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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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Functions | |
subroutine | clatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info) |
CLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow. | |
subroutine | dlahrd (n, k, nb, a, lda, tau, t, ldt, y, ldy) |
DLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. | |
subroutine | dlabrd (m, n, nb, a, lda, d, e, tauq, taup, x, ldx, y, ldy) |
DLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. | |
subroutine | dlacn2 (n, v, x, isgn, est, kase, isave) |
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. | |
subroutine | dlacon (n, v, x, isgn, est, kase) |
DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. | |
subroutine | dladiv (a, b, c, d, p, q) |
DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. | |
subroutine | dladiv1 (a, b, c, d, p, q) |
double precision function | dladiv2 (a, b, c, d, r, t) |
subroutine | dlaein (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info) |
DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. | |
subroutine | dlaexc (wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info) |
DLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. | |
subroutine | dlag2 (a, lda, b, ldb, safmin, scale1, scale2, wr1, wr2, wi) |
DLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. | |
subroutine | dlag2s (m, n, a, lda, sa, ldsa, info) |
DLAG2S converts a double precision matrix to a single precision matrix. | |
subroutine | dlags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq) |
DLAGS2 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. | |
subroutine | dlagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb) |
DLAGTM 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. | |
subroutine | dlagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr) |
DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. | |
subroutine | dlahqr (wantt, wantz, n, ilo, ihi, h, ldh, wr, wi, iloz, ihiz, z, ldz, info) |
DLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. | |
subroutine | dlahr2 (n, k, nb, a, lda, tau, t, ldt, y, ldy) |
DLAHR2 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. | |
subroutine | dlaic1 (job, j, x, sest, w, gamma, sestpr, s, c) |
DLAIC1 applies one step of incremental condition estimation. | |
subroutine | dlaln2 (ltrans, na, nw, smin, ca, a, lda, d1, d2, b, ldb, wr, wi, x, ldx, scale, xnorm, info) |
DLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form. | |
double precision function | dlangt (norm, n, dl, d, du) |
DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. | |
double precision function | dlanhs (norm, n, a, lda, work) |
DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. | |
double precision function | dlansb (norm, uplo, n, k, ab, ldab, work) |
DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. | |
double precision function | dlansp (norm, uplo, n, ap, work) |
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form. | |
double precision function | dlantb (norm, uplo, diag, n, k, ab, ldab, work) |
DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix. | |
double precision function | dlantp (norm, uplo, diag, n, ap, work) |
DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. | |
double precision function | dlantr (norm, uplo, diag, m, n, a, lda, work) |
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. | |
subroutine | dlanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn) |
DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. | |
subroutine | dlapll (n, x, incx, y, incy, ssmin) |
DLAPLL measures the linear dependence of two vectors. | |
subroutine | dlapmr (forwrd, m, n, x, ldx, k) |
DLAPMR rearranges rows of a matrix as specified by a permutation vector. | |
subroutine | dlapmt (forwrd, m, n, x, ldx, k) |
DLAPMT performs a forward or backward permutation of the columns of a matrix. | |
subroutine | dlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) |
DLAQP2 computes a QR factorization with column pivoting of the matrix block. | |
subroutine | dlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) |
DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. | |
subroutine | dlaqr0 (wantt, wantz, n, ilo, ihi, h, ldh, wr, wi, iloz, ihiz, z, ldz, work, lwork, info) |
DLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. | |
subroutine | dlaqr1 (n, h, ldh, sr1, si1, sr2, si2, v) |
DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. | |
subroutine | dlaqr2 (wantt, wantz, n, ktop, kbot, nw, h, ldh, iloz, ihiz, z, ldz, ns, nd, sr, si, v, ldv, nh, t, ldt, nv, wv, ldwv, work, lwork) |
DLAQR2 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). | |
subroutine | dlaqr3 (wantt, wantz, n, ktop, kbot, nw, h, ldh, iloz, ihiz, z, ldz, ns, nd, sr, si, v, ldv, nh, t, ldt, nv, wv, ldwv, work, lwork) |
DLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). | |
subroutine | dlaqr4 (wantt, wantz, n, ilo, ihi, h, ldh, wr, wi, iloz, ihiz, z, ldz, work, lwork, info) |
DLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. | |
subroutine | dlaqr5 (wantt, wantz, kacc22, n, ktop, kbot, nshfts, sr, si, h, ldh, iloz, ihiz, z, ldz, v, ldv, u, ldu, nv, wv, ldwv, nh, wh, ldwh) |
DLAQR5 performs a single small-bulge multi-shift QR sweep. | |
subroutine | dlaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed) |
DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. | |
subroutine | dlaqsp (uplo, n, ap, s, scond, amax, equed) |
DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. | |
subroutine | dlaqtr (ltran, lreal, n, t, ldt, b, w, scale, x, work, info) |
DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic. | |
subroutine | dlar1v (n, b1, bn, lambda, d, l, ld, lld, pivmin, gaptol, z, wantnc, negcnt, ztz, mingma, r, isuppz, nrminv, resid, rqcorr, work) |
DLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI. | |
subroutine | dlar2v (n, x, y, z, incx, c, s, incc) |
DLAR2V 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. | |
subroutine | dlarf (side, m, n, v, incv, tau, c, ldc, work) |
DLARF applies an elementary reflector to a general rectangular matrix. | |
subroutine | dlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork) |
DLARFB applies a block reflector or its transpose to a general rectangular matrix. | |
subroutine | dlarfb_gett (ident, m, n, k, t, ldt, a, lda, b, ldb, work, ldwork) |
DLARFB_GETT | |
subroutine | dlarfg (n, alpha, x, incx, tau) |
DLARFG generates an elementary reflector (Householder matrix). | |
subroutine | dlarfgp (n, alpha, x, incx, tau) |
DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. | |
subroutine | dlarft (direct, storev, n, k, v, ldv, tau, t, ldt) |
DLARFT forms the triangular factor T of a block reflector H = I - vtvH | |
subroutine | dlarfx (side, m, n, v, tau, c, ldc, work) |
DLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. | |
subroutine | dlarfy (uplo, n, v, incv, tau, c, ldc, work) |
DLARFY | |
subroutine | dlargv (n, x, incx, y, incy, c, incc) |
DLARGV generates a vector of plane rotations with real cosines and real sines. | |
subroutine | dlarrv (n, vl, vu, d, l, pivmin, isplit, m, dol, dou, minrgp, rtol1, rtol2, w, werr, wgap, iblock, indexw, gers, z, ldz, isuppz, work, iwork, info) |
DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. | |
subroutine | dlartv (n, x, incx, y, incy, c, s, incc) |
DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. | |
subroutine | dlaswp (n, a, lda, k1, k2, ipiv, incx) |
DLASWP performs a series of row interchanges on a general rectangular matrix. | |
subroutine | dlat2s (uplo, n, a, lda, sa, ldsa, info) |
DLAT2S converts a double-precision triangular matrix to a single-precision triangular matrix. | |
subroutine | dlatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info) |
DLATBS solves a triangular banded system of equations. | |
subroutine | dlatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) |
DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. | |
subroutine | dlatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info) |
DLATPS solves a triangular system of equations with the matrix held in packed storage. | |
subroutine | dlatrd (uplo, n, nb, a, lda, e, tau, w, ldw) |
DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation. | |
subroutine | dlatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info) |
DLATRS solves a triangular system of equations with the scale factor set to prevent overflow. | |
subroutine | dlatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info) |
DLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow. | |
subroutine | dlauu2 (uplo, n, a, lda, info) |
DLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm). | |
subroutine | dlauum (uplo, n, a, lda, info) |
DLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm). | |
subroutine | drscl (n, sa, sx, incx) |
DRSCL multiplies a vector by the reciprocal of a real scalar. | |
subroutine | dtprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork) |
DTPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks. | |
subroutine | slatrd (uplo, n, nb, a, lda, e, tau, w, ldw) |
SLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation. | |
subroutine | slatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info) |
SLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow. | |
subroutine | zlatrs3 (uplo, trans, diag, normin, n, nrhs, a, lda, x, ldx, scale, cnorm, work, lwork, info) |
ZLATRS3 solves a triangular system of equations with the scale factors set to prevent overflow. | |
This is the group of double other auxiliary routines