Package Modelica.​Math.​Matrices.​LAPACK
Interface to LAPACK library (should usually not directly be used but only indirectly via Modelica.Math.Matrices)

Information

This package contains external Modelica functions as interface to the LAPACK library (http://www.netlib.org/lapack) that provides FORTRAN subroutines to solve linear algebra tasks. Usually, these functions are not directly called, but only via the much more convenient interface of Modelica.Math.Matrices. The documentation of the LAPACK functions is a copy of the original FORTRAN code. The details of LAPACK are described in:

Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., and Sorensen D.:
Lapack Users' Guide. Third Edition, SIAM, 1999.

See also http://en.wikipedia.org/wiki/Lapack.

This package contains a direct interface to the LAPACK subroutines

Extends from Modelica.​Icons.​Package (Icon for standard packages).

Package Contents

NameDescription
dgbsvSolve real system of linear equations A*X=B with a B matrix
dgbsv_vecSolve real system of linear equations A*x=b with a b vector
dgeconEstimates the reciprocal of the condition number of a general real matrix A
dgeesComputes real Schur form T of real nonsymmetric matrix A, and, optionally, the matrix of Schur vectors Z as well as the eigenvalues
dgeevCompute eigenvalues and (right) eigenvectors for real nonsymmetric matrix A
dgeev_eigenValuesCompute eigenvalues for real nonsymmetric matrix A
dgeevxCompute the eigenvalues and the (real) left and right eigenvectors of matrix A, using lapack routine dgeevx
dgegvCompute generalized eigenvalues for a (A,B) system
dgehrdreduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H
dgels_vecSolves overdetermined or underdetermined real linear equations A*x=b with a b vector
dgelsxComputes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgelsx_vecComputes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgelsyComputes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgelsy_vecComputes the minimum-norm solution to a real linear least squares problem with rank deficient A
dgeqpfCompute QR factorization of square or rectangular matrix A with column pivoting (A(:,p) = Q*R)
dgeqrfcomputes a QR factorization without pivoting
dgesddDetermine singular value decomposition
dgesvSolve real system of linear equations A*X=B with a B matrix
dgesv_vecSolve real system of linear equations A*x=b with a b vector
dgesvdDetermine singular value decomposition
dgesvd_sigmaDetermine singular values
dgesvxSolve real system of linear equations op(A)*X=B, op(A) is A or A' according to the Boolean input transposed
dgetrfCompute LU factorization of square or rectangular matrix A (A = P*L*U)
dgetriComputes the inverse of a matrix using the LU factorization from dgetrf(..)
dgetrsSolves a system of linear equations with the LU decomposition from dgetrf(..)
dgetrs_vecSolves a system of linear equations with the LU decomposition from dgetrf(..)
dggevCompute generalized eigenvalues, as well as the left and right eigenvectors for a (A,B) system
dggevxCompute generalized eigenvalues for a (A,B) system, using lapack routine dggevx
dgglse_vecSolve a linear equality constrained least squares problem
dgtsvSolve real system of linear equations A*X=B with B matrix and tridiagonal A
dgtsv_vecSolve real system of linear equations A*x=b with b vector and tridiagonal A
dhgeqzCompute generalized eigenvalues for a (A,B) system
dhseqrCompute eigenvalues of a matrix H using lapack routine DHSEQR for Hessenberg form matrix
dlangeNorm of a matrix
dorghrGenerates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD
dorgqrGenerates a Real orthogonal matrix Q which is defined as the product of elementary reflectors as returned from dgeqpf
dormhroverwrites the general real M-by-N matrix C with Q * C or C * Q or Q' * C or C * Q', where Q is an orthogonal matrix as returned by dgehrd
dormqroverwrites the general real M-by-N matrix C with Q * C or C * Q or Q' * C or C * Q', where Q is an orthogonal matrix of a QR factorization as returned by dgeqrf
dpotrfComputes the Cholesky factorization of a real symmetric positive definite matrix A
dtrevcCompute the right and/or left eigenvectors of a real upper quasi-triangular matrix T
dtrsenReorder the real Schur factorization of a real matrix
dtrsmSolve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where A is triangular matrix. BLAS routine
dtrsylSolve the real Sylvester matrix equation op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C

