| *2st_kernels | | — | Is an internal routine used by the DSYTRD_SB2ST subroutine. |
| *_gbamv | | 100% | Performs a matrix-vector operation to calculate error bounds. |
| dla_gbrcond | | 100% | Estimates the Skeel condition number for a general banded matrix. |
| zla_gbrcond_c | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*inv(diag(c)) for general banded matrices. |
| zla_gbrcond_x | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*diag(x) for general banded matrices. |
| *_gbrfsx_extended | | 95% | Improves the computed solution to a general banded system using extra-precise iterative refinement. |
| *_gbrpvgrw | | 62% | Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. |
| *_geamv | | 99% | Computes a matrix-vector product using a general matrix to calculate error bounds. |
| dla_gercond | | 100% | Estimates the Skeel condition number for a general matrix. |
| zla_gercond_c | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*inv(diag(c)) for general matrices. |
| zla_gercond_x | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*diag(x) for general matrices. |
| *_gerfsx_extended | | 97% | Improves the computed solution to a general system using extra-precise iterative refinement. |
| *_gerpvgrw | | 57% | Computes the reciprocal pivot growth factor norm(A)/norm(U). |
| zla_heamv | | 100% | Computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds. |
| zla_hercond_c | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*inv(diag(c)) for Hermitian indefinite matrices. |
| zla_hercond_x | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*diag(x) for Hermitian indefinite matrices. |
| zla_herfsx_extended | | 97% | Improves the computed solution to a Hermitian indefinite system using extra-precise iterative refinement. |
| zla_herpvgrw | | 20% | Computes the reciprocal pivot growth factor norm(A)/norm(U). |
| *_lin_berr | | 100% | Computes a component-wise relative backward error. |
| dla_porcond | | 100% | Estimates the Skeel condition number for a symmetric positive-definite matrix. |
| zla_porcond_c | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*inv(diag(c)) for Hermitian positive-definite matrices. |
| zla_porcond_x | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*diag(x) for Hermitian positive-definite matrices. |
| *_porfsx_extended | | 96% | Improves the computed solution to a positive definite system using extra-precise iterative refinement. |
| *_porpvgrw | | 30% | Computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. |
| *_syamv | | 99% | Computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. |
| dla_syrcond | | 100% | Estimates the Skeel condition number for a symmetric indefinite matrix. |
| zla_syrcond_c | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*inv(diag(c)) for symmetric indefinite matrices. |
| zla_syrcond_x | | 100% | Computes the infinity norm condition number of \(\operatorname{op}(A)\)*diag(x) for symmetric indefinite matrices. |
| *_syrfsx_extended | | — | Improves the computed solution to a symmetric indefinite system using extra-precise iterative refinement. |
| *_syrpvgrw | | 18% | Computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix. |
| *_wwaddw | | 100% | Adds a vector into a doubled-single vector. |
| izmax1 | | 100% | Finds the index of the first vector element of maximum absolute value. |
| dlabad | | 100% | Is a no-op and kept for compatibility reasons. |
| *bak | | 95% | Forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL. |
| *bal | | 97% | Balances a general real matrix A. |
| *bd2 | | 100% | Reduces a general matrix to bidiagonal form using an unblocked algorithm. |
| *bdb | | — | Simultaneously bidiagonalizes the blocks of a partitioned orthogonal/unitary matrix (CS decomposition driver). |
| *bdb1 | | — | Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns (case 1). |
| *bdb2 | | — | Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns (case 2). |
| *bdb3 | | — | Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns (case 3). |
| *bdb4 | | — | Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns (case 4). |
| *bdb5 | | — | Orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] . |
| *bdb6 | | — | Orthogonalizes the column vector X = [ X1 ] [ X2 ] with respect to the columns of Q = [ Q1 ] . |
| *brd | | 74% | Reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation: \(Q^TAP = B\). |
| zcgesv | | — | Computes the solution to a system of linear equations using mixed-precision iterative refinement. |
| zlacgv | | 100% | Conjugates a complex vector. |
| ilaclc | | — | Scans a matrix for its last non-zero column. |
| ilaclr | | — | Scans a matrix for its last non-zero row. |
| *cn2 | | 60% | Estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. |
| *con | | 63% | Estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGBTRF. |
