List for LAPACK driver/computational routines

Driver routines are listed in bold type, for example**Rgbsv** and **Cgbsv**.

Driver routines are listed in bold type, for example

MLAPACK Routine | LAPACK correspondence | Description | ||

real | complex | real | complex | |

Rsteqr | Csteqr | dsteqr | zsteqr | Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix, using the implicit QL or QR algorithm. NOT CHECKED FOR EXTREME CASES and "I" |

Rsterf | dsterf | Computes all eigenvalues of a real symmetric tridiagonal matrix, using a root-free variant of the QL or QR algorithm. NOT CHECKED FOR EXTREME CASES and "I" | ||

Rorgqr | Cungqr | dorgqr | zungqr | Generates all or part of the orthogonal/unitary matrix Q from a QR factorization determined by Rgeqrf/Cgeqrf. |

Rorgql | Cungql | dorgql | zungql | Generates all or part of the orthogonal/unitary matrix Q from a QL factorization determined by Rgeqlf/Cgeqlf. |

Rsytrd | Chetrd | dsytrd | zhetrd | Reduces a symmetric/Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation. |

Rorgtr | Cungtr | dorgtr | zungtr | Generates the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by Rsytrd/Chetrd. |

Rsyev |
Cheev |
dsyev |
zheev |
Computes all eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian matrix. |

Rpotrf | Cpotrf | dpotrf | zpotrf | Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix. |

Rtrtri | Ctrtri | dtrtri | ztrtri | Computes the inverse of a triangular matrix. |

Rgetrf | Cgetrf | dgetrf | zgetrf | Computes an LU factorization of a general matrix, using partial pivoting with row interchanges. |

Rgetri | Cgetri | dgetri | zgetri | Computes the inverse of a general matrix, using the LU factorization computed by Rgetrf/Cgetrf. |

Rgetrs | Cgetrs | dgetrs | zgetrs | Solves a general system of linear equations AX=B, A^T X=B or A^H X=B, using the LU factorization computed by Rgetrf/Cgetrf. |

Rgesv |
Cgesv |
dgesv |
zgesv |
Solves a general system of linear equations AX=B. |

Rtrtrs | Ctrtrs | dtrtrs | ztrtrs | Solves a triangular system of linear equations A X=B, A^T X=B or A^H X=B. |

List for LAPACK auxliary routines

MLAPACK Routine | LAPACK correspondence | Description | ||

real | complex | real | complex | |

Rlae2 | dlae2 | Computes the eigenvalues of a 2-by-2 symmetric matrix. | ||

Rlamch | dlamch | Determines machine parameters for floating-point arithmetic. | ||

Rlaev2 | Claev2 | dlaev2 | zlaev2 | Computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. |

Rlassq | Classq | dlassq | zlassq | Updates a sum of squares represented in scaled form. |

Rlanst | Clanht | dlanst | zlanht | Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element, of a symmetric/Hermitian tridiagonal matrix. |

Rlansy | Clansy Clanhe | dlansy | zlansy,zlanhe | Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element, of a symmetric/Hermitian tridiagonal matrix. |

Rlapy2 | dlapy2 | Returns sqrt(x^2 + y^2), avoiding unnecessary overflow or harmful underflow. | ||

Rlapy3 | dlapy3 | Returns sqrt(x^2 + y^2 + z^2), avoiding unnecessary overflow or harmful underflow. | ||

Rladiv | Cladiv | dladiv | zladiv | Performs complex division in real arithmetic, avoiding unnecessary overflow. |

Rlarfg | Clarfg | dlarfg | zlarfg | Generates an elementary reflector (Householder matrix).NOT CHECKED FOR EXTREME CASES |

Rlartg | Clartg | dlartg | zlartg | Generates a plane rotation with real cosine and real/complex sine.NOT CHECKED FOR EXTREME CASES |

Rlaset | Claset | dlaset | zlaset | Initializes the off-diagonal elements of a matrix to alpha and the diagonal elements to beta. |

Rlasr | Clasr | dlasr | zlasr | Applies a sequence of plane rotations to a general rectangular matrix. |