Function Modelica.​Math.​Matrices.​LAPACK.​dgeev
Compute eigenvalues and (right) eigenvectors for real nonsymmetric matrix A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 

Outputs

TypeNameDescription
RealeigenReal[size(A, 1)]Real part of eigen values
RealeigenImag[size(A, 1)]Imaginary part of eigen values
RealeigenVectors[size(A, 1),size(A, 1)]Right eigen vectors
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgeev_eigenValues
Compute eigenvalues for real nonsymmetric matrix A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 

Outputs

TypeNameDescription
RealEigenReal[size(A, 1)] 
RealEigenImag[size(A, 1)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgegv
Compute generalized eigenvalues for a (A,B) system

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 
RealB[size(A, 1),size(A, 1)] 

Outputs

TypeNameDescription
RealalphaReal[size(A, 1)]Real part of alpha (eigenvalue=(alphaReal+i*alphaImag)/beta)
RealalphaImag[size(A, 1)]Imaginary part of alpha
Realbeta[size(A, 1)]Denominator of eigenvalue
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgelsx
Computes the minimum-norm solution to a real linear least squares problem with rank deficient A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 
RealB[size(A, 1),:] 
RealrcondReciprocal condition number to estimate rank

Outputs

TypeNameDescription
RealX[max(size(A, 1), size(A, 2)),size(B, 2)]Solution is in first size(A,2) rows
Integerinfo 
IntegerrankEffective rank of A

Function Modelica.​Math.​Matrices.​LAPACK.​dgelsx_vec
Computes the minimum-norm solution to a real linear least squares problem with rank deficient A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 
Realb[size(A, 1)] 
RealrcondReciprocal condition number to estimate rank

Outputs

TypeNameDescription
Realx[max(size(A, 1), size(A, 2))]solution is in first size(A,2) rows
Integerinfo 
IntegerrankEffective rank of A

Function Modelica.​Math.​Matrices.​LAPACK.​dgelsy
Computes the minimum-norm solution to a real linear least squares problem with rank deficient A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 
RealB[size(A, 1),:] 
RealrcondReciprocal condition number to estimate rank

Outputs

TypeNameDescription
RealX[max(size(A, 1), size(A, 2)),size(B, 2)]Solution is in first size(A,2) rows
Integerinfo 
IntegerrankEffective rank of A

Function Modelica.​Math.​Matrices.​LAPACK.​dgelsy_vec
Computes the minimum-norm solution to a real linear least squares problem with rank deficient A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 
Realb[size(A, 1)] 
RealrcondReciprocal condition number to estimate rank

Outputs

TypeNameDescription
Realx[max(size(A, 1), size(A, 2))]solution is in first size(A,2) rows
Integerinfo 
IntegerrankEffective rank of A

Function Modelica.​Math.​Matrices.​LAPACK.​dgels_vec
Solves overdetermined or underdetermined real linear equations A*x=b with a b vector

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 
Realb[size(A, 1)] 

Outputs

TypeNameDescription
Realx[max(size(A, 1), size(A, 2))]solution is in first size(A,2) rows
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgesv
Solve real system of linear equations A*X=B with a B matrix

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 
RealB[size(A, 1),:] 

Outputs

TypeNameDescription
RealX[size(A, 1),size(B, 2)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgesv_vec
Solve real system of linear equations A*x=b with a b vector

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 
Realb[size(A, 1)] 

Outputs

TypeNameDescription
Realx[size(A, 1)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgglse_vec
Solve a linear equality constrained least squares problem

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:]Minimize |A*x - c|^2
Realc[size(A, 1)] 
RealB[:,size(A, 2)]subject to B*x=d
Reald[size(B, 1)] 

