// See function Symm.
func SymmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fsymm, A, B, C, params)
if err != nil {
return
}
if ind.M == 0 || ind.N == 0 {
return
}
Aa := A.FloatArray()
Ba := B.FloatArray()
Ca := C.FloatArray()
uplo := linalg.ParamString(params.Uplo)
side := linalg.ParamString(params.Side)
dsymm(side, uplo, ind.M, ind.N, alpha, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb, beta, Ca[ind.OffsetC:], ind.LDc)
return
}
// See function Syrk2.
func Syr2kFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fsyr2k, A, B, C, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
Aa := A.FloatArray()
Ba := B.FloatArray()
Ca := C.FloatArray()
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
//diag := linalg.ParamString(params.Diag)
dsyr2k(uplo, trans, ind.N, ind.K, alpha, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb, beta, Ca[ind.OffsetC:], ind.LDc)
return
}
// See function Trsm.
func TrsmFloat(A, B *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, ftrsm, A, B, nil, params)
if err != nil {
return
}
if ind.N == 0 || ind.M == 0 {
return
}
Aa := A.FloatArray()
Ba := B.FloatArray()
uplo := linalg.ParamString(params.Uplo)
transA := linalg.ParamString(params.TransA)
side := linalg.ParamString(params.Side)
diag := linalg.ParamString(params.Diag)
dtrsm(side, uplo, transA, diag, ind.M, ind.N, alpha,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
return
}
// See function Gemm.
func GemmFloat(A, B, C *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fgemm, A, B, C, params)
if err != nil {
return
}
if ind.M == 0 || ind.N == 0 {
return
}
Aa := A.FloatArray()
Ba := B.FloatArray()
Ca := C.FloatArray()
transB := linalg.ParamString(params.TransB)
transA := linalg.ParamString(params.TransA)
//diag := linalg.ParamString(params.Diag)
dgemm(transA, transB, ind.M, ind.N, ind.K, alpha,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb, beta,
Ca[ind.OffsetC:], ind.LDc)
return
}
func GesvdFloat(A, S, U, Vt *matrix.FloatMatrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
err = checkGesvd(ind, pars, A, S, U, Vt)
if err != nil {
return err
}
if ind.M == 0 || ind.N == 0 {
return nil
}
Aa := A.FloatArray()
Sa := S.FloatArray()
var Ua, Va []float64
Ua = nil
Va = nil
if U != nil {
Ua = U.FloatArray()[ind.OffsetU:]
}
if Vt != nil {
Va = Vt.FloatArray()[ind.OffsetVt:]
}
info := dgesvd(linalg.ParamString(pars.Jobu), linalg.ParamString(pars.Jobvt),
ind.M, ind.N, Aa[ind.OffsetA:], ind.LDa, Sa[ind.OffsetS:], Ua, ind.LDu, Va, ind.LDvt)
if info != 0 {
return onError(fmt.Sprintf("GesvdFloat lapack error: %d", info))
}
return nil
}
/*
General matrix-matrix product. (L3)
PURPOSE
Computes
C := alpha*A*B + beta*C if transA = PNoTrans and transB = PNoTrans.
C := alpha*A^T*B + beta*C if transA = PTrans and transB = PNoTrans.
C := alpha*A^H*B + beta*C if transA = PConjTrans and transB = PNoTrans.
C := alpha*A*B^T + beta*C if transA = PNoTrans and transB = PTrans.
C := alpha*A^T*B^T + beta*C if transA = PTrans and transB = PTrans.
C := alpha*A^H*B^T + beta*C if transA = PConjTrans and transB = PTrans.
C := alpha*A*B^H + beta*C if transA = PNoTrans and transB = PConjTrans.
C := alpha*A^T*B^H + beta*C if transA = PTrans and transB = PConjTrans.
C := alpha*A^H*B^H + beta*C if transA = PConjTrans and transB = PConjTrans.
The number of rows of the matrix product is m. The number of columns is n.
The inner dimension is k. If k=0, this reduces to C := beta*C.
ARGUMENTS
A float or complex matrix, m*k
B float or complex matrix, k*n
C float or complex matrix, m*n
alpha number (float or complex singleton matrix)
beta number (float or complex singleton matrix)
OPTIONS
transA PNoTrans, PTrans or PConjTrans
transB PNoTrans, PTrans or PConjTrans
m integer. If negative, the default value is used. The default value is
m = A.Rows of if transA != PNoTrans m = A.Cols.
n integer. If negative, the default value is used. The default value is
n = (transB == PNoTrans) ? B.Cols : B.Rows.
k integer. If negative, the default value is used. The default value is
k=A.Cols or if transA != PNoTrans) k = A.Rows, transA=PNoTrans.
