Other Auxiliary Routines

Collaboration diagram for Other Auxiliary Routines:

Modules
	double
	real
	complex
	complex16

Namespaces
module	la_constants
	LA_CONSTANTS is a module for the scaling constants for the compiled Fortran single and double precisions

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...
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...
double precision function	dlarmm (ANORM, BNORM, CNORM)
	DLARMM 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, 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 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, 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 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	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...
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...
real function	slarmm (ANORM, BNORM, CNORM)
	SLARMM 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, 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 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, 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 2-by-2 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...

Detailed Description

This is the group of Other Auxiliary routines