LAPACK
3.10.0
LAPACK: Linear Algebra PACKage

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 kth subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. More...  
integer function  ilaslc (M, N, A, LDA) 
ILASLC scans a matrix for its last nonzero column. More...  
integer function  ilaslr (M, N, A, LDA) 
ILASLR scans a matrix for its last nonzero row. More...  
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. More...  
subroutine  slacn2 (N, V, X, ISGN, EST, KASE, ISAVE) 
SLACN2 estimates the 1norm of a square matrix, using reverse communication for evaluating matrixvector products. More...  
subroutine  slacon (N, V, X, ISGN, EST, KASE) 
SLACON estimates the 1norm of a square matrix, using reverse communication for evaluating matrixvector products. More...  
subroutine  sladiv (A, B, C, D, P, Q) 
SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. More...  
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. More...  
subroutine  slaexc (WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO) 
SLAEXC swaps adjacent diagonal blocks of a real upper quasitriangular matrix in Schur canonical form, by an orthogonal similarity transformation. More...  
subroutine  slag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI) 
SLAG2 computes the eigenvalues of a 2by2 generalized eigenvalue problem, with scaling as necessary to avoid over/underflow. More...  
subroutine  slags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ) 
SLAGS2 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  slagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB) 
SLAGTM 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  slagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR) 
SLAGV2 computes the Generalized Schur factorization of a real 2by2 matrix pencil (A,B) where B is upper triangular. More...  
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 doubleshift/singleshift QR algorithm. More...  
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. More...  
subroutine  slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) 
SLAIC1 applies one step of incremental condition estimation. More...  
subroutine  slaln2 (LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO) 
SLALN2 solves a 1by1 or 2by2 linear system of equations of the specified form. More...  
real function  slangt (NORM, N, DL, D, DU) 
SLANGT returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of a general tridiagonal matrix. More...  
real function  slanhs (NORM, N, A, LDA, WORK) 
SLANHS returns the value of the 1norm, Frobenius norm, infinitynorm, or the largest absolute value of any element of an upper Hessenberg matrix. More...  
real function  slansb (NORM, UPLO, N, K, AB, LDAB, WORK) 
SLANSB 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...  
real function  slansp (NORM, UPLO, N, AP, WORK) 
SLANSP 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...  
real function  slantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK) 
SLANTB 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...  
real function  slantp (NORM, UPLO, DIAG, N, AP, WORK) 
SLANTP 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...  
real function  slantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK) 
SLANTR 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  slanv2 (A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN) 
SLANV2 computes the Schur factorization of a real 2by2 nonsymmetric matrix in standard form. More...  
subroutine  slapll (N, X, INCX, Y, INCY, SSMIN) 
SLAPLL measures the linear dependence of two vectors. More...  
subroutine  slapmr (FORWRD, M, N, X, LDX, K) 
SLAPMR rearranges rows of a matrix as specified by a permutation vector. More...  
subroutine  slapmt (FORWRD, M, N, X, LDX, K) 
SLAPMT performs a forward or backward permutation of the columns of a matrix. More...  
subroutine  slaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK) 
SLAQP2 computes a QR factorization with column pivoting of the matrix block. More...  
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 mbyn matrix A by using BLAS level 3. More...  
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. More...  
subroutine  slaqr1 (N, H, LDH, SR1, SI1, SR2, SI2, V) 
SLAQR1 sets a scalar multiple of the first column of the product of 2by2 or 3by3 matrix H and specified shifts. More...  
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). More...  
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). More...  
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. More...  
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 smallbulge multishift QR sweep. More...  
subroutine  slaqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED) 
SLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. More...  
subroutine  slaqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED) 
SLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. More...  
subroutine  slaqtr (LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO) 
SLAQTR solves a real quasitriangular system of equations, or a complex quasitriangular system of special form, in real arithmetic. More...  
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) rth column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT  λI. More...  
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 2by2 symmetric/Hermitian matrices. More...  
subroutine  slarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK) 
SLARF applies an elementary reflector to a general rectangular matrix. More...  
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. More...  
subroutine  slarfg (N, ALPHA, X, INCX, TAU) 
SLARFG generates an elementary reflector (Householder matrix). More...  
subroutine  slarfgp (N, ALPHA, X, INCX, TAU) 
SLARFGP generates an elementary reflector (Householder matrix) with nonnegative beta. More...  
subroutine  slarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) 
SLARFT forms the triangular factor T of a block reflector H = I  vtvH More...  
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. More...  
subroutine  slarfy (UPLO, N, V, INCV, TAU, C, LDC, WORK) 
SLARFY More...  
subroutine  slargv (N, X, INCX, Y, INCY, C, INCC) 
SLARGV generates a vector of plane rotations with real cosines and real sines. More...  
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. More...  
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. More...  
subroutine  slaswp (N, A, LDA, K1, K2, IPIV, INCX) 
SLASWP performs a series of row interchanges on a general rectangular matrix. More...  
subroutine  slatbs (UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO) 
SLATBS solves a triangular banded system of equations. More...  
subroutine  slatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV) 
SLATDF uses the LU factorization of the nbyn matrix computed by sgetc2 and computes a contribution to the reciprocal Difestimate. More...  
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. More...  
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. More...  
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). More...  
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). More...  
subroutine  srscl (N, SA, SX, INCX) 
SRSCL multiplies a vector by the reciprocal of a real scalar. More...  
subroutine  stprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK) 
STPRFB applies a real or complex "triangularpentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks. More...  
This is the group of real other auxiliary routines