 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
complex
Collaboration diagram for complex:

## 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 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. More...

subroutine clacon (N, V, X, EST, KASE)
CLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. More...

subroutine clacp2 (UPLO, M, N, A, LDA, B, LDB)
CLACP2 copies all or part of a real two-dimensional array to a complex array. More...

subroutine clacpy (UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional 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 2-by-2 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 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 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 double-shift/single-shift 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 1-norm, Frobenius norm, infinity-norm, 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 1-norm, 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 1-norm, 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 1-norm, Frobenius norm, infinity-norm, 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 1-norm, 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 1-norm, 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 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...

real function clantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
CLANTB 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...

real function clantp (NORM, UPLO, DIAG, N, AP, WORK)
CLANTP 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...

real function clantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
CLANTR 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 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 m-by-n 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 2-by-2 or 3-by-3 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 small-bulge multi-shift 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) r-th 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 2-by-2 symmetric/Hermitian matrices. More...

subroutine clarcm (M, N, A, LDA, B, LDB, C, LDC, RWORK)
CLARCM copies all or part of a real two-dimensional 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 conjugate-transpose to a general rectangular matrix. More...

subroutine clarfb_gett (IDENT, M, N, K, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CLARFB_GETT 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 non-negative 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 clarfy (UPLO, N, V, INCV, TAU, C, LDC, WORK)
CLARFY 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 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 off-diagonal 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 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 n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. 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 matrix-vector product for complex vectors using a complex symmetric packed matrix More...

subroutine cspr (UPLO, N, ALPHA, X, INCX, AP)
CSPR performs the symmetrical rank-1 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 "triangular-pentagonal" 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 k-th 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 non-zero column. More...

integer function ilaclr (M, N, A, LDA)
ILACLR scans a matrix for its last non-zero 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 1-norm of the complex vector using the true absolute value. More...

## Detailed Description

This is the group of complex other auxiliary routines