Functions to port

# define sgesvd_ sgesvd

# define dgesvd_ dgesvd

# define cgesvd_ cgesvd

# define zgesvd_ zgesvd

SGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,

LWORK, INFO )

A = U*SIGMA*VT

JOBU (input) CHARACTER*1

JOBVT (input) CHARACTER*1

M (input) INTEGER

N (input) INTEGER

A (input/output) REAL array, dimension (LDA,N)

LDA (input) INTEGER

S (output) REAL array, dimension (min(M,N))

U (output) REAL array, dimension (LDU,UCOL)

LDU (input) INTEGER

VT (output) REAL array, dimension (LDVT,N)

LDVT (input) INTEGER

WORK (workspace/output) REAL array, dimension (LWORK)

LWORK (input) INTEGER

INFO (output) INTEGER

LAPACK

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/dgesvd.html

http://software.intel.com/sites/products/documentation/hpc/mkl/lapack/mkl_lapack_examples/dgesvd.htm#top

DGESVD computes the singular value decomposition (SVD) of a real M-by-N

matrix A, optionally computing the left and/or right singular vectors. The

SVD is written

A = U * SIGMA * transpose(V)

where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diag-

onal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthog-

onal matrix. The diagonal elements of SIGMA are the singular values of A;

they are real and non-negative, and are returned in descending order. The

first min(m,n) columns of U and V are the left and right singular vectors

of A.

Note that the routine returns V**T, not V.

EIGEN

http://eigen.tuxfamily.org/dox/classEigen_1_1JacobiSVD.html#_details

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/group__linalg.html#ga7f9eff151c422a9285dbb73a5ca84ff3

http://en.wikipedia.org/wiki/Singular_value_decomposition#Reduced_SVDs

# define sgesv_ sgesv

# define dgesv_ dgesv

# define cgesv_ cgesv

# define zgesv_ zgesv

LAPACK

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/dgesv.html

http://software.intel.com/sites/products/documentation/hpc/mkl/lapack/mkl_lapack_examples/dgesv.htm#top

DGESV computes the solution to a real system of linear equations

A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS

matrices.

The LU decomposition with partial pivoting and row interchanges is used to

factor A as

A = P * L * U,

where P is a permutation matrix, L is unit lower triangular, and U is upper

triangular. The factored form of A is then used to solve the system of

equations A * X = B.

EIGEN

http://eigen.tuxfamily.org/dox/TutorialLinearAlgebra.html#TutorialLinAlgBasicSolve

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/group__linalg.html#ga9f4e4329d30a3898ad93b2512da8d540

# define sgelss_ sgelss

# define dgelss_ dgelss

# define cgelss_ cgelss

# define zgelss_ zgelss

M (input) INTEGER

N (input) INTEGER

NRHS (input) INTEGER

A (input/output) DOUBLE PRECISION array, dimension (LDA,N)

LDA (input) INTEGER

B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)

LDB (input) INTEGER

S (output) DOUBLE PRECISION array, dimension (min(M,N))

RCOND (input) DOUBLE PRECISION

RANK (output) INTEGER

WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)

LWORK (input) INTEGER

INFO (output) INTEGER

LAPACK

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/dgelss.html

http://software.intel.com/sites/products/documentation/hpc/mkl/lapack/mkl_lapack_examples/dgelsd.htm#top

DGELSS computes the minimum norm solution to a real linear least squares

problem:

Minimize 2-norm(| b - A*x |).

using the singular value decomposition (SVD) of A. A is an M-by-N matrix

which may be rank-deficient.

Several right hand side vectors b and solution vectors x can be handled in

a single call; they are stored as the columns of the M-by-NRHS right hand

side matrix B and the N-by-NRHS solution matrix X.

The effective rank of A is determined by treating as zero those singular

values which are less than RCOND times the largest singular value.

EIGEN

http://eigen.tuxfamily.org/dox/TutorialLinearAlgebra.html#TutorialLinAlgLeastsquares

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/group__linalg.html#ga720de823d323fd960ce4dff0d19222a3

s/dsyev are used for real symmetric matrices;

c/zheev are used for complex Hermitian.

# define ssyev_ ssyev

# define dsyev_ dsyev

LAPACK

http://software.intel.com/sites/products/documentation/hpc/mkl/lapack/mkl_lapack_examples/dsyev.htm#top

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/dsyev.html

DSYEV - compute all eigenvalues and, optionally,

eigenvectors of a real symmetric matrix A

EIGEN

http://eigen.tuxfamily.org/dox/TutorialLinearAlgebra.html#TutorialLinAlgEigensolving

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/group__linalg.html#ga2bea055af972ccd1a6783410caaddaea

# define cheev_ cheev

# define zheev_ zheev

LAPACK

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/zheev.html

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/cheevx.html

ZHEEV - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

EIGEN

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/group__linalg.html#ga2bea055af972ccd1a6783410caaddaea

# define ssygv_ ssygv

# define dsygv_ dsygv

LAPACK

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/dsygv.html

DSYGV - compute all the eigenvalues, and optionally, the eigenvectors

of a real generalized symmetric-definite eigenproblem, of the form

A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

EIGEN

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/group__linalg.html#ga45b1f82b21b21997c5e99314197e3d7a

# define chegv_ chegv

# define zhegv_ zhegv

LAPACK

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/zhegv.html

ZHEGV - compute all the eigenvalues, and optionally, the eigenvectors of a

complex generalized Hermitian-definite eigenproblem, of the form

A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

EIGEN

MADNESS

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/zhegv.html

# define dpotrf_ dpotrf

LAPACK

http://www.netlib.org/lapack/double/dpotrf.f

http://www.physics.orst.edu/~rubin/nacphy/lapack/routines/dpotrf.html

DPOTRF - compute the Cholesky factorization

of a real symmetric positive definite matrix A

http://www.netlib.org/lapack/explore-html/d0/d8a/dpotrf_8f.html

lapack-3.3.0/SRC/cpotrf.f

EIGEN

http://eigen.tuxfamily.org/dox/classEigen_1_1LLT.html

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/namespacemadness.html#a31340b0c4ec9c440c5b77cd7a8b062d7

no longer used

# define dtrsm_ dtrsm

LAPACK

http://www.math.utah.edu/software/lapack/lapack-blas/dtrsm.html

DTRSM solves one of the matrix equations

op( A )*X = alpha*B, or X*op( A ) = alpha*B,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or

non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A or op( A ) = A'. The matrix X is overwritten on B.

http://www.netlib.org/lapack/explore-html/de/da7/dtrsm_8f.html

lapack-3.3.0/BLAS/SRC/dtrsm.f

EIGEN

MADNESS

http://code.google.com/p/m-a-d-n-e-s-s/source/browse/local/trunk/src/lib/linalg/lapack.cc

ln. 618 no longer used

# define dlamch_ dlamch

# define slamch_ slamch

LAPACK

http://www.netlib.org/lapack/explore-html/d5/dd4/dlamch_8f.html

DLAMCH determines double precision machine parameters

lapack-3.3.0/INSTALL/dlamch.f

EIGEN

MADNESS

http://harrison2.chem.utk.edu/~rjh/madness/group__linalg.html#ga59e5d613749fd9d3de9cf448c8282f85