|
subroutine | clartg (f, g, c, s, r) |
| CLARTG generates a plane rotation with real cosine and complex sine.
|
|
subroutine | classq (n, x, incx, scl, sumsq) |
| CLASSQ updates a sum of squares represented in scaled form.
|
|
logical function | disnan (din) |
| DISNAN tests input for NaN.
|
|
subroutine | dlabad (small, large) |
| DLABAD
|
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subroutine | dlacpy (uplo, m, n, a, lda, b, ldb) |
| DLACPY copies all or part of one two-dimensional array to another.
|
|
subroutine | dlae2 (a, b, c, rt1, rt2) |
| DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
|
|
subroutine | dlaebz (ijob, nitmax, n, mmax, minp, nbmin, abstol, reltol, pivmin, d, e, e2, nval, ab, c, mout, nab, work, iwork, info) |
| DLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the routine sstebz.
|
|
subroutine | dlaev2 (a, b, c, rt1, rt2, cs1, sn1) |
| DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
|
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subroutine | dlagts (job, n, a, b, c, d, in, y, tol, info) |
| DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.
|
|
logical function | dlaisnan (din1, din2) |
| DLAISNAN tests input for NaN by comparing two arguments for inequality.
|
|
integer function | dlaneg (n, d, lld, sigma, pivmin, r) |
| DLANEG computes the Sturm count.
|
|
double precision function | dlanst (norm, n, d, e) |
| DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
|
|
double precision function | dlapy2 (x, y) |
| DLAPY2 returns sqrt(x2+y2).
|
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double precision function | dlapy3 (x, y, z) |
| DLAPY3 returns sqrt(x2+y2+z2).
|
|
double precision function | dlarmm (anorm, bnorm, cnorm) |
| DLARMM
|
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subroutine | dlarnv (idist, iseed, n, x) |
| DLARNV returns a vector of random numbers from a uniform or normal distribution.
|
|
subroutine | dlarra (n, d, e, e2, spltol, tnrm, nsplit, isplit, info) |
| DLARRA computes the splitting points with the specified threshold.
|
|
subroutine | dlarrb (n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w, wgap, werr, work, iwork, pivmin, spdiam, twist, info) |
| DLARRB provides limited bisection to locate eigenvalues for more accuracy.
|
|
subroutine | dlarrc (jobt, n, vl, vu, d, e, pivmin, eigcnt, lcnt, rcnt, info) |
| DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
|
|
subroutine | dlarrd (range, order, n, vl, vu, il, iu, gers, reltol, d, e, e2, pivmin, nsplit, isplit, m, w, werr, wl, wu, iblock, indexw, work, iwork, info) |
| DLARRD computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy.
|
|
subroutine | dlarre (range, n, vl, vu, il, iu, d, e, e2, rtol1, rtol2, spltol, nsplit, isplit, m, w, werr, wgap, iblock, indexw, gers, pivmin, work, iwork, info) |
| DLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each unreduced block Ti, finds base representations and eigenvalues.
|
|
subroutine | dlarrf (n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info) |
| DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.
|
|
subroutine | dlarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info) |
| DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
|
|
subroutine | dlarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info) |
| DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
|
|
subroutine | dlarrr (n, d, e, info) |
| DLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues.
|
|
subroutine | dlartg (f, g, c, s, r) |
| DLARTG generates a plane rotation with real cosine and real sine.
|
|
subroutine | dlartgp (f, g, cs, sn, r) |
| DLARTGP generates a plane rotation so that the diagonal is nonnegative.
|
|
subroutine | dlaruv (iseed, n, x) |
| DLARUV returns a vector of n random real numbers from a uniform distribution.
|
|
subroutine | dlas2 (f, g, h, ssmin, ssmax) |
| DLAS2 computes singular values of a 2-by-2 triangular matrix.
|
|
subroutine | dlascl (type, kl, ku, cfrom, cto, m, n, a, lda, info) |
| DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
|
|
subroutine | dlasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info) |
| DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.
|
|
subroutine | dlasd1 (nl, nr, sqre, d, alpha, beta, u, ldu, vt, ldvt, idxq, iwork, work, info) |
| DLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.
|
|
subroutine | dlasd2 (nl, nr, sqre, k, d, z, alpha, beta, u, ldu, vt, ldvt, dsigma, u2, ldu2, vt2, ldvt2, idxp, idx, idxc, idxq, coltyp, info) |
| DLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
|
|
subroutine | dlasd3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2, vt, ldvt, vt2, ldvt2, idxc, ctot, z, info) |
| DLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.
