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

Functions

subroutine cbbcsd (jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, theta, phi, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, b11d, b11e, b12d, b12e, b21d, b21e, b22d, b22e, rwork, lrwork, info)
 CBBCSD
 
subroutine cbdsqr (uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, rwork, info)
 CBDSQR
 
subroutine cgghd3 (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, work, lwork, info)
 CGGHD3
 
subroutine cgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
 CGGHRD
 
subroutine cggqrf (n, m, p, a, lda, taua, b, ldb, taub, work, lwork, info)
 CGGQRF
 
subroutine cggrqf (m, p, n, a, lda, taua, b, ldb, taub, work, lwork, info)
 CGGRQF
 
subroutine cggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)
 CGGSVP3
 
subroutine cgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
 CGSVJ0 pre-processor for the routine cgesvj.
 
subroutine cgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
 CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots.
 
subroutine chbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, rwork, info)
 CHBGST
 
subroutine chbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
 CHBTRD
 
subroutine chetrd_hb2st (stage1, vect, uplo, n, kd, ab, ldab, d, e, hous, lhous, work, lwork, info)
 CHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T
 
subroutine chfrk (transr, uplo, trans, n, k, alpha, a, lda, beta, c)
 CHFRK performs a Hermitian rank-k operation for matrix in RFP format.
 
subroutine chpcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
 CHPCON
 
subroutine chpgst (itype, uplo, n, ap, bp, info)
 CHPGST
 
subroutine chprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
 CHPRFS
 
subroutine chptrd (uplo, n, ap, d, e, tau, info)
 CHPTRD
 
subroutine chptrf (uplo, n, ap, ipiv, info)
 CHPTRF
 
subroutine chptri (uplo, n, ap, ipiv, work, info)
 CHPTRI
 
subroutine chptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
 CHPTRS
 
subroutine chsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)
 CHSEIN
 
subroutine chseqr (job, compz, n, ilo, ihi, h, ldh, w, z, ldz, work, lwork, info)
 CHSEQR
 
subroutine cla_lin_berr (n, nz, nrhs, res, ayb, berr)
 CLA_LIN_BERR computes a component-wise relative backward error.
 
subroutine cla_wwaddw (n, x, y, w)
 CLA_WWADDW adds a vector into a doubled-single vector.
 
subroutine claed0 (qsiz, n, d, e, q, ldq, qstore, ldqs, rwork, iwork, info)
 CLAED0 used by CSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
 
subroutine claed7 (n, cutpnt, qsiz, tlvls, curlvl, curpbm, d, q, ldq, rho, indxq, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, rwork, iwork, info)
 CLAED7 used by CSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense.
 
subroutine claed8 (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlamda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info)
 CLAED8 used by CSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.
 
subroutine clals0 (icompq, nl, nr, sqre, nrhs, b, ldb, bx, ldbx, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, rwork, info)
 CLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd.
 
subroutine clalsa (icompq, smlsiz, n, nrhs, b, ldb, bx, ldbx, u, ldu, vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, rwork, iwork, info)
 CLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
 
subroutine clalsd (uplo, smlsiz, n, nrhs, d, e, b, ldb, rcond, rank, work, rwork, iwork, info)
 CLALSD uses the singular value decomposition of A to solve the least squares problem.
 
real function clanhf (norm, transr, uplo, n, a, work)
 CLANHF 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 matrix in RFP format.
 
subroutine clarscl2 (m, n, d, x, ldx)
 CLARSCL2 performs reciprocal diagonal scaling on a matrix.
 
subroutine clarz (side, m, n, l, v, incv, tau, c, ldc, work)
 CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
 
subroutine clarzb (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)
 CLARZB applies a block reflector or its conjugate-transpose to a general matrix.
 
subroutine clarzt (direct, storev, n, k, v, ldv, tau, t, ldt)
 CLARZT forms the triangular factor T of a block reflector H = I - vtvH.
 
subroutine clascl2 (m, n, d, x, ldx)
 CLASCL2 performs diagonal scaling on a matrix.
 
subroutine clatrz (m, n, l, a, lda, tau, work)
 CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.
 
subroutine cpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info)
 CPBCON
 
subroutine cpbequ (uplo, n, kd, ab, ldab, s, scond, amax, info)
 CPBEQU
 
subroutine cpbrfs (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x, ldx, ferr, berr, work, rwork, info)
 CPBRFS
 
subroutine cpbstf (uplo, n, kd, ab, ldab, info)
 CPBSTF
 
subroutine cpbtf2 (uplo, n, kd, ab, ldab, info)
 CPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).
 
