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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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Modules | |
double | |
real | |
complex | |
complex16 | |
Functions | |
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 | 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... | |
subroutine | ilaver (VERS_MAJOR, VERS_MINOR, VERS_PATCH) |
ILAVER returns the LAPACK version. 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 | 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