Outputs

TypeNameDescription
Realx[size(A, 2)]solution vector
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgtsv
Solve real system of linear equations A*X=B with B matrix and tridiagonal A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
Realsuperdiag[:] 
Realdiag[size(superdiag, 1) + 1] 
Realsubdiag[size(superdiag, 1)] 
RealB[size(diag, 1),:] 

Outputs

TypeNameDescription
RealX[size(B, 1),size(B, 2)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgtsv_vec
Solve real system of linear equations A*x=b with b vector and tridiagonal A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
Realsuperdiag[:] 
Realdiag[size(superdiag, 1) + 1] 
Realsubdiag[size(superdiag, 1)] 
Realb[size(diag, 1)] 

Outputs

TypeNameDescription
Realx[size(b, 1)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgbsv
Solve real system of linear equations A*X=B with a B matrix

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
IntegernNumber of equations
IntegerkLowerNumber of lower bands
IntegerkUpperNumber of upper bands
RealA[2 * kLower + kUpper + 1,n] 
RealB[n,:] 

Outputs

TypeNameDescription
RealX[n,size(B, 2)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgbsv_vec
Solve real system of linear equations A*x=b with a b vector

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
IntegernNumber of equations
IntegerkLowerNumber of lower bands
IntegerkUpperNumber of upper bands
RealA[2 * kLower + kUpper + 1,n] 
Realb[n] 

Outputs

TypeNameDescription
Realx[n] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgesvd
Determine singular value decomposition

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 

Outputs

TypeNameDescription
Realsigma[min(size(A, 1), size(A, 2))] 
RealU[size(A, 1),size(A, 1)] 
RealVT[size(A, 2),size(A, 2)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgesvd_sigma
Determine singular values

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 

Outputs

TypeNameDescription
Realsigma[min(size(A, 1), size(A, 2))] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgetrf
Compute LU factorization of square or rectangular matrix A (A = P*L*U)

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:]Square or rectangular matrix

Outputs

TypeNameDescription
RealLU[size(A, 1),size(A, 2)] 
Integerpivots[min(size(A, 1), size(A, 2))]Pivot vector
IntegerinfoInformation

Function Modelica.​Math.​Matrices.​LAPACK.​dgetrs
Solves a system of linear equations with the LU decomposition from dgetrf(..)

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealLU[:,size(LU, 1)]LU factorization of dgetrf of a square matrix
Integerpivots[size(LU, 1)]Pivot vector of dgetrf
RealB[size(LU, 1),:]Right hand side matrix B

Outputs

TypeNameDescription
RealX[size(B, 1),size(B, 2)]Solution matrix X
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgetrs_vec
Solves a system of linear equations with the LU decomposition from dgetrf(..)

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealLU[:,size(LU, 1)]LU factorization of dgetrf of a square matrix
Integerpivots[size(LU, 1)]Pivot vector of dgetrf
Realb[size(LU, 1)]Right hand side vector b

Outputs

TypeNameDescription
Realx[size(b, 1)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgetri
Computes the inverse of a matrix using the LU factorization from dgetrf(..)

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealLU[:,size(LU, 1)]LU factorization of dgetrf of a square matrix
Integerpivots[size(LU, 1)]Pivot vector of dgetrf

Outputs

TypeNameDescription
Realinv[size(LU, 1),size(LU, 2)]Inverse of matrix P*L*U
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgeqpf
Compute QR factorization of square or rectangular matrix A with column pivoting (A(:,p) = Q*R)

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:]Square or rectangular matrix

Outputs

TypeNameDescription
RealQR[size(A, 1),size(A, 2)]QR factorization in packed format
Realtau[min(size(A, 1), size(A, 2))]The scalar factors of the elementary reflectors of Q
Integerp[size(A, 2)]Pivot vector
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dorgqr
Generates a Real orthogonal matrix Q which is defined as the product of elementary reflectors as returned from dgeqpf