If the default value is used it should also be equal to
(transB == PNoTrans) ? B.Rows : B.Cols.
ldA nonnegative integer. ldA >= max(1,m) of if transA != NoTrans max(1,k).
If zero, the default value is used.
ldB nonnegative integer. ldB >= max(1,k) or if transB != NoTrans max(1,n).
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 integer
offsetC nonnegative integer;
*/
func Gemm(A, B, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fgemm, A, B, C, params)
if err != nil {
return
}
if ind.M == 0 || ind.N == 0 {
return
}
if !matrix.EqualTypes(A, B, C) {
return onError("Parameters not of same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ba := B.(*matrix.FloatMatrix).FloatArray()
Ca := C.(*matrix.FloatMatrix).FloatArray()
aval := alpha.Float()
bval := beta.Float()
if math.IsNaN(aval) || math.IsNaN(bval) {
return onError("alpha or beta not a number")
}
transB := linalg.ParamString(params.TransB)
transA := linalg.ParamString(params.TransA)
dgemm(transA, transB, ind.M, ind.N, ind.K, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb, bval,
Ca[ind.OffsetC:], ind.LDc)
case *matrix.ComplexMatrix:
Aa := A.(*matrix.ComplexMatrix).ComplexArray()
Ba := B.(*matrix.ComplexMatrix).ComplexArray()
Ca := C.(*matrix.ComplexMatrix).ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return onError("alpha not a number")
}
bval := beta.Complex()
if cmplx.IsNaN(bval) {
return onError("beta not a number")
}
transB := linalg.ParamString(params.TransB)
transA := linalg.ParamString(params.TransA)
zgemm(transA, transB, ind.M, ind.N, ind.K, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb, bval,
Ca[ind.OffsetC:], ind.LDc)
default:
return onError("Unknown type, not implemented")
}
return
}
/*
Rank-k update of symmetric matrix. (L3)
Herk(A, C, alpha, beta, uplo=PLower, trans=PNoTrans, n=-1,
k=-1, ldA=max(1,A.Rows), ldC=max(1,C.Rows), offsetA=0, offsetB=0)
Computes
C := alpha*A*A^T + beta*C, if trans is PNoTrans
C := alpha*A^T*A + beta*C, if trans is PTrans
C is symmetric (real or complex) of order n. The inner dimension of the matrix
product is k. If k=0 this is interpreted as C := beta*C.
ARGUMENTS
A float or complex matrix.
C float or complex matrix. Must have the same type as A.
alpha number (float or complex singleton matrix). Complex alpha is only
allowed if A is complex.
beta number (float or complex singleton matrix). Complex beta is only
allowed if A is complex.
OPTIONS
uplo PLower or PUpper
trans PNoTrans or PTrans
n integer. If negative, the default value is used.
The default value is n = A.Rows or if trans == PNoTrans n = A.Cols.
k integer. If negative, the default value is used.
The default value is k = A.Cols, or if trans == PNoTrans k = A.Rows.
ldA nonnegative integer.
ldA >= max(1,n) or if trans != PNoTrans ldA >= max(1,k).
If zero, the default value is used.
ldC nonnegative integer. ldC >= max(1,n).
If zero, the default value is used.