| *con_3 | | — | Estimates the reciprocal of the condition number using the bounded Bunch-Kaufman factorization. |
| *con_rook | | — | Estimates the reciprocal of the condition number using rook pivoting. |
| *conv | | 95% | Convert A given by TRF into L and D and vice-versa. |
| *convf | | 100% | Converts between factorization storage formats for symmetric/Hermitian indefinite factorizations. |
| *convf_rook | | 98% | Converts between factorization storage formats for rook-pivoted symmetric/Hermitian indefinite factorizations. |
| zlacp2 | | 100% | Copies all or part of a real two-dimensional array to a complex array. |
| zcposv | | — | Computes the solution to a positive definite system using mixed-precision iterative refinement. |
| *cpy | | 100% | Copies all or part of one two-dimensional array to another. |
| zlacrm | | — | Multiplies a complex matrix by a square real matrix. |
| zlacrt | | 100% | Performs a linear transformation of a pair of complex vectors. |
| *csd | | — | Computes the CS decomposition of a partitioned orthogonal/unitary matrix. |
| *csd2by1 | | — | Computes the CS decomposition of an M-by-Q matrix with orthonormal columns partitioned into a 2-by-1 block structure. |
| iladiag | | — | This subroutine translated from a character string specifying if a matrix has unit diagonal or not to the relevant BLAST-specified integer constant. |
| *div | | 100% | Performs complex division in real arithmetic, avoiding unnecessary overflow. |
| iladlc | | 100% | Scans a matrix for its last non-zero column. |
| iladlr | | 100% | Scans a matrix for its last non-zero row. |
| *dmd | | — | Computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices. |
| *dmdq | | — | Computes the Dynamic Mode Decomposition (DMD) for a pair of data snapshot matrices. |
| dlae2 | | 100% | Computes the eigenvalues of a 2-by-2 symmetric matrix. |
| *ebz | | 56% | Computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the routine sstebz. |
| *ed0 | | — | Used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. |
| dlaed1 | | — | Used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal. |
| dlaed2 | | 95% | Used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal. |
| dlaed3 | | — | Used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. |
| dlaed4 | | — | Used by DSTEDC. Finds a single root of the secular equation. |
| dlaed5 | | 100% | Used by DSTEDC. Solves the 2-by-2 secular equation. |
| dlaed6 | | 94% | Used by DSTEDC. Computes one Newton step in solution of the secular equation. |
| *ed7 | | — | Used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. |
| *ed8 | | — | Used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. |
| dlaed9 | | — | Used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense. |
| dlaeda | | — | Used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. |
| *edc | | — | Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. |
| ieeeck | | — | Is called from the ILAENV to verify that Infinity and possibly NaN arithmetic is safe (i.e. will not trap). |
| *egr | | — | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T. |
| *ein | | 52% | Uses inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H. |
| *emr | | — | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T. |
| ilaenv | | — | Is called from the LAPACK routines to choose problem-dependent parameters for the local environment. |
| ilaenv2stage | | — | Is called from the LAPACK routines to choose problem-dependent parameters for the local environment. |
| *eqr | | 93% | Computes the eigenvalues of a 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. |
| *equ | | 99% | Computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number. |
| *equb | | — | Computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. |
| *eqz | | 86% | Computes the eigenvalues of a real matrix pair (H,T), where H is an upper Hessenberg matrix and T is upper triangular, using the double-shift QZ method. |
| xerbla | | — | Is an error handler for the LAPACK routines. |
| xerbla_array | | — | Assists other languages in calling XERBLA, the LAPACK and BLAS error handler. |
| dsterf | | 93% | Computes all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm. |
| *es | | 73% | Computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices |
| *es3 | | — | Computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices (blocked algorithm) |
| *esx | | — | Computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE matrices |
| zlaesy | | 100% | Computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. |
| *ev | | 95% | Computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices |
| *ev2 | | 100% | Computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. |
| *ev3 | | — | Computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm) |
| *ev_2stage | | — | Computes eigenvalues and optionally eigenvectors (2-stage algorithm). |
