LAPACK
3.8.0
LAPACK: Linear Algebra PACKage

Functions  
subroutine  clabrd (M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, LDY) 
CLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. More...  
subroutine  clacgv (N, X, INCX) 
CLACGV conjugates a complex vector. More...  
subroutine  clacn2 (N, V, X, EST, KASE, ISAVE) 
CLACN2 estimates the 1norm of a square matrix, using reverse communication for evaluating matrixvector products. More...  
subroutine  clacon (N, V, X, EST, KASE) 
CLACON estimates the 1norm of a square matrix, using reverse communication for evaluating matrixvector products. More...  
subroutine  clacp2 (UPLO, M, N, A, LDA, B, LDB) 
CLACP2 copies all or part of a real twodimensional array to a complex array. More...  
subroutine  clacpy (UPLO, M, N, A, LDA, B, LDB) 
CLACPY copies all or part of one twodimensional array to another. More...  
subroutine  clacrm (M, N, A, LDA, B, LDB, C, LDC, RWORK) 
CLACRM multiplies a complex matrix by a square real matrix. More...  
subroutine  clacrt (N, CX, INCX, CY, INCY, C, S) 
CLACRT performs a linear transformation of a pair of complex vectors. More...  
complex function  cladiv (X, Y) 
CLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. More...  
subroutine  claein (RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO) 
CLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. More...  
subroutine  claev2 (A, B, C, RT1, RT2, CS1, SN1) 
CLAEV2 computes the eigenvalues and eigenvectors of a 2by2 symmetric/Hermitian matrix. More...  
subroutine  clags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ) 
CLAGS2 More...  
subroutine  clagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB) 
CLAGTM 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  clahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO) 
CLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the doubleshift/singleshift QR algorithm. More...  
subroutine  clahr2 (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) 
CLAHR2 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  claic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) 
CLAIC1 applies one step of incremental condition estimation. More...  
real function  clangt (NORM, N, DL, D, DU) 
CLANGT 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  clanhb (NORM, UPLO, N, K, AB, LDAB, WORK) 
CLANHB returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. More...  
real function  clanhp (NORM, UPLO, N, AP, WORK) 
CLANHP returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form. More...  
real function  clanhs (NORM, N, A, LDA, WORK) 
CLANHS 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  clanht (NORM, N, D, E) 
CLANHT returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix. More...  
real function  clansb (NORM, UPLO, N, K, AB, LDAB, WORK) 
CLANSB 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  clansp (NORM, UPLO, N, AP, WORK) 
CLANSP 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  clantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK) 
CLANTB 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  clantp (NORM, UPLO, DIAG, N, AP, WORK) 
CLANTP 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  clantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK) 
CLANTR 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  clapll (N, X, INCX, Y, INCY, SSMIN) 
CLAPLL measures the linear dependence of two vectors. More...  
subroutine  clapmr (FORWRD, M, N, X, LDX, K) 
CLAPMR rearranges rows of a matrix as specified by a permutation vector. More...  
subroutine  clapmt (FORWRD, M, N, X, LDX, K) 
CLAPMT performs a forward or backward permutation of the columns of a matrix. More...  
subroutine  claqhb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED) 
CLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. More...  
subroutine  claqhp (UPLO, N, AP, S, SCOND, AMAX, EQUED) 
CLAQHP scales a Hermitian matrix stored in packed form. More...  
subroutine  claqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK) 
CLAQP2 computes a QR factorization with column pivoting of the matrix block. More...  
subroutine  claqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF) 
CLAQPS computes a step of QR factorization with column pivoting of a real mbyn matrix A by using BLAS level 3. More...  
subroutine  claqr0 (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO) 
CLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. More...  
subroutine  claqr1 (N, H, LDH, S1, S2, V) 
CLAQR1 sets a scalar multiple of the first column of the product of 2by2 or 3by3 matrix H and specified shifts. More...  
subroutine  claqr2 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK) 
CLAQR2 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). More...  
subroutine  claqr3 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK) 
CLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). More...  
subroutine  claqr4 (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO) 
CLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. More...  
subroutine  claqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH) 
CLAQR5 performs a single smallbulge multishift QR sweep. More...  
subroutine  claqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED) 
CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ. More...  
subroutine  claqsp (UPLO, N, AP, S, SCOND, AMAX, EQUED) 
CLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ. More...  
subroutine  clar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR, WORK) 
CLAR1V computes the (scaled) rth column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT  λI. More...  
