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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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Functions | |
| double precision function | dlamch (CMACH) |
| DLAMCH More... | |
| double precision function | dlamc3 (A, B) |
| DLAMC3 More... | |
| subroutine | dlamc1 (BETA, T, RND, IEEE1) |
| DLAMC1 More... | |
| subroutine | dlamc2 (BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX) |
| DLAMC2 More... | |
| program | __dlamchtst.f__ |
| DLAMCHTST More... | |
| double precision function | dsecnd () |
| DSECND Using ETIME More... | |
| program | __dsecndtst.f__ |
| DSECNDTST More... | |
| subroutine | ilaver (VERS_MAJOR, VERS_MINOR, VERS_PATCH) |
| ILAVER returns the LAPACK version. More... | |
| program | __lapack_version.f__ |
| LAPACK_VERSION More... | |
| logical function | lsame (CA, CB) |
| LSAME More... | |
| program | __lsametst.f__ |
| LSAMETST More... | |
| real function | second () |
| SECOND Using ETIME More... | |
| real function | slamch (CMACH) |
| SLAMCH More... | |
| real function | slamc3 (A, B) |
| SLAMC3 More... | |
| subroutine | slamc1 (BETA, T, RND, IEEE1) |
| SLAMC1 More... | |
| subroutine | slamc2 (BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX) |
| SLAMC2 More... | |
| program | tstiee |
| TSTIEE More... | |
| logical function | disnan (DIN) |
| DISNAN tests input for NaN. More... | |
| subroutine | dlabad (SMALL, LARGE) |
| DLABAD More... | |
| subroutine | dlacpy (UPLO, M, N, A, LDA, B, LDB) |
| DLACPY copies all or part of one two-dimensional array to another. More... | |
| subroutine | dladiv (A, B, C, D, P, Q) |
| DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. More... | |
| subroutine | dlae2 (A, B, C, RT1, RT2) |
| DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. More... | |
| 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. More... | |
| subroutine | dlaev2 (A, B, C, RT1, RT2, CS1, SN1) |
| DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. More... | |
| 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. More... | |
| logical function | dlaisnan (DIN1, DIN2) |
| DLAISNAN tests input for NaN by comparing two arguments for inequality. More... | |
| integer function | dlaneg (N, D, LLD, SIGMA, PIVMIN, R) |
| DLANEG computes the Sturm count. More... | |
| 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. More... | |
| double precision function | dlapy2 (X, Y) |
| DLAPY2 returns sqrt(x2+y2). More... | |
| double precision function | dlapy3 (X, Y, Z) |
| DLAPY3 returns sqrt(x2+y2+z2). More... | |
| subroutine | dlarnv (IDIST, ISEED, N, X) |
| DLARNV returns a vector of random numbers from a uniform or normal distribution. More... | |
| subroutine | dlarra (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO) |
| DLARRA computes the splitting points with the specified threshold. More... | |
| 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. More... | |
| subroutine | dlarrc (JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO) |
| DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| subroutine | dlartg (F, G, CS, SN, R) |
| DLARTG generates a plane rotation with real cosine and real sine. More... | |
| subroutine | dlartgp (F, G, CS, SN, R) |
| DLARTGP generates a plane rotation so that the diagonal is nonnegative. More... | |
| subroutine | dlaruv (ISEED, N, X) |
| DLARUV returns a vector of n random real numbers from a uniform distribution. More... | |
| subroutine | dlas2 (F, G, H, SSMIN, SSMAX) |
| DLAS2 computes singular values of a 2-by-2 triangular matrix. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| subroutine | dlasdt (N, LVL, ND, INODE, NDIML, NDIMR, MSUB) |
| DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc. More... | |
| 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. More... | |
| subroutine | dlasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA) |
| DLASR applies a sequence of plane rotations to a general rectangular matrix. More... | |
| subroutine | dlassq (N, X, INCX, SCALE, SUMSQ) |