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealQR[:,:]QR from dgeqpf
Realtau[min(size(QR, 1), size(QR, 2))]The scalar factors of the elementary reflectors of Q

Outputs

TypeNameDescription
RealQ[size(QR, 1),size(QR, 2)]Orthogonal matrix Q
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgees
Computes real Schur form T of real nonsymmetric matrix A, and, optionally, the matrix of Schur vectors Z as well as the eigenvalues

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)]Square matrix

Outputs

TypeNameDescription
RealT[size(A, 1),size(A, 2)]Real Schur form with A = Z*T*Z'
RealZ[size(A, 1),size(A, 1)]orthogonal matrix Z of Schur vectors
Realeval_real[size(A, 1)]real part of the eigenvectors of A
Realeval_imag[size(A, 1)]imaginary part of the eigenvectors of A
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dtrsen
Reorder the real Schur factorization of a real matrix

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
StringjobSpecifies the usage of a condition number
StringcompqIs "V" if Schur vector matrix is to be updated
Booleanselect[:]Specifies the eigenvalues to reorder
RealT[:,:]Real Schur form to be reordered
RealQ[:,size(T, 2)]Matrix of the Schur vectors

Outputs

TypeNameDescription
RealTo[:,:]Reordered Schur form
RealQo[:,:]Reordered Schur vectors
Realwr[size(T, 2)]Reordered eigenvalues, real part
Realwi[size(T, 2)]Reordered eigenvalues, imaginary part
IntegermDimension of the invariant sub space spanned bei the selected eigenvalues
RealsLower bound of the reciprocal condition number. Not referenced for job==V
RealsepEstimated reciprocal condition number of the specified invariant subspace
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgesvx
Solve real system of linear equations op(A)*X=B, op(A) is A or A' according to the Boolean input transposed

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)]Real square matrix A
RealB[size(A, 1),:]Real matrix B
BooleantransposedTrue if the equation to be solved is A'*X=B

Outputs

TypeNameDescription
RealX[size(A, 1),size(B, 2)]Solution matrix
Integerinfo 
Realrcondreciprocal condition number of the matrix A

Function Modelica.​Math.​Matrices.​LAPACK.​dtrsyl
Solve the real Sylvester matrix equation op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:]Upper quais-triangular matrix
RealB[:,:]Upper quais-triangular matrix
RealC[if tranA then size(A, 1) else size(A, 2),if tranB then size(B, 1) else size(B, 2)]Right side of the Sylvester equation
BooleantranATrue if op(A)=A'
BooleantranBTrue if op(B)=B'
IntegerisgnSpecifies the sign in the equation, +1 or -1

Outputs

TypeNameDescription
RealX[size(C, 1),size(C, 2)]Solution of the Sylvester equation
RealscaleScale factor
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dhseqr
Compute eigenvalues of a matrix H using lapack routine DHSEQR for Hessenberg form matrix

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealH[:,size(H, 1)]Matrix H with Hessenberg form
BooleaneigenValuesOnlyTrue to compute the eigenvalues. False to compute the Schur form too
StringcompzSpecifies the computation of the Schur vectors
RealZ[:,:]Matrix Z

Outputs

TypeNameDescription
RealalphaReal[size(H, 1)]Real part of alpha (eigenvalue=(alphaReal+i*alphaImag))
RealalphaImag[size(H, 1)]Imaginary part of alpha (eigenvalue=(alphaReal+i*alphaImag))
Integerinfo 
RealHo[:,:]Schur decomposition (if eigenValuesOnly==false, unspecified else)
RealZo[:,:] 
Realwork[3 * max(1, size(H, 1))] 

Function Modelica.​Math.​Matrices.​LAPACK.​dlange
Norm of a matrix

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:]Real matrix A
Stringnormspecifies the norm, i.e., 1, I, F, M

