(3p) - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B sggsvp sggsvp (3p) - compute orthogonal matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0 sgtcon sgtcon (3p) - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF sgtrfs sgtrfs (3p) - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution sgtsl sgtsl (3p) - solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. sgtsv sgtsv (3p) - solve the equation A*X = B, sgtsvx sgtsvx (3p) - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, sgttrf sgttrf (3p) - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges sgttrs sgttrs (3p) - solve one of the systems of equations A*X = B or A'*X = B, shsein shsein (3p) - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H shseqr shseqr (3p) - compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors sinqb sinqb (3p) - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 * N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. sinqf sinqf (3p) - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 * N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence. sinqi sinqi (3p) - initialize the array xWSAVE, which is used in both xSINQF and xSINQB. sint sint (3p) - compute the discrete Fourier sine transform of an odd sequence. The xSINT transforms are unnormalized inverses of themselves, so a call of xSINT followed by another call of xSINT will multiply the input sequence by 2 * (N+1). The VxSINT transforms are normalized, so a call of VxSINT followed by a call of VxSINT will return the original sequence. sinti sinti (3p) - initialize the array xWSAVE, which is used in subroutine xSINT. slabad slabad (3p) - take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large slabrd slabrd (3p) - reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A slacon slacon (3p) - estimate the 1-norm of a square, real matrix A slacpy slacpy (3p) - copie all or part of a two-dimensional matrix A to another matrix B slae2 slae2 (3p) - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] slaebz slaebz (3p) - contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w slaed0 slaed0 (3p) - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method slaed1 slaed1 (3p) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix slaed2 slaed2 (3p) - merge the two sets of eigenvalues together into a the solution sgerq2 sgerq2 (3p) - compute an RQ factorization of a real m by n matrix A sgerqf sgerqf (3p) - compute an RQ factorization of a real M-by-N matrix A sgesl sgesl (3p) - solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. sgesv sgesv (3p) - compute the solution to a real system of linear equations A * X = B, sgesvd sgesvd (3p) - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors sgesvx sgesvx (3p) - use the LU factorization to compute the solution to a real system of linear equations A * X = B, sgetf2 sgetf2 (3p) - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges sgetrf sgetrf (3p) - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges sgetri sgetri (3p) - compute the inverse of a matrix using the LU factorization computed by SGETRF sgetrs sgetrs (3p) - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF sggbak sggbak (3p) - form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL sggbal sggbal (3p) - balance a pair of general real matrices (A,B) sggglm sggglm (3p) - solve a general Gauss-Markov linear model (GLM) problem sgghrd sgghrd (3p) - reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular sgglse sgglse (3p) - solve the linear equality-constrained least squares (LSE) problem sggqrf sggqrf (3p) - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B sggrqf sggrqf (3p) - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B sggsvd sggsvd