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LAPACK
3.9.0
LAPACK: Linear Algebra PACKage
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| program | __secondtst.f__ |
| | SECONDTST More...
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| program | __slamchtst.f__ |
| | SLAMCHTST More...
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| character *1 function | chla_transtype (TRANS) |
| | CHLA_TRANSTYPE More...
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| subroutine | dbdsdc (UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO) |
| | DBDSDC More...
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| subroutine | dbdsqr (UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO) |
| | DBDSQR More...
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| subroutine | ddisna (JOB, M, N, D, SEP, INFO) |
| | DDISNA More...
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| subroutine | dlaed0 (ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) |
| | DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. More...
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| subroutine | dlaed1 (N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO) |
| | DLAED1 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. More...
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| subroutine | dlaed2 (K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO) |
| | DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal. More...
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| subroutine | dlaed3 (K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO) |
| | DLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. More...
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| subroutine | dlaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) |
| | DLAED4 used by sstedc. Finds a single root of the secular equation. More...
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| subroutine | dlaed5 (I, D, Z, DELTA, RHO, DLAM) |
| | DLAED5 used by sstedc. Solves the 2-by-2 secular equation. More...
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| subroutine | dlaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO) |
| | DLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. More...
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| 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 sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. More...
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| 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 sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. More...
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| subroutine | dlaed9 (K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO) |
| | DLAED9 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense. More...
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| subroutine | dlaeda (N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO) |
| | DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| subroutine | dlasq1 (N, D, E, WORK, INFO) |
| | DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| subroutine | dlasrt (ID, N, D, INFO) |
| | DLASRT sorts numbers in increasing or decreasing order. More...
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| subroutine | dstebz (RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) |
| | DSTEBZ More...
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| subroutine | dstedc (COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) |
| | DSTEDC More...
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| subroutine | dsteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO) |
| | DSTEQR More...
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| subroutine | dsterf (N, D, E, INFO) |
| | DSTERF More...
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| integer function | iladiag (DIAG) |
| | ILADIAG More...
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| integer function | ilaprec (PREC) |
| | ILAPREC More...
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| integer function | ilatrans (TRANS) |
| | ILATRANS More...
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| integer function | ilauplo (UPLO) |
| | ILAUPLO More...
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| subroutine | sbdsdc (UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO) |
| | SBDSDC More...
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| subroutine | sbdsqr (UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO) |
| | SBDSQR More...
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| subroutine | sdisna (JOB, M, N, D, SEP, INFO) |
| | SDISNA More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| subroutine | slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) |
| | SLAED4 used by sstedc. Finds a single root of the secular equation. More...
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| subroutine | slaed5 (I, D, Z, DELTA, RHO, DLAM) |
| | SLAED5 used by sstedc. Solves the 2-by-2 secular equation. More...
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| subroutine | slaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO) |
| | SLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| subroutine | slasq1 (N, D, E, WORK, INFO) |
| | SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| 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. More...
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| subroutine | slasrt (ID, N, D, INFO) |
| | SLASRT sorts numbers in increasing or decreasing order. More...
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| subroutine | spttrf (N, D, E, INFO) |
| | SPTTRF More...
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| subroutine | sstebz (RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO) |
| | SSTEBZ More...
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| subroutine | sstedc (COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) |
| | SSTEDC More...
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| subroutine | ssteqr (COMPZ, N, D, E, Z, LDZ, WORK, INFO) |
| | SSTEQR More...
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| subroutine | ssterf (N, D, E, INFO) |
| | SSTERF More...
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This is the group of auxiliary Computational routines
real function snrm2(N, X, INCX)
SNRM2
subroutine dlaed6(KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO)
DLAED6 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 ...
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 ...
real function slamc3(A, B)
SLAMC3
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 dlaed4(N, I, D, Z, DELTA, RHO, DLAM, INFO)
DLAED4 used by sstedc. Finds a single root of the secular equation.
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....
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 dlaed9(K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO)
DLAED9 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors....
integer function ilaprec(PREC)
ILAPREC
double precision function dlanst(NORM, N, D, E)
DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
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....
integer function idamax(N, DX, INCX)
IDAMAX
subroutine dlaed3(K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO)
DLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors....
subroutine dlartg(F, G, CS, SN, R)
DLARTG generates a plane rotation with real cosine and real sine.
