A123) RightEV

func (A123) RightEV() blas64.General

type AntisymRandom

type AntisymRandom struct {
	// contains filtered or unexported fields
}

AntisymRandom is a anti-symmetric random matrix. All its eigenvalues are imaginary with one zero if the order is odd.

func NewAntisymRandom

func NewAntisymRandom(n int, rnd *rand.Rand) AntisymRandom

func (AntisymRandom) Eigenvalues

func (AntisymRandom) Eigenvalues() []complex128

func (AntisymRandom) Matrix

func (a AntisymRandom) Matrix() blas64.General

type Circulant

type Circulant int

Circulant is a generally non-symmetric matrix given by

A[i,j] = 1 + (j-i+n)%n.

For example, for n=5,

    [ 1 2 3 4 5 ]
    [ 5 1 2 3 4 ]
A = [ 4 5 1 2 3 ]
    [ 3 4 5 1 2 ]
    [ 2 3 4 5 1 ]

It has real and complex eigenvalues, some possibly repeated.

func (Circulant) Eigenvalues

func (c Circulant) Eigenvalues() []complex128

func (Circulant) Matrix

func (c Circulant) Matrix() blas64.General

type Clement

type Clement int

Clement is a generally non-symmetric matrix given by

A[i,j] = i+1  if j == i+1,
       = n-i  if j == i-1,
       = 0    otherwise.

For example, for n=5,

    [ . 1 . . . ]
    [ 4 . 2 . . ]
A = [ . 3 . 3 . ]
    [ . . 2 . 4 ]
    [ . . . 1 . ]

It has n distinct real eigenvalues.

func (Clement) Eigenvalues

func (c Clement) Eigenvalues() []complex128

func (Clement) Matrix

func (c Clement) Matrix() blas64.General

type Creation

type Creation int

Creation is a singular non-symmetric matrix given by

A[i,j] = i  if j == i-1,
       = 0  otherwise.

For example, for n=5,

    [ . . . . . ]
    [ 1 . . . . ]
A = [ . 2 . . . ]
    [ . . 3 . . ]
    [ . . . 4 . ]

Zero is its only eigenvalue.

func (Creation) Eigenvalues

func (c Creation) Eigenvalues() []complex128

func (Creation) Matrix

func (c Creation) Matrix() blas64.General

type Dbdsqrer

type Dbdsqrer interface {
	Dbdsqr(uplo blas.Uplo, n, ncvt, nru, ncc int, d, e, vt []float64, ldvt int, u []float64, ldu int, c []float64, ldc int, work []float64) (ok bool)
}

type Dcombssqer

type Dcombssqer interface {
	Dcombssq(scale1, ssq1, scale2, ssq2 float64) (scale, ssq float64)
}

type Dgebaker

type Dgebaker interface {
	Dgebak(job lapack.BalanceJob, side lapack.EVSide, n, ilo, ihi int, scale []float64, m int, v []float64, ldv int)
}

type Dgebaler

type Dgebaler interface {
	Dgebal(job lapack.BalanceJob, n int, a []float64, lda int, scale []float64) (int, int)
}

type Dgebd2er

type Dgebd2er interface {
	Dgebd2(m, n int, a []float64, lda int, d, e, tauq, taup, work []float64)
}

type Dgebrder

type Dgebrder interface {
	Dgebrd(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64, lwork int)
	Dgebd2er
}

type Dgeconer

type Dgeconer interface {
	Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64

	Dgetrier
	Dlanger
}

type Dgeever

type Dgeever interface {
	Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, n int, a []float64, lda int,
		wr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) int
}

type Dgehd2er

type Dgehd2er interface {
	Dgehd2(n, ilo, ihi int, a []float64, lda int, tau, work []float64)
}

type Dgehrder

type Dgehrder interface {
	Dgehrd(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int)

	Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
}

type Dgelq2er

type Dgelq2er interface {
	Dgelq2(m, n int, a []float64, lda int, tau, work []float64)
}

type Dgelqfer

type Dgelqfer interface {
	Dgelq2er
	Dgelqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
}

type Dgelser

type Dgelser interface {
	Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
}

type Dgeql2er

type Dgeql2er interface {
	Dgeql2(m, n int, a []float64, lda int, tau, work []float64)
}

type Dgeqp3er

type Dgeqp3er interface {
	Dlapmter
	Dgeqp3(m, n int, a []float64, lda int, jpvt []int, tau, work []float64, lwork int)
}

type Dgeqr2er

type Dgeqr2er interface {
	Dgeqr2(m, n int, a []float64, lda int, tau []float64, work []float64)
}

type Dgeqrfer

type Dgeqrfer interface {
	Dgeqr2er
	Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
}

type Dgerq2er

type Dgerq2er interface {
	Dgerq2(m, n int, a []float64, lda int, tau []float64, work []float64)
}

type Dgerqfer

type Dgerqfer interface {
	Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
}

type Dgesvder

type Dgesvder interface {
	Dgesvd(jobU, jobVT lapack.SVDJob, m, n int, a []float64, lda int, s, u []float64, ldu int, vt []float64, ldvt int, work []float64, lwork int) (ok bool)
}

type Dgetf2er

type Dgetf2er interface {
	Dgetf2(m, n int, a []float64, lda int, ipiv []int) bool
}

type Dgetrfer

type Dgetrfer interface {
	Dgetrf(m, n int, a []float64, lda int, ipiv []int) bool
}

type Dgetrier

type Dgetrier interface {
	Dgetrfer
	Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) bool
}

type Dgetrser

type Dgetrser interface {
	Dgetrfer
	Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int)
}

type Dggsvd3er

type Dggsvd3er interface {
	Dggsvd3(jobU, jobV, jobQ lapack.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)
}

type Dggsvp3er

type Dggsvp3er interface {
	Dlanger
	Dggsvp3(jobU, jobV, jobQ lapack.GSVDJob, m, p, n int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, iwork []int, tau, work []float64, lwork int) (k, l int)
}

type Dhseqrer

type Dhseqrer interface {
	Dhseqr(job lapack.SchurJob, compz lapack.SchurComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64,
		z []float64, ldz int, work []float64, lwork int) int
}

type Diagonal

type Diagonal int

Diagonal is a diagonal matrix given by

A[i,j] = i+1  if i == j,
       = 0    otherwise.

For example, for n=5,

    [ 1 . . . . ]
    [ . 2 . . . ]
A = [ . . 3 . . ]
    [ . . . 4 . ]
    [ . . . . 5 ]

It has n real eigenvalues {1,...,n}.

func (Diagonal) Eigenvalues

func (d Diagonal) Eigenvalues() []complex128

func (Diagonal) Matrix

func (d Diagonal) Matrix() blas64.General

type Dlabrder

type Dlabrder interface {
	Dlabrd(m, n, nb int, a []float64, lda int, d, e, tauq, taup, x []float64, ldx int, y []float64, ldy int)
}

type Dlacn2er

type Dlacn2er interface {
	Dlacn2(n int, v, x []float64, isgn []int, est float64, kase int, isave *[3]int) (float64, int)
}

type Dlacpyer

type Dlacpyer interface {
	Dlacpy(uplo blas.Uplo, m, n int, a []float64, lda int, b []float64, ldb int)
}

type Dlae2er

type Dlae2er interface {
	Dlae2(a, b, c float64) (rt1, rt2 float64)
}

type Dlaev2er

type Dlaev2er interface {
	Dlaev2(a, b, c float64) (rt1, rt2, cs1, sn1 float64)
}

type Dlaexcer

type Dlaexcer interface {
	Dlaexc(wantq bool, n int, t []float64, ldt int, q []float64, ldq int, j1, n1, n2 int, work []float64) bool
}

type Dlags2er

type Dlags2er interface {
	Dlags2(upper bool, a1, a2, a3, b1, b2, b3 float64) (csu, snu, csv, snv, csq, snq float64)
}

type Dlahqrer

type Dlahqrer interface {
	Dlahqr(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int) int
}

type Dlahr2er

type Dlahr2er interface {
	Dlahr2(n, k, nb int, a []float64, lda int, tau, t []float64, ldt int, y []float64, ldy int)
}

type Dlaln2er

type Dlaln2er interface {
	Dlaln2(trans bool, na, nw int, smin, ca float64, a []float64, lda int, d1, d2 float64, b []float64, ldb int, wr, wi float64, x []float64, ldx int) (scale, xnorm float64, ok bool)
}

type Dlanger

type Dlanger interface {
	Dlange(norm lapack.MatrixNorm, m, n int, a []float64, lda int, work []float64) float64
}

type Dlansber

type Dlansber interface {
	Dlansb(norm lapack.MatrixNorm, uplo blas.Uplo, n, kd int, ab []float64, ldab int, work []float64) float64
}

