x. cgbsv cgbsv (3p) - 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 (3p) - 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 (3p) - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges cgbtrf cgbtrf (3p) - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges cgbtrs cgbtrs (3p) - 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 (3p) - 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 (3p) - balance a general complex matrix A cgebd2 cgebd2 (3p) - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation cgebrd cgebrd (3p) - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation cgeco cgeco (3p) - compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then xGEFA is slightly faster. It is typical to follow a call to xGECO with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant and inverse of A. cgecon cgecon (3p) - 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 cgedi cgedi (3p) - compute the determinant and inverse of a general matrix A, which has been LU-factored by xGECO or xGEFA. cgeequ cgeequ (3p) - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number cgees cgees (3p) - 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 (3p) - 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 (3p) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors cgeevx cgeevx (3p) - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors cgefa cgefa (3p) - compute the LU factorization of a general matrix A. It is typical to follow a call to xGEFA with a call to xGESL to solve Ax = b or to xGEDI to compute the determinant of A. cgegs cgegs (3p) - compute for a pair of N-by-N complex nonsymmetric matrices A, cgegv cgegv (3p) - compute for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, beta), and optionally, cgehd2 cgehd2 (3p) - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation cgehrd cgehrd (3p) - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation cgelq2 cgelq2 (3p) - compute an LQ factorization of a complex m by n matrix A cgelqf cgelqf (3p) - compute an LQ factorization of a complex M-by-N matrix A cgels cgels (3p) - 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 (3p) - compute the minimum norm solution to a complex linear least squares problem cgelsx cgelsx (3p) - compute the minimum-norm solution to a complex linear least squares problem cgemm cgemm (3p) - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C cgemv cgemv (3p) - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y cgeql2 cgeql2 (3p) - compute a QL factorization of a complex m by n matrix A cgeqlf cgeqlf (3p) - compute a QL factorization of a complex M-by-N matrix A cgeqpf cgeqpf (3p) - compute a QR factorization with column pivoting of a complex M-by-N matrix A cgeqr2 cgeqr2 (3p) - compute a QR factorization of a complex m by n matrix A cgeqrf cgeqrf (3p) - compute a QR factorization of a complex M-by-N matrix A cgerc cgerc (3p) - perform the rank 1 operation A := alpha*x*conjg( y' ) + A cgerfs cgerfs (3p) - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution cgerq2 cgerq2 (3p) - compute an RQ factorization of a complex m by n matrix A cgerqf cgerqf (3p) - compute an RQ factorization of a complex M-by-N matrix A cgeru cgeru (3p) - perform the rank 1 operation A := alpha*x*y' + A cgesl cgesl (3p) - solve the linear system Ax = b for a general matrix A, which has been LU- factored by xGECO or xGEFA, and vectors b and x. cgesv cgesv (3p) - compute the solution to a complex system of linear equations A * X = B, cgesvd cgesvd (3p) - 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 (3p) - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, cgetf2 cgetf2 (3p) - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges cgetrf cgetrf (3p) - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges cgetri cgetri (3p) - compute the inverse of a matrix using the LU factorization computed by CGETRF cgetrs cgetrs (3p) - 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 (3p) - 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 (3p) - balance a pair of general complex matrices (A,B) cggglm cggglm (3p) - solve a general Gauss-Markov linear model (GLM) problem cgghrd cgghrd (3p) - 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 (3p) - solve the linear equality-constrained least squares (LSE) problem cggqrf cggqrf (3p) - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B cggrqf cggrqf (3p) - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B cggsvd cggsvd (3p) - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B cggsvp cggsvp (3p) - 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 (3p) - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF cgtrfs cgtrfs (3p) - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution cgtsl cgtsl (3p) - solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x. cgtsv cgtsv (3p) - solve the equation A*X = B, cgtsvx cgtsvx (3p) - 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 (3p) - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges cgttrs cgttrs (3p) - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, chbev chbev (3p) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A chbevd chbevd (3p) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A chbevx chbevx (3p) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A chbgst chbgst (3p) - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, chbgv chbgv (3p) - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x chbmv chbmv (3p) - perform the matrix-vector operation y := alpha*A*x + beta*y chbtrd chbtrd (3p) - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation checon checon (3p) - 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 (3p) - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A cheevd cheevd (3p) - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A cheevx cheevx (3p) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A chegs2 chegs2 (3p) - reduce a complex Hermitian-definite generalized eigenproblem to standard form chegst chegst (3p) - reduce a complex Hermitian-definite generalized eigenproblem to standard form chegv chegv (3p) - 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 chemm chemm (3p) - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C chemv chemv (3p) - perform the matrix-vector operation y := alpha*A*x + beta*y cher cher (3p) - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A cher2 cher2 (3p) - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A cher2k cher2k (3p) - perform one of the Hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C cherfs cherfs (3p) - 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 cherk cherk (3p) - perform one of the Hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A + beta*C chesv chesv (3p) - compute the solution to a complex system of linear equations A * X = B, chesvx chesvx (3p) - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B, chetd2 chetd2 (3p) - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation chetf2 chetf2 (3p) - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method chetrd chetrd (3p) - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation chetrf chetrf (3p) - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method chetri chetri (3p) - 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 (3p) - 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 chico chico (3p) - compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. chidi chidi (3p) - compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA. chifa chifa (3p) - compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to xHIFA with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A. chisl chisl (3p) - solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by xHICO or xHIFA, and vectors b and x. chpco chpco (3p) - compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. chpcon chpcon (3p) - 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 chpdi chpdi (3p) - compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA. chpev chpev (3p) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage chpevd chpevd (3p) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage chpevx chpevx (3p) - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage chpfa chpfa (3p) - compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to xHPFA with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A. chpgst chpgst (3p) - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage chpgv chpgv (3p) - 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 chpmv chpmv (3p) - perform the m