This table shows some of the Lapack functions (only the Single Precision REAL Routines are shown), and Matlab, Mathematica and Ada calls which closely provide that functionality.
lapack 
description 
Matlab 
Mathematica 
Ada 
SGESV 
Solves a general system of linear equations 
A\b f=factorize(A) S=inverse(A) pinv(A)* b 
LinearSolve[A,B] 
x:=solve(A,b) 
SGBSV 
Solves a general banded system of linear equations 
A\b 
LinearSolve[A,B] 
x:=solve(A,b) 
SGTSV 
Solves a general tridiagonal system of linear equations 
A\b 
LinearSolve[A,B] 
x:=solve(A,b) 
SPOSV 
Solves a symmetric positive definite system of linear 
A\b 
LinearSolve[A,B] 
x:=solve(A,b) 
SPPSV 
Solves a symmetric positive definite system of linear equations , where is held in packed storage 
A\b 
LinearSolve[A,B] 
x:=solve(A,b) 
SPBSV 
Solves a symmetric positive definite banded system 
see
above.
Or 
see
above.
Or 
x:=solve(A,b) 
SPTSV 
Solves a symmetric positive definite tridiagonal system 
A\b 
LinearSolve[A,B] 
x:=solve(A,b) 
SSYSV 
Solves a real symmetric indefinite system of linear equations 
A\b 
LinearSolve[A,B] 
x:=solve(A,b) 
SSPSV 
Solves a real symmetric indefinite system of linear equations where is held in packed storage 
A\b 
LinearSolve[A,B] 
x:=solve(A,b) 
SGELS 
Computes the least squares solution to an overdetermined system of linear equations, or , or the minimum norm solution of an underdetermined system, where A is a general rectangular matrix of full rank, using a QR or LQ factorization of A 
for
overdetermined: for
underdetermined: or lsqlin(A,b) 
for
overdetermined: for
underdetermined: PseudoInverse[A].b or LeastSquares[A,b] 
x:=solve(A,b) 
SGELSD 
Computes the least squares solution to an overdetermined system of linear equations, or , or the minimum norm solution of an underdetermined system, where is a general rectangular matrix of full rank, using singular value decomposition (SVD) 
Can
also
use [u,s,v]=svd(A) 
x=LinearSolve[A,b] u,w,v=SingularValueDecomposition[A] 
No SVD. Can use x:=solve(A,b) 
SGGLSE 
Solves the LSE (Constrained Linear Least Squares Problem) using the Generalized RQ factorization 
lsqlin() 
FindMinimum[] 
Missing? 
SGGGLM 
Solves the GLM (Generalized Linear Regression Model) using the GQR (Generalized QR) factorization 
glmfit() 
see
GeneralizedLinearModelFit[] 
Missing?

SSYEV 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric matrix 
eig() or eigs() 
Eigensystem[] 
eigenvalues() 
SSYEVD 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric matrix If eigenvectors are desired, it uses a divide and conquer algorithm 
eig() or eigs() 
Eigensystem[] 
eigenvalues() 
SSPEV 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric matrix in packed storage 
eig() or eigs() 
Eigensystem[] 
eigenvalues() 
SSPEVD 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric matrix in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm 
eig() or eigs() 
Eigensystem[] 
eigenvalues() 
SSBEV 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric band matrix 
eig() or eigs() 
Eigensystem[] 
eigenvalues()

SSBEVD 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric band matrix. If eigenvectors are desired, it uses a divide and conquer algorithm 
eig() or eigs() 
Eigensystem[] 
eigenvalues()

SSTEV 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric tridiagonal matrix 
eig() or eigs() 
Eigensystem[] 
eigenvalues() 
SSTEVD 
Computes all eigenvalues and optionally, eigenvectors of a real symmetric tridiagonal matrix. If eigenvectors are desired, it uses a divide and conquer algorithm 
eig() or eigs() 
Eigensystem[] 
eigenvalues()

SGEES 
Computes all eigenvalues and Schur factorization of a general matrix and orders the factorization so that selected eigenvalues are at the top left of the Schur form 
schur() 
SchurDecomposition[] 
missing? 
SGEEV 
Computes the eigenvalues and left and right eigenvectors of a general matrix 
For
right
eigenvectors
use
[V,D]
=
eig(A) 
For
right
eigenvectors
use
D,V=Eigensystem[A] For
left
eigenvectors
of
A
D,W=Eigensystem[Transpose[A]] 
For right eigenvectors use eigensystem(A,values,vectors) and for left eigenvectors, use transpose() on A and call eigensystem() again then call conjugate(). See annex G for the exact calls.

