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Index
- 1.
- This index
lists related pairs of real and complex routines together,
in the same style as in Appendix A.
- 2.
- Routines are listed in alphanumeric order
of the real (single precision) routine name (which always begins with S-).
(See subsection 2.2.3 for details of the LAPACK naming scheme.)
- 3.
- A few complex routines have no real equivalents, and they are listed
first; routines listed in italics (for example, CROT), have real
equivalents in the Level 1 or Level 2 BLAS.
- 4.
- Double precision routines are not listed here;
they have names beginning with D- instead of
S-, or Z- instead of C-.
The only exceptions to this simple rule are that
the double precision versions of ICMAX1, SCSUM1 and CSRSCL
are named IZMAX1, DZSUM1 and ZDRSCL.
- 5.
- A few routines in the list have names that are independent of data type:
ILAENV, LSAME, LSAMEN and XERBLA.
- 6.
- This index gives only a brief description of the purpose of each
routine. For a precise description consult the leading comments in the code,
which have been written in the same style as for the driver and
computational routines.
Routine
Description
real
complex
CLACGV
Conjugates a complex vector.
CLACRM
Performs a matrix multiplication $C~=~A \ast B,ドル
where A is complex, B is
real, and C is complex.
CLAESY
Computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix,
and checks that the norm of the matrix of eigenvectors is larger than
a threshold value.
CROT
Applies a plane rotation with real cosine and complex sine
to a pair of complex vectors.
CSPMV
Computes the matrix-vector product
$y = \alpha Ax + \beta y,ドル
where $\alpha$
and $\beta$
are complex scalars,
x and y are complex vectors and
A is a complex symmetric matrix in packed storage.
CSPR
Performs the symmetric rank-1 update
[
画像:$A = \alpha x x^T + A$],
where $\alpha$
is a complex scalar,
x is a complex vector and
A is a complex symmetric matrix in packed storage.
CSROT
Applies a plane rotation with real cosine and sine
to a pair of complex vectors.
CSYMV
Computes the matrix-vector product
$y = \alpha Ax + \beta y,ドル
where $\alpha$
and $\beta$
are complex scalars,
x and y are complex vectors and
A is a complex symmetric matrix.
CSYR
Performs the symmetric rank-1 update
[
画像:$A = \alpha x x^T + A$],
where $\alpha$
is a complex scalar,
x is a complex vector and
A is a complex symmetric matrix.
ICMAX1
Finds the index of the element whose real part has maximum absolute value
(similar to the Level 1 BLAS ICAMAX,
but using the absolute value of the real part).
ILAENV
Environmental enquiry function which returns values for tuning
algorithmic performance.
LSAME
Tests two characters for equality regardless of case.
LSAMEN
Tests two character strings for equality regardless of case.
SCSUM1
Forms the 1-norm of a complex vector
(similar to the Level 1 BLAS SCASUM,
but using the true absolute value).
SGBTF2
CGBTF2
Computes an LU factorization of a general band matrix,
using partial pivoting with row interchanges
(unblocked algorithm).
SGEBD2
CGEBD2
Reduces a general rectangular matrix to real bidiagonal form
by an orthogonal/unitary transformation
(unblocked algorithm).
SGEHD2
CGEHD2
Reduces a general matrix to upper Hessenberg form
by an orthogonal/unitary similarity transformation
(unblocked algorithm).
SGELQ2
CGELQ2
Computes an LQ factorization of a general rectangular matrix
(unblocked algorithm).
Routine
Description
real
complex
SGEQL2
CGEQL2
Computes a QL factorization of a general rectangular matrix
(unblocked algorithm).
SGEQR2
CGEQR2
Computes a QR factorization of a general rectangular matrix
(unblocked algorithm).
SGERQ2
CGERQ2
Computes an RQ factorization of a general rectangular matrix
(unblocked algorithm).
