LAPACK
3.10.1
LAPACK: Linear Algebra PACKage

Functions  
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 kth 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 1norm of a square matrix, using reverse communication for evaluating matrixvector products. More...  
subroutine  dlacon (N, V, X, ISGN, EST, KASE) 
DLACON estimates the 1norm of a square matrix, using reverse communication for evaluating matrixvector 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 quasitriangular 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 2by2 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 2by2 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 matrixmatrix 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 2by2 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 doubleshift/singleshift 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 1by1 or 2by2 linear system of equations of the specified form. More...  
double precision function  dlangt (NORM, N, DL, D, DU) 
DLANGT returns the value of the 1norm, Frobenius norm, infinitynorm, 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 1norm, Frobenius norm, infinitynorm, 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 1norm, 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 1norm, 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 1norm, 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 1norm, 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 1norm, 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 2by2 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 mbyn 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 2by2 or 3by3 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 smallbulge multishift 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 quasitriangular system of equations, or a complex quasitriangular 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) rth 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 2by2 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 nonnegative 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 doubleprecision triangular matrix to a singleprecision 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 nbyn matrix computed by sgetc2 and computes a contribution to the reciprocal Difestimate. 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  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 or complex "triangularpentagonal" blocked reflector to a real or complex 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...  
This is the group of double other auxiliary routines