auxiliary Computational routines

Collaboration diagram for auxiliary Computational routines:

Functions
program	__secondtst_f__
	SECONDTST
program	__slamchtst_f__
	SLAMCHTST
character *1 function	chla_transtype (trans)
	CHLA_TRANSTYPE
subroutine	dbdsdc (uplo, compq, n, d, e, u, ldu, vt, ldvt, q, iq, work, iwork, info)
	DBDSDC
subroutine	dbdsqr (uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info)
	DBDSQR
subroutine	ddisna (job, m, n, d, sep, info)
	DDISNA
subroutine	dlaed0 (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info)
	DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
subroutine	dlaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info)
	DLAED1 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.
subroutine	dlaed2 (k, n, n1, d, q, ldq, indxq, rho, z, dlamda, w, q2, indx, indxc, indxp, coltyp, info)
	DLAED2 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.
subroutine	dlaed3 (k, n, n1, d, q, ldq, rho, dlamda, q2, indx, ctot, w, s, info)
	DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.
subroutine	dlaed4 (n, i, d, z, delta, rho, dlam, info)
	DLAED4 used by DSTEDC. Finds a single root of the secular equation.
subroutine	dlaed5 (i, d, z, delta, rho, dlam)
	DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.
subroutine	dlaed6 (kniter, orgati, rho, d, z, finit, tau, info)
	DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation.
subroutine	dlaed7 (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info)
	DLAED7 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense.
subroutine	dlaed8 (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z, dlamda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx, info)
	DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.
subroutine	dlaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlamda, w, s, lds, info)
	DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
subroutine	dlaeda (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info)
	DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.
subroutine	dlagtf (n, a, lambda, b, c, tol, d, in, info)
	DLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix, and λ a scalar, using partial pivoting with row interchanges.
subroutine	dlamrg (n1, n2, a, dtrd1, dtrd2, index)
	DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a single set sorted in ascending order.
subroutine	dlartgs (x, y, sigma, cs, sn)
	DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.
subroutine	dlasq1 (n, d, e, work, info)
	DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
subroutine	dlasq2 (n, z, info)
	DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr.
subroutine	dlasq3 (i0, n0, z, pp, dmin, sigma, desig, qmax, nfail, iter, ndiv, ieee, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
	DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.
subroutine	dlasq4 (i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
	DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr.
subroutine	dlasq5 (i0, n0, z, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2, ieee, eps)
	DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr.
subroutine	dlasq6 (i0, n0, z, pp, dmin, dmin1, dmin2, dn, dnm1, dnm2)
	DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
subroutine	dlasrt (id, n, d, info)
	DLASRT sorts numbers in increasing or decreasing order.
subroutine	dstebz (range, order, n, vl, vu, il, iu, abstol, d, e, m, nsplit, w, iblock, isplit, work, iwork, info)
	DSTEBZ
subroutine	dstedc (compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
	DSTEDC
subroutine	dsteqr (compz, n, d, e, z, ldz, work, info)
	DSTEQR
subroutine	dsterf (n, d, e, info)
	DSTERF
integer function	iladiag (diag)
	ILADIAG
integer function	ilaprec (prec)
	ILAPREC
integer function	ilatrans (trans)
	ILATRANS
integer function	ilauplo (uplo)
	ILAUPLO
subroutine	sbdsdc (uplo, compq, n, d, e, u, ldu, vt, ldvt, q, iq, work, iwork, info)
	SBDSDC
subroutine	sbdsqr (uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info)
	SBDSQR
subroutine	sdisna (job, m, n, d, sep, info)
	SDISNA
subroutine	slaed0 (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info)
	SLAED0 used by SSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
subroutine	slaed1 (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info)
	SLAED1 used by SSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.
subroutine	slaed2 (k, n, n1, d, q, ldq, indxq, rho, z, dlamda, w, q2, indx, indxc, indxp, coltyp, info)
	SLAED2 used by SSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.
subroutine	slaed3 (k, n, n1, d, q, ldq, rho, dlamda, q2, indx, ctot, w, s, info)
	SLAED3 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.
subroutine	slaed4 (n, i, d, z, delta, rho, dlam, info)
	SLAED4 used by SSTEDC. Finds a single root of the secular equation.
subroutine	slaed5 (i, d, z, delta, rho, dlam)
	SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.
subroutine	slaed6 (kniter, orgati, rho, d, z, finit, tau, info)
	SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation.
subroutine	slaed7 (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info)
	SLAED7 used by SSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense.
subroutine	slaed8 (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z, dlamda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx, info)
	SLAED8 used by SSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.
subroutine	slaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlamda, w, s, lds, info)
	SLAED9 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
subroutine	slaeda (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info)
	SLAEDA used by SSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.
subroutine	slagtf (n, a, lambda, b, c, tol, d, in, info)
	SLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix, and λ a scalar, using partial pivoting with row interchanges.
subroutine	slamrg (n1, n2, a, strd1, strd2, index)
	SLAMRG creates a permutation list to merge the entries of two independently sorted sets into a single set sorted in ascending order.
subroutine	slartgs (x, y, sigma, cs, sn)
	SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.
subroutine	slasq1 (n, d, e, work, info)
	SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
subroutine	slasq2 (n, z, info)
	SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr.
subroutine	slasq3 (i0, n0, z, pp, dmin, sigma, desig, qmax, nfail, iter, ndiv, ieee, ttype, dmin1, dmin2, dn, dn1, dn2, g, tau)
	SLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr.
subroutine	slasq4 (i0, n0, z, pp, n0in, dmin, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g)
	SLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr.
subroutine	slasq5 (i0, n0, z, pp, tau, sigma, dmin, dmin1, dmin2, dn, dnm1, dnm2, ieee, eps)
	SLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr.
subroutine	slasq6 (i0, n0, z, pp, dmin, dmin1, dmin2, dn, dnm1, dnm2)
	SLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
subroutine	slasrt (id, n, d, info)
	SLASRT sorts numbers in increasing or decreasing order.
subroutine	spttrf (n, d, e, info)
	SPTTRF
subroutine	sstebz (range, order, n, vl, vu, il, iu, abstol, d, e, m, nsplit, w, iblock, isplit, work, iwork, info)
	SSTEBZ
subroutine	sstedc (compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
	SSTEDC
subroutine	ssteqr (compz, n, d, e, z, ldz, work, info)
	SSTEQR
subroutine	ssterf (n, d, e, info)
	SSTERF

Detailed Description

This is the group of auxiliary Computational routines