SGESC2
CGESC2
Solves a system of linear equations
$A \ast X = scale \ast RHS$
using
the LU factorization with complete pivoting computed by xGETC2.
SGETC2
CGETC2
Computes an LU factorization with complete pivoting of the
general n-by-n matrix A
SGETF2
CGETF2
Computes an LU factorization of a general matrix,
using partial pivoting with row interchanges
(unblocked algorithm).
SGTTS2
CGTTS2
Solves one of the systems of equations $A \ast X = B$
or
$A^H \ast X = B,ドル
with a tridiagonal matrix A using the LU factorization computed
by SGTTRF/CGTTRF.
SLABAD
Returns the square root of the underflow and overflow thresholds
if the exponent-range is very large.
SLABRD
CLABRD
Reduces the first nb rows and columns of a general rectangular matrix A
to real bidiagonal form by an orthogonal/unitary transformation,
and returns auxiliary matrices
which are needed to apply the transformation to the unreduced part of A.
SLACON
CLACON
Estimates the 1-norm of a square matrix,
using reverse communication for evaluating matrix-vector products.
SLACPY
CLACPY
Copies all or part of one two-dimensional array to another.
SLADIV
CLADIV
Performs complex division in real arithmetic,
avoiding unnecessary overflow.
SLAE2
Computes the eigenvalues of a 2-by-2 symmetric matrix.
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.
SLAED0
CLAED0
Used by xSTEDC.
Computes all eigenvalues and corresponding eigenvectors of an
unreduced symmetric tridiagonal matrix using the divide and conquer
method.
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.
SLAED2
Used by SSTEDC.
Merges eigenvalues and deflates secular equation.
Used when the original matrix is tridiagonal.
SLAED3
Used by SSTEDC.
Finds the roots of the secular equation and updates the eigenvectors.
Used when the original matrix is tridiagonal.
SLAED4
Used by SSTEDC.
Finds a single root of the secular equation.
Routine
Description
real
complex
SLAED5
Used by SSTEDC.
Solves the 2-by-2 secular equation.
SLAED6
Used by SSTEDC.
Computes one Newton step in solution of secular equation.
SLAED7
CLAED7
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.
SLAED8
CLAED8
Used by xSTEDC.
Merges eigenvalues and deflates secular equation.
Used when the original matrix is dense.
SLAED9
Used by SSTEDC.
Finds the roots of the secular equation and updates the eigenvectors.
Used when the original matrix is dense.
SLAEDA
Used by SSTEDC.
Computes the Z vector determining the rank-one modification of the
diagonal matrix.
Used when the original matrix is dense.
SLAEIN
CLAEIN
Computes a specified right or left eigenvector of an upper Hessenberg matrix
by inverse iteration.
SLAEV2
CLAEV2
Computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian
matrix.
SLAEXC
Swaps adjacent diagonal blocks of a real upper quasi-triangular matrix
in Schur canonical form,
by an orthogonal similarity transformation.
SLAG2
Computes the eigenvalues of a 2-by-2 generalized eigenvalue problem
$A~-~w\ast B,ドル
with scaling as necessary to avoid over-/underflow.
SLAGS2
Computes 2-by-2 orthogonal matrices U, V, and Q, and applies
them to matrices A and B such that the rows of the transformed
A and B are parallel.
SLAGTF
Computes an LU factorization of a matrix
$(T - \lambda I),ドル
where T is a general tridiagonal matrix, and $\lambda$
a scalar,
using partial pivoting with row interchanges.
SLAGTM
CLAGTM
Performs a matrix-matrix product of the form
$C = \alpha A B + \beta C,ドル
where A is a tridiagonal matrix,
B and C are rectangular matrices,
and $\alpha$
and $\beta$
are scalars, which may be 0, 1, or -1.
SLAGTS
Solves the system of equations
$(T - \lambda I) x = y$
or
[
画像:$(T - \lambda I)^T x = y$],
where
T is a general tridiagonal matrix and $\lambda$
a scalar,
using the
LU factorization computed by SLAGTF.