| DLASSQ updates a sum of squares represented in scaled form. More... | |
| subroutine | dlasv2 (F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL) |
| DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. More... | |
| integer function | ieeeck (ISPEC, ZERO, ONE) |
| IEEECK More... | |
| integer function | iladlc (M, N, A, LDA) |
| ILADLC scans a matrix for its last non-zero column. More... | |
| integer function | iladlr (M, N, A, LDA) |
| ILADLR scans a matrix for its last non-zero row. More... | |
| integer function | ilaenv (ISPEC, NAME, OPTS, N1, N2, N3, N4) |
| ILAENV More... | |
| integer function | iparmq (ISPEC, NAME, OPTS, N, ILO, IHI, LWORK) |
| IPARMQ More... | |
| logical function | lsamen (N, CA, CB) |
| LSAMEN More... | |
| logical function | sisnan (SIN) |
| SISNAN tests input for NaN. More... | |
| subroutine | slabad (SMALL, LARGE) |
| SLABAD More... | |
| subroutine | slacpy (UPLO, M, N, A, LDA, B, LDB) |
| SLACPY copies all or part of one two-dimensional array to another. More... | |
| subroutine | sladiv (A, B, C, D, P, Q) |
| SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. More... | |
| subroutine | slae2 (A, B, C, RT1, RT2) |
| SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. More... | |
| 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. More... | |
| subroutine | slaev2 (A, B, C, RT1, RT2, CS1, SN1) |
| SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. More... | |
| subroutine | slag2d (M, N, SA, LDSA, A, LDA, INFO) |
| SLAG2D converts a single precision matrix to a double precision matrix. More... | |
| 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. More... | |
| logical function | slaisnan (SIN1, SIN2) |
| SLAISNAN tests input for NaN by comparing two arguments for inequality. More... | |
| integer function | slaneg (N, D, LLD, SIGMA, PIVMIN, R) |
| SLANEG computes the Sturm count. More... | |
| 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. More... | |
| real function | slapy2 (X, Y) |
| SLAPY2 returns sqrt(x2+y2). More... | |
| real function | slapy3 (X, Y, Z) |
| SLAPY3 returns sqrt(x2+y2+z2). More... | |
| subroutine | slarnv (IDIST, ISEED, N, X) |
| SLARNV returns a vector of random numbers from a uniform or normal distribution. More... | |
| subroutine | slarra (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO) |
| SLARRA computes the splitting points with the specified threshold. More... | |
| 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. More... | |
| subroutine | slarrc (JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO) |
| SLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| subroutine | slartg (F, G, CS, SN, R) |
| SLARTG generates a plane rotation with real cosine and real sine. More... | |
| subroutine | slartgp (F, G, CS, SN, R) |
| SLARTGP generates a plane rotation so that the diagonal is nonnegative. More... | |
| subroutine | slaruv (ISEED, N, X) |
| SLARUV returns a vector of n random real numbers from a uniform distribution. More... | |
| subroutine | slas2 (F, G, H, SSMIN, SSMAX) |
| SLAS2 computes singular values of a 2-by-2 triangular matrix. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| subroutine | slasdt (N, LVL, ND, INODE, NDIML, NDIMR, MSUB) |
| SLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc. More... | |
| 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. More... | |
| subroutine | slasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA) |
| SLASR applies a sequence of plane rotations to a general rectangular matrix. More... | |
| subroutine | slassq (N, X, INCX, SCALE, SUMSQ) |
| SLASSQ updates a sum of squares represented in scaled form. More... | |
| subroutine | slasv2 (F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL) |
| SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. More... | |
| subroutine | xerbla (SRNAME, INFO) |
| XERBLA More... | |
| subroutine | xerbla_array (SRNAME_ARRAY, SRNAME_LEN, INFO) |
| XERBLA_ARRAY More... | |
This is the group of Other Auxiliary routines
1.8.10 