offsetA nonnegative integer
offsetC nonnegative integer;
*/
func Herk(A, C matrix.Matrix, alpha, beta matrix.Scalar, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, fsyrk, A, nil, C, params)
if e != nil || err != nil {
return
}
if !matrix.EqualTypes(A, C) {
return onError("Parameters not of same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ca := C.(*matrix.FloatMatrix).FloatArray()
aval := alpha.Float()
bval := beta.Float()
if math.IsNaN(aval) || math.IsNaN(bval) {
return onError("alpha or beta not a number")
}
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
dsyrk(uplo, trans, ind.N, ind.K, aval, Aa[ind.OffsetA:], ind.LDa, bval,
Ca[ind.OffsetC:], ind.LDc)
case *matrix.ComplexMatrix:
Aa := A.(*matrix.ComplexMatrix).ComplexArray()
Ca := C.(*matrix.ComplexMatrix).ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return onError("alpha not a real or complex number")
}
bval := beta.Float()
if math.IsNaN(bval) {
return onError("beta not a real number")
}
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
zherk(uplo, trans, ind.N, ind.K, aval, Aa[ind.OffsetA:], ind.LDa, bval,
Ca[ind.OffsetC:], ind.LDc)
default:
return onError("Unknown type, not implemented")
}
return
}
func GbtrsFloat(A, B *matrix.FloatMatrix, ipiv []int32, KL int, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
ind.Kl = KL
err = checkGbtrs(ind, A, B, ipiv)
if err != nil {
return err
}
if ind.N == 0 || ind.Nrhs == 0 {
return nil
}
Aa := A.FloatArray()
Ba := B.FloatArray()
trans := linalg.ParamString(pars.Trans)
info := dgbtrs(trans, ind.N, ind.Kl, ind.Ku, ind.Nrhs,
Aa[ind.OffsetA:], ind.LDa, ipiv, Ba[ind.OffsetB:], ind.LDb)
if info != 0 {
return onError(fmt.Sprintf("Gbtrs: lapack error: %d", info))
}
return nil
}
// See function Gbmv.
func GbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {
var params *linalg.Parameters
params, err = linalg.GetParameters(opts...)
if err != nil {
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level2_func(ind, fgbmv, X, Y, A, params)
if err != nil {
return
}
if ind.M == 0 && ind.N == 0 {
return
}
Xa := X.FloatArray()
Ya := Y.FloatArray()
Aa := A.FloatArray()
if params.Trans == linalg.PNoTrans && ind.N == 0 {
dscal(ind.M, beta, Ya[ind.OffsetY:], ind.IncY)
} else if params.Trans == linalg.PTrans && ind.M == 0 {
dscal(ind.N, beta, Ya[ind.OffsetY:], ind.IncY)
} else {
trans := linalg.ParamString(params.Trans)
dgbmv(trans, ind.M, ind.N, ind.Kl, ind.Ku,
alpha, Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:], ind.IncX,
beta, Ya[ind.OffsetY:], ind.IncY)
}
return
}
/*
Solves a general real or complex set of linear equations.
PURPOSE
Solves A*X=B with A m by n real or complex.
ARGUMENTS.
A float or complex matrix
B float or complex matrix. Must have the same type as A.
OPTIONS:
trans
m nonnegative integer. If negative, the default value is used.
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.
*/
func Gels(A, B matrix.Matrix, opts ...linalg.Option) error {
pars, _ := linalg.GetParameters(opts...)
ind := linalg.GetIndexOpts(opts...)
arows := ind.LDa
brows := ind.LDb
if ind.M < 0 {
ind.M = A.Rows()
}
if ind.N < 0 {
ind.N = A.Cols()
}
if ind.Nrhs < 0 {
ind.Nrhs = B.Cols()
}
if ind.M == 0 || ind.N == 0 || ind.Nrhs == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.LeadingIndex())
arows = max(1, A.Rows())
}
if ind.LDa < max(1, ind.M) {
return onError("Gesv: ldA")
}
if ind.LDb == 0 {
ind.LDb = max(1, B.LeadingIndex())
brows = max(1, B.Rows())
}
if ind.LDb < max(ind.M, ind.N) {
return onError("Gesv: ldB")
}
if !matrix.EqualTypes(A, B) {
return onError("Gesv: arguments not of same type")
}
_, _ = arows, brows // todo!! something
info := -1
trans := linalg.ParamString(pars.Trans)
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ba := B.(*matrix.FloatMatrix).FloatArray()
info = dgels(trans, ind.M, ind.N, ind.Nrhs, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
Aa := A.(*matrix.ComplexMatrix).ComplexArray()
Ba := B.(*matrix.ComplexMatrix).ComplexArray()
info = zgels(trans, ind.M, ind.N, ind.Nrhs, Aa[ind.OffsetA:], ind.LDa,
Ba[ind.OffsetB:], ind.LDb)
}
if info != 0 {
return onError(fmt.Sprintf("Gels: lapack error: %d", info))
}
return nil
}
func SyevdFloat(A, W *matrix.FloatMatrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