SLAGV2
Computes the Generalized Schur factorization of a real 2-by-2
matrix pencil (A,B) where B is upper triangular.
SLAHQR
CLAHQR
Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix,
using the double-shift/single-shift QR algorithm.
SLAHRD
CLAHRD
Reduces the first nb columns of a general rectangular matrix A
so that elements below the kth subdiagonal are zero,
by an orthogonal/unitary transformation,
and returns auxiliary matrices
which are needed to apply the transformation to the unreduced part of A.
SLAIC1
CLAIC1
Applies one step of incremental condition estimation.
Routine
Description
real
complex
SLALN2
Solves a 1-by-1 or 2-by-2 system of equations of the form
$(\gamma A - \lambda D ) x = \sigma b$
or
[
画像:$(\gamma A^T - \lambda D) x = \sigma b$],
where
D is a diagonal matrix,
$\lambda,ドル
b and
x may be complex,
and $\sigma$
is a scale factor set to avoid overflow.
SLALS0
CLALS0
Used by xGELSD.
Applies back the multiplying factors of either the left or the right
singular vector matrix of a diagonal matrix appended by a row to
the right hand side matrix B in solving the least squares problem
using the divide and conquer SVD approach.
SLALSA
CLALSA
Used by xGELSD.
An intermediate step in solving the least squares problem
by computing the SVD of the coefficient matrix in compact form.
SLALSD
CLALSD
Used by xGELSD.
Uses the singular value decomposition of A to solve the least
squares problem of finding X to minimize the Euclidean norm of each
column of $A \ast X-B$.
SLAMCH
Determines machine parameters for floating-point arithmetic.
SLAMRG
Creates a permutation list which will merge the entries of
two independently sorted sets into a single set which is sorted
in ascending order.
SLANGB
CLANGB
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a general band matrix.
SLANGE
CLANGE
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a general rectangular matrix.
SLANGT
CLANGT
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a general tridiagonal matrix.
SLANHS
CLANHS
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of an upper Hessenberg matrix.
SLANSB
CLANSB CLANHB
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a real symmetric/complex symmetric/complex Hermitian band matrix.
SLANSP
CLANSP CLANHP
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a real symmetric/complex symmetric/complex Hermitian matrix
in packed storage.
SLANST
CLANHT
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a symmetric/Hermitian tridiagonal matrix.
SLANSY
CLANSY CLANHE
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a real symmetric/complex symmetric/complex Hermitian matrix.
SLANTB
CLANTB
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a triangular band matrix.
Routine
Description
real
complex
SLANTP
CLANTP
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a triangular matrix in packed storage.
SLANTR
CLANTR
Returns the value of the 1-norm, Frobenius norm, infinity-norm,
or the largest absolute value of any element,
of a triangular matrix.
SLANV2
Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix
in Schur canonical form.
SLAPLL
CLAPLL
Measures the linear dependence of two vectors X and Y.
SLAPMT
CLAPMT
Performs a forward or backward permutation of the columns of a matrix.
SLAQGB
CLAQGB
Scales a general band matrix,
using row and column scaling factors computed by SGBEQU/CGBEQU.
SLAQGE
CLAQGE
Scales a general rectangular matrix,
using row and column scaling factors computed by SGEEQU/CGEEQU.
SLAQP2
CLAQP2
Computes a QR factorization with column pivoting of the block
A(OFFSET+1:M,1:N). The block
A(1:OFFSET,1:N) is accordingly pivoted,
but not factorized.
SLAQPS
CLAQPS
Computes a step of QR factorization with column pivoting
of a real M-by-N matrix A by using Level 3 Blas.
SLAQSB
CLAQSB
Scales a symmetric/Hermitian band matrix,
using scaling factors computed by SPBEQU/CPBEQU.
