CBDSQR CBDSQR (l) - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B CGBBRD CGBBRD (l) - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation CGBCON CGBCON (l) - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, CGBEQU CGBEQU (l) - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number CGBRFS CGBRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution CGBSV CGBSV (l) - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices CGBSVX CGBSVX (l) - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, CGBTF2 CGBTF2 (l) - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges CGBTRF CGBTRF (l) - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges CGBTRS CGBTRS (l) - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by CGBTRF CGEBAK CGEBAK (l) - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL CGEBAL CGEBAL (l) - balance a general complex matrix A CGEBD2 CGEBD2 (l) - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation CGEBRD CGEBRD (l) - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation CGECON CGECON (l) - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF CGEEQU CGEEQU (l) - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number CGEES CGEES (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z CGEESX CGEESX (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z CGEEV CGEEV (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors CGEEVX CGEEVX (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors CGEGS CGEGS (l) - compute for a pair of N-by-N complex nonsymmetric matrices A, CGEGV CGEGV (l) - compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, CGEHD2 CGEHD2 (l) - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation CGEHRD CGEHRD (l) - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation CGELQ2 CGELQ2 (l) - compute an LQ factorization of a complex m by n matrix A CGELQF CGELQF (l) - compute an LQ factorization of a complex M-by-N matrix A CGELS CGELS (l) - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A CGELSS CGELSS (l) - compute the minimum norm solution to a complex linear least squares problem CGELSX CGELSX (l) - compute the minimum-norm solution to a complex linear least squares problem CGEQL2 CGEQL2 (l) - compute a QL factorization of a complex m by n matrix A CGEQLF CGEQLF (l) - compute a QL factorization of a complex M-by-N matrix A CGEQPF CGEQPF (l) - compute a QR factorization with column pivoting of a complex M-by-N matrix A CGEQR2 CGEQR2 (l) - compute a QR factorization of a complex m by n matrix A CGEQRF CGEQRF (l) - compute a QR factorization of a complex M-by-N matrix A CGERFS CGERFS (l) - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution CGERQ2 CGERQ2 (l) - compute an RQ factorization of a complex m by n matrix A CGERQF CGERQF (l) - compute an RQ factorization of a complex M-by-N matrix A CGESV CGESV (l) - compute the solution to a complex system of linear equations A * X = B, CGESVD CGESVD (l) - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors CGESVX CGESVX (l) - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, CGETF2 CGETF2 (l) - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges CGETRF CGETRF (l) - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges CGETRI CGETRI (l) - compute the inverse of a matrix using the LU factorization computed by CGETRF CGETRS CGETRS (l) - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF CGGBAK CGGBAK (l) - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL CGGBAL CGGBAL (l) - balance a pair of general complex matrices (A,B) CGGGLM CGGGLM (l) - solve a general Gauss-Markov linear model (GLM) problem CGGHRD CGGHRD (l) - reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular CGGLSE CGGLSE (l) - solve the linear equality-constrained least squares (LSE) problem CGGQRF CGGQRF (l) - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B CGGRQF CGGRQF (l) - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B CGGSVD CGGSVD (l) - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B CGGSVP CGGSVP (l) - compute unitary matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0 CGTCON CGTCON (l) - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF CGTRFS CGTRFS (l) - 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 CGTSV CGTSV (l) - solve the equation A*X = B, CGTSVX CGTSVX (l) - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, CGTTRF CGTTRF (l) - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges CGTTRS CGTTRS (l) - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, CHBEV CHBEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A CHBEVD CHBEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A CHBEVX CHBEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A CHBGST CHBGST (l) - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, CHBGV CHBGV (l) - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x CHBTRD CHBTRD (l) - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation CHECON CHECON (l) - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF CHEEV CHEEV (l) - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A CHEEVD CHEEVD (l) - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A CHEEVX CHEEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A CHEGS2 CHEGS2 (l) - reduce a complex Hermitian-definite generalized eigenproblem to standard form CHEGST CHEGST (l) - reduce a complex Hermitian-definite generalized eigenproblem to standard form CHEGV CHEGV (l) - 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 CHERFS CHERFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution CHESV CHESV (l) - compute the solution to a complex system of linear equations A * X = B, CHESVX CHESVX (l) - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B, CHETD2 CHETD2 (l) - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation CHETF2 CHETF2 (l) - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method CHETRD CHETRD (l) - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation CHETRF CHETRF (l) - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method CHETRI CHETRI (l) - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF CHETRS CHETRS (l) - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF CHPCON CHPCON (l) - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF CHPEV CHPEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage CHPEVD CHPEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage CHPEVX CHPEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage CHPGST CHPGST (l) - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage CHPGV CHPGV (l) - 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 CHPRFS CHPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution CHPSV CHPSV (l) - compute the solution to a complex system of linear equations A * X = B, CHPSVX CHPSVX (l) - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices CHPTRD CHPTRD (l) - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation CHPTRF CHPTRF (l) - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method CHPTRI CHPTRI (l) - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF CHPTRS CHPTRS (l) - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF CHSEIN CHSEIN (l) - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H CHSEQR CHSEQR (l) - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors CLABRD CLABRD (l) - reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A CLACGV CLACGV (l) - conjugate a complex vector of length N CLACON CLACON (l) - estimate the 1-norm of a square, complex matrix A CLACPY CLACPY (l) - copie all or part of a two-dimensional matrix A to another matrix B CLACRM CLACRM (l) - perform a very simple matrix-matrix multiplication CLACRT CLACRT (l) - applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex CLADIV CLADIV (l) - := X / Y, where X and Y are complex CLAED0 CLAED0 (l) - the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix CLAED7 CLAED7 (l) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix CLAED8 CLAED8 (l) - merge the two sets of eigenvalues together into a single sorted set CLAEIN CLAEIN (l) - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H CLAESY CLAESY (l) - compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value CLAEV2 CLAEV2 (l) - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] CLAGS2 CLAGS2 (l) - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), CLAHEF CLAHEF (l) - compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method CLAHQR CLAHQR (l) - i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI CLAHRD CLAHRD (l) - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero CLAIC1 CLAIC1 (l) - applie one step of incremental condition estimation in its simplest version CLANGB CLANGB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals CLANGE CLANGE (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A CLANGT CLANGT (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A CLANHB CLANHB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals CLANHE CLANHE (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A CLANHP CLANHP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form CLANHS CLANHS (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A CLANHT CLANHT (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A CLANSB CLANSB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals CLANSP CLANSP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form CLANSY CLANSY (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A CLANTB CLANTB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals CLANTP CLANTP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form CLANTR CLANTR (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A CLAPLL CLAPLL (l) - two column vectors X and Y, let A = ( X Y ) CLAPMT CLAPMT (l) - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N CLAQGB CLAQGB (l) - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C CLAQGE CLAQGE (l) - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C CLAQHB CLAQHB (l) - equilibrate a symmetric band matrix A using the scaling factors in the vector S CLAQHE CLAQHE (l) - equilibrate a Hermitian matrix A using the scaling factors in the vector S CLAQHP CLAQHP (l) - equilibrate a Hermitian matrix A using the scaling factors in the vector S CLAQSB CLAQSB (l) - equilibrate a symmetric band matrix A using the scaling factors in the vector S CLAQSP CLAQSP (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S CLAQSY CLAQSY (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S CLAR2V CLAR2V (l) - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, CLARF CLARF (l) - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right CLARFB CLARFB (l) - applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right CLARFG CLARFG (l) - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I CLARFT CLARFT (l) - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors CLARFX CLARFX (l) - applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right CLARGV CLARGV (l) - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y CLARNV CLARNV (l) - return a vector of n random complex numbers from a uniform or normal distribution CLARTG CLARTG (l) - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] CLARTV CLARTV (l) - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y CLASCL CLASCL (l) - multiplie the M by N complex matrix A by the real scalar CTO/CFROM CLASET CLASET (l) - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals CLASR CLASR (l) - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix, CLASSQ CLASSQ (l) - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, CLASWP CLASWP (l) - perform a series of row interchanges on the matrix A CLASYF CLASYF (l) - compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method CLATBS CLATBS (l) - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b, CLATPS CLATPS (l) - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b, CLATRD CLATRD (l) - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A CLATRS CLATRS (l) - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b, CLATZM CLATZM (l) - applie a Householder matrix generated by CTZRQF to a matrix CLAUU2 CLAUU2 (l) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A CLAUUM CLAUUM (l) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A CPBCON CPBCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF CPBEQU CPBEQU (l) - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm) CPBRFS CPBRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution CPBSTF CPBSTF (l) - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A CPBSV CPBSV (l) - compute the solution to a complex system of linear equations A * X = B, CPBSVX CPBSVX (l) - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B, CPBTF2 CPBTF2 (l) - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A CPBTRF CPBTRF (l) - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A CPBTRS CPBTRS (l) - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF CPOCON CPOCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF CPOEQU CPOEQU (l) - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm) CPORFS CPORFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, CPOSV CPOSV (l) - compute the solution to a complex system of linear equations A * X = B, CPOSVX CPOSVX (l) - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B, CPOTF2 CPOTF2 (l) - compute the Cholesky factorization of a complex Hermitian positive definite matrix A CPOTRF CPOTRF (l) - compute the Cholesky factorization of a complex Hermitian positive definite matrix A CPOTRI CPOTRI (l) - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF CPOTRS CPOTRS (l) - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF CPPCON CPPCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF CPPEQU CPPEQU (l) - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) CPPRFS CPPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution CPPSV CPPSV (l) - compute the solution to a complex system of linear equations A * X = B, CPPSVX CPPSVX (l) - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B, CPPTRF CPPTRF (l) - compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format CPPTRI CPPTRI (l) - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF CPPTRS CPPTRS (l) - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF CPTCON CPTCON (l) - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF CPTEQR CPTEQR (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor CPTRFS CPTRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution CPTSV CPTSV (l) - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices CPTSVX CPTSVX (l) - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices CPTTRF CPTTRF (l) - compute the factorization of a complex Hermitian positive definite tridiagonal matrix A CPTTRS CPTTRS (l) - solve a system of linear equations A * X = B with a Hermitian positive definite tridiagonal matrix A using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF CROT CROT (l) - applie a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex CSPCON CSPCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF CSPMV CSPMV (l) - perform the matrix-vector operation y := alpha*A*x + beta*y, CSPR CSPR (l) - perform the symmetric rank 1 operation A := alpha*x*conjg( x' ) + A, CSPRFS CSPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution CSPSV CSPSV (l) - compute the solution to a complex system of linear equations A * X = B, CSPSVX CSPSVX (l) - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices CSPTRF CSPTRF (l) - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method CSPTRI CSPTRI (l) - compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF CSPTRS CSPTRS (l) - solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF CSRSCL CSRSCL (l) - multiplie an n-element complex vector x by the real scalar 1/a CSTEDC CSTEDC (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method CSTEIN CSTEIN (l) - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration CSTEQR CSTEQR (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method CSYCON CSYCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF CSYMV CSYMV (l) - perform the matrix-vector operation y := alpha*A*x + beta*y, CSYR CSYR (l) - perform the symmetric rank 1 operation A := alpha*x*( x' ) + A, CSYRFS CSYRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution CSYSV CSYSV (l) - compute the solution to a complex system of linear equations A * X = B, CSYSVX CSYSVX (l) - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B, CSYTF2 CSYTF2 (l) - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method CSYTRF CSYTRF (l) - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method CSYTRI CSYTRI (l) - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF CSYTRS CSYTRS (l) - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF CTBCON CTBCON (l) - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm CTBRFS CTBRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix CTBTRS CTBTRS (l) - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B, CTGEVC CTGEVC (l) - compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B) CTGSJA CTGSJA (l) - compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B CTPCON CTPCON (l) - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm CTPRFS CTPRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix CTPTRI CTPTRI (l) - compute the inverse of a complex upper or lower triangular matrix A stored in packed format CTPTRS CTPTRS (l) - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B, CTRCON CTRCON (l) - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm CTREVC CTREVC (l) - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T CTREXC CTREXC (l) - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST CTRRFS CTRRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix CTRSEN CTRSEN (l) - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace CTRSNA CTRSNA (l) - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary) CTRSYL CTRSYL (l) - solve the complex Sylvester matrix equation CTRTI2 CTRTI2 (l) - compute the inverse of a complex upper or lower triangular matrix CTRTRI CTRTRI (l) - compute the inverse of a complex upper or lower triangular matrix A CTRTRS CTRTRS (l) - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B, CTZRQF