subroutine  clar2v (N, X, Y, Z, INCX, C, S, INCC) 
CLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2by2 symmetric/Hermitian matrices. More...  
subroutine  clarcm (M, N, A, LDA, B, LDB, C, LDC, RWORK) 
CLARCM copies all or part of a real twodimensional array to a complex array. More...  
subroutine  clarf (SIDE, M, N, V, INCV, TAU, C, LDC, WORK) 
CLARF applies an elementary reflector to a general rectangular matrix. More...  
subroutine  clarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK) 
CLARFB applies a block reflector or its conjugatetranspose to a general rectangular matrix. More...  
subroutine  clarfg (N, ALPHA, X, INCX, TAU) 
CLARFG generates an elementary reflector (Householder matrix). More...  
subroutine  clarfgp (N, ALPHA, X, INCX, TAU) 
CLARFGP generates an elementary reflector (Householder matrix) with nonnegative beta. More...  
subroutine  clarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) 
CLARFT forms the triangular factor T of a block reflector H = I  vtvH More...  
subroutine  clarfx (SIDE, M, N, V, TAU, C, LDC, WORK) 
CLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. More...  
subroutine  clargv (N, X, INCX, Y, INCY, C, INCC) 
CLARGV generates a vector of plane rotations with real cosines and complex sines. More...  
subroutine  clarnv (IDIST, ISEED, N, X) 
CLARNV returns a vector of random numbers from a uniform or normal distribution. More...  
subroutine  clarrv (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) 
CLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. More...  
subroutine  clartg (F, G, CS, SN, R) 
CLARTG generates a plane rotation with real cosine and complex sine. More...  
subroutine  clartv (N, X, INCX, Y, INCY, C, S, INCC) 
CLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors. More...  
subroutine  clascl (TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO) 
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. More...  
subroutine  claset (UPLO, M, N, ALPHA, BETA, A, LDA) 
CLASET initializes the offdiagonal elements and the diagonal elements of a matrix to given values. More...  
subroutine  clasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA) 
CLASR applies a sequence of plane rotations to a general rectangular matrix. More...  
subroutine  classq (N, X, INCX, SCALE, SUMSQ) 
CLASSQ updates a sum of squares represented in scaled form. More...  
subroutine  claswp (N, A, LDA, K1, K2, IPIV, INCX) 
CLASWP performs a series of row interchanges on a general rectangular matrix. More...  
subroutine  clatbs (UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO) 
CLATBS solves a triangular banded system of equations. More...  
subroutine  clatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV) 
CLATDF uses the LU factorization of the nbyn matrix computed by sgetc2 and computes a contribution to the reciprocal Difestimate. More...  
subroutine  clatps (UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO) 
CLATPS solves a triangular system of equations with the matrix held in packed storage. More...  
subroutine  clatrd (UPLO, N, NB, A, LDA, E, TAU, W, LDW) 
CLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an unitary similarity transformation. More...  
subroutine  clatrs (UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO) 
CLATRS solves a triangular system of equations with the scale factor set to prevent overflow. More...  
subroutine  clauu2 (UPLO, N, A, LDA, INFO) 
CLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm). More...  
subroutine  clauum (UPLO, N, A, LDA, INFO) 
CLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm). More...  
subroutine  crot (N, CX, INCX, CY, INCY, C, S) 
CROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors. More...  
subroutine  cspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY) 
CSPMV computes a matrixvector product for complex vectors using a complex symmetric packed matrix More...  
subroutine  cspr (UPLO, N, ALPHA, X, INCX, AP) 
CSPR performs the symmetrical rank1 update of a complex symmetric packed matrix. More...  
subroutine  csrscl (N, SA, SX, INCX) 
CSRSCL multiplies a vector by the reciprocal of a real scalar. More...  
subroutine  ctprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK) 
CTPRFB applies a real or complex "triangularpentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks. More...  
subroutine  clahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) 
CLAHRD 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  icmax1 (N, CX, INCX) 
ICMAX1 finds the index of the first vector element of maximum absolute value. More...  
integer function  ilaclc (M, N, A, LDA) 
ILACLC scans a matrix for its last nonzero column. More...  
integer function  ilaclr (M, N, A, LDA) 
ILACLR scans a matrix for its last nonzero row. More...  
integer function  izmax1 (N, ZX, INCX) 
IZMAX1 finds the index of the first vector element of maximum absolute value. More...  
real function  scsum1 (N, CX, INCX) 
SCSUM1 forms the 1norm of the complex vector using the true absolute value. More...  
This is the group of complex other auxiliary routines