Пример #1
0
// Copies a vector X to a vector Y (Y := X).
//
// ARGUMENTS
//  X         float or complex matrix
//  Y         float or complex matrix.  Must have the same type as X.
//
// OPTIONS
//  n         integer.  If n<0, the default value of n is used.
//            The default value is given by 1+(len(x)-offsetx-1)/incx or 0
//            if len(x) > offsetx+1
//  incx      nonzero integer
//  incy      nonzero integer
//  offsetx   nonnegative integer
//  offsety   nonnegative integer;
//
func Copy(X, Y matrix.Matrix, opts ...linalg.Option) (err error) {
	ind := linalg.GetIndexOpts(opts...)
	err = check_level1_func(ind, fcopy, X, Y)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		return
	}
	sameType := matrix.EqualTypes(X, Y)
	if !sameType {
		err = onError("arrays not same type")
		return
	}
	switch X.(type) {
	case *matrix.ComplexMatrix:
		Xa := X.(*matrix.ComplexMatrix).ComplexArray()
		Ya := Y.(*matrix.ComplexMatrix).ComplexArray()
		zcopy(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY)
	case *matrix.FloatMatrix:
		Xa := X.(*matrix.FloatMatrix).FloatArray()
		Ya := Y.(*matrix.FloatMatrix).FloatArray()
		dcopy(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY)
	default:
		err = onError("not implemented for parameter types")
	}
	return
}
Пример #2
0
// Returns Y = X^H*Y for real or complex X, Y.
//
// ARGUMENTS
//  X         float or complex matrix
//  Y         float or complex matrix.  Must have the same type as X.
//
// OPTIONS
//  n         integer.  If n<0, the default value of n is used.
//            The default value is equal to nx = 1+(len(x)-offsetx-1)/incx or 0 if
//            len(x) > offsetx+1.  If the default value is used, it must be equal to
//            ny = 1+(len(y)-offsetx-1)/|incy| or 0 if len(y) > offsety+1
//  incx      nonzero integer [default=1]
//  incy      nonzero integer [default=1]
//  offsetx   nonnegative integer [default=0]
//  offsety   nonnegative integer [default=0]
//
func Dot(X, Y matrix.Matrix, opts ...linalg.Option) (v matrix.Scalar) {
	v = matrix.FScalar(math.NaN())
	//cv = cmplx.NaN()
	ind := linalg.GetIndexOpts(opts...)
	err := check_level1_func(ind, fdot, X, Y)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		return matrix.FScalar(0.0)
	}
	sameType := matrix.EqualTypes(X, Y)
	if !sameType {
		err = onError("arrays not of same type")
		return
	}
	switch X.(type) {
	case *matrix.ComplexMatrix:
		Xa := X.(*matrix.ComplexMatrix).ComplexArray()
		Ya := Y.(*matrix.ComplexMatrix).ComplexArray()
		v = matrix.CScalar(zdotc(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY))
	case *matrix.FloatMatrix:
		Xa := X.(*matrix.FloatMatrix).FloatArray()
		Ya := Y.(*matrix.FloatMatrix).FloatArray()
		v = matrix.FScalar(ddot(ind.Nx, Xa[ind.OffsetX:], ind.IncX, Ya[ind.OffsetY:], ind.IncY))
		//default:
		//	err = onError("not implemented for parameter types", )
	}
	return
}
Пример #3
0
/*
 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
}
Пример #4
0
/*
 LU factorization of a real or complex tridiagonal matrix.

 PURPOSE

 Factors an n by n real or complex tridiagonal matrix A as A = P*L*U.

 A is specified by its lower diagonal dl, diagonal d, and upper
 diagonal du.  On exit dl, d, du, du2 and ipiv contain the details
 of the factorization.