CTZRQF (l) - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations CUNG2L CUNG2L (l) - generate an m by n complex matrix Q with orthonormal columns, CUNG2R CUNG2R (l) - generate an m by n complex matrix Q with orthonormal columns, CUNGBR CUNGBR (l) - generate one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form CUNGHR CUNGHR (l) - generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD CUNGL2 CUNGL2 (l) - generate an m-by-n complex matrix Q with orthonormal rows, CUNGLQ CUNGLQ (l) - generate an M-by-N complex matrix Q with orthonormal rows, CUNGQL CUNGQL (l) - generate an M-by-N complex matrix Q with orthonormal columns, CUNGQR CUNGQR (l) - generate an M-by-N complex matrix Q with orthonormal columns, CUNGR2 CUNGR2 (l) - generate an m by n complex matrix Q with orthonormal rows, CUNGRQ CUNGRQ (l) - generate an M-by-N complex matrix Q with orthonormal rows, CUNGTR CUNGTR (l) - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD CUNM2L CUNM2L (l) - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C', CUNM2R CUNM2R (l) - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C', CUNMBR CUNMBR (l) - VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' CUNMHR CUNMHR (l) - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' CUNML2 CUNML2 (l) - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C', CUNMLQ CUNMLQ (l) - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' CUNMQL CUNMQL (l) - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' CUNMQR CUNMQR (l) - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' CUNMR2 CUNMR2 (l) - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C', CUNMRQ CUNMRQ (l) - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' CUNMTR CUNMTR (l) - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' CUPGTR CUPGTR (l) - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage CUPMTR CUPMTR (l) - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DBDSQR DBDSQR (l) - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B DDISNA DDISNA (l) - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix DGBBRD DGBBRD (l) - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation DGBCON DGBCON (l) - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, DGBEQU DGBEQU (l) - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number DGBRFS DGBRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution DGBSV DGBSV (l) - compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices DGBSVX DGBSVX (l) - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B, DGBTF2 DGBTF2 (l) - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges DGBTRF DGBTRF (l) - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges DGBTRS DGBTRS (l) - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factorization computed by DGBTRF DGEBAK DGEBAK (l) - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL DGEBAL DGEBAL (l) - balance a general real matrix A DGEBD2 DGEBD2 (l) - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation DGEBRD DGEBRD (l) - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation DGECON DGECON (l) - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF DGEEQU DGEEQU (l) - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number DGEES DGEES (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z DGEESX DGEESX (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z DGEEV DGEEV (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors DGEEVX DGEEVX (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors DGEGS DGEGS (l) - compute for a pair of N-by-N real nonsymmetric matrices A, B DGEGV DGEGV (l) - compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai*i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR) DGEHD2 DGEHD2 (l) - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation DGEHRD DGEHRD (l) - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation DGELQ2 DGELQ2 (l) - compute an LQ factorization of a real m by n matrix A DGELQF DGELQF (l) - compute an LQ factorization of a real M-by-N matrix A DGELS DGELS (l) - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A DGELSS DGELSS (l) - compute the minimum norm solution to a real linear least squares problem DGELSX DGELSX (l) - compute the minimum-norm solution to a real linear least squares problem DGEQL2 DGEQL2 (l) - compute a QL factorization of a real m by n matrix A DGEQLF DGEQLF (l) - compute a QL factorization of a real M-by-N matrix A DGEQPF DGEQPF (l) - compute a QR factorization with column pivoting of a real M-by-N matrix A DGEQR2 DGEQR2 (l) - compute a QR factorization of a real m by n matrix A DGEQRF DGEQRF (l) - compute a QR factorization of a real M-by-N matrix A DGERFS DGERFS (l) - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution DGERQ2 DGERQ2 (l) - compute an RQ factorization of a real m by n matrix A DGERQF DGERQF (l) - compute an RQ factorization of a real M-by-N matrix A DGESV DGESV (l) - compute the solution to a real system of linear equations A * X = B, DGESVD DGESVD (l) - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors DGESVX DGESVX (l) - use the LU factorization to compute the solution to a real system of linear equations A * X = B, DGETF2 DGETF2 (l) - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges DGETRF DGETRF (l) - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges DGETRI DGETRI (l) - compute the inverse of a matrix using the LU factorization computed by DGETRF DGETRS DGETRS (l) - 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 DGETRF DGGBAK DGGBAK (l) - 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 DGGBAL DGGBAL DGGBAL (l) - balance a pair of general real matrices (A,B) DGGGLM DGGGLM (l) - solve a general Gauss-Markov linear model (GLM) problem DGGHRD DGGHRD (l) - 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 DGGLSE DGGLSE (l) - solve the linear equality-constrained least squares (LSE) problem DGGQRF DGGQRF (l) - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B DGGRQF DGGRQF (l) - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B DGGSVD DGGSVD (l) - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B DGGSVP DGGSVP (l) - 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 DGTCON DGTCON (l) - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF DGTRFS DGTRFS (l) - 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 DGTSV DGTSV (l) - solve the equation A*X = B, DGTSVX DGTSVX (l) - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, DGTTRF DGTTRF (l) - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges DGTTRS DGTTRS (l) - solve one of the systems of equations A*X = B or A'*X = B, DHSEIN DHSEIN (l) - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H DHSEQR DHSEQR (l) - 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 DLABAD DLABAD (l) - 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 DLABRD DLABRD (l) - 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 DLACON DLACON (l) - estimate the 1-norm of a square, real matrix A DLACPY DLACPY (l) - copie all or part of a two-dimensional matrix A to another matrix B DLAE2 DLAE2 (l) - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] DLAEBZ DLAEBZ (l) - 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 DLAED0 DLAED0 (l) - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method DLAED1 DLAED1 (l) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix DLAED2 DLAED2 (l) - merge the two sets of eigenvalues together into a single sorted set DLAED3 DLAED3 (l) - find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP DLAED4 DLAED4 (l) - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0 DLAED5 DLAED5 (l) - subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j DLAED7 DLAED7 (l) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix DLAED8 DLAED8 (l) - merge the two sets of eigenvalues together into a single sorted set DLAED9 DLAED9 (l) - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP DLAEDA DLAEDA (l) - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem DLAEIN DLAEIN (l) - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H DLAEV2 DLAEV2 (l) - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] DLAEXC DLAEXC (l) - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation DLAHQR DLAHQR (l) - i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI DLAHRD DLAHRD (l) - reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero DLAIC1 DLAIC1 (l) - applie one step of incremental condition estimation in its simplest version DLAMCH DLAMCH (l) - determine double precision machine parameters DLAMRG DLAMRG (l) - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order DLANGB DLANGB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals DLANGE DLANGE (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A DLANGT DLANGT (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A DLANHS DLANHS (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A DLANSB DLANSB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals DLANSP DLANSP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form DLANST DLANST (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A DLANSY DLANSY (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A DLANTB DLANTB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals DLANTP DLANTP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form DLANTR DLANTR (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A DLANV2 DLANV2 (l) - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form DLAPLL DLAPLL (l) - two column vectors X and Y, let A = ( X Y ) DLAPMT DLAPMT (l) - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N DLAPY2 DLAPY2 (l) - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow DLAPY3 DLAPY3 (l) - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow DLAQGB DLAQGB (l) - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C DLAQGE DLAQGE (l) - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C DLAQSB DLAQSB (l) - equilibrate a symmetric band matrix A using the scaling factors in the vector S DLAQSP DLAQSP (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S DLAQSY DLAQSY (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S DLAQTR DLAQTR (l) - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE DLAR2V DLAR2V (l) - applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z DLARF DLARF (l) - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right DLARFB DLARFB (l) - applie a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right DLARFG DLARFG (l) - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I DLARFT DLARFT (l) - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors DLARFX DLARFX (l) - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right DLARGV DLARGV (l) - generate a vector of real plane rotations, determined by elements of the real vectors x and y DLARNV DLARNV (l) - return a vector of n random real numbers from a uniform or normal distribution DLARTG DLARTG (l) - generate a plane rotation so that [ CS SN ] DLARTV DLARTV (l) - applie a vector of real plane rotations to elements of the real vectors x and y DLARUV DLARUV (l) - return a vector of n random real numbers from a uniform (0,1) DLAS2 DLAS2 (l) - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] DLASCL DLASCL (l) - multiplie the M by N real matrix A by the real scalar CTO/CFROM DLASET DLASET (l) - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals DLASQ1 DLASQ1 (l) - DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E DLASQ2 DLASQ2 (l) - DLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E DLASQ3 DLASQ3 (l) - DLASQ3 is the workhorse of the whole bidiagonal SVD algorithm DLASQ4 DLASQ4 (l) - DLASQ4 estimates TAU, the smallest eigenvalue of a matrix DLASR DLASR (l) - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix, DLASRT DLASRT (l) - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' ) DLASSQ DLASSQ (l) - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, DLASV2 DLASV2 (l) - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] DLASWP DLASWP (l) - perform a series of row interchanges on the matrix A DLASY2 DLASY2 (l) - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B, DLASYF DLASYF (l) - compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method DLATBS DLATBS (l) - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix DLATPS DLATPS (l) - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form DLATRD DLATRD (l) - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A DLATRS DLATRS (l) - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow DLATZM DLATZM (l) - applie a Householder matrix generated by DTZRQF to a matrix DLAUU2 DLAUU2 (l) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A DLAUUM DLAUUM (l) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A DOPGTR DOPGTR (l) - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage DOPMTR DOPMTR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DORG2L DORG2L (l) - generate an m by n real matrix Q with orthonormal columns, DORG2R DORG2R (l) - generate an m by n real matrix Q with orthonormal columns, DORGBR DORGBR (l) - generate one of the real orthogonal matrices Q or P**T determined by DGEBRD when reducing a real matrix A to bidiagonal form DORGHR DORGHR (l) - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD DORGL2 DORGL2 (l) - generate an m by n real matrix Q with orthonormal rows, DORGLQ DORGLQ (l) - generate an M-by-N real matrix Q with orthonormal rows, DORGQL DORGQL (l) - generate an M-by-N real matrix Q with orthonormal columns, DORGQR DORGQR (l) - generate an M-by-N real matrix Q with orthonormal columns, DORGR2 DORGR2 (l) - generate an m by n real matrix Q with orthonormal rows, DORGRQ DORGRQ (l) - generate an M-by-N real matrix Q with orthonormal rows, DORGTR DORGTR (l) - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD DORM2L DORM2L (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', DORM2R DORM2R (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', DORMBR DORMBR (l) - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DORMHR DORMHR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DORML2 DORML2 (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', DORMLQ DORMLQ (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DORMQL DORMQL (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DORMQR DORMQR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DORMR2 DORMR2 (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', DORMRQ DORMRQ (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DORMTR DORMTR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' DPBCON DPBCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF DPBEQU DPBEQU (l) - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm) DPBRFS DPBRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution DPBSTF DPBSTF (l) - compute a split Cholesky factorization of a real symmetric positive definite band matrix A DPBSV DPBSV (l) - compute the solution to a real system of linear equations A * X = B, DPBSVX DPBSVX (l) - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B, DPBTF2 DPBTF2 (l) - compute the Cholesky factorization of a real symmetric positive definite band matrix A DPBTRF DPBTRF (l) - compute the Cholesky factorization of a real symmetric positive definite band matrix A DPBTRS DPBTRS (l) - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF DPOCON DPOCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF DPOEQU DPOEQU (l) - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm) DPORFS DPORFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, DPOSV DPOSV (l) - compute the solution to a real system of linear equations A * X = B, DPOSVX DPOSVX (l) - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B, DPOTF2 DPOTF2 (l) - compute the Cholesky factorization of a real symmetric positive definite matrix A DPOTRF DPOTRF (l) - compute the Cholesky factorization of a real symmetric positive definite matrix A DPOTRI DPOTRI (l) - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF DPOTRS DPOTRS (l) - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF DPPCON DPPCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF DPPEQU DPPEQU (l) - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) DPPRFS DPPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution DPPSV DPPSV (l) - compute the solution to a real system of linear equations A * X = B, DPPSVX DPPSVX (l) - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B, DPPTRF DPPTRF (l) - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format DPPTRI DPPTRI (l) - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF DPPTRS DPPTRS (l) - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF DPTCON DPTCON (l) - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF DPTEQR DPTEQR (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor DPTRFS DPTRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution DPTSV DPTSV (l) - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices DPTSVX DPTSVX (l) - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices DPTTRF DPTTRF (l) - compute the factorization of a real symmetric positive definite tridiagonal matrix A DPTTRS DPTTRS (l) - solve a system of linear equations A * X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF DRSCL DRSCL (l) - multiplie an n-element real vector x by the real scalar 1/a DSBEV DSBEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A DSBEVD DSBEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A DSBEVX DSBEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A DSBGST DSBGST (l) - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, DSBGV DSBGV (l) - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x DSBTRD DSBTRD (l) - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation DSECND DSECND (l) - return the user time for a process in seconds DSPCON DSPCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF DSPEV DSPEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage DSPEVD DSPEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage DSPEVX DSPEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage DSPGST DSPGST (l) - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage DSPGV DSPGV (l) - 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 DSPRFS DSPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution DSPSV DSPSV (l) - compute the solution to a real system of linear equations A * X = B, DSPSVX DSPSVX (l) - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices DSPTRD DSPTRD (l) - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation DSPTRF DSPTRF (l) - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method DSPTRI DSPTRI (l) - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF DSPTRS DSPTRS (l) - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF DSTEBZ DSTEBZ (l) - compute the eigenvalues of a symmetric tridiagonal matrix T DSTEDC DSTEDC (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method DSTEIN DSTEIN (l) - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration DSTEQR DSTEQR (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method DSTERF DSTERF (l) - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm DSTEV DSTEV (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A DSTEVD DSTEVD (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix DSTEVX DSTEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A DSYCON DSYCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF DSYEV DSYEV (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A DSYEVD DSYEVD (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A DSYEVX DSYEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A DSYGS2 DSYGS2 (l) - reduce a real symmetric-definite generalized eigenproblem to standard form DSYGST DSYGST (l) - reduce a real symmetric-definite generalized eigenproblem to standard form DSYGV DSYGV (l) - 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 DSYRFS DSYRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution DSYSV DSYSV (l) - compute the solution to a real system of linear equations A * X = B, DSYSVX DSYSVX (l) - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B, DSYTD2 DSYTD2 (l) - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation DSYTF2 DSYTF2 (l) - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method DSYTRD DSYTRD (l) - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation DSYTRF DSYTRF (l) - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method DSYTRI DSYTRI (l) - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF DSYTRS DSYTRS (l) - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF DTBCON DTBCON (l) - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm DTBRFS DTBRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix DTBTRS DTBTRS (l) - solve a triangular system of the form A * X = B or A**T * X = B, DTGEVC DTGEVC (l) - compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) DTGSJA DTGSJA (l) - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B DTPCON DTPCON (l) - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm DTPRFS DTPRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix DTPTRI DTPTRI (l) - compute the inverse of a real upper or lower triangular matrix A stored in packed format DTPTRS DTPTRS (l) - solve a triangular system of the form A * X = B or A**T * X = B, DTRCON DTRCON (l) - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm DTREVC DTREVC (l) - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T DTREXC DTREXC (l) - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST DTRRFS DTRRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix DTRSEN DTRSEN (l) - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, DTRSNA DTRSNA (l) - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal) DTRSYL DTRSYL (l) - solve the real Sylvester matrix equation DTRTI2 DTRTI2 (l) - compute the inverse of a real upper or lower triangular matrix DTRTRI DTRTRI (l) - compute the inverse of a real upper or lower triangular matrix A DTRTRS DTRTRS (l) - solve a triangular system of the form A * X = B or A**T * X = B, DTZRQF DTZRQF (l) - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations DZSUM1 DZSUM1 (l) - take the sum of the absolute values of a complex vector and returns a double precision result ICMAX1 ICMAX1 (l) - find the index of the element whose real part has maximum absolute value ILAENV ILAENV (l) - i called from the LAPACK routines to choose problem-dependent parameters for the local environment IZMAX1 IZMAX1 (l) - find the index of the element whose real part has maximum absolute value LSAME LSAME (l) - return .TRUE LSAMEN LSAMEN (l) - test if the first N letters of CA are the same as the first N letters of CB, regardless of case SBDSQR SBDSQR (l) - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B SCSUM1 SCSUM1 (l) - take the sum of the absolute values of a complex vector and returns a single precision result SDISNA SDISNA (l) - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix SECOND SECOND (l) - return the user time for a process in seconds SGBBRD SGBBRD (l) - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation SGBCON SGBCON (l) - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, SGBEQU SGBEQU (l) - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number SGBRFS SGBRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution SGBSV SGBSV (l) - compute the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices SGBSVX SGBSVX (l) - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B, SGBTF2 SGBTF2 (l) - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges SGBTRF SGBTRF (l) - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges SGBTRS SGBTRS (l) - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factorization computed by SGBTRF SGEBAK SGEBAK (l) - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL SGEBAL SGEBAL (l) - balance a general real matrix A SGEBD2 SGEBD2 (l) - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation SGEBRD SGEBRD (l) - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation SGECON SGECON (l) - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF SGEEQU SGEEQU (l) - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number SGEES SGEES (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z SGEESX SGEESX (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z SGEEV SGEEV (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors SGEEVX SGEEVX (l) - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors SGEGS SGEGS (l) - compute for a pair of N-by-N real nonsymmetric matrices A, B SGEGV SGEGV (l) - compute for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai*i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR) SGEHD2 SGEHD2 (l) - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation SGEHRD SGEHRD (l) - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation SGELQ2 SGELQ2 (l) - compute an LQ factorization of a real m by n matrix A SGELQF SGELQF (l) - compute an LQ factorization of a real M-by-N matrix A SGELS SGELS (l) - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A SGELSS SGELSS (l) - compute the minimum norm solution to a real linear least squares problem SGELSX SGELSX (l) - compute the minimum-norm solution to a real linear least squares problem SGEQL2 SGEQL2 (l) - compute a QL factorization of a real m by n matrix A SGEQLF SGEQLF (l) - compute a QL factorization of a real M-by-N matrix A SGEQPF SGEQPF (l) - compute a QR factorization with column pivoting of a real M-by-N matrix A SGEQR2 SGEQR2 (l) - compute a QR factorization of a real m by n matrix A SGEQRF SGEQRF (l) - compute a QR factorization of a real M-by-N matrix A SGERFS SGERFS (l) - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution SGERQ2 SGERQ2 (l) - compute an RQ factorization of a real m by n matrix A SGERQF SGERQF (l) - compute an RQ factorization of a real M-by-N matrix A SGESV SGESV (l) - compute the solution to a real system of linear equations A * X = B, SGESVD SGESVD (l) - 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 (l) - use the LU factorization to compute the solution to a real system of linear equations A * X = B, SGETF2 SGETF2 (l) - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges SGETRF SGETRF (l) - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges SGETRI SGETRI (l) - compute the inverse of a matrix using the LU factorization computed by SGETRF SGETRS SGETRS (l) - 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 (l) - 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 (l) - balance a pair of general real matrices (A,B) SGGGLM SGGGLM (l) - solve a general Gauss-Markov linear model (GLM) problem SGGHRD SGGHRD (l) - 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 (l) - solve the linear equality-constrained least squares (LSE) problem SGGQRF SGGQRF (l) - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B SGGRQF SGGRQF (l) - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B SGGSVD SGGSVD (l) - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B SGGSVP SGGSVP (l) - 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 (l) - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF SGTRFS SGTRFS (l) - 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 SGTSV SGTSV (l) - solve the equation A*X = B, SGTSVX SGTSVX (l) - 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 (l) - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges SGTTRS