type Dlanster

type Dlanster interface {
	Dlanst(norm lapack.MatrixNorm, n int, d, e []float64) float64
	Dlanger
}

type Dlansyer

type Dlansyer interface {
	Dlanger
	Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
}

type Dlantrer

type Dlantrer interface {
	Dlanger
	Dlantr(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64
}

type Dlanv2er

type Dlanv2er interface {
	Dlanv2(a, b, c, d float64) (aa, bb, cc, dd float64, rt1r, rt1i, rt2r, rt2i float64, cs, sn float64)
}

type Dlapller

type Dlapller interface {
	Dgesvder
	Dlapll(n int, x []float64, incX int, y []float64, incY int) float64
}

type Dlapmter

type Dlapmter interface {
	Dlapmt(forward bool, m, n int, x []float64, ldx int, k []int)
}

type Dlapy2er

type Dlapy2er interface {
	Dlapy2(float64, float64) float64
}

type Dlaqp2er

type Dlaqp2er interface {
	Dlapmter
	Dlaqp2(m, n, offset int, a []float64, lda int, jpvt []int, tau, vn1, vn2, work []float64)
}

type Dlaqpser

type Dlaqpser interface {
	Dlapmter
	Dlaqps(m, n, offset, nb int, a []float64, lda int, jpvt []int, tau, vn1, vn2, auxv, f []float64, ldf int) (kb int)
}

type Dlaqr04er

type Dlaqr04er interface {
	Dlaqr04(wantt, wantz bool, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64, iloz, ihiz int, z []float64, ldz int, work []float64, lwork int, recur int) int

	Dlahqrer
}

type Dlaqr1er

type Dlaqr1er interface {
	Dlaqr1(n int, h []float64, ldh int, sr1, si1, sr2, si2 float64, v []float64)
}

type Dlaqr23er

type Dlaqr23er interface {
	Dlaqr23(wantt, wantz bool, n, ktop, kbot, nw int, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, sr, si []float64, v []float64, ldv int, nh int, t []float64, ldt int, nv int, wv []float64, ldwv int, work []float64, lwork int, recur int) (ns, nd int)
}

type Dlaqr5er

type Dlaqr5er interface {
	Dlaqr5(wantt, wantz bool, kacc22 int, n, ktop, kbot, nshfts int, sr, si []float64, h []float64, ldh int, iloz, ihiz int, z []float64, ldz int, v []float64, ldv int, u []float64, ldu int, nh int, wh []float64, ldwh int, nv int, wv []float64, ldwv int)
}

type Dlarfber

type Dlarfber interface {
	Dlarfter
	Dlarfb(side blas.Side, trans blas.Transpose, direct lapack.Direct,
		store lapack.StoreV, m, n, k int, v []float64, ldv int, t []float64, ldt int,
		c []float64, ldc int, work []float64, ldwork int)
}

type Dlarfer

type Dlarfer interface {
	Dlarf(side blas.Side, m, n int, v []float64, incv int, tau float64, c []float64, ldc int, work []float64)
}

type Dlarfger

type Dlarfger interface {
	Dlarfg(n int, alpha float64, x []float64, incX int) (beta, tau float64)
}

type Dlarfter

type Dlarfter interface {
	Dgeqr2er
	Dlarft(direct lapack.Direct, store lapack.StoreV, n, k int, v []float64, ldv int, tau []float64, t []float64, ldt int)
}

type Dlarfxer

type Dlarfxer interface {
	Dlarfx(side blas.Side, m, n int, v []float64, tau float64, c []float64, ldc int, work []float64)
}

type Dlartger

type Dlartger interface {
	Dlartg(f, g float64) (cs, sn, r float64)
}

type Dlas2er

type Dlas2er interface {
	Dlas2(f, g, h float64) (min, max float64)
}

type Dlascler

type Dlascler interface {
	Dlascl(kind lapack.MatrixType, kl, ku int, cfrom, cto float64, m, n int, a []float64, lda int)
}

type Dlaseter

type Dlaseter interface {
	Dlaset(uplo blas.Uplo, m, n int, alpha, beta float64, a []float64, lda int)
}

type Dlasq1er

type Dlasq1er interface {
	Dlasq1(n int, d, e, work []float64) int

	Dgebrd(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64, lwork int)
}

type Dlasq2er

type Dlasq2er interface {
	Dlasq2(n int, z []float64) (info int)