err = checkSyevd(ind, A, W)
if err != nil {
return err
}
if ind.N == 0 {
return nil
}
jobz := linalg.ParamString(pars.Jobz)
uplo := linalg.ParamString(pars.Uplo)
Aa := A.FloatArray()
Wa := W.FloatArray()
info := dsyevd(jobz, uplo, ind.N, Aa[ind.OffsetA:], ind.LDa, Wa[ind.OffsetW:])
if info != 0 {
return onError(fmt.Sprintf("Syevd: lapack error %d", info))
}
return nil
}
/*
Solution of a triangular system of equations with multiple righthand sides. (L3)
Trsm(A, B, alpha, side=PLeft, uplo=PLower, transA=PNoTrans, diag=PNonUnit,
m=-1, n=-1, ldA=max(1,A.Rows), ldB=max(1,B.Rows), offsetA=0, offsetB=0)
Computes
B := alpha*A^{-1}*B if transA is PNoTrans and side = PLeft
B := alpha*B*A^{-1} if transA is PNoTrans and side = PRight
B := alpha*A^{-T}*B if transA is PTrans and side = PLeft
B := alpha*B*A^{-T} if transA is PTrans and side = PRight
B := alpha*A^{-H}*B if transA is PConjTrans and side = PLeft
B := alpha*B*A^{-H} if transA is PConjTrans and side = PRight
B is m by n and A is triangular. The code does not verify whether A is nonsingular.
ARGUMENTS
A float or complex matrix.
B float or complex matrix. Must have the same type as A.
alpha number (float or complex). Complex alpha is only
allowed if A is complex.
OPTIONS
side PLeft or PRight
uplo PLower or PUpper
transA PNoTrans or PTrans
diag PNonUnit or PUnit
m integer. If negative, the default value is used.
The default value is m = A.Rows or if side == PRight m = B.Rows
If the default value is used and side is PLeft, m must be equal to A.Cols.
n integer. If negative, the default value is used.
The default value is n = B.Cols or if side )= PRight n = A.Rows.
If the default value is used and side is PRight, n must be equal to A.Cols.
ldA nonnegative integer.
ldA >= max(1,m) of if side == PRight lda >= max(1,n).
If zero, the default value is used.
ldB nonnegative integer. ldB >= max(1,m).
If zero, the default value is used.
offsetA nonnegative integer
offsetB nonnegative integer
*/
func Trsm(A, B matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error) {
params, e := linalg.GetParameters(opts...)
if e != nil {
err = e
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level3_func(ind, ftrsm, A, B, nil, params)
if err != nil {
return
}
if !matrix.EqualTypes(A, B) {
return onError("Parameters not of same type")
}
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ba := B.(*matrix.FloatMatrix).FloatArray()
aval := alpha.Float()
if math.IsNaN(aval) {
return onError("alpha or beta not a number")
}
uplo := linalg.ParamString(params.Uplo)
transA := linalg.ParamString(params.TransA)
side := linalg.ParamString(params.Side)
diag := linalg.ParamString(params.Diag)
dtrsm(side, uplo, transA, diag, ind.M, ind.N, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
Aa := A.(*matrix.ComplexMatrix).ComplexArray()
Ba := B.(*matrix.ComplexMatrix).ComplexArray()
aval := alpha.Complex()
if cmplx.IsNaN(aval) {
return onError("alpha not a number")
}
uplo := linalg.ParamString(params.Uplo)
transA := linalg.ParamString(params.TransA)
side := linalg.ParamString(params.Side)
diag := linalg.ParamString(params.Diag)
ztrsm(side, uplo, transA, diag, ind.M, ind.N, aval,
Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
default:
return onError("Unknown type, not implemented")
}
return
}
// See function Tbsv.
func TbsvFloat(A, X *matrix.FloatMatrix, opts ...linalg.Option) (err error) {
var params *linalg.Parameters
params, err = linalg.GetParameters(opts...)
if err != nil {
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level2_func(ind, ftbsv, X, nil, A, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
Xa := X.FloatArray()
Aa := A.FloatArray()
uplo := linalg.ParamString(params.Uplo)
trans := linalg.ParamString(params.Trans)
diag := linalg.ParamString(params.Diag)
dtbsv(uplo, trans, diag, ind.N, ind.K,
Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:], ind.IncX)
return
}
func PotrfFloat(A *matrix.FloatMatrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
err = checkPotrf(ind, A)
if ind.N == 0 {
return nil
}
Aa := A.FloatArray()
uplo := linalg.ParamString(pars.Uplo)
info := dpotrf(uplo, ind.N, Aa[ind.OffsetA:], ind.LDa)
if info != 0 {
return onError(fmt.Sprintf("Potrf: lapack error %d", info))
}
return nil
}
// See function Syr.