| *evc | | 92% | Computes some or all of the right and/or left eigenvectors of a pair of real matrices (S,P), where S is a quasi-triangular matrix and P is upper triangular. |
| *evc3 | | 92% | Computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. |
| *evd | | — | Computes eigenvalues and optionally eigenvectors using divide and conquer. |
| *evd_2stage | | — | Computes eigenvalues and optionally eigenvectors using divide and conquer (2-stage algorithm). |
| *evr | | 94% | Computes eigenvalues and optionally eigenvectors using the MRRR algorithm. |
| *evr_2stage | | — | Computes eigenvalues and optionally eigenvectors using the MRRR algorithm (2-stage). |
| *evx | | 85% | Computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices |
| *evx_2stage | | — | Computes selected eigenvalues and optionally eigenvectors (2-stage algorithm). |
| *ex2 | | 97% | Swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an orthogonal equivalence transformation. |
| *exc | | 85% | Swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. |
| dlag2 | | 99% | Computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. |
| zlag2c | | 100% | Converts a complex double precision matrix to a complex single precision matrix. |
| *g2l | | 100% | Generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). |
| *g2r | | 100% | Generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). |
| dlag2s | | 100% | Converts a double precision matrix to a single precision matrix. |
| *gbr | | 100% | Generates one of the real orthogonal matrices Q or \(P^T\) determined by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q * B * \(P^T\). |
| *ghr | | 100% | Generates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD: Q = H(ilo) H(ilo+1) . |
| *gl2 | | 100% | Generates an m by n real matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n Q = H(k) . |
| *glm | | — | Solves a general Gauss-Markov linear model (GLM) problem. |
| *glq | | 100% | Generates an M-by-N real matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k) . |
| *gql | | 81% | Generates an M-by-N real matrix Q with orthonormal columns, which is defined as the last N columns of a product of K elementary reflectors of order M Q = H(k) . |
| *gqr | | 100% | Generates an M-by-N real matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2) . |
| *gr2 | | 100% | Generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). |
| *grq | | — | Generates an M-by-N real matrix Q with orthonormal rows, which is defined as the last M rows of a product of K elementary reflectors of order N Q = H(1) H(2) . |
| *gs2 | | 99% | Computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel. |
| *gst | | 92% | Reduces a real symmetric-definite banded generalized eigenproblem A*x = \(\lambda\)*B*x to standard form C*y = \(\lambda\)*y, such that C has the same bandwidth as A. |
| dlagtf | | 93% | Computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix, and λ a scalar, using partial pivoting with row interchanges. |
| *gtm | | 99% | Performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. |
| *gtr | | 100% | Generates 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: if UPLO = 'U', Q = H(n-1) . |
| dlagts | | 77% | Solves the system of equations (T-λI)x = y |
| *gtsqr | | — | Generates an M-by-N real matrix Q_out with orthonormal columns, which are the first N columns of a product of real orthogonal matrices of order M which are returned by DLATSQR Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ). |
| *gtsqr_row | | — | Generates an M-by-N real matrix Q_out with orthonormal columns from the output of DLATSQR. |
| *gv | | 98% | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form \(Ax=\lambda\,Bx\). |
| dlagv2 | | 100% | Computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. |
| *gv_2stage | | — | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form \(Ax=\lambda\,Bx\), A*Bx=(\(\lambda\))*x, or B*A*x=(\(\lambda\))*x. |
| *gvd | | — | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form \(Ax=\lambda\,Bx\). |
| *gvx | | 96% | Computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form \(Ax=\lambda\,Bx\). |
| *hd2 | | 100% | Reduces a general square matrix to upper Hessenberg form using an unblocked algorithm. |
| *hd3 | | — | Reduces 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. |
| zlahef | | 94% | Computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). |
| zlahef_aa | | — | DLAHEF_AA factorizes a panel of a complex hermitian matrix A using the Aasen's algorithm. |
| zlahef_rk | | — | Computes a partial factorization of a complex Hermitian indefinite matrix using bounded Bunch-Kaufman (rook) diagonal pivoting method. |
| zlahef_rook | | — | Computes a partial factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). |
| *hqr | | 95% | Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. |
| *hr2 | | 100% | Reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. |