SGTTRS (l) - solve one of the systems of equations A*X = B or A'*X = B, SHSEIN SHSEIN (l) - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H SHSEQR SHSEQR (l) - 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 SLABAD SLABAD (l) - 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 (l) - 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 (l) - estimate the 1-norm of a square, real matrix A SLACPY SLACPY (l) - copie all or part of a two-dimensional matrix A to another matrix B SLAE2 SLAE2 (l) - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] SLAEBZ SLAEBZ (l) - 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 (l) - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method SLAED1 SLAED1 (l) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix SLAED2 SLAED2 (l) - merge the two sets of eigenvalues together into a single sorted set SLAED3 SLAED3 (l) - find the roots of the secular equation, as defined by the values in D, W, and RHO, between KSTART and KSTOP SLAED4 SLAED4 (l) - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0 SLAED5 SLAED5 (l) - subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j SLAED7 SLAED7 (l) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix SLAED8 SLAED8 (l) - merge the two sets of eigenvalues together into a single sorted set SLAED9 SLAED9 (l) - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP SLAEDA SLAEDA (l) - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem SLAEIN SLAEIN (l) - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H SLAEV2 SLAEV2 (l) - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ] SLAEXC SLAEXC (l) - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation SLAHQR SLAHQR (l) - i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI SLAHRD SLAHRD (l) - reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero SLAIC1 SLAIC1 (l) - applie one step of incremental condition estimation in its simplest version SLAMCH SLAMCH (l) - determine single precision machine parameters SLAMRG SLAMRG (l) - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order SLANGB SLANGB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals SLANGE SLANGE (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A SLANGT SLANGT (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A SLANHS SLANHS (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A SLANSB SLANSB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals SLANSP SLANSP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form SLANST SLANST (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A SLANSY SLANSY (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A SLANTB SLANTB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals SLANTP SLANTP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form SLANTR SLANTR (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A SLANV2 SLANV2 (l) - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form SLAPLL SLAPLL (l) - two column vectors X and Y, let A = ( X Y ) SLAPMT SLAPMT (l) - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N SLAPY2 SLAPY2 (l) - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow SLAPY3 SLAPY3 (l) - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow SLAQGB SLAQGB (l) - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C SLAQGE SLAQGE (l) - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C SLAQSB SLAQSB (l) - equilibrate a symmetric band matrix A using the scaling factors in the vector S SLAQSP SLAQSP (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S SLAQSY SLAQSY (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S SLAQTR SLAQTR (l) - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE SLAR2V SLAR2V (l) - applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z SLARF SLARF (l) - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right SLARFB SLARFB (l) - applie a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right SLARFG SLARFG (l) - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I SLARFT SLARFT (l) - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors SLARFX SLARFX (l) - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right SLARGV SLARGV (l) - generate a vector of real plane rotations, determined by elements of the real vectors x and y SLARNV SLARNV (l) - return a vector of n random real numbers from a uniform or normal distribution SLARTG SLARTG (l) - generate a plane rotation so that [ CS SN ] SLARTV SLARTV (l) - applie a vector of real plane rotations to elements of the real vectors x and y SLARUV SLARUV (l) - return a vector of n random real numbers from a uniform (0,1) SLAS2 SLAS2 (l) - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] SLASCL SLASCL (l) - multiplie the M by N real matrix A by the real scalar CTO/CFROM SLASET SLASET (l) - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals SLASQ1 SLASQ1 (l) - SLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E SLASQ2 SLASQ2 (l) - SLASQ2 computes the singular values of a real N-by-N unreduced bidiagonal matrix with squared diagonal elements in Q and squared off-diagonal elements in E SLASQ3 SLASQ3 (l) - SLASQ3 is the workhorse of the whole bidiagonal SVD algorithm SLASQ4 SLASQ4 (l) - SLASQ4 estimates TAU, the smallest eigenvalue of a matrix SLASR SLASR (l) - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix, SLASRT SLASRT (l) - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' ) SLASSQ SLASSQ (l) - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, SLASV2 SLASV2 (l) - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ] SLASWP SLASWP (l) - perform a series of row interchanges on the matrix A SLASY2 SLASY2 (l) - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B, SLASYF SLASYF (l) - compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method SLATBS SLATBS (l) - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix SLATPS SLATPS (l) - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form SLATRD SLATRD (l) - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A SLATRS SLATRS (l) - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow SLATZM SLATZM (l) - applie a Householder matrix generated by STZRQF to a matrix SLAUU2 SLAUU2 (l) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A SLAUUM SLAUUM (l) - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A SOPGTR SOPGTR (l) - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage SOPMTR SOPMTR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SORG2L SORG2L (l) - generate an m by n real matrix Q with orthonormal columns, SORG2R SORG2R (l) - generate an m by n real matrix Q with orthonormal columns, SORGBR SORGBR (l) - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form SORGHR SORGHR (l) - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD SORGL2 SORGL2 (l) - generate an m by n real matrix Q with orthonormal rows, SORGLQ SORGLQ (l) - generate an M-by-N real matrix Q with orthonormal rows, SORGQL SORGQL (l) - generate an M-by-N real matrix Q with orthonormal columns, SORGQR SORGQR (l) - generate an M-by-N real matrix Q with orthonormal columns, SORGR2 SORGR2 (l) - generate an m by n real matrix Q with orthonormal rows, SORGRQ SORGRQ (l) - generate an M-by-N real matrix Q with orthonormal rows, SORGTR SORGTR (l) - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD SORM2L SORM2L (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', SORM2R SORM2R (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', SORMBR SORMBR (l) - VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SORMHR SORMHR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SORML2 SORML2 (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', SORMLQ SORMLQ (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SORMQL SORMQL (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SORMQR SORMQR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SORMR2 SORMR2 (l) - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T', SORMRQ SORMRQ (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SORMTR SORMTR (l) - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SPBCON SPBCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF SPBEQU SPBEQU (l) - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm) SPBRFS SPBRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution SPBSTF SPBSTF (l) - compute a split Cholesky factorization of a real symmetric positive definite band matrix A SPBSV SPBSV (l) - compute the solution to a real system of linear equations A * X = B, SPBSVX SPBSVX (l) - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B, SPBTF2 SPBTF2 (l) - compute the Cholesky factorization of a real symmetric positive definite band matrix A SPBTRF SPBTRF (l) - compute the Cholesky factorization of a real symmetric positive definite band matrix A SPBTRS SPBTRS (l) - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF SPOCON SPOCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF SPOEQU SPOEQU (l) - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm) SPORFS SPORFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, SPOSV SPOSV (l) - compute the solution to a real system of linear equations A * X = B, SPOSVX SPOSVX (l) - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B, SPOTF2 SPOTF2 (l) - compute the Cholesky factorization of a real symmetric positive definite matrix A SPOTRF SPOTRF (l) - compute the Cholesky factorization of a real symmetric positive definite matrix A SPOTRI SPOTRI (l) - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF SPOTRS SPOTRS (l) - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF SPPCON SPPCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF SPPEQU SPPEQU (l) - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) SPPRFS SPPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution SPPSV SPPSV (l) - compute the solution to a real system of linear equations A * X = B, SPPSVX SPPSVX (l) - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B, SPPTRF SPPTRF (l) - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format SPPTRI SPPTRI (l) - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF SPPTRS SPPTRS (l) - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF SPTCON SPTCON (l) - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF SPTEQR SPTEQR (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor SPTRFS SPTRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution SPTSV SPTSV (l) - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices SPTSVX SPTSVX (l) - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices SPTTRF SPTTRF (l) - compute the factorization of a real symmetric positive definite tridiagonal matrix A SPTTRS SPTTRS (l) - solve a system of linear equations A * X = B with a symmetric positive definite tridiagonal matrix A using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF SRSCL SRSCL (l) - multiplie an n-element real vector x by the real scalar 1/a SSBEV SSBEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A SSBEVD SSBEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A SSBEVX SSBEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A SSBGST SSBGST (l) - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, SSBGV SSBGV (l) - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x SSBTRD SSBTRD (l) - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation SSPCON SSPCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF SSPEV SSPEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage SSPEVD SSPEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage SSPEVX SSPEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage SSPGST SSPGST (l) - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage SSPGV SSPGV (l) - 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 SSPRFS SSPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution SSPSV SSPSV (l) - compute the solution to a real system of linear equations A * X = B, SSPSVX SSPSVX (l) - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices SSPTRD SSPTRD (l) - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation SSPTRF SSPTRF (l) - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method SSPTRI SSPTRI (l) - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF SSPTRS SSPTRS (l) - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF SSTEBZ SSTEBZ (l) - compute the eigenvalues of a symmetric tridiagonal matrix T SSTEDC SSTEDC (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method SSTEIN SSTEIN (l) - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration SSTEQR SSTEQR (l) - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method SSTERF SSTERF (l) - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm SSTEV SSTEV (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A SSTEVD SSTEVD (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix SSTEVX SSTEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A SSYCON SSYCON (l) - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF SSYEV SSYEV (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A SSYEVD SSYEVD (l) - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A SSYEVX SSYEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A SSYGS2 SSYGS2 (l) - reduce a real symmetric-definite generalized eigenproblem to standard form SSYGST SSYGST (l) - reduce a real symmetric-definite generalized eigenproblem to standard form SSYGV SSYGV (l) - 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 SSYRFS SSYRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution SSYSV SSYSV (l) - compute the solution to a real system of linear equations A * X = B, SSYSVX SSYSVX (l) - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B, SSYTD2 SSYTD2 (l) - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation SSYTF2 SSYTF2 (l) - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method SSYTRD SSYTRD (l) - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation SSYTRF SSYTRF (l) - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method SSYTRI SSYTRI (l) - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF SSYTRS SSYTRS (l) - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF STBCON STBCON (l) - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm STBRFS STBRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix STBTRS STBTRS (l) - solve a triangular system of the form A * X = B or A**T * X = B, STGEVC STGEVC (l) - compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) STGSJA STGSJA (l) - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B STPCON STPCON (l) - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm STPRFS STPRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix STPTRI STPTRI (l) - compute the inverse of a real upper or lower triangular matrix A stored in packed format STPTRS STPTRS (l) - solve a triangular system of the form A * X = B or A**T * X = B, STRCON STRCON (l) - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm STREVC STREVC (l) - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T STREXC STREXC (l) - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST STRRFS STRRFS (l) - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix STRSEN STRSEN (l) - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, STRSNA STRSNA (l) - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal) STRSYL STRSYL (l) - solve the real Sylvester matrix equation STRTI2 STRTI2 (l) - compute the inverse of a real upper or lower triangular matrix STRTRI STRTRI (l) - compute the inverse of a real upper or lower triangular matrix A STRTRS STRTRS (l) - solve a triangular system of the form A * X = B or A**T * X = B, STZRQF STZRQF (l) - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations XERBLA XERBLA (l) - i an error handler for the LAPACK routines ZBDSQR ZBDSQR (l) - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B ZDRSCL ZDRSCL (l) - multiplie an n-element complex vector x by the real scalar 1/a ZGBBRD ZGBBRD (l) - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation ZGBCON ZGBCON (l) - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, ZGBEQU ZGBEQU (l) - compute row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number ZGBRFS ZGBRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution ZGBSV ZGBSV (l) - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices ZGBSVX ZGBSVX (l) - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, ZGBTF2 ZGBTF2 (l) - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges ZGBTRF ZGBTRF (l) - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges ZGBTRS ZGBTRS (l) - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by ZGBTRF ZGEBAK ZGEBAK (l) - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL ZGEBAL ZGEBAL (l) - balance a general complex matrix A ZGEBD2 ZGEBD2 (l) - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation ZGEBRD ZGEBRD (l) - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation ZGECON ZGECON (l) - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF ZGEEQU ZGEEQU (l) - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number ZGEES ZGEES (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z ZGEESX ZGEESX (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z ZGEEV ZGEEV (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors ZGEEVX ZGEEVX (l) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors ZGEGS ZGEGS (l) - compute for a pair of N-by-N complex nonsymmetric matrices A, ZGEGV ZGEGV (l) - compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, ZGEHD2 ZGEHD2 (l) - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation ZGEHRD ZGEHRD (l) - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation ZGELQ2 ZGELQ2 (l) - compute an LQ factorization of a complex m by n matrix A ZGELQF ZGELQF (l) - compute an LQ factorization of a complex M-by-N matrix A ZGELS ZGELS (l) - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A ZGELSS ZGELSS (l) - compute the minimum norm solution to a complex linear least squares problem ZGELSX ZGELSX (l) - compute the minimum-norm solution to a complex linear least squares problem ZGEQL2 ZGEQL2 (l) - compute a QL factorization of a complex m by n matrix A ZGEQLF ZGEQLF (l) - compute a QL factorization of a complex M-by-N matrix A ZGEQPF ZGEQPF (l) - compute a QR factorization with column pivoting of a complex M-by-N