 ARGUMENTS.
  DL        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 of length at least n-2.  Must have the
            same type as DL.
  ipiv      int vector of length at least n

 OPTIONS
  n         nonnegative integer.  If negative, the default value is used.
  offsetdl  nonnegative integer
  offsetd   nonnegative integer
  offsetdu  nonnegative integer
*/
func Gtrrf(DL, D, DU, DU2 matrix.Matrix, ipiv []int32, opts ...linalg.Option) error {
	ind := linalg.GetIndexOpts(opts...)
	if ind.OffsetD < 0 {
		return onError("Gttrf: offset D")
	}
	if ind.N < 0 {
		ind.N = D.NumElements() - ind.OffsetD
	}
	if ind.N < 0 {
		return onError("Gttrf: size D")
	}
	if ind.N == 0 {
		return nil
	}
	if ind.OffsetDL < 0 {
		return onError("Gttrf: offset DL")
	}
	sizeDL := DL.NumElements()
	if sizeDL < ind.OffsetDL+ind.N-1 {
		return onError("Gttrf: sizeDL")
	}
	if ind.OffsetDU < 0 {
		return onError("Gttrf: offset DU")
	}
	sizeDU := DU.NumElements()
	if sizeDU < ind.OffsetDU+ind.N-1 {
		return onError("Gttrf: sizeDU")
	}
	sizeDU2 := DU2.NumElements()
	if sizeDU2 < ind.N-2 {
		return onError("Gttrf: sizeDU2")
	}
	if len(ipiv) < ind.N {
		return onError("Gttrf: size ipiv")
	}
	info := -1
	if !matrix.EqualTypes(DL, D, DU, DU2) {
		return onError("Gttrf: arguments not same type")
	}
	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()
		info = dgttrf(ind.N, DLa[ind.OffsetDL:], Da[ind.OffsetD:], DUa[ind.OffsetDU:],
			DU2a, ipiv)
	case *matrix.ComplexMatrix:
		return onError("Gttrf: complex not yet implemented")
	}
	if info != 0 {
		return onError(fmt.Sprintf("Gttrf lapack error: %d", info))
	}
	return nil
}
Пример #5
0
/*
 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
}
Пример #6
0
/*
 Computes selected eigenvalues and eigenvectors of a real symmetric
 matrix (RRR driver).

 PURPOSE

 Computes selected eigenvalues/vectors of a real symmetric n by n
 matrix A.

 If range is PRangeAll, all eigenvalues are computed.
 If range is PRangeV all eigenvalues in the interval (vlimit[0],vlimit[1]] are
 computed.
 If range is PRangeI, all eigenvalues ilimit[0] through ilimit[1] are computed
 (sorted in ascending order with 1 <= ilimit[0] <= ilimit[1] <= n).

 If jobz is PJobNo, only the eigenvalues are returned in W.
 If jobz is PJobV, the eigenvectors are also returned in Z.
 On exit, the content of A is destroyed.

 Syevr is usually the fastest of the four eigenvalue routines.

 ARGUMENTS
  A         float matrix
  W         float matrix of length at least n.  On exit, contains
            the computed eigenvalues in ascending order.
  Z         float matrix or nil.  Only required when jobz = PJobV.
            If range is PRangeAll or PRangeV, Z must have at least n columns.
            If range is PRangeI, Z must have at least iu-il+1 columns.
            On exit the first m columns of Z contain the computed
            (normalized) eigenvectors.
  abstol    double.  Absolute error tolerance for eigenvalues.
            If nonpositive, the LAPACK default value is used.
  vlmit     []float or nil.  Only required when range is PRangeV.
  ilimit    []int or nil.  Only required when range is PRangeI.

