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void | PTEQR (const char COMPZ, const OrdinalType n, ScalarType *D, ScalarType *E, ScalarType *Z, const OrdinalType ldz, ScalarType *WORK, OrdinalType *info) const |
| Computes the eigenvalues and, optionally, eigenvectors of a symmetric positive-definite tridiagonal n by n matrix A using BDSQR, after factoring the matrix with PTTRF.
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| LAPACK (void) |
| Default Constructor.
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| LAPACK (const LAPACK< OrdinalType, ScalarType > &lapack) |
| Copy Constructor.
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virtual | ~LAPACK (void) |
| Destructor.
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void | PTTRF (const OrdinalType n, ScalarType *d, ScalarType *e, OrdinalType *info) const |
| Computes the L*D*L' factorization of a Hermitian/symmetric positive definite tridiagonal matrix A .
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void | PTTRS (const OrdinalType n, const OrdinalType nrhs, const ScalarType *d, const ScalarType *e, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Solves a tridiagonal system A*X=B using the *D*L' factorization of A computed by PTTRF.
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void | POTRF (const char UPLO, const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *info) const |
| Computes Cholesky factorization of a real symmetric positive definite matrix A .
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void | POTRS (const char UPLO, const OrdinalType n, const OrdinalType nrhs, const ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Solves a system of linear equations A*X=B , where A is a symmetric positive definite matrix factored by POTRF and the nrhs solutions are returned in B .
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void | POTRI (const char UPLO, const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *info) const |
| Computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A from POTRF.
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void | POCON (const char UPLO, const OrdinalType n, const ScalarType *A, const OrdinalType lda, const ScalarType anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Estimates the reciprocal of the condition number (1-norm) of a real symmetric positive definite matrix A using the Cholesky factorization from POTRF.
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void | POSV (const char UPLO, const OrdinalType n, const OrdinalType nrhs, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Computes the solution to a real system of linear equations A*X=B , where A is a symmetric positive definite matrix and the nrhs solutions are returned in B .
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void | POEQU (const OrdinalType n, const ScalarType *A, const OrdinalType lda, MagnitudeType *S, MagnitudeType *scond, MagnitudeType *amax, OrdinalType *info) const |
| Computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (w.r.t. 2-norm).
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void | PORFS (const char UPLO, const OrdinalType n, const OrdinalType nrhs, const ScalarType *A, const OrdinalType lda, const ScalarType *AF, const OrdinalType ldaf, const ScalarType *B, const OrdinalType ldb, ScalarType *X, const OrdinalType ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and provides error bounds and backward error estimates for the solution.
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void | POSVX (const char FACT, const char UPLO, const OrdinalType n, const OrdinalType nrhs, ScalarType *A, const OrdinalType lda, ScalarType *AF, const OrdinalType ldaf, char EQUED, ScalarType *S, ScalarType *B, const OrdinalType ldb, ScalarType *X, const OrdinalType ldx, ScalarType *rcond, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Uses the Cholesky factorization to compute the solution to a real system of linear equations A*X=B , where A is symmetric positive definite. System can be equilibrated by POEQU and iteratively refined by PORFS, if requested.
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void | GELS (const char TRANS, const OrdinalType m, const OrdinalType n, const OrdinalType nrhs, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Solves an over/underdetermined real m by n linear system A using QR or LQ factorization of A.
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void | GELSS (const OrdinalType m, const OrdinalType n, const OrdinalType nrhs, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, MagnitudeType *S, const MagnitudeType rcond, OrdinalType *rank, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *info) const |
| Use the SVD to solve a possibly rank-deficient linear least-squares problem. More...
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void | GELSS (const OrdinalType m, const OrdinalType n, const OrdinalType nrhs, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, ScalarType *S, const ScalarType rcond, OrdinalType *rank, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Legacy GELSS interface for real-valued ScalarType.
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void | GGLSE (const OrdinalType m, const OrdinalType n, const OrdinalType p, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, ScalarType *C, ScalarType *D, ScalarType *X, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Solves the linear equality-constrained least squares (LSE) problem where A is an m by n matrix,B is a p by n matrix C is a given m-vector , and D is a given p-vector .
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void | GEQRF (const OrdinalType m, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *TAU, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Computes a QR factorization of a general m by n matrix A .
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void | GETRF (const OrdinalType m, const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *IPIV, OrdinalType *info) const |
| Computes an LU factorization of a general m by n matrix A using partial pivoting with row interchanges.