	Dsyev(jobz lapack.EVJob, uplo blas.Uplo, n int, a []float64, lda int, w, work []float64, lwork int) (ok bool)
}

type Dlasrer

type Dlasrer interface {
	Dlasr(side blas.Side, pivot lapack.Pivot, direct lapack.Direct, m, n int, c, s, a []float64, lda int)
}

type Dlasrter

type Dlasrter interface {
	Dlasrt(s lapack.Sort, n int, d []float64)
}

type Dlassqer

type Dlassqer interface {
	Dlassq(n int, x []float64, incx int, scale, ssq float64) (float64, float64)
}

type Dlasv2er

type Dlasv2er interface {
	Dlasv2(f, g, h float64) (ssmin, ssmax, snr, csr, snl, csl float64)
}

type Dlaswper

type Dlaswper interface {
	Dlaswp(n int, a []float64, lda, k1, k2 int, ipiv []int, incX int)
}

type Dlasy2er

type Dlasy2er interface {
	Dlasy2(tranl, tranr bool, isgn, n1, n2 int, tl []float64, ldtl int, tr []float64, ldtr int, b []float64, ldb int, x []float64, ldx int) (scale, xnorm float64, ok bool)
}

type Dlatbser

type Dlatbser interface {
	Dlatbs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, normin bool, n, kd int, ab []float64, ldab int, x []float64, cnorm []float64) float64
}

type Dlatrder

type Dlatrder interface {
	Dlatrd(uplo blas.Uplo, n, nb int, a []float64, lda int, e, tau, w []float64, ldw int)
}

type Dlatrser

type Dlatrser interface {
	Dlatrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, normin bool, n int, a []float64, lda int, x []float64, cnorm []float64) (scale float64)
}

type Dlauu2er

type Dlauu2er interface {
	Dlauu2(uplo blas.Uplo, n int, a []float64, lda int)
}

type Dlauumer

type Dlauumer interface {
	Dlauum(uplo blas.Uplo, n int, a []float64, lda int)
}

type Dorg2ler

type Dorg2ler interface {
	Dorg2l(m, n, k int, a []float64, lda int, tau, work []float64)
	Dgeql2er
}

type Dorg2rer

type Dorg2rer interface {
	Dgeqrfer
	Dorg2r(m, n, k int, a []float64, lda int, tau []float64, work []float64)
}

type Dorgbrer

type Dorgbrer interface {
	Dorgbr(vect lapack.GenOrtho, m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
	Dgebrder
}

type Dorghrer

type Dorghrer interface {
	Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int)

	Dgehrder
}

type Dorgl2er

type Dorgl2er interface {
	Dgelqfer
	Dorgl2(m, n, k int, a []float64, lda int, tau []float64, work []float64)
}

type Dorglqer

type Dorglqer interface {
	Dorgl2er
	Dorglq(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
}

type Dorgqler

type Dorgqler interface {
	Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)

	Dlarfger
}

type Dorgqrer

type Dorgqrer interface {
	Dorg2rer
	Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
}

type Dorgtrer

type Dorgtrer interface {
	Dorgtr(uplo blas.Uplo, n int, a []float64, lda int, tau, work []float64, lwork int)
	Dsytrder
}

type Dorm2rer

type Dorm2rer interface {
	Dgeqrfer
	Dorm2r(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64)
}

type Dormbrer

type Dormbrer interface {
	Dormbr(vect lapack.ApplyOrtho, side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
	Dgebrder
}

type Dormhrer

type Dormhrer interface {
	Dormhr(side blas.Side, trans blas.Transpose, m, n, ilo, ihi int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)

	Dgehrder
}

type Dorml2er

type Dorml2er interface {
	Dgelqfer
	Dorml2(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64)
}

type Dormlqer

type Dormlqer interface {
	Dorml2er
	Dormlq(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
}

type Dormqrer

type Dormqrer interface {
	Dorm2rer
	Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
}

type Dormr2er

type Dormr2er interface {
	Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
	Dormr2(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64)
}

type Downshift

type Downshift int

Downshift is a non-singular upper Hessenberg matrix given by

A[i,j] = 1  if (i-j+n)%n == 1,
       = 0  otherwise.

