LAPACK
3.8.0
LAPACK: Linear Algebra PACKage

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 kth 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 1norm of the complex vector using the true absolute value. More...  
integer function  ilazlc (M, N, A, LDA) 
ILAZLC scans a matrix for its last nonzero column. More...  
integer function  ilazlr (M, N, A, LDA) 
ILAZLR scans a matrix for its last nonzero 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 1norm of a square matrix, using reverse communication for evaluating matrixvector products. More...  
subroutine  zlacon (N, V, X, EST, KASE) 
ZLACON estimates the 1norm of a square matrix, using reverse communication for evaluating matrixvector products. More...  
subroutine  zlacp2 (UPLO, M, N, A, LDA, B, LDB) 
ZLACP2 copies all or part of a real twodimensional array to a complex array. More...  
subroutine  zlacpy (UPLO, M, N, A, LDA, B, LDB) 
ZLACPY copies all or part of one twodimensional 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 2by2 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 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  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 doubleshift/singleshift 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 1norm, Frobenius norm, infinitynorm, 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 1norm, 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 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...  
double precision function  zlanhs (NORM, N, A, LDA, WORK) 
ZLANHS 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  zlanht (NORM, N, D, E) 
ZLANHT 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...  
double precision function  zlansb (NORM, UPLO, N, K, AB, LDAB, WORK) 
ZLANSB 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  zlansp (NORM, UPLO, N, AP, WORK) 
ZLANSP 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  zlantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK) 
ZLANTB 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  zlantp (NORM, UPLO, DIAG, N, AP, WORK) 
ZLANTP 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  zlantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK) 
ZLANTR 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  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 mbyn 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 2by2 or 3by3 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 smallbulge multishift 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) rth 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 2by2 symmetric/Hermitian matrices. More...  
subroutine  zlarcm (M, N, A, LDA, B, LDB, C, LDC, RWORK) 
ZLARCM copies all or part of a real twodimensional 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 conjugatetranspose to a general rectangular matrix. 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 nonnegative 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  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  zlartg (F, G, CS, SN, R) 
ZLARTG generates a plane rotation with real cosine and complex sine. 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 offdiagonal 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  zlassq (N, X, INCX, SCALE, SUMSQ) 
ZLASSQ updates a sum of squares represented in scaled form. 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 nbyn matrix computed by sgetc2 and computes a contribution to the reciprocal Difestimate. 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 matrixvector product for complex vectors using a complex symmetric packed matrix More...  
subroutine  zspr (UPLO, N, ALPHA, X, INCX, AP) 
ZSPR performs the symmetrical rank1 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 real or complex "triangularpentagonal" blocked reflector to a real or complex matrix, which is composed of two blocks. More...  
This is the group of complex16 other auxiliary routines