Outputs

TypeNameDescription
Realanormnorm of A

Function Modelica.​Math.​Matrices.​LAPACK.​dgecon
Estimates the reciprocal of the condition number of a general real matrix A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealLU_of_A[:,:]LU factorization of a real matrix A
BooleaninfIs true if infinity norm is used and false for 1-norm
Realanormnorm of A

Outputs

TypeNameDescription
RealrcondReciprocal condition number of A
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgehrd
reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 
Integerilolowest index where the original matrix had been Hessenbergform
Integerihihighest index where the original matrix had been Hessenbergform

Outputs

TypeNameDescription
RealAout[size(A, 1),size(A, 2)]contains the Hessenberg form in the upper triangle and the first subdiagonal and below the first subdiagonal it contains the elementary reflectors which represents (with array tau) as a product the orthogonal matrix Q
Realtau[max(size(A, 1), 1) - 1]scalar factors of the elementary reflectors
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgeqrf
computes a QR factorization without pivoting

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:]Square or rectangular matrix

Outputs

TypeNameDescription
RealAout[size(A, 1),size(A, 2)]the upper triangle of the array contains the upper trapezoidal matrix R; the elements below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors
Realtau[min(size(A, 1), size(A, 2))]scalar factors of the elementary reflectors
Integerinfo 
Realwork[3 * max(1, size(A, 2))] 

Function Modelica.​Math.​Matrices.​LAPACK.​dgeevx
Compute the eigenvalues and the (real) left and right eigenvectors of matrix A, using lapack routine dgeevx

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 

Outputs

TypeNameDescription
RealalphaReal[size(A, 1)]Real part of alpha (eigenvalue=(alphaReal+i*alphaImag))
RealalphaImag[size(A, 1)]Imaginary part of alpha (eigenvalue=(alphaReal+i*alphaImag))
ReallEigenVectors[size(A, 1),size(A, 1)]left eigenvectors of matrix A
RealrEigenVectors[size(A, 1),size(A, 1)]right eigenvectors of matrix A
RealAS[size(A, 1),size(A, 2)]AS iss the real Schur form of the balanced version of the input matrix A
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dgesdd
Determine singular value decomposition

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:] 

Outputs

TypeNameDescription
Realsigma[min(size(A, 1), size(A, 2))] 
RealU[size(A, 1),size(A, 1)] 
RealVT[size(A, 2),size(A, 2)] 
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dggev
Compute generalized eigenvalues, as well as the left and right eigenvectors for a (A,B) system

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 
RealB[size(A, 1),size(A, 1)] 
IntegernAThe actual dimensions of matrices A and B (the computation is performed for A[1:nA,1:nA], B[1:nA,1:nA])

Outputs

TypeNameDescription
RealalphaReal[size(A, 1)]Real part of alpha (eigenvalue=(alphaReal+i*alphaImag)/beta)
RealalphaImag[size(A, 1)]Imaginary part of alpha
Realbeta[size(A, 1)]Denominator of eigenvalue
ReallEigenVectors[size(A, 1),size(A, 1)]left eigenvectors of matrix A
RealrEigenVectors[size(A, 1),size(A, 1)]right eigenvectors of matrix A
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dggevx
Compute generalized eigenvalues for a (A,B) system, using lapack routine dggevx

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 
RealB[size(A, 1),size(A, 1)] 

Outputs

TypeNameDescription
RealalphaReal[size(A, 1)]Real part of alpha (eigenvalue=(alphaReal+i*alphaImag)/beta)
RealalphaImag[size(A, 1)]Imaginary part of alpha
Realbeta[size(A, 1)]Denominator of eigenvalue
ReallEigenVectors[size(A, 1),size(A, 1)]left eigenvectors of matrix A
RealrEigenVectors[size(A, 1),size(A, 1)]right eigenvectors of matrix A
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dhgeqz
Compute generalized eigenvalues for a (A,B) system

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)] 
RealB[size(A, 1),size(A, 1)] 