func SyrFloat(X, A *matrix.FloatMatrix, alpha float64, opts ...linalg.Option) (err error) {
var params *linalg.Parameters
params, err = linalg.GetParameters(opts...)
if err != nil {
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level2_func(ind, fsyr, X, nil, A, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
Xa := X.FloatArray()
Aa := A.FloatArray()
uplo := linalg.ParamString(params.Uplo)
dsyr(uplo, ind.N, alpha, Xa[ind.OffsetX:], ind.IncX, Aa[ind.OffsetA:], ind.LDa)
return
}
func PosvFloat(A, B *matrix.FloatMatrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
err = checkPosv(ind, A, B)
if err != nil {
return err
}
if ind.N == 0 || ind.Nrhs == 0 {
return nil
}
Aa := A.FloatArray()
Ba := B.FloatArray()
uplo := linalg.ParamString(pars.Uplo)
info := dposv(uplo, ind.N, ind.Nrhs, Aa[ind.OffsetA:], ind.LDa, Ba[ind.OffsetB:], ind.LDb)
if info != 0 {
return onError(fmt.Sprintf("Posv: lapack error %d", info))
}
return nil
}
// See function Sbmv.
func SbmvFloat(A, X, Y *matrix.FloatMatrix, alpha, beta float64, opts ...linalg.Option) (err error) {
var params *linalg.Parameters
params, err = linalg.GetParameters(opts...)
if err != nil {
return
}
ind := linalg.GetIndexOpts(opts...)
err = check_level2_func(ind, fsbmv, X, Y, A, params)
if err != nil {
return
}
if ind.N == 0 {
return
}
Xa := X.FloatArray()
Ya := Y.FloatArray()
Aa := A.FloatArray()
uplo := linalg.ParamString(params.Uplo)
dsbmv(uplo, ind.N, ind.K, alpha, Aa[ind.OffsetA:], ind.LDa, Xa[ind.OffsetX:],
ind.IncX, beta, Ya[ind.OffsetY:], ind.IncY)
return
}
/*
Solves a real or complex tridiagonal set of linear equations,
given the LU factorization computed by gttrf().
PURPOSE
solves A*X=B, if trans is PNoTrans
solves A^T*X=B, if trans is PTrans
solves A^H*X=B, if trans is PConjTrans
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 float or complex matrix
D float or complex matrix. Must have the same type as dl.
DU float or complex matrix. Must have the same type as dl.
DU2 float or complex matrix. Must have the same type as dl.
B float or complex matrix. Must have the same type oas dl.
ipiv int vector
OPTIONS
trans PNoTrans, PTrans, PConjTrans
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 integer
*/
func Gtrrs(DL, D, DU, DU2, B matrix.Matrix, ipiv []int32, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
brows := ind.LDb
if ind.OffsetD < 0 {
return onError("Gttrs: offset D")
}
if ind.N < 0 {
ind.N = D.NumElements() - ind.OffsetD
}
if ind.N < 0 {
return onError("Gttrs: size D")
}
if ind.N == 0 {
return nil
}
if ind.OffsetDL < 0 {
return onError("Gttrs: offset DL")
}
sizeDL := DL.NumElements()
if sizeDL < ind.OffsetDL+ind.N-1 {
return onError("Gttrs: sizeDL")
}
if ind.OffsetDU < 0 {
return onError("Gttrs: offset DU")
}
sizeDU := DU.NumElements()
if sizeDU < ind.OffsetDU+ind.N-1 {
return onError("Gttrs: sizeDU")
}
sizeDU2 := DU2.NumElements()
if sizeDU2 < ind.N-2 {
return onError("Gttrs: sizeDU2")
}
if ind.Nrhs < 0 {
ind.Nrhs = B.Cols()
}
if ind.Nrhs == 0 {
return nil
}
if ind.LDb == 0 {
ind.LDb = max(1, B.LeadingIndex())
brows = max(1, B.Rows())
}
if ind.LDb < max(1, ind.N) {
return onError("Gttrs: ldB")
}
if ind.OffsetB < 0 {
return onError("Gttrs: offset B")
}