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void | GETRS (const char TRANS, const OrdinalType n, const OrdinalType nrhs, const ScalarType *A, const OrdinalType lda, const OrdinalType *IPIV, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Solves 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 GETRF.
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void | LASCL (const char TYPE, const OrdinalType kl, const OrdinalType ku, const MagnitudeType cfrom, const MagnitudeType cto, const OrdinalType m, const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *info) const |
| Multiplies the m by n matrix A by the real scalar cto/cfrom .
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void | GEQP3 (const OrdinalType m, const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *jpvt, ScalarType *TAU, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *info) const |
| Computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.
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void | LASWP (const OrdinalType N, ScalarType A[], const OrdinalType LDA, const OrdinalType K1, const OrdinalType K2, const OrdinalType IPIV[], const OrdinalType INCX) const |
| Apply a series of row interchanges to the matrix A.
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void | GBTRF (const OrdinalType m, const OrdinalType n, const OrdinalType kl, const OrdinalType ku, ScalarType *A, const OrdinalType lda, OrdinalType *IPIV, OrdinalType *info) const |
| Computes an LU factorization of a general banded m by n matrix A using partial pivoting with row interchanges.
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void | GBTRS (const char TRANS, const OrdinalType n, const OrdinalType kl, const OrdinalType ku, const OrdinalType nrhs, const ScalarType *A, const OrdinalType lda, const OrdinalType *IPIV, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Solves a system of linear equations A*X=B or A'*X=B with a general banded n by n matrix A using the LU factorization computed by GBTRF.
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void | GTTRF (const OrdinalType n, ScalarType *dl, ScalarType *d, ScalarType *du, ScalarType *du2, OrdinalType *IPIV, OrdinalType *info) const |
| Computes an LU factorization of a n by n tridiagonal matrix A using partial pivoting with row interchanges.
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void | GTTRS (const char TRANS, const OrdinalType n, const OrdinalType nrhs, const ScalarType *dl, const ScalarType *d, const ScalarType *du, const ScalarType *du2, const OrdinalType *IPIV, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Solves a system of linear equations A*X=B or A'*X=B or A^H*X=B with a tridiagonal matrix A using the LU factorization computed by GTTRF.
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void | GETRI (const OrdinalType n, ScalarType *A, const OrdinalType lda, const OrdinalType *IPIV, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Computes the inverse of a matrix A using the LU factorization computed by GETRF.
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void | LATRS (const char UPLO, const char TRANS, const char DIAG, const char NORMIN, const OrdinalType N, ScalarType *A, const OrdinalType LDA, ScalarType *X, MagnitudeType *SCALE, MagnitudeType *CNORM, OrdinalType *INFO) const |
| Robustly solve a possibly singular triangular linear system. More...
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void | GECON (const char NORM, const OrdinalType n, const ScalarType *A, const OrdinalType lda, const ScalarType anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Estimates 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 GETRF.
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void | GBCON (const char NORM, const OrdinalType n, const OrdinalType kl, const OrdinalType ku, const ScalarType *A, const OrdinalType lda, OrdinalType *IPIV, const ScalarType anorm, ScalarType *rcond, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Estimates the reciprocal of the condition number of a general banded real matrix A , in either the 1-norm or the infinity-norm, using the LU factorization computed by GETRF.
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ScalarTraits< ScalarType >
::magnitudeType | LANGB (const char NORM, const OrdinalType n, const OrdinalType kl, const OrdinalType ku, const ScalarType *A, const OrdinalType lda, MagnitudeType *WORK) const |
| Returns 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.
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void | GESV (const OrdinalType n, const OrdinalType nrhs, ScalarType *A, const OrdinalType lda, OrdinalType *IPIV, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Computes the solution to a real system of linear equations A*X=B , where A is factored through GETRF and the nrhs solutions are computed through GETRS.
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void | GEEQU (const OrdinalType m, const OrdinalType n, const ScalarType *A, const OrdinalType lda, MagnitudeType *R, MagnitudeType *C, MagnitudeType *rowcond, MagnitudeType *colcond, MagnitudeType *amax, OrdinalType *info) const |
| Computes row and column scalings intended to equilibrate an m by n matrix A and reduce its condition number.
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void | GERFS (const char TRANS, const OrdinalType n, const OrdinalType nrhs, const ScalarType *A, const OrdinalType lda, const ScalarType *AF, const OrdinalType ldaf, const OrdinalType *IPIV, const ScalarType *B, const OrdinalType ldb, ScalarType *X, const OrdinalType ldx, MagnitudeType *FERR, MagnitudeType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. Use after GETRF/GETRS.