For example, for n=5,

    [ . . . . 1 ]
    [ 1 . . . . ]
A = [ . 1 . . . ]
    [ . . 1 . . ]
    [ . . . 1 . ]

Its eigenvalues are the complex roots of unity.

func (Downshift) Eigenvalues

func (d Downshift) Eigenvalues() []complex128

func (Downshift) Matrix

func (d Downshift) Matrix() blas64.General

type Dpbconer

type Dpbconer interface {
	Dpbcon(uplo blas.Uplo, n, kd int, ab []float64, ldab int, anorm float64, work []float64, iwork []int) float64

	Dpbtrser
	Dlanger
	Dlansber
}

type Dpbtf2er

type Dpbtf2er interface {
	Dpbtf2(uplo blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
}

type Dpbtrfer

type Dpbtrfer interface {
	Dpbtrf(uplo blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
}

type Dpbtrser

type Dpbtrser interface {
	Dpbtrs(uplo blas.Uplo, n, kd, nrhs int, ab []float64, ldab int, b []float64, ldb int)

	Dpbtrfer
}

type Dpoconer

type Dpoconer interface {
	Dpotrfer
	Dgeconer
	Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
	Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
}

type Dpotf2er

type Dpotf2er interface {
	Dpotf2(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
}

type Dpotrfer

type Dpotrfer interface {
	Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool)
}

type Dpotrier

type Dpotrier interface {
	Dpotri(uplo blas.Uplo, n int, a []float64, lda int) bool

	Dpotrf(uplo blas.Uplo, n int, a []float64, lda int) bool
}

type Dpotrser

type Dpotrser interface {
	Dpotrs(uplo blas.Uplo, n, nrhs int, a []float64, lda int, b []float64, ldb int)

	Dpotrf(uplo blas.Uplo, n int, a []float64, lda int) bool
}

type Drscler

type Drscler interface {
	Drscl(n int, a float64, x []float64, incX int)
}

type Dsteqrer

type Dsteqrer interface {
	Dsteqr(compz lapack.EVComp, n int, d, e, z []float64, ldz int, work []float64) (ok bool)
	Dorgtrer
}

type Dsterfer

type Dsterfer interface {
	Dsteqrer
	Dlansyer
	Dsterf(n int, d, e []float64) (ok bool)
}

type Dsyever

type Dsyever interface {
	Dsyev(jobz lapack.EVJob, uplo blas.Uplo, n int, a []float64, lda int, w, work []float64, lwork int) (ok bool)
}

type Dsytd2er

type Dsytd2er interface {
	Dsytd2(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau []float64)
}

type Dsytrder

type Dsytrder interface {
	Dsytrd(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau, work []float64, lwork int)

	Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
	Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int)
}

type Dtgsjaer

type Dtgsjaer interface {
	Dlanger
	Dtgsja(jobU, jobV, jobQ lapack.GSVDJob, m, p, n, k, l int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64) (cycles int, ok bool)
}

type Dtrconer

type Dtrconer interface {
	Dtrcon(norm lapack.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) bool
	Dlantr(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64
}

type Dtrevc3er

type Dtrevc3er interface {
	Dtrevc3(side lapack.EVSide, howmny lapack.EVHowMany, selected []bool, n int, t []float64, ldt int, vl []float64, ldvl int, vr []float64, ldvr int, mm int, work []float64, lwork int) int
}

type Dtrexcer

type Dtrexcer interface {
	Dtrexc(compq lapack.UpdateSchurComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool)
}

type Dtrti2er

type Dtrti2er interface {
	Dtrti2(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int)
}

type Dtrtrier

type Dtrtrier interface {
	Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) bool
}

type Fibonacci

type Fibonacci int

Fibonacci is an upper Hessenberg matrix with 3 distinct real eigenvalues. For example, for n=5,

    [ . 1 . . . ]
    [ 1 1 . . . ]
A = [ . 1 1 . . ]
    [ . . 1 1 . ]
    [ . . . 1 1 ]

func (Fibonacci) Eigenvalues

func (f Fibonacci) Eigenvalues() []complex128

func (Fibonacci) Matrix

func (f Fibonacci) Matrix() blas64.General

type Gear

type Gear int

Gear is a singular non-symmetric matrix with real eigenvalues. For example, for n=5,

    [ . 1 . . 1 ]
    [ 1 . 1 . . ]
A = [ . 1 . 1 . ]
    [ . . 1 . 1 ]
    [-1 . . 1 . ]

func (Gear) Eigenvalues

func (g Gear) Eigenvalues() []complex128

func (Gear) Matrix

func (g Gear) Matrix() blas64.General

type Grcar

type Grcar struct {
	N int
	K int
}

Grcar is an upper Hessenberg matrix given by

A[i,j] = -1  if i == j+1,
       = 1   if i <= j and j <= i+k,
       = 0   otherwise.