sizeB := B.NumElements()
if sizeB < ind.OffsetB+(ind.Nrhs-1)*brows+ind.N {
return onError("Gttrs: sizeB")
}
if len(ipiv) < ind.N {
return onError("Gttrs: size ipiv")
}
if !matrix.EqualTypes(DL, D, DU, DU2, B) {
return onError("Gttrs: matrix types")
}
var info int = -1
switch DL.(type) {
case *matrix.FloatMatrix:
DLa := DL.(*matrix.FloatMatrix).FloatArray()
Da := D.(*matrix.FloatMatrix).FloatArray()
DUa := DU.(*matrix.FloatMatrix).FloatArray()
DU2a := DU2.(*matrix.FloatMatrix).FloatArray()
Ba := B.(*matrix.FloatMatrix).FloatArray()
trans := linalg.ParamString(pars.Trans)
info = dgttrs(trans, ind.N, ind.Nrhs,
DLa[ind.OffsetDL:], Da[ind.OffsetD:], DUa[ind.OffsetDU:], DU2a,
ipiv, Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
return onError("Gttrs: complex valued not yet implemented")
}
if info != 0 {
return onError(fmt.Sprintf("Gttrs lapack error: %d", info))
}
return nil
}
/*
Solves a real or complex set of linear equations with a banded
coefficient matrix, given the LU factorization computed by gbtrf()
or gbsv().
PURPOSE
Solves linear equations
A*X = B, if trans is PNoTrans
A^T*X = B, if trans is PTrans
A^H*X = B, if trans is PConjTrans
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 float or complex matrix
B float or complex matrix. Must have the same type as A.
ipiv int vector
kl nonnegative integer
OPTIONS
trans PNoTrans, PTrans or PConjTrans
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 value is used.
offsetA nonnegative integer
offsetB nonnegative integer;
*/
func Gbtrs(A, B matrix.Matrix, ipiv []int32, KL int, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
ind.Kl = KL
arows := ind.LDa
brows := ind.LDb
if ind.Kl < 0 {
return onError("Gbtrs: invalid kl")
}
if ind.N < 0 {
ind.N = A.Rows()
}
if ind.Nrhs < 0 {
ind.Nrhs = A.Cols()
}
if ind.N == 0 || ind.Nrhs == 0 {
return nil
}
if ind.Ku < 0 {
ind.Ku = A.Rows() - 2*ind.Kl - 1
}
if ind.Ku < 0 {
return onError("Gbtrs: invalid ku")
}
if ind.LDa == 0 {
ind.LDa = max(1, A.LeadingIndex())
arows = max(1, A.Rows())
}
if ind.LDa < 2*ind.Kl+ind.Ku+1 {
return onError("Gbtrs: ldA")
}
if ind.OffsetA < 0 {
return onError("Gbtrs: offsetA")
}
sizeA := A.NumElements()
if sizeA < ind.OffsetA+(ind.N-1)*arows+2*ind.Kl+ind.Ku+1 {
return onError("Gbtrs: sizeA")
}
if ind.LDb == 0 {
ind.LDb = max(1, B.LeadingIndex())
brows = max(1, B.Rows())
}
if ind.OffsetB < 0 {
return onError("Gbtrs: offsetB")
}
sizeB := B.NumElements()
if sizeB < ind.OffsetB+(ind.Nrhs-1)*brows+ind.N {
return onError("Gbtrs: sizeB")
}
if ipiv != nil && len(ipiv) < ind.N {
return onError("Gbtrs: size ipiv")
}
if !matrix.EqualTypes(A, B) {
return onError("Gbtrs: arguments not of same type")
}
info := -1
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ba := B.(*matrix.FloatMatrix).FloatArray()
trans := linalg.ParamString(pars.Trans)
info = dgbtrs(trans, ind.N, ind.Kl, ind.Ku, ind.Nrhs,
Aa[ind.OffsetA:], ind.LDa, ipiv, Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
return onError("Gbtrs: complex not yet implemented")
}
if info != 0 {
return onError(fmt.Sprintf("Gbtrs lapack error: %d", info))
}
return nil
}
/*
Solves a real or complex symmetric set of linear equations,
given the LDL^T factorization computed by sytrf() or sysv().
