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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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Functions | |
subroutine | slahrd (n, k, nb, a, lda, tau, t, ldt, y, ldy) |
SLAHRD 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. | |
integer function | ilaslc (m, n, a, lda) |
ILASLC scans a matrix for its last non-zero column. | |
integer function | ilaslr (m, n, a, lda) |
ILASLR scans a matrix for its last non-zero row. | |
subroutine | slabrd (m, n, nb, a, lda, d, e, tauq, taup, x, ldx, y, ldy) |
SLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. | |
subroutine | slacn2 (n, v, x, isgn, est, kase, isave) |
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. | |
subroutine | slacon (n, v, x, isgn, est, kase) |
SLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. | |
subroutine | sladiv (a, b, c, d, p, q) |
SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. | |
subroutine | sladiv1 (a, b, c, d, p, q) |
real function | sladiv2 (a, b, c, d, r, t) |
subroutine | slaein (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info) |
SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. | |
subroutine | slaexc (wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info) |
SLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. | |
subroutine | slag2 (a, lda, b, ldb, safmin, scale1, scale2, wr1, wr2, wi) |
SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. | |
subroutine | slags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq) |
SLAGS2 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 | slagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb) |
SLAGTM 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 | slagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr) |
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. | |
subroutine | slahqr (wantt, wantz, n, ilo, ihi, h, ldh, wr, wi, iloz, ihiz, z, ldz, info) |
SLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. | |
subroutine | slahr2 (n, k, nb, a, lda, tau, t, ldt, y, ldy) |
SLAHR2 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 | slaic1 (job, j, x, sest, w, gamma, sestpr, s, c) |
SLAIC1 applies one step of incremental condition estimation. | |
subroutine | slaln2 (ltrans, na, nw, smin, ca, a, lda, d1, d2, b, ldb, wr, wi, x, ldx, scale, xnorm, info) |
SLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form. | |
real function | slangt (norm, n, dl, d, du) |
SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. | |
real function | slanhs (norm, n, a, lda, work) |
SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. | |
real function | slansb (norm, uplo, n, k, ab, ldab, work) |
SLANSB 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. | |
real function | slansp (norm, uplo, n, ap, work) |
SLANSP 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. | |
real function | slantb (norm, uplo, diag, n, k, ab, ldab, work) |
SLANTB 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. | |
real function | slantp (norm, uplo, diag, n, ap, work) |
SLANTP 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. | |
real function | slantr (norm, uplo, diag, m, n, a, lda, work) |
SLANTR 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 | slanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn) |
SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. | |
subroutine | slapll (n, x, incx, y, incy, ssmin) |
SLAPLL measures the linear dependence of two vectors. | |
subroutine | slapmr (forwrd, m, n, x, ldx, k) |
SLAPMR rearranges rows of a matrix as specified by a permutation vector. | |
subroutine | slapmt (forwrd, m, n, x, ldx, k) |
SLAPMT performs a forward or backward permutation of the columns of a matrix. | |
subroutine | slaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) |
SLAQP2 computes a QR factorization with column pivoting of the matrix block. | |
subroutine | slaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) |
SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. | |
subroutine | slaqr0 (wantt, wantz, n, ilo, ihi, h, ldh, wr, wi, iloz, ihiz, z, ldz, work, lwork, info) |
SLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. | |
subroutine | slaqr1 (n, h, ldh, sr1, si1, sr2, si2, v) |
SLAQR1 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 | slaqr2 (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) |
SLAQR2 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 | slaqr3 (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) |
SLAQR3 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 | slaqr4 (wantt, wantz, n, ilo, ihi, h, ldh, wr, wi, iloz, ihiz, z, ldz, work, lwork, info) |
SLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. | |
subroutine | slaqr5 (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) |
SLAQR5 performs a single small-bulge multi-shift QR sweep. | |
subroutine | slaqsb (uplo, n, kd, ab, ldab, s, scond, amax, equed) |
SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. | |
subroutine | slaqsp (uplo, n, ap, s, scond, amax, equed) |
SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. | |
subroutine | slaqtr (ltran, lreal, n, t, ldt, b, w, scale, x, work, info) |
SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic. | |
subroutine | slar1v (n, b1, bn, lambda, d, l, ld, lld, pivmin, gaptol, z, wantnc, negcnt, ztz, mingma, r, isuppz, nrminv, resid, rqcorr, work) |
SLAR1V computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI. | |
subroutine | slar2v (n, x, y, z, incx, c, s, incc) |
SLAR2V 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 | slarf (side, m, n, v, incv, tau, c, ldc, work) |
SLARF applies an elementary reflector to a general rectangular matrix. | |
subroutine | slarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork) |
SLARFB applies a block reflector or its transpose to a general rectangular matrix. | |
subroutine | slarfg (n, alpha, x, incx, tau) |
SLARFG generates an elementary reflector (Householder matrix). | |
subroutine | slarfgp (n, alpha, x, incx, tau) |
SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. | |
subroutine | slarft (direct, storev, n, k, v, ldv, tau, t, ldt) |
SLARFT forms the triangular factor T of a block reflector H = I - vtvH | |
subroutine | slarfx (side, m, n, v, tau, c, ldc, work) |
SLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. | |
subroutine | slarfy (uplo, n, v, incv, tau, c, ldc, work) |
SLARFY | |
subroutine | slargv (n, x, incx, y, incy, c, incc) |
SLARGV generates a vector of plane rotations with real cosines and real sines. | |
subroutine | slarrv (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) |
SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. | |
subroutine | slartv (n, x, incx, y, incy, c, s, incc) |
SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. | |
subroutine | slaswp (n, a, lda, k1, k2, ipiv, incx) |
SLASWP performs a series of row interchanges on a general rectangular matrix. | |
subroutine | slatbs (uplo, trans, diag, normin, n, kd, ab, ldab, x, scale, cnorm, info) |
SLATBS solves a triangular banded system of equations. | |
subroutine | slatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv) |
SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. | |
subroutine | slatps (uplo, trans, diag, normin, n, ap, x, scale, cnorm, info) |
SLATPS solves a triangular system of equations with the matrix held in packed storage. | |
subroutine | slatrs (uplo, trans, diag, normin, n, a, lda, x, scale, cnorm, info) |
SLATRS solves a triangular system of equations with the scale factor set to prevent overflow. | |
subroutine | slauu2 (uplo, n, a, lda, info) |
SLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm). | |
subroutine | slauum (uplo, n, a, lda, info) |
SLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm). | |
subroutine | srscl (n, sa, sx, incx) |
SRSCL multiplies a vector by the reciprocal of a real scalar. | |
subroutine | stprfb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, a, lda, b, ldb, work, ldwork) |
STPRFB applies a real "triangular-pentagonal" block reflector to a real matrix, which is composed of two blocks. | |
This is the group of real other auxiliary routines