|
|
subroutine | dlasd4 (n, i, d, z, delta, rho, sigma, work, info) |
| DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc.
|
|
subroutine | dlasd5 (i, d, z, delta, rho, dsigma, work) |
| DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.
|
|
subroutine | dlasd6 (icompq, nl, nr, sqre, d, vf, vl, alpha, beta, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, work, iwork, info) |
| DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by sbdsdc.
|
|
subroutine | dlasd7 (icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw, alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, c, s, info) |
| DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.
|
|
subroutine | dlasd8 (icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info) |
| DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.
|
|
subroutine | dlasda (icompq, smlsiz, n, sqre, d, e, u, ldu, vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, work, iwork, info) |
| DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
|
|
subroutine | dlasdq (uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info) |
| DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
|
|
subroutine | dlasdt (n, lvl, nd, inode, ndiml, ndimr, msub) |
| DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc.
|
|
subroutine | dlaset (uplo, m, n, alpha, beta, a, lda) |
| DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
|
|
subroutine | dlasr (side, pivot, direct, m, n, c, s, a, lda) |
| DLASR applies a sequence of plane rotations to a general rectangular matrix.
|
|
subroutine | dlassq (n, x, incx, scl, sumsq) |
| DLASSQ updates a sum of squares represented in scaled form.
|
|
subroutine | dlasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl) |
| DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
|
|
integer function | ieeeck (ispec, zero, one) |
| IEEECK
|
|
integer function | iladlc (m, n, a, lda) |
| ILADLC scans a matrix for its last non-zero column.
|
|
integer function | iladlr (m, n, a, lda) |
| ILADLR scans a matrix for its last non-zero row.
|
|
integer function | ilaenv (ispec, name, opts, n1, n2, n3, n4) |
| ILAENV
|
|
integer function | ilaenv2stage (ispec, name, opts, n1, n2, n3, n4) |
| ILAENV2STAGE
|
|
integer function | iparmq (ispec, name, opts, n, ilo, ihi, lwork) |
| IPARMQ
|
|
logical function | lsamen (n, ca, cb) |
| LSAMEN
|
|
logical function | sisnan (sin) |
| SISNAN tests input for NaN.
|
|
subroutine | slabad (small, large) |
| SLABAD
|
|
subroutine | slacpy (uplo, m, n, a, lda, b, ldb) |
| SLACPY copies all or part of one two-dimensional array to another.
|
|
subroutine | slae2 (a, b, c, rt1, rt2) |
| SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
|
|
subroutine | slaebz (ijob, nitmax, n, mmax, minp, nbmin, abstol, reltol, pivmin, d, e, e2, nval, ab, c, mout, nab, work, iwork, info) |
| SLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the routine sstebz.
|
|
subroutine | slaev2 (a, b, c, rt1, rt2, cs1, sn1) |
| SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
|
|
subroutine | slag2d (m, n, sa, ldsa, a, lda, info) |
| SLAG2D converts a single precision matrix to a double precision matrix.
|
|
subroutine | slagts (job, n, a, b, c, d, in, y, tol, info) |
| SLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.
|
|
logical function | slaisnan (sin1, sin2) |
| SLAISNAN tests input for NaN by comparing two arguments for inequality.
|
|
integer function | slaneg (n, d, lld, sigma, pivmin, r) |
| SLANEG computes the Sturm count.
|
|
real function | slanst (norm, n, d, e) |
| SLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
|
|
real function | slapy2 (x, y) |
| SLAPY2 returns sqrt(x2+y2).
|
|
real function | slapy3 (x, y, z) |
| SLAPY3 returns sqrt(x2+y2+z2).
|
|
real function | slarmm (anorm, bnorm, cnorm) |
| SLARMM
|
|
subroutine | slarnv (idist, iseed, n, x) |
| SLARNV returns a vector of random numbers from a uniform or normal distribution.
|
|
subroutine | slarra (n, d, e, e2, spltol, tnrm, nsplit, isplit, info) |
| SLARRA computes the splitting points with the specified threshold.
|
|
subroutine | slarrb (n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w, wgap, werr, work, iwork, pivmin, spdiam, twist, info) |
| SLARRB provides limited bisection to locate eigenvalues for more accuracy.