| *hr_col | | — | Takes an M-by-N real matrix Q_in with orthonormal columns as input, stored in A, and performs Householder Reconstruction (HR), i.e. |
| *hrd | | 100% | Reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: \(Q^TAQ = H\) . |
| *ic1 | | 100% | Applies one step of incremental condition estimation. |
| *isnan | | 100% | Tests input for NaN. |
| *jsv | | — | Computes the singular value decomposition (SVD) of a real M-by-N matrix [A], where M >= N. |
| dlaln2 | | 84% | Solves a 1-by-1 or 2-by-2 linear system of equations of the specified form. |
| *lq | | — | Computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N. |
| *lq2 | | 100% | Computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. |
| *lqf | | 100% | Computes an LQ factorization of a real M-by-N matrix A: A = ( L 0 ) * Q where: Q is a N-by-N orthogonal matrix; L is a lower-triangular M-by-M matrix; 0 is a M-by-(N-M) zero matrix, if M < N. |
| *lqt | | — | Computes a blocked LQ factorization of a real M-by-N matrix A using the compact WY representation of Q. |
| *lqt2 | | — | Computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. |
| *lqt3 | | — | Recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q. |
| *ls | | 98% | Solves overdetermined or underdetermined systems for GE matrices |
| *ls0 | | — | Applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. |
| *lsa | | — | Computes the SVD of the coefficient matrix in compact form. Used by sgelsd. |
| *lsd | | — | Computes the minimum-norm solution to a linear least squares problem for GE matrices |
| *lse | | — | Solves overdetermined or underdetermined systems for OTHER matrices |
| *lss | | 58% | Solves overdetermined or underdetermined systems for GE matrices |
| *lst | | — | Solves overdetermined or underdetermined systems for GE matrices using QR or LQ factorization with compact WY representation of Q. |
| *lsy | | — | Solves overdetermined or underdetermined systems for GE matrices |
| *m22 | | 100% | Multiplies a general matrix by a banded orthogonal matrix. |
| *m2l | | 100% | Multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). |
| *m2r | | 100% | Multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm). |
| *mbr | | 100% | Multiplies a general matrix by the orthogonal/unitary matrix Q or P from a bidiagonal reduction. |
| *mhr | | 100% | Multiplies a general matrix by the orthogonal/unitary matrix Q from a Hessenberg reduction. |
| *ml2 | | 100% | Multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). |
| *mlq | | 99% | Multiplies a general matrix by the orthogonal/unitary matrix Q from an LQ factorization. |
| *mlqt | | — | Multiplies a general matrix by the orthogonal/unitary matrix Q from a blocked LQ factorization. |
| *mql | | 99% | Multiplies a general matrix by the orthogonal/unitary matrix Q from a QL factorization. |
| *mqr | | 99% | Multiplies a general matrix by the orthogonal/unitary matrix Q from a QR factorization. |
| *mqrt | | — | Multiplies a general matrix by the orthogonal/unitary matrix Q from a blocked QR factorization. |
| *mr2 | | 100% | Multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm). |
| *mr3 | | — | Multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm). |
| dlamrg | | 100% | Creates a permutation list to merge the entries of two independently sorted sets into a single set sorted in ascending order. |
| *mrq | | 98% | Multiplies a general matrix by the orthogonal/unitary matrix Q from an RQ factorization. |
| *mrz | | — | Multiplies a general matrix by the orthogonal/unitary matrix Q from an RZ factorization. |
| *mswlq | | — | Multiplies a general matrix by the orthogonal/unitary matrix Q from a short-wide LQ factorization. |
| *mtr | | 100% | Multiplies a general matrix by the orthogonal/unitary matrix Q stored in a triangular factorization. |
| *mtsqr | | — | Multiplies a general matrix by the orthogonal/unitary matrix Q from a tall-skinny QR factorization. |
| *mv | | 100% | Computes a matrix-vector product for complex vectors using a complex symmetric packed matrix |
| *n | | 32% | Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. |
| dlaneg | | 100% | Computes the Sturm count. |
| zlanht | | 37% | Returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix. |
| dlanv2 | | 93% | Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. |
| dlaorhr_col_getrfnp | | — | Computes the modified LU factorization without pivoting of a real general M-by-N matrix A. |
| dlaorhr_col_getrfnp2 | | — | Computes the modified LU factorization without pivoting of a real general M-by-N matrix A. |
| dsposv | | — | Computes the solution to system of linear equations \(AX = B\) for PO matrices |
| iparmq | | — | This program sets problem and machine dependent parameters useful for xHSEQR and related subroutines for eigenvalue problems. |
| *pll | | 100% | Measures the linear dependence of two vectors. |