SLAQSP
CLAQSP
Scales a symmetric/Hermitian matrix in packed storage,
using scaling factors computed by SPPEQU/CPPEQU.
SLAQSY
CLAQSY
Scales a symmetric/Hermitian matrix,
using scaling factors computed by SPOEQU/CPOEQU.
SLAQTR
Solves a real quasi-triangular system of equations,
or a complex quasi-triangular system of special form,
in real arithmetic.
SLAR1V
CLAR1V
Computes the (scaled) r
th column of the inverse of
the sumbmatrix in rows B1 through BN of the tridiagonal matrix
[
画像:$L D L^T - \sigma I$].
SLAR2V
CLAR2V
Applies a vector of plane rotations with real cosines and real/complex sines
from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
SLARF
CLARF
Applies an elementary reflector to a general rectangular matrix.
SLARFB
CLARFB
Applies a block reflector or its transpose/conjugate-transpose
to a general rectangular matrix.
SLARFG
CLARFG
Generates an elementary reflector (Householder matrix).
SLARFT
CLARFT
Forms the triangular factor T of a block reflector
H = I - V T VH.
Routine
Description
real
complex
SLARFX
CLARFX
Applies an elementary reflector to a general rectangular matrix,
with loop unrolling when the reflector has order $\leq 10$.
SLARGV
CLARGV
Generates a vector of plane rotations with real cosines and real/complex
sines.
SLARNV
CLARNV
Returns a vector of random numbers from a uniform or normal distribution.
SLARRB
Given the relatively robust representation(RRR) L D LT, SLARRB
does ``limited'' bisection to locate the eigenvalues of L D LT,
W(IFIRST) through W(ILAST), to more accuracy.
SLARRE
Given the tridiagonal matrix
T, SLARRE sets ``small'' off-diagonal
elements to zero, and for each unreduced block
Ti, it finds
the numbers $\sigma _ i ,ドル
the base
[
画像:$T_i - \sigma_i I~=~L_i D_i L_i^T$]
representations and the eigenvalues of each
Li Di LiT.
SLARRV
CLARRV
Computes the eigenvectors of the tridiagonal matrix
T = L D LT given L, D and the eigenvalues of L D LT.
SLARTG
CLARTG
Generates a plane rotation with real cosine and real/complex sine.
SLARTV
CLARTV
Applies a vector of plane rotations with real cosines and real/complex sines
to the elements of a pair of vectors.
SLARUV
Returns a vector of n random real numbers from a uniform (0,1) distribution
($n \leq 128$).
SLARZ
CLARZ
Applies an elementary reflector (as returned by xTZRZF) to a general
matrix.
SLARZB
CLARZB
Applies a block reflector or its transpose/conjugate-transpose to a
general matrix.
SLARZT
CLARZT
Forms the triangular factor T of a block reflector
H = I - V T VH.
SLAS2
Computes the singular values of a 2-by-2 triangular matrix.
SLASCL
CLASCL
Multiplies a general rectangular matrix by a real scalar defined as
cto/cfrom.
SLASD0
Used by SBDSDC. Computes via a divide and conquer method the singular values
of a real upper bidiagonal n-by-m matrix with diagonal D and offdiagonal
E, where M = N + SQRE.
SLASD1
Used by SBDSDC. Computes the SVD of an upper bidiagonal N-by-M matrix,
where
N = NL + NR + 1 and M = N + SQRE.
SLASD2
Used by SBDSDC. Merges the two sets of singular values together into a
single sorted set, and then it tries to deflate the size of the problem.
SLASD3
Used by SBDSDC. Finds all the 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.
Routine
Description
real
complex
SLASD4
Used by SBDSDC. Computes the square root of the I-th updated
eigenvalue of a positive symmetric rank-one modification to
a positive diagonal matrix.
SLASD5
Used by SBDSDC. Computes the square root of the I-th eigenvalue
of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix.
