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	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	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 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	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 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