| *pmr | | 100% | Rearranges rows of a matrix as specified by a permutation vector. |
| *pmt | | 100% | Performs a forward or backward permutation of the columns of a matrix. |
| ilaprec | | — | This subroutine translated from a character string specifying an intermediate precision to the relevant BLAST-specified integer constant. |
| dlapy2 | | 100% | Returns \(\sqrt{x^2+y^2}\). |
| dlapy3 | | 100% | Returns \(\sqrt{x^2+y^2+z^2}\). |
| *qgb | | 100% | Scales a general band matrix, using row and column scaling factors computed by sgbequ. |
| *qge | | 100% | Scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. |
| zlaqhb | | 100% | Scales a Hermitian band matrix, using scaling factors computed by cpbequ. |
| zlaqhe | | 100% | Scales a Hermitian matrix. |
| zlaqhp | | 100% | Scales a Hermitian matrix stored in packed form. |
| *ql2 | | 100% | Computes the QL factorization of a general rectangular matrix using an unblocked algorithm. |
| *qlf | | 100% | Computes a QL factorization of a real M-by-N matrix A: A = Q * L. |
| *qp2 | | 99% | Computes a QR factorization with column pivoting of the matrix block. |
| *qp2rk | | — | Computes truncated QR factorization with column pivoting of a real matrix block using Level 2 BLAS and overwrites a real m-by-nrhs matrix B with \(Q^T\) * B. |
| *qp3 | | 100% | Computes a QR factorization with column pivoting of a matrix A: \(AP = Q\)*R using Level 3 BLAS. |
| *qp3rk | | — | Computes a truncated Householder QR factorization with column pivoting of a real m-by-n matrix A by using Level 3 BLAS and overwrites a real m-by-nrhs matrix B with \(Q^T\) * B. |
| *qps | | 98% | Computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. |
| *qr | | — | Computes a QR factorization of a real M-by-N matrix A: A = Q * ( R ), ( 0 ) where: Q is a M-by-M orthogonal matrix; R is an upper-triangular N-by-N matrix; 0 is a (M-N)-by-N zero matrix, if M > N. |
| *qr0 | | 81% | Computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. |
| *qr1 | | 100% | Sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. |
| *qr2 | | 97% | Computes the QR factorization of a general rectangular matrix using an unblocked algorithm. |
| *qr2p | | 100% | Computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm. |
| *qr3 | | 98% | Performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). |
| *qr4 | | 80% | Computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. |
| *qr5 | | 81% | Performs a single small-bulge multi-shift QR sweep. |
| *qrf | | 100% | Computes a QR factorization of a real M-by-N matrix A: A = Q * ( R ), ( 0 ) where: Q is a M-by-M orthogonal matrix; R is an upper-triangular N-by-N matrix; 0 is a (M-N)-by-N zero matrix, if M > N. |
| *qrfp | | 98% | Computes a QR factorization with non-negative diagonal entries. |
| *qrt | | — | Computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q. |
| *qrt2 | | — | Computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. |
| *qrt3 | | — | Recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. |
| *qsb | | 100% | Scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. |
| *qsp | | 100% | Scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. |
| *qsy | | 100% | Scales a symmetric/Hermitian matrix, using scaling factors computed by spoequ. |
| dlaqtr | | 17% | Solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic. |
| *qz0 | | — | Computes the eigenvalues of a real matrix pair (H,T), where H is an upper Hessenberg matrix and T is upper triangular, using the double-shift QZ method. |
| *qz1 | | — | Given a 3-by-3 matrix pencil (A,B), DLAQZ1 sets v to a scalar multiple of the first column of the product (*) K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1). |
| *qz2 | | — | Chases a 2x2 shift bulge in a matrix pencil down a single position |
| *qz3 | | — | Performs aggressive early deflation in the QZ algorithm. |
| dlaqz4 | | — | Executes a single multishift QZ sweep |
| *r | | 100% | Performs the symmetrical rank-1 update of a complex symmetric packed matrix. |
| *r1v | | — | Computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI. |
| *r2v | | 100% | Applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices. |
| zlarcm | | — | Copies all or part of a real two-dimensional array to a complex array. |
| *rf | | 100% | Applies an elementary reflector to a general rectangular matrix. |
| *rfb | | 61% | Applies a block reflector or its transpose to a general rectangular matrix. |
| *rfb_gett | | 100% | Applies a block Householder reflector to a triangular-pentagonal matrix. |
| *rfg | | 100% | Generates an elementary reflector (Householder matrix). |
| *rfgp | | 91% | Generates an elementary reflector (Householder matrix) with non-negative \(\beta\). |
| *rfs | | 95% | Improves 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. |
| *rfsx | | — | Improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. |