SLASD6
Used by SBDSDC. Computes the SVD of an updated upper bidiagonal matrix
obtained by merging two smaller ones by appending a row.
SLASD7
Used by SBDSDC. Merges the two sets of singular values together into a
single sorted set, and then it tries to deflate the size of the problem.
SLASD8
Used by SBDSDC. 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 (elements in DSIGMA).
SLASD9
Used by SBDSDC. 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 (elements in DSIGMA).
SLASDA
Used by SBDSDC. Computes the singular value decomposition (SVD) of a
real upper bidiagonal N-by-M matrix with diagonal D and offdiagonal E,
where M = N + SQRE.
SLASDQ
Used by SBDSDC. Computes the singular value decomposition (SVD) of a real
(upper or lower) bidiagonal matrix with diagonal D and
offdiagonal E, accumulating the transformations if desired.
SLASDT
Used by SBDSDC. Creates a tree of subproblems for bidiagonal divide and
conquer.
SLASET
CLASET
Initializes the off-diagonal elements of a matrix to $\alpha$
and the diagonal elements to $\beta$.
SLASQ1
Used by SBDSQR.
Computes the singular values of a real n-by-n bidiagonal
matrix with diagonal D and offdiagonal E.
SLASQ2
Used by SBDSQR and SSTEGR.
Computes all the eigenvalues of the symmetric positive
definite tridiagonal matrix associated with the qd array Z to high
relative accuracy.
SLASQ3
Used by SBDSQR.
Checks for deflation, computes a shift (TAU) and calls dqds.
SLASQ4
Used by SBDSQR.
Computes an approximation TAU to the smallest eigenvalue
using values of d from the previous transform.
SLASQ5
Used by SBDSQR and SSTEGR.
Computes one dqds transform in ping-pong form.
SLASQ6
Used by SBDSQR and SSTEGR.
computes one dqds transform in ping-pong form.
SLASR
CLASR
Applies a sequence of plane rotations to a general rectangular
matrix.
Routine
Description
real
complex
SLASRT
Sorts numbers in increasing or decreasing order using Quick Sort,
reverting to Insertion sort on arrays of size $\leq$
20.
SLASSQ
CLASSQ
Updates a sum of squares represented in scaled form.
SLASV2
Computes the singular value decomposition of a 2-by-2 triangular matrix.
SLASWP
CLASWP
Performs a sequence of row interchanges on a general rectangular matrix.
SLASY2
Solves the Sylvester matrix equation
$A X \pm X B = \sigma C$
where A and B are of order 1 or 2,
and may be transposed,
and $\sigma$
is a scale factor.
SLASYF
CLASYF CLAHEF
Computes a partial factorization of
a real symmetric/complex symmetric/complex Hermitian indefinite matrix,
using the diagonal pivoting method.
SLATBS
CLATBS
Solves a triangular banded system of equations
$A x = \sigma b,ドル
$A^T x = \sigma b,ドル
or
$A^H x = \sigma b,ドル
where $\sigma$
is a scale factor set to prevent overflow.
SLATDF
CLATDF
Uses the LU factorization of the n-by-n matrix computed by
SGETC2 and computes a contribution to the reciprocal Dif-estimate.
SLATPS
CLATPS
Solves a triangular system of equations
$A x = \sigma b,ドル
$A^T x = \sigma b,ドル
or
$A^H x = \sigma b,ドル
where A is held in packed storage,
and $\sigma$
is a scale factor set to prevent overflow.
SLATRD
CLATRD
Reduces the first nb rows and columns of a symmetric/Hermitian matrix A
to real tridiagonal form by an orthogonal/unitary similarity transformation,
and returns auxiliary matrices
which are needed to apply the transformation to the unreduced part of A.
SLATRS
CLATRS
Solves a triangular system of equations
$A x = \sigma b,ドル
$A^T x = \sigma b,ドル
or
$A^H x = \sigma b,ドル
where $\sigma$
is a scale factor set to prevent overflow.