 OPTIONS
  jobz      PJobNo or PJobV
  range     PRangeAll, PRangeV or PRangeI
  uplo      PLower or PUpper
  n         integer.  If negative, the default value is used.
  ldA       nonnegative integer.  ldA >= max(1,n).
            If zero, the default value is used.
  ldZ       nonnegative integer.  ldZ >= 1 if jobz is 'N' and
            ldZ >= max(1,n) if jobz is PJobV.  The default value
            is 1 if jobz is PJobNo and max(1,Z.Rows) if jobz =PJboV.
            If zero, the default value is used.
  offsetA   nonnegative integer
  offsetW   nonnegative integer
  offsetZ   nonnegative integer
  m         the number of eigenvalues computed

*/
func Syevr(A, W, Z matrix.Matrix, abstol float64, vlimit []float64, ilimit []int, opts ...linalg.Option) error {
	if !matrix.EqualTypes(A, W, Z) {
		return onError("Syevr: arguments not of same type")
	}
	switch A.(type) {
	case *matrix.FloatMatrix:
		Am := A.(*matrix.FloatMatrix)
		Wm := W.(*matrix.FloatMatrix)
		Zm := Z.(*matrix.FloatMatrix)
		return SyevrFloat(Am, Wm, Zm, abstol, vlimit, ilimit, opts...)
	}
	return onError("Syevr: unknown types")
}
Пример #7
0
/*
 Eigenvalue decomposition of a real symmetric matrix
 (divide-and-conquer driver).

 PURPOSE

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

 ARGUMENTS
  A         float matrix
  W         float matrix of length at least n.  On exit, contains
            the computed eigenvalues in ascending order.

 OPTIONS
  jobz      PJobNo or PJobV
  uplo      PLower or PUpper
  n         integer.  If negative, the default value is used.
  ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
            default value is used.
  offsetA   nonnegative integer
  offsetB   nonnegative integer;
*/
func Syevd(A, W matrix.Matrix, opts ...linalg.Option) error {
	if !matrix.EqualTypes(A, W) {
		return onError("Syevd: arguments not of same type")
	}
	switch A.(type) {
	case *matrix.FloatMatrix:
		Am := A.(*matrix.FloatMatrix)
		Wm := W.(*matrix.FloatMatrix)
		return SyevdFloat(Am, Wm, opts...)
	case *matrix.ComplexMatrix:
		return onError("Syevd: not a complex function")
	}
	return onError("Syevd: unknown types")
}
Пример #8
0
/*
 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
}
Пример #9
0
/*
 Solves a real or complex set of linear equations with a banded
 coefficient matrix.

 PURPOSE

 Solves A*X = B

 A an n by n real or complex band matrix with kl subdiagonals and
 ku superdiagonals.

 If ipiv is provided, then on entry the kl+ku+1 diagonals of the
 matrix are stored in rows kl+1 to 2*kl+ku+1 of A, in the BLAS
 format for general band matrices.  On exit, A and ipiv contain the
 details of the factorization.  If ipiv is not provided, then on
 entry the diagonals of the matrix are stored in rows 1 to kl+ku+1
 of A, and Gbsv() does not return the factorization and does not
 modify A.  On exit B is replaced with solution X.

 ARGUMENTS.
  A         float or complex banded matrix
  B         float or complex matrix.  Must have the same type as A.
  kl        nonnegative integer
  ipiv      int array of length at least n

 OPTIONS
  ku        nonnegative integer.  If negative, the default value is
            used.  The default value is A.Rows-kl-1 if ipiv is
            not provided, and A.Rows-2*kl-1 otherwise.
  n         nonnegative integer.  If negative, the default value is used.
  nrhs      nonnegative integer.  If negative, the default value is used.
  ldA       positive integer.  ldA >= kl+ku+1 if ipiv is not provided
            and ldA >= 2*kl+ku+1 if ipiv is provided.  If zero, the
            default value is used.
  ldB       positive integer.  ldB >= max(1,n).  If zero, the default
            default value is used.
  offsetA   nonnegative integer
  offsetB   nonnegative integer;

*/
func Gbsv(A, B matrix.Matrix, ipiv []int32, kl int, opts ...linalg.Option) error {
	if !matrix.EqualTypes(A, B) {
		return onError("Gbsv: not same type")
	}
	switch A.(type) {
	case *matrix.FloatMatrix:
		Am := A.(*matrix.FloatMatrix)
		Bm := B.(*matrix.FloatMatrix)
		return GbsvFloat(Am, Bm, ipiv, kl, opts...)
	case *matrix.ComplexMatrix:
		Am := A.(*matrix.ComplexMatrix)
		Bm := B.(*matrix.ComplexMatrix)
		return GbsvComplex(Am, Bm, ipiv, kl, opts...)
	}
	return onError("Gbsv: unknown types types!")
}
Пример #10
0
/*
 Solves a real symmetric or complex Hermitian positive definite set
 of linear equations.