Clacgv | zlacgv | Conjugates a complex vector. | ||

Rpotf2 | Cpotf2 | dpotf2 | zpotf2 | Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm). |

Rlascl | Clascl | dlascl | zlascl | Multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. NOT CHECKED FOR EXTREME CASES |

Rlasrt | dlasrt | Sorts numbers in increasing or decreasing order using Quick Sort. | ||

Rsytd2 | Chetd2 | dsytd2 | zhetd2 | Reduces a symmetric/Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation (unblocked algorithm). |

Rlarf | Clarf | dlarf | zlarf | Applies an elementary reflector to a general rectangular matrix. |

Rorg2l | Cung2l | dorg2l | zung2l | Generates all or part of the orthogonal/unitary matrix Q from a QL factorization determined by Rgeqlf/Cgeqlf (unblocked algorithm). |

Rorg2r | Cung2r | dorg2r | zung2r | Generates all or part of the orthogonal/unitary matrix Q from a QR factorization determined by Rgeqrf/Cgeqrf (unblocked algorithm). |

Rlarft | Clarft | dlarft | zlarft | Forms the triangular factor T of a block reflector H = I - V^T V^H. NOT CHECKED FOR TAU[i]=0 for some CASES |

Rlarfb | Clarfb | dlarfb | zlarfb | Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix. |

Rlatrd | Clatrd | dlatrd | zlatrd | Reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal/unitary similarity transformation, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. |

Rtrti2 | Ctrti2 | dtrti2 | ztrti2 | Computes the inverse of a triangular matrix (unblocked algorithm). |

Rgetf2 | Cgetf2 | dgetf2 | zgetf2 | Computes the inverse of a triangular matrix (unblocked algorithm). |

Rlaswp | Claswp | dlaswp | zlaswp | Computes the inverse of a triangular matrix (unblocked algorithm). |

Rlasyf | Clasyf, Clahef | dlasyf | zlasyf, zlahef | Computes a partial factorization of a real symmetric/complex symmetric/complex Hermitian indefinite matrix, using the diagonal pivoting method. |

Clacrm | zlacrm | Performs the transformation ... where c, s, x, and y are complex. | ||

Claesy | zlaesy | Computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix, and checks that the norm of the matrix of eigenvectors is larger than a threshold value.NOT CHECKED FOR EXTREME CASES" | ||

Crot | zrot | Applies a plane rotation with real cosine and complex sine to a pair of complex vectors. | ||

Cspmv | zspmv | Computes the matrix-vector product y = alpha Ax + beta y, where alpha and beta are complex scalars, x and y are complex vectors and A is a complex symmetric matrix in packed storage. | ||

Cspr | zspr | Performs the symmetric rank-1 update A = alpha x x^T + A, where alpha is a complex scalar, x is a complex vector and A is a complex symmetric matrix in packed storage. | ||

Csymv | zsymv | Computes the matrix-vector product y = alpha Ax + beta y, where alpha and beta are complex scalars, x and y are complex vectors and A is a complex symmetric matrix. | ||

Csyr | zsyr | Performs the symmetric rank-1 update A = alpha x x^T + A, where alpha is a complex scalar, x is a complex vector and A is a complex symmetric matrix. | ||

iCmax1 | izmax1 | Finds the index of the element whose real part has maximum absolute value (similar to the Level 1 MBLAS iCamax, but using the absolute value of the real part). | ||

RCsum1 | dzsum1 | Forms the 1-norm of a complex vector (similar to the Level 1 MBLAS RCasum, but using the true absolute value). | ||

Rpotrs | dpotrs | - | Rpotrs solves a system of linear equations A*X = B with a symmetric positive definite matrix A | |

Rposv | dposv | - | Rposv computes the solution to a real system of linear equations A * X = B. | |

Rgeequ | dgeequ | - | Rgeequ computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. | |

Rlatrs | dlatrs | - | Rlatrs solves one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow. | |

Rlacn2 | Clacn2 | dlacn2 | zlacn2 | Estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. These routinese are thread safe version of Rlacon/Clacon. |

Rgecon | -- | dgecon | - | Rgecon estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm |

$Id: mlapack_routines.html,v 1.16 2010/08/13 03:50:41 nakatamaho Exp $