SLATRZ
CLATRZ
Factors an upper trapezoidal matrix by means of orthogonal/unitary
transformations.
SLAUU2
CLAUU2
Computes the product U UH or LH L,
where U and L are upper or lower triangular matrices
(unblocked algorithm).
SLAUUM
CLAUUM
Computes the product U UH or LH L,
where U and L are upper or lower triangular matrices.
SORG2L
CUNG2L
Generates all or part of the orthogonal/unitary matrix Q
from a QL factorization determined by SGEQLF/CGEQLF
(unblocked algorithm).
SORG2R
CUNG2R
Generates all or part of the orthogonal/unitary matrix Q
from a QR factorization determined by SGEQRF/CGEQRF
(unblocked algorithm).
SORGL2
CUNGL2
Generates all or part of the orthogonal/unitary matrix Q
from an LQ factorization determined by SGELQF/CGELQF
(unblocked algorithm).
Routine
Description
real
complex
SORGR2
CUNGR2
Generates all or part of the orthogonal/unitary matrix Q
from an RQ factorization determined by SGERQF/CGERQF
(unblocked algorithm).
SORM2L
CUNM2L
Multiplies a general matrix by the orthogonal/unitary matrix
from a QL factorization determined by SGEQLF/CGEQLF
(unblocked algorithm).
SORM2R
CUNM2R
Multiplies a general matrix by the orthogonal/unitary matrix
from a QR factorization determined by SGEQRF/CGEQRF
(unblocked algorithm).
SORML2
CUNML2
Multiplies a general matrix by the orthogonal/unitary matrix
from an LQ factorization determined by SGELQF/CGELQF
(unblocked algorithm).
SORMR2
CUNMR2
Multiplies a general matrix by the orthogonal/unitary matrix
from an RQ factorization determined by SGERQF/CGERQF
(unblocked algorithm).
SORMR3
CUNMR3
Multiplies a general matrix by the orthogonal/unitary matrix
from an RZ factorization determined by STZRZF/CTZRZF
(unblocked algorithm).
SPBTF2
CPBTF2
Computes the Cholesky factorization of
a symmetric/Hermitian positive definite band matrix
(unblocked algorithm).
SPOTF2
CPOTF2
Computes the Cholesky factorization of
a symmetric/Hermitian positive definite matrix
(unblocked algorithm).
SPTTS2
CPTTS2
Solves a tridiagonal system of the form
$A \ast X = B$
using the
$L \ast D \ast L^H$
factorization of A computed by
SPTTRF/CPTTRF.
SRSCL
CSRSCL
Multiplies a vector by the reciprocal of a real scalar.
SSYGS2
CHEGS2
Reduces a symmetric/Hermitian definite generalized eigenproblem
$Ax = \lambda Bx,ドル
$ABx=\lambda x,ドル
or $BAx=\lambda x,ドル
to standard form, where B has been factorized by SPOTRF/CPOTRF
(unblocked algorithm).
SSYTD2
CHETD2
Reduces a symmetric/Hermitian matrix to
real symmetric tridiagonal form
by an orthogonal/unitary similarity transformation
(unblocked algorithm).
SSYTF2
CSYTF2 CHETF2
Computes the factorization of
a real symmetric/complex symmetric/complex Hermitian indefinite matrix,
using the diagonal pivoting method
(unblocked algorithm).
STGEX2
CTGEX2
Swaps adjacent diagonal blocks (A11, B11) and (A22, B22)
of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair
(A, B) by an orthogonal/unitary equivalence transformation.
STGSY2
CTGSY2
Solves the generalized Sylvester equation (unblocked algorithm).
STRTI2
CTRTI2
Computes the inverse of a triangular matrix
(unblocked algorithm).
XERBLA
Error handling routine called by LAPACK routines
if an input parameter has an invalid value.
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Susan Blackford
1999年10月01日