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 float or complex matrix
B float or complex matrix. Must have the same type as A.
ipiv int vector
OPTIONS
uplo PLower or PUpper
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 integer;
*/
func Sytrs(A, B matrix.Matrix, ipiv []int32, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
arows := ind.LDa
brows := ind.LDb
if ind.N < 0 {
ind.N = A.Rows()
if ind.N != A.Cols() {
return onError("Sytrs: A not square")
}
}
if ind.Nrhs < 0 {
ind.Nrhs = B.Cols()
}
if ind.N == 0 || ind.Nrhs == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.LeadingIndex())
arows = max(1, A.Rows())
}
if ind.LDa < max(1, ind.N) {
return onError("Sytrs: ldA")
}
if ind.LDb == 0 {
ind.LDb = max(1, B.LeadingIndex())
brows = max(1, B.Rows())
}
if ind.LDb < max(1, ind.N) {
return onError("Sytrs: ldB")
}
if ind.OffsetA < 0 {
return onError("Sytrs: offsetA")
}
sizeA := A.NumElements()
if sizeA < ind.OffsetA+(ind.N-1)*arows+ind.N {
return onError("Sytrs: sizeA")
}
if ind.OffsetB < 0 {
return onError("Sytrs: offsetB")
}
sizeB := B.NumElements()
if sizeB < ind.OffsetB+(ind.Nrhs-1)*brows+ind.N {
return onError("Sytrs: sizeB")
}
if ipiv != nil && len(ipiv) < ind.N {
return onError("Sytrs: size ipiv")
}
if !matrix.EqualTypes(A, B) {
return onError("Sytrs: arguments not of same type")
}
info := -1
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ba := B.(*matrix.FloatMatrix).FloatArray()
uplo := linalg.ParamString(pars.Uplo)
info = dsytrs(uplo, ind.N, ind.Nrhs, Aa[ind.OffsetA:], ind.LDa, ipiv,
Ba[ind.OffsetB:], ind.LDb)
case *matrix.ComplexMatrix:
return onError("Sytrs: complex not yet implemented")
}
if info != 0 {
return onError(fmt.Sprintf("Sytrs lapack error: %d", info))
}
return nil
}
/*
Product with a real orthogonal matrix.
PURPOSE
Computes
C := Q*C if side = PLeft and trans = PNoTrans
C := Q^T*C if side = PLeft and trans = PTrans
C := C*Q if side = PRight and trans = PNoTrans
C := C*Q^T if side = PRight and trans = PTrans
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 float matrix
tau float matrix of length at least k
C float matrix
OPTIONS
side PLeft or PRight
trans PNoTrans or PTrans
m integer. If negative, the default value is used.
n integer. If negative, the default value is used.
k integer. k <= m if side = PRight and k <= n if side = PLeft.
If negative, the default value is used.
ldA nonnegative integer. ldA >= max(1,m) if side = PLeft
and ldA >= max(1,n) if side = PRight. 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 integer
*/
func Ormqr(A, tau, C matrix.Matrix, opts ...linalg.Option) error {
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
arows := ind.LDa
crows := ind.LDc
if ind.N < 0 {
ind.N = C.Cols()
}
if ind.M < 0 {
ind.M = C.Rows()
}
if ind.K < 0 {
ind.K = tau.NumElements()
}
if ind.N == 0 || ind.M == 0 || ind.K == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.LeadingIndex())
arows = max(1, A.Rows())
}
if ind.LDc == 0 {
ind.LDc = max(1, C.LeadingIndex())
crows = max(1, C.Rows())
}
switch pars.Side {
case linalg.PLeft:
if ind.K > ind.M {
onError("Ormqf: K")
}
if ind.LDa < max(1, ind.M) {
return onError("Ormqf: ldA")
}
case linalg.PRight:
if ind.K > ind.N {
onError("Ormqf: K")
}
if ind.LDa < max(1, ind.N) {
return onError("Ormqf: ldA")
}
}
if ind.OffsetA < 0 {
return onError("Ormqf: offsetA")
}
if A.NumElements() < ind.OffsetA+ind.K*arows {
return onError("Ormqf: sizeA")
}
if ind.OffsetC < 0 {
return onError("Ormqf: offsetC")
}
if C.NumElements() < ind.OffsetC+(ind.N-1)*crows+ind.M {
return onError("Ormqf: sizeC")
}
if tau.NumElements() < ind.K {
return onError("Ormqf: sizeTau")
}
if !matrix.EqualTypes(A, C, tau) {
return onError("Ormqf: arguments not of same type")
}
info := -1
side := linalg.ParamString(pars.Side)
trans := linalg.ParamString(pars.Trans)
switch A.(type) {
case *matrix.FloatMatrix:
Aa := A.(*matrix.FloatMatrix).FloatArray()
Ca := C.(*matrix.FloatMatrix).FloatArray()
taua := tau.(*matrix.FloatMatrix).FloatArray()
info = dormqr(side, trans, ind.M, ind.N, ind.K, Aa[ind.OffsetA:], ind.LDa,
taua, Ca[ind.OffsetC:], ind.LDc)
case *matrix.ComplexMatrix:
return onError("Ormqf: complex not implemented yet")
}
if info != 0 {
return onError(fmt.Sprintf("Ormqr: lapack error %d", info))
}
return nil
}
func SyevxFloat(A, W, Z matrix.Matrix, abstol float64, vlimit []float64, ilimit []int, opts ...linalg.Option) error {
var vl, vu float64
var il, iu int
pars, err := linalg.GetParameters(opts...)