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void | GBEQU (const OrdinalType m, const OrdinalType n, const OrdinalType kl, const OrdinalType ku, const ScalarType *A, const OrdinalType lda, MagnitudeType *R, MagnitudeType *C, MagnitudeType *rowcond, MagnitudeType *colcond, MagnitudeType *amax, OrdinalType *info) const |
| Computes row and column scalings intended to equilibrate an m by n banded matrix A and reduce its condition number.
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void | GBRFS (const char TRANS, const OrdinalType n, const OrdinalType kl, const OrdinalType ku, const OrdinalType nrhs, const ScalarType *A, const OrdinalType lda, const ScalarType *AF, const OrdinalType ldaf, const OrdinalType *IPIV, const ScalarType *B, const OrdinalType ldb, ScalarType *X, const OrdinalType ldx, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Improves the computed solution to a banded system of linear equations and provides error bounds and backward error estimates for the solution. Use after GBTRF/GBTRS.
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void | GESVX (const char FACT, const char TRANS, const OrdinalType n, const OrdinalType nrhs, ScalarType *A, const OrdinalType lda, ScalarType *AF, const OrdinalType ldaf, OrdinalType *IPIV, char EQUED, ScalarType *R, ScalarType *C, ScalarType *B, const OrdinalType ldb, ScalarType *X, const OrdinalType ldx, ScalarType *rcond, ScalarType *FERR, ScalarType *BERR, ScalarType *WORK, OrdinalType *IWORK, OrdinalType *info) const |
| Uses the LU factorization to compute the solution to a real system of linear equations A*X=B , returning error bounds on the solution and a condition estimate.
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void | SYTRD (const char UPLO, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *D, ScalarType *E, ScalarType *TAU, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Reduces a real symmetric matrix A to tridiagonal form by orthogonal similarity transformations. More...
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void | GEHRD (const OrdinalType n, const OrdinalType ilo, const OrdinalType ihi, ScalarType *A, const OrdinalType lda, ScalarType *TAU, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Reduces a real general matrix A to upper Hessenberg form by orthogonal similarity transformations.
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void | TRTRS (const char UPLO, const char TRANS, const char DIAG, const OrdinalType n, const OrdinalType nrhs, const ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, OrdinalType *info) const |
| Solves a triangular linear system of the form A*X=B or A**T*X=B , where A is a triangular matrix.
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void | TRTRI (const char UPLO, const char DIAG, const OrdinalType n, const ScalarType *A, const OrdinalType lda, OrdinalType *info) const |
| Computes the inverse of an upper or lower triangular matrix A .
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void | SPEV (const char JOBZ, const char UPLO, const OrdinalType n, ScalarType *AP, ScalarType *W, ScalarType *Z, const OrdinalType ldz, ScalarType *WORK, OrdinalType *info) const |
| Computes the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A in packed storage. More...
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void | SYEV (const char JOBZ, const char UPLO, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *W, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Computes all the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix A. More...
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void | SYGV (const OrdinalType itype, const char JOBZ, const char UPLO, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, ScalarType *W, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Computes all the eigenvalues and, optionally, eigenvectors of a symmetric n by n matrix pencil {A ,B}, where A is symmetric and B is symmetric positive-definite. More...
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void | HEEV (const char JOBZ, const char UPLO, const OrdinalType n, ScalarType *A, const OrdinalType lda, MagnitudeType *W, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *info) const |
| Computes all the eigenvalues and, optionally, eigenvectors of a Hermitian n by n matrix A. More...
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void | HEGV (const OrdinalType itype, const char JOBZ, const char UPLO, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, MagnitudeType *W, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *info) const |
| Computes all the eigenvalues and, optionally, eigenvectors of a generalized Hermitian-definite n by n matrix pencil {A ,B}, where A is Hermitian and B is Hermitian positive-definite. More...
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void | STEQR (const char COMPZ, const OrdinalType n, ScalarType *D, ScalarType *E, ScalarType *Z, const OrdinalType ldz, ScalarType *WORK, OrdinalType *info) const |
| Computes the eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal n by n matrix A using implicit QL/QR. The eigenvectors can only be computed if A was reduced to tridiagonal form by SYTRD.
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void | HSEQR (const char JOB, const char COMPZ, const OrdinalType n, const OrdinalType ilo, const OrdinalType ihi, ScalarType *H, const OrdinalType ldh, ScalarType *WR, ScalarType *WI, ScalarType *Z, const OrdinalType ldz, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Computes the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition, where T is an upper quasi-triangular matrix and Z contains the Schur vectors.