| *rft | | 100% | Forms the triangular factor T of a block reflector. |
| *rfx | | 98% | Applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. |
| *rfy | | 100% | Applies an elementary reflector, or Householder matrix, H, to an n x n symmetric matrix C, from both the left and the right. |
| *rgv | | 97% | Generates a vector of plane rotations with real cosines and real sines. |
| *rk | | 100% | Performs a symmetric rank-k operation for matrix in RFP format. |
| dlarmm | | 100% | Computes a scaling factor to prevent overflow in triangular matrix multiplication. |
| *rnv | | 100% | Returns a vector of random numbers from a uniform or normal distribution. |
| zrot | | 100% | Applies a plane rotation with real cosine and complex sine to a pair of complex vectors. |
| *rq2 | | 100% | Computes the RQ factorization of a general rectangular matrix using an unblocked algorithm. |
| *rqf | | 100% | Computes an RQ factorization of a real M-by-N matrix A: A = R * Q. |
| dlarra | | 54% | Computes the splitting points with the specified threshold. |
| dlarrb | | — | Provides limited bisection to locate eigenvalues for more accuracy. |
| dlarrc | | 99% | Computes the number of eigenvalues of the symmetric tridiagonal matrix. |
| dlarrd | | 80% | Computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy. |
| dlarre | | — | Given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each unreduced block Ti, finds base representations and eigenvalues. |
| dlarrf | | 64% | Finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. |
| dlarrj | | 100% | Performs refinement of the initial estimates of the eigenvalues of the matrix T. |
| dlarrk | | 98% | Computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. |
| dlarrr | | 100% | Performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues. |
| *rrv | | — | Computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. |
| *rscl | | 99% | Multiplies a vector by the reciprocal of a real scalar. |
| *rscl2 | | 100% | Performs reciprocal diagonal scaling on a matrix. |
| *rtg | | 98% | Generates a plane rotation with real cosine and real sine. |
| dlartgp | | 97% | Generates a plane rotation so that the diagonal is nonnegative. |
| dlartgs | | 76% | Generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem. |
| *rtv | | 100% | Applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. |
| dlaruv | | 99% | Returns a vector of n random real numbers from a uniform distribution. |
| *rz | | 99% | Applies an elementary reflector (as returned by stzrzf) to a general matrix. |
| *rzb | | — | Applies a block reflector or its transpose to a general matrix. |
| *rzf | | — | Reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. |
| *rzt | | 100% | Forms the triangular factor T of a block reflector H = I - vtvH. |
| dlas2 | | 100% | Computes singular values of a 2-by-2 triangular matrix. |
| lsamen | | — | Tests if the first N letters of CA are the same as the first N letters of CB, regardless of case. |
| *sc2 | | 97% | Solves a system of linear equations using the LU factorization with complete pivoting computed by sgetc2. |
| *scl | | 100% | Multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. |
| *scl2 | | 100% | Performs diagonal scaling on a matrix. |
| dlasd0 | | — | Computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc. |
| dlasd1 | | — | Computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc. |
| dlasd2 | | 98% | Merges the two sets of singular values together into a single sorted set. Used by sbdsdc. |
| dlasd3 | | — | Finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc. |
| dlasd4 | | — | Computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc. |
| dlasd5 | | 100% | Computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. |
| dlasd6 | | — | Computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by sbdsdc. |
| dlasd7 | | 98% | Merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc. |
| dlasd8 | | — | Finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. |
| dlasda | | — | Computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. |
| dbdsdc | | — | Computes the SVD of a bidiagonal matrix using a divide and conquer method. |
| *sdd | | — | Computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors. |
| dlasdq | | — | Computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. |
| dlasdt | | 100% | Creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc. |
| *sen | | 62% | Reorders the generalized Schur decomposition and computes reciprocal condition numbers. |
| *set | | 100% | Initializes the off-diagonal elements and the diagonal elements of a matrix to given values. |
| dsgesv | | — | Computes the solution to a system of linear equations using mixed-precision iterative refinement. |
| *sja | | 97% | Computes the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B. |