 PURPOSE

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

 ARGUMENTS.
  A         float or complex matrix
  B         float or complex matrix.  Must have the same type as A.

 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       positive integer.  ldB >= max(1,n).  If zero, the default value is used.
  offsetA   nonnegative integer
  offsetB   nonnegative integer
*/
func Posv(A, B matrix.Matrix, opts ...linalg.Option) error {
	if !matrix.EqualTypes(A, B) {
		return onError("Posv: arguments not same type")
	}
	switch A.(type) {
	case *matrix.FloatMatrix:
		Am := A.(*matrix.FloatMatrix)
		Bm := B.(*matrix.FloatMatrix)
		return PosvFloat(Am, Bm, opts...)
	case *matrix.ComplexMatrix:
		Am := A.(*matrix.ComplexMatrix)
		Bm := B.(*matrix.ComplexMatrix)
		return PosvComplex(Am, Bm, opts...)
	}
	return onError("Posv: unknown types")
}
Пример #11
0
/*
 Computes selected eigenvalues and eigenvectors of a real symmetric
 matrix (expert driver).

 PURPOSE

 Computes selected eigenvalues/vectors of a real symmetric n by n
 matrix A.

 If range is OptRangeAll, all eigenvalues are computed.
 If range is OptRangeValue, all eigenvalues in the interval (vlimit[0],vlimit[1]] are
 computed.
 If range is OptRangeInt, all eigenvalues il through iu are computed
 (sorted in ascending order with 1 <= il <= iu <= n).

 If jobz is OptJobNo, only the eigenvalues are returned in W.
 If jobz is OptJobValue, the eigenvectors are also returned in Z.

 On exit, the content of A is destroyed.

 ARGUMENTS
  A         float matrix
  W         float matrix of length at least n.  On exit, contains
            the computed eigenvalues in ascending order.
  Z         float matrix.  Only required when jobz is PJobValue.  If range
            is PRangeAll or PRangeValue, Z must have at least n columns.  If
            range is PRangeInt, Z must have at least iu-il+1 columns.
            On exit the first m columns of Z contain the computed (normalized) eigenvectors.
  vlimit    []float64 or nul.  Only required when range is PRangeValue
  ilimit    []int or nil.  Only required when range is PRangeInt.
  abstol    double.  Absolute error tolerance for eigenvalues.
            If nonpositive, the LAPACK default value is used.

 OPTIONS
  jobz      linalg.OptJobNo or linalg.OptJobValue
  range     linalg.OptRangeAll, linalg.OptRangeValue or linalg.OptRangeInt
  uplo      linalg.OptLower or linalg.OptUpper
  n         integer.  If negative, the default value is used.
  m         the number of eigenvalues computed;
  ldA       nonnegative integer.  ldA >= max(1,n).  If zero, the
            default value is used.
  ldZ       nonnegative integer.  ldZ >= 1 if jobz is PJobNo and
            ldZ >= max(1,n) if jobz is PJobValue.  The default value
            is 1 if jobz is PJobNo and max(1,Z.size[0]) if jobz =PJobValue.
            If zero, the default value is used.
  offsetA   nonnegative integer
  offsetW   nonnegative integer
  offsetZ   nonnegative integer
*/
func Syevx(A, W, Z matrix.Matrix, abstol float64, vlimit []float64, ilimit []int, opts ...linalg.Option) error {
	if !matrix.EqualTypes(A, W, Z) {
		return onError("Syevx: not same type")
	}
	switch A.(type) {
	case *matrix.FloatMatrix:
		Am := A.(*matrix.FloatMatrix)
		Wm := W.(*matrix.FloatMatrix)
		var Zm *matrix.FloatMatrix = nil
		if Z != nil {
			Zm = Z.(*matrix.FloatMatrix)
		}
		return SyevrFloat(Am, Wm, Zm, abstol, vlimit, ilimit, opts...)
	}
	return onError("Syevr: unknown types")
}
Пример #12
0
/*
 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
}
Пример #13
0
/*
 QR factorization.