if err != nil {
return err
}
ind := linalg.GetIndexOpts(opts...)
arows := ind.LDa
if ind.N < 0 {
ind.N = A.Rows()
if ind.N != A.Cols() {
return onError("Syevr: A not square")
}
}
// Check indexes
if ind.N == 0 {
return nil
}
if ind.LDa == 0 {
ind.LDa = max(1, A.LeadingIndex())
arows = max(1, A.Rows())
}
if ind.LDa < max(1, A.Rows()) {
return onError("Syevr: lda")
}
if pars.Range == linalg.PRangeValue {
if vlimit == nil {
return onError("Syevx: vlimit is nil")
}
vl = vlimit[0]
vu = vlimit[1]
if vl >= vu {
return onError("Syevx: must be: vl < vu")
}
} else if pars.Range == linalg.PRangeInt {
if ilimit == nil {
return onError("Syevx: ilimit is nil")
}
il = ilimit[0]
iu = ilimit[1]
if il < 1 || il > iu || iu > ind.N {
return onError("Syevx: must be:1 <= il <= iu <= N")
}
}
if pars.Jobz == linalg.PJobValue {
if Z == nil {
return onError("Syevx: Z is nil")
}
if ind.LDz == 0 {
ind.LDz = max(1, Z.LeadingIndex())
}
if ind.LDz < max(1, ind.N) {
return onError("Syevx: ldz")
}
} else {
if ind.LDz == 0 {
ind.LDz = 1
}
if ind.LDz < 1 {
return onError("Syevx: ldz")
}
}
if ind.OffsetA < 0 {
return onError("Syevx: OffsetA")
}
sizeA := A.NumElements()
if sizeA < ind.OffsetA+(ind.N-1)*arows+ind.N {
return onError("Syevx: sizeA")
}
if ind.OffsetW < 0 {
return onError("Syevx: OffsetW")
}
sizeW := W.NumElements()
if sizeW < ind.OffsetW+ind.N {
return onError("Syevx: sizeW")
}
if pars.Jobz == linalg.PJobValue {
if ind.OffsetZ < 0 {
return onError("Syevx: OffsetW")
}
zrows := max(1, Z.Rows())
minZ := ind.OffsetZ + (ind.N-1)*zrows + ind.N
if pars.Range == linalg.PRangeInt {
minZ = ind.OffsetZ + (iu-il)*zrows + ind.N
}
if Z.NumElements() < minZ {
return onError("Syevx: sizeZ")
}
}
Aa := A.(*matrix.FloatMatrix).FloatArray()
Wa := W.(*matrix.FloatMatrix).FloatArray()
var Za []float64
if pars.Jobz == linalg.PJobValue {
Za = Z.(*matrix.FloatMatrix).FloatArray()
} else {
Za = nil
}
jobz := linalg.ParamString(pars.Jobz)
rnge := linalg.ParamString(pars.Range)
uplo := linalg.ParamString(pars.Uplo)
info := dsyevx(jobz, rnge, uplo, ind.N, Aa[ind.OffsetA:], ind.LDa,
vl, vu, il, iu, ind.M, Wa[ind.OffsetW:], Za, ind.LDz)
if info != 0 {
return onError(fmt.Sprintf("Syevx: call failed %d", info))
}
return nil
}