matrix A ZGEQR2 ZGEQR2 (l) - compute a QR factorization of a complex m by n matrix A ZGEQRF ZGEQRF (l) - compute a QR factorization of a complex M-by-N matrix A ZGERFS ZGERFS (l) - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution ZGERQ2 ZGERQ2 (l) - compute an RQ factorization of a complex m by n matrix A ZGERQF ZGERQF (l) - compute an RQ factorization of a complex M-by-N matrix A ZGESV ZGESV (l) - compute the solution to a complex system of linear equations A * X = B, ZGESVD ZGESVD (l) - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors ZGESVX ZGESVX (l) - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, ZGETF2 ZGETF2 (l) - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges ZGETRF ZGETRF (l) - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges ZGETRI ZGETRI (l) - compute the inverse of a matrix using the LU factorization computed by ZGETRF ZGETRS ZGETRS (l) - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by ZGETRF ZGGBAK ZGGBAK (l) - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL ZGGBAL ZGGBAL (l) - balance a pair of general complex matrices (A,B) ZGGGLM ZGGGLM (l) - solve a general Gauss-Markov linear model (GLM) problem ZGGHRD ZGGHRD (l) - reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular ZGGLSE ZGGLSE (l) - solve the linear equality-constrained least squares (LSE) problem ZGGQRF ZGGQRF (l) - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B ZGGRQF ZGGRQF (l) - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B ZGGSVD ZGGSVD (l) - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B ZGGSVP ZGGSVP (l) - compute unitary matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0 ZGTCON ZGTCON (l) - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF ZGTRFS ZGTRFS (l) - 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 ZGTSV ZGTSV (l) - solve the equation A*X = B, ZGTSVX ZGTSVX (l) - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B, ZGTTRF ZGTTRF (l) - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges ZGTTRS ZGTTRS (l) - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, ZHBEV ZHBEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A ZHBEVD ZHBEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A ZHBEVX ZHBEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A ZHBGST ZHBGST (l) - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, ZHBGV ZHBGV (l) - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x ZHBTRD ZHBTRD (l) - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation ZHECON ZHECON (l) - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF ZHEEV ZHEEV (l) - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A ZHEEVD ZHEEVD (l) - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A ZHEEVX ZHEEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A ZHEGS2 ZHEGS2 (l) - reduce a complex Hermitian-definite generalized eigenproblem to standard form ZHEGST ZHEGST (l) - reduce a complex Hermitian-definite generalized eigenproblem to standard form ZHEGV ZHEGV (l) - 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 ZHERFS ZHERFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution ZHESV ZHESV (l) - compute the solution to a complex system of linear equations A * X = B, ZHESVX ZHESVX (l) - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B, ZHETD2 ZHETD2 (l) - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation ZHETF2 ZHETF2 (l) - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method ZHETRD ZHETRD (l) - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation ZHETRF ZHETRF (l) - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method ZHETRI ZHETRI (l) - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF ZHETRS ZHETRS (l) - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF ZHPCON ZHPCON (l) - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF ZHPEV ZHPEV (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage ZHPEVD ZHPEVD (l) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage ZHPEVX ZHPEVX (l) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage ZHPGST ZHPGST (l) - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage ZHPGV ZHPGV (l) - 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 ZHPRFS ZHPRFS (l) - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution ZHPSV ZHPSV (l) - compute the solution to a complex system of linear equations A * X = B, ZHPSVX ZHPSVX (l) - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices ZHPTRD ZHPTRD (l) - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation ZHPTRF ZHPTRF (l) - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method ZHPTRI ZHPTRI (l) - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF ZHPTRS ZHPTRS (l) - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF ZHSEIN ZHSEIN (l) - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H ZHSEQR ZHSEQR (l) - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors ZLABRD ZLABRD (l) - reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A ZLACGV ZLACGV (l) - conjugate a complex vector of length N ZLACON ZLACON (l) - estimate the 1-norm of a square, complex matrix A ZLACPY ZLACPY (l) - copie all or part of a two-dimensional matrix A to another matrix B ZLACRM ZLACRM (l) - perform a very simple matrix-matrix multiplication ZLACRT ZLACRT (l) - applie a plane rotation, where the cos and sin (C and S) are complex and the vectors CX and CY are complex ZLADIV ZLADIV (l) - := X / Y, where X and Y are complex ZLAED0 ZLAED0 (l) - the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix ZLAED7 ZLAED7 (l) - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix ZLAED8 ZLAED8 (l) - merge the two sets of eigenvalues together into a single sorted set ZLAEIN ZLAEIN (l) - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H ZLAESY ZLAESY (l) - compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value ZLAEV2 ZLAEV2 (l) - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] ZLAGS2 ZLAGS2 (l) - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ), ZLAHEF ZLAHEF (l) - compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method ZLAHQR ZLAHQR (l) - i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI ZLAHRD ZLAHRD (l) - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero ZLAIC1 ZLAIC1 (l) - applie one step of incremental condition estimation in its simplest version ZLANGB ZLANGB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals ZLANGE ZLANGE (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A ZLANGT ZLANGT (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A ZLANHB ZLANHB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals ZLANHE ZLANHE (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A ZLANHP ZLANHP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form ZLANHS ZLANHS (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A ZLANHT ZLANHT (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A ZLANSB ZLANSB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals ZLANSP ZLANSP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form ZLANSY ZLANSY (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A ZLANTB ZLANTB (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals ZLANTP ZLANTP (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form ZLANTR ZLANTR (l) - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A ZLAPLL ZLAPLL (l) - two column vectors X and Y, let A = ( X Y ) ZLAPMT ZLAPMT (l) - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N ZLAQGB ZLAQGB (l) - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C ZLAQGE ZLAQGE (l) - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C ZLAQHB ZLAQHB (l) - equilibrate a symmetric band matrix A using the scaling factors in the vector S ZLAQHE ZLAQHE (l) - equilibrate a Hermitian matrix A using the scaling factors in the vector S ZLAQHP ZLAQHP (l) - equilibrate a Hermitian matrix A using the scaling factors in the vector S ZLAQSB ZLAQSB (l) - equilibrate a symmetric band matrix A using the scaling factors in the vector S ZLAQSP ZLAQSP (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S ZLAQSY ZLAQSY (l) - equilibrate a symmetric matrix A using the scaling factors in the vector S ZLAR2V ZLAR2V (l) - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices, ZLARF ZLARF (l) - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right ZLARFB ZLARFB (l) - applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right ZLARFG ZLARFG (l) - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I ZLARFT ZLARFT (l) - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors ZLARFX ZLARFX (l) - applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right ZLARGV ZLARGV (l) - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y ZLARNV ZLARNV (l) - return a vector of n random complex numbers from a uniform or normal distribution ZLARTG ZLARTG (l) - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ] ZLARTV ZLARTV (l) - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y ZLASCL ZLASCL (l) - multiplie the M by N complex matrix A by the real scalar CTO/CFROM ZLASET ZLASET (l) - initialize a 2-D array A to BETA on the diagonal and ALPHA on the off