subroutine cpbtrf (uplo, n, kd, ab, ldab, info)
 CPBTRF
 
subroutine cpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
 CPBTRS
 
subroutine cpftrf (transr, uplo, n, a, info)
 CPFTRF
 
subroutine cpftri (transr, uplo, n, a, info)
 CPFTRI
 
subroutine cpftrs (transr, uplo, n, nrhs, a, b, ldb, info)
 CPFTRS
 
subroutine cppcon (uplo, n, ap, anorm, rcond, work, rwork, info)
 CPPCON
 
subroutine cppequ (uplo, n, ap, s, scond, amax, info)
 CPPEQU
 
subroutine cpprfs (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, rwork, info)
 CPPRFS
 
subroutine cpptrf (uplo, n, ap, info)
 CPPTRF
 
subroutine cpptri (uplo, n, ap, info)
 CPPTRI
 
subroutine cpptrs (uplo, n, nrhs, ap, b, ldb, info)
 CPPTRS
 
subroutine cpstf2 (uplo, n, a, lda, piv, rank, tol, work, info)
 CPSTF2 computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix.
 
subroutine cpstrf (uplo, n, a, lda, piv, rank, tol, work, info)
 CPSTRF computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix.
 
subroutine cspcon (uplo, n, ap, ipiv, anorm, rcond, work, info)
 CSPCON
 
subroutine csprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)
 CSPRFS
 
subroutine csptrf (uplo, n, ap, ipiv, info)
 CSPTRF
 
subroutine csptri (uplo, n, ap, ipiv, work, info)
 CSPTRI
 
subroutine csptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info)
 CSPTRS
 
subroutine cstedc (compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
 CSTEDC
 
subroutine cstegr (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz, work, lwork, iwork, liwork, info)
 CSTEGR
 
subroutine cstein (n, d, e, m, w, iblock, isplit, z, ldz, work, iwork, ifail, info)
 CSTEIN
 
subroutine cstemr (jobz, range, n, d, e, vl, vu, il, iu, m, w, z, ldz, nzc, isuppz, tryrac, work, lwork, iwork, liwork, info)
 CSTEMR
 
subroutine csteqr (compz, n, d, e, z, ldz, work, info)
 CSTEQR
 
subroutine ctbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
 CTBCON
 
subroutine ctbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, rwork, info)
 CTBRFS
 
subroutine ctbtrs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, info)
 CTBTRS
 
subroutine ctfsm (transr, side, uplo, trans, diag, m, n, alpha, a, b, ldb)
 CTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
 
subroutine ctftri (transr, uplo, diag, n, a, info)
 CTFTRI
 
subroutine ctfttp (transr, uplo, n, arf, ap, info)
 CTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
 
subroutine ctfttr (transr, uplo, n, arf, a, lda, info)
 CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
 
subroutine ctgsen (ijob, wantq, wantz, select, n, a, lda, b, ldb, alpha, beta, q, ldq, z, ldz, m, pl, pr, dif, work, lwork, iwork, liwork, info)
 CTGSEN
 
subroutine ctgsja (jobu, jobv, jobq, m, p, n, k, l, a, lda, b, ldb, tola, tolb, alpha, beta, u, ldu, v, ldv, q, ldq, work, ncycle, info)
 CTGSJA
 
subroutine ctgsna (job, howmny, select, n, a, lda, b, ldb, vl, ldvl, vr, ldvr, s, dif, mm, m, work, lwork, iwork, info)
 CTGSNA
 
subroutine ctpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
 CTPCON
 
subroutine ctpmqrt (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
 CTPMQRT
 
subroutine ctpqrt (m, n, l, nb, a, lda, b, ldb, t, ldt, work, info)
 CTPQRT
 
subroutine ctpqrt2 (m, n, l, a, lda, b, ldb, t, ldt, info)
 CTPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.
 
subroutine ctprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, rwork, info)
 CTPRFS
 
subroutine ctptri (uplo, diag, n, ap, info)
 CTPTRI
 
subroutine ctptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
 CTPTRS
 
subroutine ctpttf (transr, uplo, n, ap, arf, info)
 CTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).
 
subroutine ctpttr (uplo, n, ap, a, lda, info)
 CTPTTR copies a triangular matrix from the standard packed format (TP) to the standard full format (TR).
 