 PURPOSE

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

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

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

 ARGUMENTS
  A         float or complex matrix
  tau       float or complex  matrix of length at least min(m,n).  Must
            have the same type as A.
  m         integer.  If negative, the default value is used.
  n         integer.  If negative, the default value is used.
  ldA       nonnegative integer.  ldA >= max(1,m).  If zero, the
            default value is used.
  offsetA   nonnegative integer

*/
func Geqrf(A, tau matrix.Matrix, opts ...linalg.Option) error {
	ind := linalg.GetIndexOpts(opts...)
	arows := ind.LDa
	if ind.N < 0 {
		ind.N = A.Cols()
	}
	if ind.M < 0 {
		ind.M = A.Rows()
	}
	if ind.N == 0 || ind.M == 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("Geqrf: ldA")
	}
	if ind.OffsetA < 0 {
		return onError("Geqrf: offsetA")
	}
	if A.NumElements() < ind.OffsetA+ind.K*arows {
		return onError("Geqrf: sizeA")
	}
	if tau.NumElements() < min(ind.M, ind.N) {
		return onError("Geqrf: sizeTau")
	}
	if !matrix.EqualTypes(A, tau) {
		return onError("Geqrf: arguments not of same type")
	}
	info := -1
	switch A.(type) {
	case *matrix.FloatMatrix:
		Aa := A.(*matrix.FloatMatrix).FloatArray()
		taua := tau.(*matrix.FloatMatrix).FloatArray()
		info = dgeqrf(ind.M, ind.N, Aa[ind.OffsetA:], ind.LDa, taua)
	case *matrix.ComplexMatrix:
		return onError("Geqrf: complex not yet implemented")
	}
	if info != 0 {
		return onError(fmt.Sprintf("Geqrf lapack error: %d", info))
	}
	return nil
}
Пример #14
0
/*
 Singular value decomposition of a real or complex matrix.

 PURPOSE

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

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

  PJobNo : no left singular vectors are computed.
  PJobAll: all left singular vectors are computed and returned as
           columns of U.
  PJobS  : the first min(m,n) left singular vectors are computed and
           returned as columns of U.
  PJobO  : the first min(m,n) left singular vectors are computed and
           returned as columns of A.

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

  PJobNo : no right singular vectors are computed.
  PJobAll: all right singular vectors are computed and returned as
           rows of Vt.
  PJobS  : the first min(m,n) right singular vectors are computed and
           returned as rows of Vt.
  PJobO  : the first min(m,n) right singular vectors are computed and
           returned as rows of A.

 Note that the (conjugate) transposes of the right singular
 vectors are returned in Vt or A.
 On exit (in all cases), the contents of A are destroyed.