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 of...
subroutine slas2(F, G, H, SSMIN, SSMAX)
SLAS2 computes singular values of a 2-by-2 triangular matrix.
subroutine slaev2(A, B, C, RT1, RT2, CS1, SN1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
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...
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....
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
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 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 sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a ...
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 matri...
subroutine dlaev2(A, B, C, RT1, RT2, CS1, SN1)
DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian 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 ...
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 dlaed2(K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO)
DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matri...
logical function disnan(DIN)
DISNAN tests input for NaN.
subroutine slasr(SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
SLASR applies a sequence of plane rotations to a general rectangular matrix.
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 diagona...
double precision function dlapy2(X, Y)
DLAPY2 returns sqrt(x2+y2).
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 dsterf(N, D, E, INFO)
DSTERF
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
real function slanst(NORM, N, D, E)
SLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
integer function isamax(N, SX, INCX)
ISAMAX
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
integer function ilatrans(TRANS)
ILATRANS
subroutine dlasq2(N, Z, INFO)
DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated ...
subroutine srot(N, SX, INCX, SY, INCY, C, S)
SROT
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 sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
subroutine dsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
DSTEQR
logical function sisnan(SIN)
SISNAN tests input for NaN.
subroutine slasq1(N, D, E, WORK, INFO)
SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
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 of...
double precision function dnrm2(N, X, INCX)
DNRM2
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 scopy(N, SX, INCX, SY, INCY)
SCOPY
integer function ilauplo(UPLO)
ILAUPLO
subroutine dlas2(F, G, H, SSMIN, SSMAX)
DLAS2 computes singular values of a 2-by-2 triangular matrix.
subroutine ssterf(N, D, E, INFO)
SSTERF
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....
subroutine dlasq1(N, D, E, WORK, INFO)
DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr.
integer function iladiag(DIAG)
ILADIAG
subroutine sscal(N, SA, SX, INCX)
SSCAL
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 sstedc. Merges eigenvalues and deflates secular equation. Used when the original matri...
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
double precision function dlamc3(A, B)
DLAMC3
subroutine xerbla(SRNAME, INFO)
XERBLA
subroutine slaed4(N, I, D, Z, DELTA, RHO, DLAM, INFO)
SLAED4 used by sstedc. Finds a single root of the secular equation.
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 ma...
logical function lsame(CA, CB)
LSAME
real function slapy2(X, Y)
SLAPY2 returns sqrt(x2+y2).
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 drot(N, DX, INCX, DY, INCY, C, S)
DROT
real function slamch(CMACH)
SLAMCH
subroutine dlaed0(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO)
DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmet...
subroutine slaed5(I, D, Z, DELTA, RHO, DLAM)
SLAED5 used by sstedc. Solves the 2-by-2 secular equation.
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
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 dswap(N, DX, INCX, DY, INCY)
DSWAP
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 matri...
subroutine dlaed1(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO)
DLAED1 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a ...
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 dlasr(SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
DLASR applies a sequence of plane rotations to a general rectangular matrix.
subroutine dlasv2(F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL)
DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
subroutine slasq2(N, Z, INFO)
SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated ...
subroutine ssteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
SSTEQR
subroutine slartg(F, G, CS, SN, R)
SLARTG generates a plane rotation with real cosine and real sine.
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
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 symmet...
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 dlartgp(F, G, CS, SN, R)
DLARTGP generates a plane rotation so that the diagonal is nonnegative.
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...
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 diagona...
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 trans...
subroutine dlaed5(I, D, Z, DELTA, RHO, DLAM)
DLAED5 used by sstedc. Solves the 2-by-2 secular equation.
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 ...
subroutine slartgp(F, G, CS, SN, R)
SLARTGP generates a plane rotation so that the diagonal is nonnegative.
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 dscal(N, DA, DX, INCX)
DSCAL
subroutine dlasrt(ID, N, D, INFO)
DLASRT sorts numbers in increasing or decreasing order.
subroutine dlaeda(N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO)
DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the diagonal ma...
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 trans...
subroutine slasrt(ID, N, D, INFO)
SLASRT sorts numbers in increasing or decreasing order.
double precision function dlamch(CMACH)
DLAMCH
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.
character *1 function chla_transtype(TRANS)
CHLA_TRANSTYPE
1.8.16