| ilaslc | | — | Scans a matrix for its last non-zero column. |
| ilaslr | | — | Scans a matrix for its last non-zero row. |
| *sm | | 100% | Solves a matrix equation (one operand is a triangular matrix in RFP format). |
| *sna | | 45% | Computes 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. |
| dlasq1 | | 91% | Computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. |
| dlasq2 | | 87% | Computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. |
| dlasq3 | | 90% | Checks for deflation, computes a shift and calls dqds. Used by sbdsqr. |
| dlasq4 | | 98% | Computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr. |
| dlasq5 | | 100% | Computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. |
| dlasq6 | | 100% | Computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr. |
| *sqr | | 95% | Computes singular values and vectors from the SVD of a bidiagonal matrix. |
| *sr | | 100% | Applies a sequence of plane rotations to a general rectangular matrix. |
| dlasrt | | 98% | Sorts numbers in increasing or decreasing order. |
| *ssq | | 100% | Updates a sum of squares represented in scaled form. |
| *stf | | 97% | Computes a split Cholesky factorization of a real symmetric positive definite band matrix A. |
| dzsum1 | | 100% | Forms the 1-norm of the complex vector using the true absolute value. |
| *sv | | 100% | Computes the solution to system of linear equations \(AX = B\) for GB matrices (simple driver) |
| dlasv2 | | 100% | Computes the singular value decomposition of a 2-by-2 triangular matrix. |
| *sv_aa | | — | Computes the solution to system of linear equations \(AX = B\) for SY matrices |
| *sv_aa_2stage | | — | Computes the solution to system of linear equations \(AX = B\) for SY matrices |
| *sv_rk | | — | Computes the solution to system of linear equations \(AX = B\) for SY matrices |
| *sv_rook | | — | Computes the solution to system of linear equations \(AX = B\) for SY matrices |
| *svd | | 99% | Computes the singular value decomposition (SVD) for GE matrices |
| *svd3 | | 98% | Computes the singular value decomposition (SVD) for OTHER matrices |
| *svdq | | — | Computes the singular value decomposition (SVD) with a QR-Preconditioned QR SVD Method for GE matrices |
| *svdx | | — | Computes selected singular values and vectors of a bidiagonal matrix. |
| *svj | | — | Computes the singular value decomposition (SVD) of a real M-by-N matrix A, where M >= N. |
| *svp3 | | 67% | Computes the generalized singular value decomposition (GSVD). |
| *svx | | 97% | Computes the solution to system of linear equations \(AX = B\) for GB matrices |
| *svxx | | — | Computes the solution to system of linear equations \(AX = B\) for GB matrices |
| *swapr | | 100% | Applies an elementary permutation on the rows and columns of a symmetric matrix. |
| *swlq | | — | Computes a blocked short-wide LQ factorization. |
| *swp | | 100% | Performs a series of row interchanges on a general rectangular matrix. |
| *sy2 | | 92% | Solves the Sylvester matrix equation where the matrices are of order 1 or 2. |
| *syf | | 92% | Computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method. |
| *syf_aa | | — | DLATRF_AA factorizes a panel of a real symmetric matrix A using the Aasen's algorithm. |
| *syf_rk | | — | Computes a partial factorization of a real symmetric indefinite matrix using bounded Bunch-Kaufman (rook) diagonal pivoting method. |
| *syf_rook | | — | Computes a partial factorization of a symmetric matrix using rook pivoting (blocked). |
| *syl | | 70% | Solves the generalized Sylvester equation. |
| *syl3 | | — | Solves the Sylvester matrix equation (blocked algorithm). |
| zlat2c | | 100% | Converts a double complex triangular matrix to a complex triangular matrix. |
| dlat2s | | 100% | Converts a double-precision triangular matrix to a single-precision triangular matrix. |
| *tbs | | 54% | Solves a triangular banded system of equations. |
| *tc2 | | 97% | Computes the LU factorization with complete pivoting of the general n-by-n matrix. |
| *td2 | | 100% | Reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm). |
| *tdf | | 99% | Uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. |
| *tf2 | | 98% | Computes the LU factorization of a general band matrix using the unblocked version of the algorithm. |
| *tf2_rk | | — | Computes the factorization of a real symmetric indefinite matrix using the bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS2 unblocked algorithm). |
| *tf2_rook | | — | Computes the factorization of a real symmetric indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm). |
| *ti2 | | 100% | Computes the inverse of a triangular matrix (unblocked algorithm). |
| *tps | | 18% | Solves a triangular system of equations with the matrix held in packed storage. |
| ilatrans | | — | This subroutine translates from a character string specifying a transposition operation to the relevant BLAST-specified integer constant. |