subroutine ctrcon (norm, uplo, diag, n, a, lda, rcond, work, rwork, info)
 CTRCON
 
subroutine ctrevc (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, rwork, info)
 CTREVC
 
subroutine ctrevc3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, mm, m, work, lwork, rwork, lrwork, info)
 CTREVC3
 
subroutine ctrexc (compq, n, t, ldt, q, ldq, ifst, ilst, info)
 CTREXC
 
subroutine ctrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
 CTRRFS
 
subroutine ctrsen (job, compq, select, n, t, ldt, q, ldq, w, m, s, sep, work, lwork, info)
 CTRSEN
 
subroutine ctrsna (job, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr, s, sep, mm, m, work, ldwork, rwork, info)
 CTRSNA
 
subroutine ctrti2 (uplo, diag, n, a, lda, info)
 CTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
 
subroutine ctrtri (uplo, diag, n, a, lda, info)
 CTRTRI
 
subroutine ctrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)
 CTRTRS
 
subroutine ctrttf (transr, uplo, n, a, lda, arf, info)
 CTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
 
subroutine ctrttp (uplo, n, a, lda, ap, info)
 CTRTTP copies a triangular matrix from the standard full format (TR) to the standard packed format (TP).
 
subroutine ctzrzf (m, n, a, lda, tau, work, lwork, info)
 CTZRZF
 
subroutine cunbdb (trans, signs, m, p, q, x11, ldx11, x12, ldx12, x21, ldx21, x22, ldx22, theta, phi, taup1, taup2, tauq1, tauq2, work, lwork, info)
 CUNBDB
 
subroutine cunbdb1 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)
 CUNBDB1
 
subroutine cunbdb2 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)
 CUNBDB2
 
subroutine cunbdb3 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, work, lwork, info)
 CUNBDB3
 
subroutine cunbdb4 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, phantom, work, lwork, info)
 CUNBDB4
 
subroutine cunbdb5 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
 CUNBDB5
 
subroutine cunbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
 CUNBDB6
 
recursive subroutine cuncsd (jobu1, jobu2, jobv1t, jobv2t, trans, signs, m, p, q, x11, ldx11, x12, ldx12, x21, ldx21, x22, ldx22, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, work, lwork, rwork, lrwork, iwork, info)
 CUNCSD
 
subroutine cuncsd2by1 (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, rwork, lrwork, iwork, info)
 CUNCSD2BY1
 
subroutine cung2l (m, n, k, a, lda, tau, work, info)
 CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).
 
subroutine cung2r (m, n, k, a, lda, tau, work, info)
 CUNG2R
 
subroutine cunghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
 CUNGHR
 
subroutine cungl2 (m, n, k, a, lda, tau, work, info)
 CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
 
subroutine cunglq (m, n, k, a, lda, tau, work, lwork, info)
 CUNGLQ
 
subroutine cungql (m, n, k, a, lda, tau, work, lwork, info)
 CUNGQL
 
subroutine cungqr (m, n, k, a, lda, tau, work, lwork, info)
 CUNGQR
 
subroutine cungr2 (m, n, k, a, lda, tau, work, info)
 CUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).
 
subroutine cungrq (m, n, k, a, lda, tau, work, lwork, info)
 CUNGRQ
 
subroutine cungtr (uplo, n, a, lda, tau, work, lwork, info)
 CUNGTR
 
subroutine cungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
 CUNGTSQR
 
subroutine cungtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
 CUNGTSQR_ROW
 
subroutine cunhr_col (m, n, nb, a, lda, t, ldt, d, info)
 CUNHR_COL
 
subroutine cunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
 CUNM22 multiplies a general matrix by a banded unitary matrix.
 
subroutine cunm2l (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
 CUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm).
 
subroutine cunm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
 CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).
 
subroutine cunmbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
 CUNMBR
 
subroutine cunmhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
 CUNMHR
 
subroutine cunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
 CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm).
 
subroutine cunmlq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
 CUNMLQ
 
subroutine cunmql (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
 CUNMQL
 
subroutine cunmqr (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
 CUNMQR
 
subroutine cunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
 CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).
 
subroutine cunmr3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
 CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).
 
subroutine cunmrq (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
 CUNMRQ
 
subroutine cunmrz (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)
 CUNMRZ
 
subroutine cunmtr (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
 CUNMTR
 
subroutine cupgtr (uplo, n, ap, tau, q, ldq, work, info)
 CUPGTR
 
subroutine cupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
 CUPMTR
 
subroutine cggsvp (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, info)
 CGGSVP
 
subroutine clatzm (side, m, n, v, incv, tau, c1, c2, ldc, work)
 CLATZM
 
subroutine ctzrqf (m, n, a, lda, tau, info)
 CTZRQF
 
subroutine dorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
 DORM22 multiplies a general matrix by a banded orthogonal matrix.
 
subroutine sorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
 SORM22 multiplies a general matrix by a banded orthogonal matrix.
 
subroutine zunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
 ZUNM22 multiplies a general matrix by a banded unitary matrix.
 

Detailed Description

This is the group of complex other Computational routines