SGESVD 
Computes the singular value decomposition (SVD) a general matrix 
svd() 
SingularValueDecomposition[] 
missing? 
SGESDD 
Computes the singular value decomposition (SVD) a general matrix using divideandconquer 
svd() 
SingularValueDecomposition[] 
missing? 
SSYGV 
Computes all eigenvalues and the eigenvectors of a generalized symmetricdefinite generalized eigenproblem 
[V,D]=eig(A,B,’chol’) 
D,V=Eigensystem[A,B] 
missing?

SSYGVD 
Computes all eigenvalues and the eigenvectors of a generalized symmetricdefinite generalized eigenproblem , , If eigenvectors are desired, it uses a divide and conquer algorithm 
[V,D]=eig(A,B,’chol’) 
D,V=Eigensystem[A,B] 
missing? 
SSPGV 
Computes all eigenvalues and the eigenvectors of a generalized symmetricdefinite generalized eigenproblem , , where A and B are in packed storage 
[V,D]=eig(A,B,’chol’) 
D,V=Eigensystem[A,B] 
missing? 
SSPGVD 
Computes all eigenvalues and the eigenvectors of a generalized symmetricdefinite generalized eigenproblem , , , where A and B are in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm 
[V,D]=eig(A,B,’chol’) 
D,V=Eigensystem[A,B] 
missing? 
SSBGV 
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric of the form the form A and B are assumed to be symmetric and banded, and B is also positive definite 
[V,D]=eig(A,B,’chol’) 
D,V=Eigensystem[A,B] 
missing? 
SSBGVD 
Computes all eigenvalues and optionally, the eigenvectors of a real generalized symmetric definite banded eigenproblem of the form A and B are assumed to be symmetric and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm 
[V,D]=eig(A,B,’chol’) 
D,V=Eigensystem[A,B] 
missing? 
SGGES 
Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for a pair of nonsymmetric matrices 
schur() 
SchurDecomposition[] 
missing? 
SGGEV 
Computes the generalized eigenvalues, and left and/or right generalized eigenvectors for a pair of nonsymmetric matrices 
[V,D]=eig(A,B,’qz’) 
D,V=Eigensystem[A,B] 
missing? 
SGGSVD 
Computes the Generalized Singular Value Decomposition 
gsvd() 
SingularValueList[] 
missing?

SGESVX 
Solve a general system of linear equations, , , or and provides an estimate of the condition number, and error bounds on the solution 
A\b 
LinearSolve[A,b] 
Use transpose or conjuagte on A first, then call solve(). But missing condition number function. 
SGBSVX 
Solves a general banded system of linear equations , , or ,and provides an estimate of the condition number and error bounds on the solution. 
A\b 
LinearSolve[A,b] 
Use transpose or conjuagte on A first, then call solve(). But missing condition number function. 
SGTSVX 
Solves a general tridiagonal system of linear equations , , or , and provides an estimate of the condition ,number and error bounds on the solution 
A\b 
LinearSolve[A,b] 
Use transpose or conjuagte on A first, then call solve(). But missing condition number function. 
SPOSVX 
Solves a symmetric positive definite system of linear equations , and provides an estimate of the condition number and error bounds on the solution. 
A\b 
LinearSolve[A,b] 
x:solve(A,b). But missing condition number function. 
SPPSVX 
Solves a symmetric positive definite system of linear equations , where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution 
A\b 
LinearSolve[A,b] 
x:solve(A,b). But missing condition number function. 
SPBSVX 
Solves a symmetric positive definite banded system of linear equations , where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution. 
A\b 
LinearSolve[A,b] 
x:solve(A,b). But missing condition number function. 
SPTSVX 
Solves a symmetric positive definite tridiagonal system of linear equations , where is held in packed storage, and provides an estimate of the condition number and error bounds on the solution. 
A\b 
LinearSolve[A,b] 
x:solve(A,b). But missing condition number function. 
SSYSVX 
Solves a real symmetric indefinite system of linear equations , and provides an estimate of the condition number and error bounds on the solution. 
A\b 
LinearSolve[A,b] 
x:solve(A,b). But missing condition number function. 
SSPSVX 
Solves a real symmetric indefinite system of linear equations , where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution. 
A\b 
LinearSolve[A,b] 
x:solve(A,b). But missing condition number function. 
SGELSY 
Computes the minimum norm least squares solution to an overor underdetermined system of linear equations , using a complete orthogonal factorization of A 
for
overdetermined: for
underdetermined: or lsqlin(A,b) 
for
overdetermined: for
underdetermined: PseudoInverse[A].b or LeastSquares[A,b] 
x:=solve(A,b) 
SGELSS 
Computes the minimum norm least squares solution to an over or underdetermined system of linear equations , using the singular value decomposition of A. 
for
overdetermined: for
underdetermined: or lsqlin(A,b) 
for
overdetermined: for
underdetermined: PseudoInverse[A].b or LeastSquares[A,b] 
x:=solve(A,b) 
SSYEVX 
Computes selected eigenvalues and eigenvectors of a symmetric matrix. 
use eig() then user selects 
Eigenvalues[] then user selects 
eigenvalues(A) then user selects 
SSYEVR 
Computes selected eigenvalues, and optionally, eigenvectors of a real, symmetric matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" , representations (also known as Relatively Robust Representations). 
No direct support, but can use eig() then user selects 
No direct support, but can use Eigensystem() then user selects 
No direct support, but can use eigensystem() then user selects 
SSYGVX 
Computes selected eigenvalues and and optionally, the eigenvectors of a generalized symmetricdefinite generalized eigenproblem , , 
No direct support, [V,D]=eig(A,B,’chol’) then user selects 
No direct support, but can use D,V=Eigensystem[A,B] or D,V=Eigensystem[A,B,k] then user selects 
missing? 
SSPEVX 
Computes selected eigenvalues and eigenvectors of a symmetric matrix in packed storage. 
No direct support, but can use eig() then user selects 
No direct support, but can use Eigensystem() then user selects 
No direct support, but can use eigensystem() then user selects