| *trd | | 97% | Reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation. |
| *trd_2stage | | — | Reduces a real symmetric matrix A to real symmetric tridiagonal form T by a orthogonal similarity transformation: Q1**T Q2**T* A * Q2 * Q1 = T. |
| zhetrd_he2hb | | — | Reduces a complex Hermitian matrix A to complex Hermitian band-diagonal form AB by a unitary similarity transformation: \(Q^H\) * A * Q = AB. |
| dsytrd_sy2sb | | — | Reduces a real symmetric matrix A to real symmetric band-diagonal form AB by a orthogonal similarity transformation: \(Q^T\) * A * Q = AB. |
| *trf | | 96% | Computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges. |
| *trf2 | | 100% | Computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. |
| *trf_aa | | — | Computes the factorization of a real symmetric matrix A using the Aasen's algorithm. |
| *trf_aa_2stage | | — | Computes the factorization of a real symmetric matrix A using the Aasen's algorithm. |
| *trf_rk | | — | Computes the factorization of a real symmetric indefinite matrix using the bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS3 blocked algorithm). |
| *trf_rook | | — | Computes the factorization of a real symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. |
| *tri | | 90% | Computes the inverse of a matrix using the LU factorization computed by DGETRF. |
| *tri2 | | — | Computes the inverse of a DOUBLE PRECISION symmetric indefinite matrix A using the factorization \(A = UDU^T\) or \(A = LDL^T\) computed by DSYTRF. |
| *tri2x | | — | Computes the inverse of a real symmetric indefinite matrix A using the factorization \(A = UDU^T\) or \(A = LDL^T\) computed by DSYTRF. |
| *tri_3 | | — | Computes the inverse of a symmetric/Hermitian indefinite matrix using the bounded Bunch-Kaufman factorization. |
| *tri_3x | | — | Computes the inverse of a symmetric/Hermitian indefinite matrix using the bounded Bunch-Kaufman factorization (expert). |
| *tri_rook | | — | Computes the inverse of a real symmetric matrix A using the factorization \(A = UDU^T\) or \(A = LDL^T\) computed by DSYTRF_ROOK. |
| *trs | | 98% | Solves a system of linear equations \(AX = B\) or \(A^TX = B\) with a general band matrix A using the LU factorization computed by DGBTRF. |
| *trs2 | | 97% | Solves a system of linear equations \(AX = B\) with a real symmetric matrix A using the factorization \(A = UDU^T\) or \(A = LDL^T\) computed by DSYTRF and converted by DSYCONV. |
| *trs3 | | — | Solves a triangular system of equations with the scale factors set to prevent overflow. |
| *trs_3 | | — | Solves a system of linear equations using the bounded Bunch-Kaufman factorization. |
| *trs_aa | | — | Solves a system of linear equations \(AX = B\) with a real symmetric matrix A using the factorization \(A = U^TTU\) or \(A = LTL^T\) computed by DSYTRF_AA. |
| *trs_aa_2stage | | — | Solves a system of linear equations \(AX = B\) with a real symmetric matrix A using the factorization \(A = U^TTU\) or \(A = LTL^T\) computed by DSYTRF_AA_2STAGE. |
| *trs_rook | | — | Solves a system of linear equations \(AX = B\) with a real symmetric matrix A using the factorization \(A = UDU^T\) or \(A = LDL^T\) computed by DSYTRF_ROOK. |
| *trz | | — | Factors an upper trapezoidal matrix by means of orthogonal transformations. |
| *ts2 | | 99% | Solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. |
| *tsls | | — | Solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, using a tall skinny QR or short wide LQ factorization of A. |
| *tsqr | | — | Computes a blocked tall-skinny QR factorization. |
| *tsqrhrt | | — | Computes an upper-triangular factor of an orthogonal/unitary matrix from a tall-skinny QR factorization. |
| *ttf | | 100% | Copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF). |
| *ttp | | 100% | Copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP). |
| *ttr | | 100% | Copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). |
| zlaunhr_col_getrfnp | | — | Computes the modified LU factorization without pivoting of a complex general M-by-N matrix A. |
| zlaunhr_col_getrfnp2 | | — | Computes the modified LU factorization without pivoting of a complex general M-by-N matrix A. |
| ilauplo | | — | This subroutine translated from a character string specifying a upper- or lower-triangular matrix to the relevant BLAST-specified integer constant. |
| *uu2 | | 100% | Computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm). |
| *uum | | 100% | Computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm). |
| *vj0 | | 59% | Pre-processor for the routine dgesvj. |
| *vj1 | | — | Pre-processor for the routine dgesvj, applies Jacobi rotations targeting only particular pivots. |
| ilazlc | | 100% | Scans a matrix for its last non-zero column. |
| ilazlr | | 100% | Scans a matrix for its last non-zero row. |