LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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Collaboration diagram for double:

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. More...

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. More...

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. More...

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. More...

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. More...

subroutine dladiv (A, B, C, D, P, Q)
DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. More...

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. More...

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. More...

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. More...

subroutine dlag2s (M, N, A, LDA, SA, LDSA, INFO)
DLAG2S converts a double precision matrix to a single precision matrix. More...

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. More...

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. More...

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. More...

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. More...

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. More...

subroutine dlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
DLAIC1 applies one step of incremental condition estimation. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

subroutine dlapll (N, X, INCX, Y, INCY, SSMIN)
DLAPLL measures the linear dependence of two vectors. More...

subroutine dlapmr (FORWRD, M, N, X, LDX, K)
DLAPMR rearranges rows of a matrix as specified by a permutation vector. More...

subroutine dlapmt (FORWRD, M, N, X, LDX, K)
DLAPMT performs a forward or backward permutation of the columns of a matrix. More...

subroutine dlaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK)
DLAQP2 computes a QR factorization with column pivoting of the matrix block. More...

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. More...

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. More...

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. More...

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). More...

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). More...

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. More...

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. More...

subroutine dlaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
DLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. More...

subroutine dlaqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED)
DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. More...

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. More...

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. More...

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. More...

subroutine dlarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix. More...

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. More...

subroutine dlarfb_gett (IDENT, M, N, K, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
DLARFB_GETT More...

subroutine dlarfg (N, ALPHA, X, INCX, TAU)
DLARFG generates an elementary reflector (Householder matrix). More...

subroutine dlarfgp (N, ALPHA, X, INCX, TAU)
DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. More...

subroutine dlarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
DLARFT forms the triangular factor T of a block reflector H = I - vtvH More...

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. More...

subroutine dlarfy (UPLO, N, V, INCV, TAU, C, LDC, WORK)
DLARFY More...

subroutine dlargv (N, X, INCX, Y, INCY, C, INCC)
DLARGV generates a vector of plane rotations with real cosines and real sines. More...

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. More...

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. More...

subroutine dlaswp (N, A, LDA, K1, K2, IPIV, INCX)
DLASWP performs a series of row interchanges on a general rectangular matrix. More...

subroutine dlat2s (UPLO, N, A, LDA, SA, LDSA, INFO)
DLAT2S converts a double-precision triangular matrix to a single-precision triangular matrix. More...

subroutine dlatbs (UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
DLATBS solves a triangular banded system of equations. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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). More...

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). More...

subroutine drscl (N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar. More...

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. More...

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. More...

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. More...

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. More...

Detailed Description

This is the group of double other auxiliary routines