SSPGVX 
Computes selected eigenvalues and and optionally, the eigenvectors of a generalized symmetricdefinite generalized eigenproblem , , where A and B are in packed storage. 
No direct support, [V,D]=eig(A,B,’chol’) then user selects 
No direct support, but can use D,V=Eigensystem[A,B] or D,V=Eigensystem[A,B,k] then user selects 
missing?

SSBEVX 
Computes selected eigenvalues and eigenvectors of a symmetric band matrix. 
No direct support, but can use eig() then user selects 
No direct support, but can use Eigensystem() then user selects 
No direct support, but can use eigensystem() then user selects

SSBGVX 
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite banded eigenproblem, of the form A*x=(lambda)*B*x. A and B are assumed to be symmetric and banded, and B is also positive definite. 
No direct support, [V,D]=eig(A,B,’chol’) then user selects 
No direct support, but can use D,V=Eigensystem[A,B] or D,V=Eigensystem[A,B,k] then user selects 
missing? 
SSTEVX 
Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. 
No direct support, but can use eig() then user selects 
No direct support, but can use Eigensystem() then user selects 
No direct support, but can use eigensystem() then user selects 
SSTEVR 
Computes selected eigenvalues, and optionally, eigenvectors of a real symmetric tridiagonal matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" representations (also known as Relatively Robust Representations). 
No direct support, but can use eig() then user selects 
No direct support, but can use Eigensystem() then user selects 
No direct support, but can use eigensystem() then user selects 
SGEESX 
Computes the eigenvalues and Schur factorization of a general matrix, orders the factorization so that selected eigenvalues, are at the top left of the Schur form, and computes reciprocal condition numbers for the average of the selected eigenvalues and for the associated right invariant subspace. 
No direct support, but can use eig(), shur(), then user selects 
No direct support, but can use Eigensystem(), SchurDecomposition[], then user selects 
No direct support, but can use eigensystem() then user selects 
SGGESX 
Computes the generalized eigenvalues, the real Schur form, and optionally, the left and/or right matrices of Schur vectors. 
No direct support, but can use eig(), shur(), then user selects 
No direct support, but can use Eigensystem[], SchurDecomposition[], then user selects 
No support for generalized eigenvalues. No shur decomposition 
SGEEVX 
Computes the eigenvalues and left and right eigenvectors of a general matrix, with preliminary balancing of the matrix, and computes reciprocal condition numbers for the eigenvalues and right eigenvectors. 
No direct support, but can use eig() and cond() 
No direct support, but can use Eigensystem[], and LinearAlgebra‘MatrixConditionNumber[A] 
No support but can use eigensystem(), no condition number. 
SGGEVX 
Computes the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors. 
[V,D]=eig(A,B,’chol’) 
[D,V]=Eigensystem[A,B] 
No support for generalized eigenvalues 