For example, for n=5 and k=2,

    [  1  1  1  .  . ]
    [ -1  1  1  1  . ]
A = [  . -1  1  1  1 ]
    [  .  . -1  1  1 ]
    [  .  .  . -1  1 ]

The matrix has sensitive eigenvalues but they are not given explicitly.

func (Grcar) Eigenvalues

func (Grcar) Eigenvalues() []complex128

func (Grcar) Matrix

func (g Grcar) Matrix() blas64.General

type Hanowa

type Hanowa struct {
	N     int // Order of the matrix, must be even.
	Alpha float64
}

Hanowa is a non-symmetric non-singular matrix of even order given by

A[i,j] = alpha    if i == j,
       = -i-1     if i < n/2 and j == i + n/2,
       = i+1-n/2  if i >= n/2 and j == i - n/2,
       = 0        otherwise.

The matrix has complex eigenvalues.

func (Hanowa) Eigenvalues

func (h Hanowa) Eigenvalues() []complex128

func (Hanowa) Matrix

func (h Hanowa) Matrix() blas64.General

type Iladlcer

type Iladlcer interface {
	Iladlc(m, n int, a []float64, lda int) int
}

type Iladlrer

type Iladlrer interface {
	Iladlr(m, n int, a []float64, lda int) int
}

type Lesp

type Lesp int

Lesp is a tridiagonal, generally non-symmetric matrix given by

A[i,j] = -2*i-5   if i == j,
       = 1/(i+1)  if i == j-1,
       = j+1      if i == j+1.

For example, for n=5,

    [  -5    2    .    .    . ]
    [ 1/2   -7    3    .    . ]
A = [   .  1/3   -9    4    . ]
    [   .    .  1/4  -11    5 ]
    [   .    .    .  1/5  -13 ].

The matrix has sensitive eigenvalues but they are not given explicitly.

func (Lesp) Eigenvalues

func (Lesp) Eigenvalues() []complex128

func (Lesp) Matrix

func (l Lesp) Matrix() blas64.General

type Rutis

type Rutis struct{}

Rutis is the 4×4 non-symmetric matrix

    [ 4 -5  0  3 ]
A = [ 0  4 -3 -5 ]
    [ 5 -3  4  0 ]
    [ 3  0  5  4 ]

It has two distinct real eigenvalues and a pair of complex eigenvalues.

func (Rutis) Eigenvalues

func (Rutis) Eigenvalues() []complex128

func (Rutis) Matrix

func (Rutis) Matrix() blas64.General

type Tris

type Tris struct {
	N       int
	X, Y, Z float64
}

Tris is a tridiagonal matrix given by

A[i,j] = x  if i == j-1,
       = y  if i == j,
       = z  if i == j+1.

If x*z is negative, the matrix has complex eigenvalues.

func (Tris) Eigenvalues

func (t Tris) Eigenvalues() []complex128

func (Tris) Matrix

func (t Tris) Matrix() blas64.General

type Wilk12

type Wilk12 struct{}

Wilk12 is a 12×12 lower Hessenberg matrix with 12 distinct real eigenvalues.

func (Wilk12) Eigenvalues

func (Wilk12) Eigenvalues() []complex128

func (Wilk12) Matrix

func (Wilk12) Matrix() blas64.General

type Wilk20

type Wilk20 float64

Wilk20 is a 20×20 lower Hessenberg matrix. If the parameter is 0, the matrix has 20 distinct real eigenvalues. If the parameter is 1e-10, the matrix has 6 real eigenvalues and 7 pairs of complex eigenvalues.

func (Wilk20) Eigenvalues

func (w Wilk20) Eigenvalues() []complex128

func (Wilk20) Matrix

func (w Wilk20) Matrix() blas64.General

type Wilk4

type Wilk4 struct{}

Wilk4 is a 4×4 lower triangular matrix with 4 distinct real eigenvalues.

func (Wilk4) Eigenvalues

func (Wilk4) Eigenvalues() []complex128

func (Wilk4) Matrix

func (Wilk4) Matrix() blas64.General

type Zero

type Zero int

Zero is a matrix with all elements equal to zero.

func (Zero) Eigenvalues

func (z Zero) Eigenvalues() []complex128

func (Zero) Matrix

func (z Zero) Matrix() blas64.General

Package Files

Documentation was rendered with GOOS=linux and GOARCH=amd64.

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