 ARGUMENTS
  A         float or complex matrix
  S         float matrix of length at least min(m,n).  On exit,
            contains the computed singular values in descending order.
  jobu      PJobNo, PJobAll, PJobS or PJobO
  jobvt     PJobNo, PJobAll, PJobS or PJobO
  U         float or complex matrix.  Must have the same type as A.
            Not referenced if jobu is PJobNo or PJobO.  If jobu is PJobAll,
            a matrix with at least m columns.   If jobu is PJobS, a
            matrix with at least min(m,n) columns.
            On exit (with jobu PJobAll or PJobS), the columns of U
            contain the computed left singular vectors.
  Vt        float or complex matrix.  Must have the same type as A.
            Not referenced if jobvt is PJobNo or PJobO.  If jobvt is
            PJobAll or PJobS, a matrix with at least n columns.
            On exit (with jobvt PJobAll or PJobS), the rows of Vt
            contain the computed right singular vectors, or, in
            the complex case, their complex conjugates.
  m         integer.  If negative, the default value is used.
  n         integer.  If negative, the default value is used.
  ldA       nonnegative integer.  ldA >= max(1,m).
            If zero, the default value is used.
  ldU       nonnegative integer.
            ldU >= 1        if jobu is PJobNo or PJobO
            ldU >= max(1,m) if jobu is PJobAll or PJobS.
            The default value is max(1,U.Rows) if jobu is PJobAll
            or PJobS, and 1 otherwise.
            If zero, the default value is used.
  ldVt      nonnegative integer.
            ldVt >= 1 if jobvt is PJobNo or PJobO.
            ldVt >= max(1,n) if jobvt is PJobAll.
            ldVt >= max(1,min(m,n)) if ldVt is PJobS.
            The default value is max(1,Vt.Rows) if jobvt is PJobAll
            or PJobS, and 1 otherwise.
            If zero, the default value is used.
  offsetA   nonnegative integer
  offsetS   nonnegative integer
  offsetU   nonnegative integer
  offsetVt  nonnegative integer

*/
func Gesvd(A, S, U, Vt matrix.Matrix, opts ...linalg.Option) error {
	if !matrix.EqualTypes(A, S, U, Vt) {
		return onError("Gesvd: arguments not of same type")
	}
	switch A.(type) {
	case *matrix.FloatMatrix:
		Am := A.(*matrix.FloatMatrix)
		Sm := S.(*matrix.FloatMatrix)
		Um := U.(*matrix.FloatMatrix)
		Vm := Vt.(*matrix.FloatMatrix)
		return GesvdFloat(Am, Sm, Um, Vm, opts...)
	case *matrix.ComplexMatrix:
		Am := A.(*matrix.ComplexMatrix)
		Sm := S.(*matrix.ComplexMatrix)
		Um := U.(*matrix.ComplexMatrix)
		Vm := Vt.(*matrix.ComplexMatrix)
		return GesvdComplex(Am, Sm, Um, Vm, opts...)
	}
	return onError("Gesvd: unknown parameter types")
}
Пример #15
0
// Constant times a vector plus a vector (Y := alpha*X+Y).
//
// ARGUMENTS
//   X         float or complex matrix
//   Y         float or complex matrix.  Must have the same type as X.
//   alpha     number (float or complex singleton matrix).  Complex alpha is only
//             allowed if x is complex.
//
// OPTIONS
//   n         integer.  If n<0, the default value of n is used.
//             The default value is equal to 1+(len(x)-offsetx-1)/incx
//             or 0 if  len(x) >= offsetx+1
//   incx      nonzero integer
//   incy      nonzero integer
//   offsetx   nonnegative integer
//   offsety   nonnegative integer;
//
func Axpy(X, Y matrix.Matrix, alpha matrix.Scalar, opts ...linalg.Option) (err error) {
	ind := linalg.GetIndexOpts(opts...)
	err = check_level1_func(ind, faxpy, X, Y)
	if err != nil {
		return
	}
	if ind.Nx == 0 {
		return
	}
	sameType := matrix.EqualTypes(X, Y)
	if !sameType {
		err = onError("arrays not same type")
		return
	}
	switch X.(type) {
	case *matrix.ComplexMatrix:
		Xa := X.(*matrix.ComplexMatrix).ComplexArray()
		Ya := Y.(*matrix.ComplexMatrix).ComplexArray()
		aval := alpha.Complex()
		if cmplx.IsNaN(aval) {
			return onError("alpha not complex value")
		}
		zaxpy(ind.Nx, aval, Xa[ind.OffsetX:],
			ind.IncX, Ya[ind.OffsetY:], ind.IncY)
	case *matrix.FloatMatrix:
		Xa := X.(*matrix.FloatMatrix).FloatArray()
		Ya := Y.(*matrix.FloatMatrix).FloatArray()
		aval := alpha.Float()
		if math.IsNaN(aval) {
			return onError("alpha not float value")
		}
		daxpy(ind.Nx, aval, Xa[ind.OffsetX:],
			ind.IncX, Ya[ind.OffsetY:], ind.IncY)
	default:
		err = onError("not implemented for parameter types")
	}
	return
}
Пример #16
0
/*
 Solves a general real or complex set of linear equations.