Outputs

TypeNameDescription
RealalphaReal[size(A, 1)]Real part of alpha (eigenvalue=(alphaReal+i*alphaImag)/beta)
RealalphaImag[size(A, 1)]Imaginary part of alpha
Realbeta[size(A, 1)]Denominator of eigenvalue
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dormhr
overwrites the general real M-by-N matrix C with Q * C or C * Q or Q' * C or C * Q', where Q is an orthogonal matrix as returned by dgehrd

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealC[:,:] 
RealA[:,:] 
Realtau[if side == "L" then size(C, 2) - 1 else size(C, 1) - 1] 
Stringside 
Stringtrans 
Integerilolowest index where the original matrix had been Hessenbergform
Integerihihighest index where the original matrix had been Hessenbergform

Outputs

TypeNameDescription
RealCout[size(C, 1),size(C, 2)]contains the Hessenberg form in the upper triangle and the first subdiagonal and below the first subdiagonal it contains the elementary reflectors which represents (with array tau) as a product the orthogonal matrix Q
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dormqr
overwrites the general real M-by-N matrix C with Q * C or C * Q or Q' * C or C * Q', where Q is an orthogonal matrix of a QR factorization as returned by dgeqrf

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealC[:,:] 
RealA[:,:] 
Realtau[:] 
Stringside 
Stringtrans 

Outputs

TypeNameDescription
RealCout[size(C, 1),size(C, 2)]contains Q*C or Q**T*C or C*Q**T or C*Q
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dtrevc
Compute the right and/or left eigenvectors of a real upper quasi-triangular matrix T

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealT[:,size(T, 1)]Upper quasi triangular matrix
StringsideSpecify which eigenvectors
StringhowmnySpecify how many eigenvectors
RealQ[size(T, 1),size(T, 1)]Orthogonal matrix Q of Schur vectors returned by DHSEQR

Outputs

TypeNameDescription
ReallEigenVectors[size(T, 1),size(T, 1)]left eigenvectors of matrix T
RealrEigenVectors[size(T, 1),size(T, 1)]right eigenvectors of matrix T
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dpotrf
Computes the Cholesky factorization of a real symmetric positive definite matrix A

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)]Real symmetric positive definite matrix A
BooleanupperTrue if the upper triangle of A is provided

Outputs

TypeNameDescription
RealAcholesky[size(A, 1),size(A, 1)]Cholesky factor
Integerinfo 

Function Modelica.​Math.​Matrices.​LAPACK.​dtrsm
Solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where A is triangular matrix. BLAS routine

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,:]Input matrix A
RealB[:,:]Input matrix B
RealalphaFactor alpha
BooleanrightTrue if A is right multiplication
BooleanupperTrue if A is upper triangular
BooleantransTrue if op(A) means transposed(A)
BooleanunitTriangularTrue if A is unit triangular, i.e., all diagonal elements of A are equal to 1

Outputs

TypeNameDescription
RealX[size(B, 1),size(B, 2)]Matrix Bout=alpha*op( A )*B, or B := alpha*B*op( A )

Function Modelica.​Math.​Matrices.​LAPACK.​dorghr
Generates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD

Information

Extends from Modelica.​Icons.​Function (Icon for functions).

Inputs

TypeNameDescription
RealA[:,size(A, 1)]Square matrix with the elementary reflectors
Integerilolowest index where the original matrix had been Hessenbergform - ilo must have the same value as in the previous call of DGEHRD
Integerihihighest index where the original matrix had been Hessenbergform - ihi must have the same value as in the previous call of DGEHRD
Realtau[max(0, size(A, 1) - 1)]scalar factors of the elementary reflectors

Outputs

TypeNameDescription
RealAout[size(A, 1),size(A, 2)]Orthogonal matrix as a result of elementary reflectors
Integerinfo 

Generated 2018-12-12 12:14:35 EST by MapleSim.