LAPACK
3.10.0
LAPACK: Linear Algebra PACKage

Modules  
double  
real  
complex  
complex16  
Functions  
subroutine  clartg (f, g, c, s, r) 
CLARTG generates a plane rotation with real cosine and complex sine. More...  
subroutine  classq (n, x, incx, scl, sumsq) 
CLASSQ updates a sum of squares represented in scaled form. More...  
subroutine  dcombssq (V1, V2) 
DCOMBSSQ adds two scaled sum of squares quantities. 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 twodimensional array to another. More...  
subroutine  dlae2 (A, B, C, RT1, RT2) 
DLAE2 computes the eigenvalues of a 2by2 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 2by2 symmetric/Hermitian matrix. More...  
subroutine  dlagts (JOB, N, A, B, C, D, IN, Y, TOL, INFO) 
DLAGTS solves the system of equations (TλI)x = y or (TλI)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 1norm, 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 offdiagonal 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, c, s, 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 2by2 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 nbym matrix B with diagonal d and offdiagonal 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 ith updated eigenvalue of a positive symmetric rankone 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 ith eigenvalue of a positive symmetric rankone modification of a 2by2 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 offdiagonal 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 offdiagonal 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 offdiagonal 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, scl, 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 2by2 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 nonzero column. More...  
integer function  iladlr (M, N, A, LDA) 
ILADLR scans a matrix for its last nonzero row. More...  
integer function  ilaenv (ISPEC, NAME, OPTS, N1, N2, N3, N4) 
ILAENV More...  
integer function  ilaenv2stage (ISPEC, NAME, OPTS, N1, N2, N3, N4) 
ILAENV2STAGE More...  
integer function  iparmq (ISPEC, NAME, OPTS, N, ILO, IHI, LWORK) 
IPARMQ More...  
logical function  lsamen (N, CA, CB) 
LSAMEN More...  
subroutine  scombssq (V1, V2) 
SCOMBSSQ adds two scaled sum of squares quantities 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 twodimensional array to another. More...  
subroutine  slae2 (A, B, C, RT1, RT2) 
SLAE2 computes the eigenvalues of a 2by2 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 2by2 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 (TλI)x = y or (TλI)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 1norm, 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 offdiagonal 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, c, s, 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 2by2 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 nbym matrix B with diagonal d and offdiagonal 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 ith updated eigenvalue of a positive symmetric rankone 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 ith eigenvalue of a positive symmetric rankone modification of a 2by2 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 offdiagonal 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 offdiagonal 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 offdiagonal 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, scl, 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 2by2 triangular matrix. More...  
subroutine  xerbla (SRNAME, INFO) 
XERBLA More...  
subroutine  xerbla_array (SRNAME_ARRAY, SRNAME_LEN, INFO) 
XERBLA_ARRAY More...  
subroutine  zlartg (f, g, c, s, r) 
ZLARTG generates a plane rotation with real cosine and complex sine. More...  
subroutine  zlassq (n, x, incx, scl, sumsq) 
ZLASSQ updates a sum of squares represented in scaled form. More...  
This is the group of Other Auxiliary routines