|
|
subroutine | slarrc (jobt, n, vl, vu, d, e, pivmin, eigcnt, lcnt, rcnt, info) |
| SLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
|
|
subroutine | slarrd (range, order, n, vl, vu, il, iu, gers, reltol, d, e, e2, pivmin, nsplit, isplit, m, w, werr, wl, wu, iblock, indexw, work, iwork, info) |
| SLARRD computes the eigenvalues of a symmetric tridiagonal matrix to suitable accuracy.
|
|
subroutine | slarre (range, n, vl, vu, il, iu, d, e, e2, rtol1, rtol2, spltol, nsplit, isplit, m, w, werr, wgap, iblock, indexw, gers, pivmin, work, iwork, info) |
| SLARRE given the tridiagonal matrix T, sets small off-diagonal elements to zero and for each unreduced block Ti, finds base representations and eigenvalues.
|
|
subroutine | slarrf (n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info) |
| SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.
|
|
subroutine | slarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info) |
| SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
|
|
subroutine | slarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info) |
| SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
|
|
subroutine | slarrr (n, d, e, info) |
| SLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues.
|
|
subroutine | slartg (f, g, c, s, r) |
| SLARTG generates a plane rotation with real cosine and real sine.
|
|
subroutine | slartgp (f, g, cs, sn, r) |
| SLARTGP generates a plane rotation so that the diagonal is nonnegative.
|
|
subroutine | slaruv (iseed, n, x) |
| SLARUV returns a vector of n random real numbers from a uniform distribution.
|
|
subroutine | slas2 (f, g, h, ssmin, ssmax) |
| SLAS2 computes singular values of a 2-by-2 triangular matrix.
|
|
subroutine | slascl (type, kl, ku, cfrom, cto, m, n, a, lda, info) |
| SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
|
|
subroutine | slasd0 (n, sqre, d, e, u, ldu, vt, ldvt, smlsiz, iwork, work, info) |
| SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.
|
|
subroutine | slasd1 (nl, nr, sqre, d, alpha, beta, u, ldu, vt, ldvt, idxq, iwork, work, info) |
| SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.
|
|
subroutine | slasd2 (nl, nr, sqre, k, d, z, alpha, beta, u, ldu, vt, ldvt, dsigma, u2, ldu2, vt2, ldvt2, idxp, idx, idxc, idxq, coltyp, info) |
| SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.
|
|
subroutine | slasd3 (nl, nr, sqre, k, d, q, ldq, dsigma, u, ldu, u2, ldu2, vt, ldvt, vt2, ldvt2, idxc, ctot, z, info) |
| SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.
|
|
subroutine | slasd4 (n, i, d, z, delta, rho, sigma, work, info) |
| SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.
|
|
subroutine | slasd5 (i, d, z, delta, rho, dsigma, work) |
| SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.
|
|
subroutine | slasd6 (icompq, nl, nr, sqre, d, vf, vl, alpha, beta, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, poles, difl, difr, z, k, c, s, work, iwork, info) |
| SLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by sbdsdc.
|
|
subroutine | slasd7 (icompq, nl, nr, sqre, k, d, z, zw, vf, vfw, vl, vlw, alpha, beta, dsigma, idx, idxp, idxq, perm, givptr, givcol, ldgcol, givnum, ldgnum, c, s, info) |
| SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc.
|
|
subroutine | slasd8 (icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info) |
| SLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.
|
|
subroutine | slasda (icompq, smlsiz, n, sqre, d, e, u, ldu, vt, k, difl, difr, z, poles, givptr, givcol, ldgcol, perm, givnum, c, s, work, iwork, info) |
| SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
|
|
subroutine | slasdq (uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info) |
| SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.
|
|
subroutine | slasdt (n, lvl, nd, inode, ndiml, ndimr, msub) |
| SLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc.
|
|
subroutine | slaset (uplo, m, n, alpha, beta, a, lda) |
| SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
|
|
subroutine | slasr (side, pivot, direct, m, n, c, s, a, lda) |
| SLASR applies a sequence of plane rotations to a general rectangular matrix.
|
|
subroutine | slassq (n, x, incx, scl, sumsq) |
| SLASSQ updates a sum of squares represented in scaled form.
|
|
subroutine | slasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl) |
| SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
|
|
subroutine | xerbla (srname, info) |
| XERBLA
|
|
subroutine | xerbla_array (srname_array, srname_len, info) |
| XERBLA_ARRAY
|
|
subroutine | zlartg (f, g, c, s, r) |
| ZLARTG generates a plane rotation with real cosine and complex sine.
|
|
subroutine | zlassq (n, x, incx, scl, sumsq) |
| ZLASSQ updates a sum of squares represented in scaled form.
|
|