LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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complex16
Collaboration diagram for complex16:

## Functions

subroutine clag2z (M, N, SA, LDSA, A, LDA, INFO)
CLAG2Z converts a complex single precision matrix to a complex double precision matrix. More...

subroutine zlahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY)
ZLAHRD 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...

double precision function dzsum1 (N, CX, INCX)
DZSUM1 forms the 1-norm of the complex vector using the true absolute value. More...

integer function ilazlc (M, N, A, LDA)
ILAZLC scans a matrix for its last non-zero column. More...

integer function ilazlr (M, N, A, LDA)
ILAZLR scans a matrix for its last non-zero row. More...

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

subroutine zlabrd (M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, LDY)
ZLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. More...

subroutine zlacgv (N, X, INCX)
ZLACGV conjugates a complex vector. More...

subroutine zlacn2 (N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. More...

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

subroutine zlacp2 (UPLO, M, N, A, LDA, B, LDB)
ZLACP2 copies all or part of a real two-dimensional array to a complex array. More...

subroutine zlacpy (UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another. More...

subroutine zlacrm (M, N, A, LDA, B, LDB, C, LDC, RWORK)
ZLACRM multiplies a complex matrix by a square real matrix. More...

subroutine zlacrt (N, CX, INCX, CY, INCY, C, S)
ZLACRT performs a linear transformation of a pair of complex vectors. More...

complex *16 function zladiv (X, Y)
ZLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. More...

subroutine zlaein (RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO)
ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. More...

subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. More...

subroutine zlag2c (M, N, A, LDA, SA, LDSA, INFO)
ZLAG2C converts a complex double precision matrix to a complex single precision matrix. More...

subroutine zlags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
ZLAGS2 More...

subroutine zlagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
ZLAGTM 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 zlahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO)
ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. More...

subroutine zlahr2 (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY)
ZLAHR2 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 zlaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C)
ZLAIC1 applies one step of incremental condition estimation. More...

double precision function zlangt (NORM, N, DL, D, DU)
ZLANGT 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 zlanhb (NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB 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...

double precision function zlanhp (NORM, UPLO, N, AP, WORK)
ZLANHP 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...

double precision function zlanhs (NORM, N, A, LDA, WORK)
ZLANHS 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 zlanht (NORM, N, D, E)
ZLANHT 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...

double precision function zlansb (NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANSB 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 zlansp (NORM, UPLO, N, AP, WORK)
ZLANSP 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 zlantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
ZLANTB 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 zlantp (NORM, UPLO, DIAG, N, AP, WORK)
ZLANTP 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 zlantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
ZLANTR 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 zlapll (N, X, INCX, Y, INCY, SSMIN)
ZLAPLL measures the linear dependence of two vectors. More...

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

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

subroutine zlaqhb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
ZLAQHB scales a Hermitian band matrix, using scaling factors computed by cpbequ. More...

subroutine zlaqhp (UPLO, N, AP, S, SCOND, AMAX, EQUED)
ZLAQHP scales a Hermitian matrix stored in packed form. More...

subroutine zlaqp2 (M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK)
ZLAQP2 computes a QR factorization with column pivoting of the matrix block. More...

subroutine zlaqps (M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, VN2, AUXV, F, LDF)
ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. More...

subroutine zlaqr0 (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO)
ZLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. More...

subroutine zlaqr1 (N, H, LDH, S1, S2, V)
ZLAQR1 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 zlaqr2 (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)
ZLAQR2 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 zlaqr3 (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)
ZLAQR3 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 zlaqr4 (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO)
ZLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. More...

subroutine zlaqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)
ZLAQR5 performs a single small-bulge multi-shift QR sweep. More...

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

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

subroutine zlar1v (N, B1, BN, LAMBDA, D, L, LD, LLD, PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, R, ISUPPZ, NRMINV, RESID, RQCORR, WORK)
ZLAR1V 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 zlar2v (N, X, Y, Z, INCX, C, S, INCC)
ZLAR2V 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 zlarcm (M, N, A, LDA, B, LDB, C, LDC, RWORK)
ZLARCM copies all or part of a real two-dimensional array to a complex array. More...

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

subroutine zlarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. More...

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

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

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

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

subroutine zlarfx (SIDE, M, N, V, TAU, C, LDC, WORK)
ZLARFX applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order ≤ 10. More...

subroutine zlarfy (UPLO, N, V, INCV, TAU, C, LDC, WORK)
ZLARFY More...

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

subroutine zlarnv (IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution. More...

subroutine zlarrv (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)
ZLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the eigenvalues of L D LT. More...

subroutine zlartv (N, X, INCX, Y, INCY, C, S, INCC)
ZLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors. More...

subroutine zlascl (TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. More...

subroutine zlaset (UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values. More...

subroutine zlasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
ZLASR applies a sequence of plane rotations to a general rectangular matrix. More...

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

subroutine zlat2c (UPLO, N, A, LDA, SA, LDSA, INFO)
ZLAT2C converts a double complex triangular matrix to a complex triangular matrix. More...

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

subroutine zlatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate. More...

subroutine zlatps (UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
ZLATPS solves a triangular system of equations with the matrix held in packed storage. More...

subroutine zlatrd (UPLO, N, NB, A, LDA, E, TAU, W, LDW)
ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an unitary similarity transformation. More...

subroutine zlatrs (UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow. More...

subroutine zlauu2 (UPLO, N, A, LDA, INFO)
ZLAUU2 computes the product UUH or LHL, where U and L are upper or lower triangular matrices (unblocked algorithm). More...

subroutine zlauum (UPLO, N, A, LDA, INFO)
ZLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm). More...

subroutine zrot (N, CX, INCX, CY, INCY, C, S)
ZROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors. More...

subroutine zspmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix More...

subroutine zspr (UPLO, N, ALPHA, X, INCX, AP)
ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix. More...

subroutine ztprfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
ZTPRFB applies a complex "triangular-pentagonal" block reflector to a complex matrix, which is composed of two blocks. More...

## Detailed Description

This is the group of complex16 other auxiliary routines