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void | GEES (const char JOBVS, const char SORT, OrdinalType(*ptr2func)(ScalarType *, ScalarType *), const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *sdim, ScalarType *WR, ScalarType *WI, ScalarType *VS, const OrdinalType ldvs, ScalarType *WORK, const OrdinalType lwork, OrdinalType *BWORK, OrdinalType *info) const |
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void | GEES (const char JOBVS, const char SORT, OrdinalType(*ptr2func)(ScalarType *), const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *sdim, ScalarType *W, ScalarType *VS, const OrdinalType ldvs, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *BWORK, OrdinalType *info) const |
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void | GEES (const char JOBVS, const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType *sdim, MagnitudeType *WR, MagnitudeType *WI, ScalarType *VS, const OrdinalType ldvs, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *BWORK, OrdinalType *info) const |
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void | GEEV (const char JOBVL, const char JOBVR, const OrdinalType n, ScalarType *A, const OrdinalType lda, MagnitudeType *WR, MagnitudeType *WI, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *info) const |
| Computes for an n by n real nonsymmetric matrix A , the eigenvalues and, optionally, the left and/or right eigenvectors. More...
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void | GEEVX (const char BALANC, const char JOBVL, const char JOBVR, const char SENSE, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *WR, ScalarType *WI, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *SCALE, MagnitudeType *abnrm, MagnitudeType *RCONDE, MagnitudeType *RCONDV, ScalarType *WORK, const OrdinalType lwork, OrdinalType *IWORK, OrdinalType *info) const |
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void | GGEVX (const char BALANC, const char JOBVL, const char JOBVR, const char SENSE, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType *BETA, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, OrdinalType *ilo, OrdinalType *ihi, MagnitudeType *lscale, MagnitudeType *rscale, MagnitudeType *abnrm, MagnitudeType *bbnrm, MagnitudeType *RCONDE, MagnitudeType *RCONDV, ScalarType *WORK, const OrdinalType lwork, OrdinalType *IWORK, OrdinalType *BWORK, OrdinalType *info) const |
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void | GGEV (const char JOBVL, const char JOBVR, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, ScalarType *BETA, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
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void | TRSEN (const char JOB, const char COMPQ, const OrdinalType *SELECT, const OrdinalType n, ScalarType *T, const OrdinalType ldt, ScalarType *Q, const OrdinalType ldq, MagnitudeType *WR, MagnitudeType *WI, OrdinalType *M, ScalarType *S, MagnitudeType *SEP, ScalarType *WORK, const OrdinalType lwork, OrdinalType *IWORK, const OrdinalType liwork, OrdinalType *info) const |
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void | TGSEN (const OrdinalType ijob, const OrdinalType wantq, const OrdinalType wantz, const OrdinalType *SELECT, const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType *Q, const OrdinalType ldq, ScalarType *Z, const OrdinalType ldz, OrdinalType *M, MagnitudeType *PL, MagnitudeType *PR, MagnitudeType *DIF, ScalarType *WORK, const OrdinalType lwork, OrdinalType *IWORK, const OrdinalType liwork, OrdinalType *info) const |
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void | GGES (const char JOBVL, const char JOBVR, const char SORT, OrdinalType(*ptr2func)(ScalarType *, ScalarType *, ScalarType *), const OrdinalType n, ScalarType *A, const OrdinalType lda, ScalarType *B, const OrdinalType ldb, OrdinalType *sdim, MagnitudeType *ALPHAR, MagnitudeType *ALPHAI, MagnitudeType *BETA, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, ScalarType *WORK, const OrdinalType lwork, OrdinalType *BWORK, OrdinalType *info) const |
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void | GESVD (const char JOBU, const char JOBVT, const OrdinalType m, const OrdinalType n, ScalarType *A, const OrdinalType lda, MagnitudeType *S, ScalarType *U, const OrdinalType ldu, ScalarType *V, const OrdinalType ldv, ScalarType *WORK, const OrdinalType lwork, MagnitudeType *RWORK, OrdinalType *info) const |
| Computes the singular values (and optionally, vectors) of a real matrix A .
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void | ORMQR (const char SIDE, const char TRANS, const OrdinalType m, const OrdinalType n, const OrdinalType k, ScalarType *A, const OrdinalType lda, const ScalarType *TAU, ScalarType *C, const OrdinalType ldc, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
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void | UNMQR (const char SIDE, const char TRANS, const OrdinalType m, const OrdinalType n, const OrdinalType k, ScalarType *A, const OrdinalType lda, const ScalarType *TAU, ScalarType *C, const OrdinalType ldc, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Apply Householder reflectors (complex case). More...