 PURPOSE

 Solves A*X=B with A n by n real or complex.

 If ipiv is provided, then on exit A is overwritten with the details
 of the LU factorization, and ipiv contains the permutation matrix.
 If ipiv is not provided, then gesv() does not return the
 factorization and does not modify A.  On exit B is replaced with
 the solution X.

 ARGUMENTS.
  A         float or complex matrix
  B         float or complex matrix.  Must have the same type as A.
  ipiv      int vector of length at least n

 OPTIONS:
  n         nonnegative integer.  If negative, the default value is used.
  nrhs      nonnegative integer.  If negative, the default value is used.
  ldA       positive integer.  ldA >= max(1,n).  If zero, the default value is used.
  ldB       positive integer.  ldB >= max(1,n).  If zero, the default value is used.
  offsetA   nonnegative integer
  offsetA   nonnegative integer;
*/
func Gesv(A, B matrix.Matrix, ipiv []int32, opts ...linalg.Option) error {
	//pars, err := linalg.GetParameters(opts...)
	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("Gesv: 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("Gesv: 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("Gesv: ldB")
	}
	if ind.OffsetA < 0 {
		return onError("Gesv: offsetA")
	}
	if ind.OffsetB < 0 {
		return onError("Gesv: offsetB")
	}
	sizeA := A.NumElements()
	if sizeA < ind.OffsetA+(ind.N-1)*arows+ind.N {
		return onError("Gesv: sizeA")
	}
	sizeB := B.NumElements()
	if sizeB < ind.OffsetB+(ind.Nrhs-1)*brows+ind.N {
		return onError("Gesv: sizeB")
	}
	if ipiv != nil && len(ipiv) < ind.N {
		return onError("Gesv: size ipiv")
	}
	if !matrix.EqualTypes(A, B) {
		return onError("Gesv: arguments not of same type")
	}
	info := -1
	if ipiv == nil {
		ipiv = make([]int32, ind.N)
		// Do not overwrite A.
		A = A.MakeCopy()
	}
	switch A.(type) {
	case *matrix.FloatMatrix:
		Aa := A.(*matrix.FloatMatrix).FloatArray()
		Aa = Aa[ind.OffsetA:]
		// Ensure there are sufficient elements in A.
		Aa = Aa[:ind.LDa*ind.LDb]
		Ba := B.(*matrix.FloatMatrix).FloatArray()
		Ba = Ba[ind.OffsetB:]
		info = dgesv(ind.N, ind.Nrhs, Aa, ind.LDa, ipiv, Ba, ind.LDb)
	case *matrix.ComplexMatrix:
		Aa := A.(*matrix.ComplexMatrix).ComplexArray()
		Aa = Aa[ind.OffsetA:]
		// Ensure there are sufficient elements in A.
		Aa = Aa[:ind.LDa*ind.LDb]
		Ba := B.(*matrix.ComplexMatrix).ComplexArray()
		Ba = Ba[ind.OffsetB:]
		info = zgesv(ind.N, ind.Nrhs, Aa, ind.LDa, ipiv, Ba, ind.LDb)
	}
	if info != 0 {
		return onError(fmt.Sprintf("Gesv: lapack error: %d", info))
	}
	return nil
}
Пример #17
0
/*
 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
}
Пример #18
0
/*
 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
}
Пример #19
0
/*
 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
}
Пример #20
0
/*
 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
}