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void | ORGQR (const OrdinalType m, const OrdinalType n, const OrdinalType k, ScalarType *A, const OrdinalType lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Compute explicit Q factor from QR factorization (GEQRF) (real case). More...
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void | UNGQR (const OrdinalType m, const OrdinalType n, const OrdinalType k, ScalarType *A, const OrdinalType lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Compute explicit QR factor from QR factorization (GEQRF) (complex case). More...
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void | ORGHR (const OrdinalType n, const OrdinalType ilo, const OrdinalType ihi, ScalarType *A, const OrdinalType lda, const ScalarType *TAU, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Generates a real orthogonal matrix Q which is the product of ihi-ilo elementary reflectors of order n , as returned by GEHRD. On return Q is stored in A . More...
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void | ORMHR (const char SIDE, const char TRANS, const OrdinalType m, const OrdinalType n, const OrdinalType ilo, const OrdinalType ihi, const ScalarType *A, const OrdinalType lda, const ScalarType *TAU, ScalarType *C, const OrdinalType ldc, ScalarType *WORK, const OrdinalType lwork, OrdinalType *info) const |
| Overwrites the general real m by n matrix C with the product of C and Q , which is a product of ihi-ilo elementary reflectors, as returned by GEHRD. More...
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void | TREVC (const char SIDE, const char HOWMNY, OrdinalType *select, const OrdinalType n, const ScalarType *T, const OrdinalType ldt, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, const OrdinalType mm, OrdinalType *m, ScalarType *WORK, OrdinalType *info) const |
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void | TREVC (const char SIDE, const OrdinalType n, const ScalarType *T, const OrdinalType ldt, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, const OrdinalType mm, OrdinalType *m, ScalarType *WORK, MagnitudeType *RWORK, OrdinalType *info) const |
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void | TREXC (const char COMPQ, const OrdinalType n, ScalarType *T, const OrdinalType ldt, ScalarType *Q, const OrdinalType ldq, OrdinalType ifst, OrdinalType ilst, ScalarType *WORK, OrdinalType *info) const |
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void | TGEVC (const char SIDE, const char HOWMNY, const OrdinalType *SELECT, const OrdinalType n, ScalarType *S, const OrdinalType lds, ScalarType *P, const OrdinalType ldp, ScalarType *VL, const OrdinalType ldvl, ScalarType *VR, const OrdinalType ldvr, const OrdinalType mm, OrdinalType *M, ScalarType *WORK, OrdinalType *info) const |
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void | LARTG (const ScalarType f, const ScalarType g, MagnitudeType *c, ScalarType *s, ScalarType *r) const |
| Gnerates a plane rotation that zeros out the second component of the input vector.
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void | LARFG (const OrdinalType n, ScalarType *alpha, ScalarType *x, const OrdinalType incx, ScalarType *tau) const |
| Generates an elementary reflector of order n that zeros out the last n-1 components of the input vector.
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void | GEBAL (const char JOBZ, const OrdinalType n, ScalarType *A, const OrdinalType lda, OrdinalType ilo, OrdinalType ihi, MagnitudeType *scale, OrdinalType *info) const |
| Balances a general matrix A, through similarity transformations to make the rows and columns as close in norm as possible.
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void | GEBAK (const char JOBZ, const char SIDE, const OrdinalType n, const OrdinalType ilo, const OrdinalType ihi, const MagnitudeType *scale, const OrdinalType m, ScalarType *V, const OrdinalType ldv, OrdinalType *info) const |
| Forms the left or right eigenvectors of a general matrix that has been balanced by GEBAL by backward transformation of the computed eigenvectors V .
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ScalarType | LARND (const OrdinalType idist, OrdinalType *seed) const |
| Returns a random number from a uniform or normal distribution.
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void | LARNV (const OrdinalType idist, OrdinalType *seed, const OrdinalType n, ScalarType *v) const |
| Returns a vector of random numbers from a chosen distribution.
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ScalarType | LAMCH (const char CMACH) const |
| Determines machine parameters for floating point characteristics. More...
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OrdinalType | ILAENV (const OrdinalType ispec, const std::string &NAME, const std::string &OPTS, const OrdinalType N1=-1, const OrdinalType N2=-1, const OrdinalType N3=-1, const OrdinalType N4=-1) const |
| Chooses problem-dependent parameters for the local environment. More...
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ScalarType | LAPY2 (const ScalarType x, const ScalarType y) const |
| Computes x^2 + y^2 safely, to avoid overflow. More...
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