This code provides a wrapper for the LAPACK routines currently used at the NWTC (mainly codes in the FAST framework). More...

Data Types
interface	lapack_axpy

interface	lapack_copy
	straight-up lapack routines (from ExtPtfm_MCKF): More...

interface	lapack_gbsv
	Computes the solution to system of linear equations A * X = B for GB matrices. More...

interface	lapack_gemm
	Computes scalar1op( A )op( B ) + scalar2C where op(x) = x or op(x) = x*T for matrices A, B, and C. More...

interface	lapack_gemv

interface	lapack_gesv
	Computes the solution to system of linear equations A * X = B for GE matrices. More...

interface	lapack_gesvd
	Compute the SVD for a general matrix A = USV^T. More...

interface	lapack_getrf
	Factor matrix into A=PLU. More...

interface	lapack_getri
	Compute the inverse of a matrix using the LU factorization. More...

interface	lapack_getrs
	Solve system(s) of linear equations Ax=PLUx=b. More...

interface	lapack_ggev
	Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B). More...

interface	lapack_posv
	Compute the solution to system of linear equations A * X = B for PO matrices. More...

interface	lapack_pptrf
	Compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. More...

interface	lapack_tpttr
	Unpack packed (1D) to regular matrix format (2D) More...

Functions/Subroutines
subroutine	lapack_dgbsv (N, KL, KU, NRHS, AB, IPIV, B, ErrStat, ErrMsg)
	general banded solve: Computes the solution to system of linear equations A * X = B for GB (general, banded) matrices. More...

subroutine	lapack_sgbsv (N, KL, KU, NRHS, AB, IPIV, B, ErrStat, ErrMsg)
	general banded solve: Computes the solution to system of linear equations A * X = B for GB (general, banded) matrices. More...

subroutine	lapack_dgemm (TRANSA, TRANSB, ALPHA, A, B, BETA, C, ErrStat, ErrMsg)
	general matrix multiply: computes C = alphaop( A )op( B ) + betaC where op(x) = x or op(x) = x*T for matrices A, B, and C use LAPACK_GEMM (nwtc_lapack::lapack_gemm) instead of this specific function. More...

subroutine	lapack_sgemm (TRANSA, TRANSB, ALPHA, A, B, BETA, C, ErrStat, ErrMsg)
	general matrix multiply: computes C = alphaop( A )op( B ) + betaC where op(x) = x or op(x) = x*T for matrices A, B, and C use LAPACK_GEMM (nwtc_lapack::lapack_gemm) instead of this specific function. More...

subroutine	lapack_dgesv (N, A, IPIV, B, ErrStat, ErrMsg)
	general solve: Computes the solution to system of linear equations A * X = B for GE matrices. More...

subroutine	lapack_sgesv (N, A, IPIV, B, ErrStat, ErrMsg)
	general solve: Computes the solution to system of linear equations A * X = B for GE matrices. More...

subroutine	lapack_dgetrf (M, N, A, IPIV, ErrStat, ErrMsg)
	general matrix factorization: Factor matrix into A=PLU. More...

subroutine	lapack_sgetrf (M, N, A, IPIV, ErrStat, ErrMsg)
	general matrix factorization: Factor matrix into A=PLU. More...

subroutine	lapack_dgetrs (TRANS, N, A, IPIV, B, ErrStat, ErrMsg)
	general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b. More...

subroutine	lapack_dgetrs1 (TRANS, N, A, IPIV, B, ErrStat, ErrMsg)
	general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b. More...

subroutine	lapack_sgetrs (TRANS, N, A, IPIV, B, ErrStat, ErrMsg)
	general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b. More...

subroutine	lapack_sgetrs1 (TRANS, N, A, IPIV, B, ErrStat, ErrMsg)
	general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b. More...

subroutine	lapack_dgetri (N, A, IPIV, WORK, LWORK, ErrStat, ErrMsg)
	Compute the inverse of a general matrix using the LU factorization. More...

subroutine	lapack_sgetri (N, A, IPIV, WORK, LWORK, ErrStat, ErrMsg)
	Compute the inverse of a general matrix using the LU factorization. More...

subroutine	lapack_dggev (JOBVL, JOBVR, N, A, B, ALPHAR, ALPHAI, BETA, VL, VR, WORK, LWORK, ErrStat, ErrMsg)
	Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B). More...

subroutine	lapack_sggev (JOBVL, JOBVR, N, A, B, ALPHAR, ALPHAI, BETA, VL, VR, WORK, LWORK, ErrStat, ErrMsg)
	Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B). More...

subroutine	lapack_dposv (UPLO, N, NRHS, A, B, ErrStat, ErrMsg)
	Compute the solution to system of linear equations A * X = B for PO (positive-definite) matrices. More...

subroutine	lapack_sposv (UPLO, N, NRHS, A, B, ErrStat, ErrMsg)
	Compute the solution to system of linear equations A * X = B for PO (positive-definite) matrices. More...

subroutine	lapack_dpptrf (UPLO, N, AP, ErrStat, ErrMsg)
	Compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. More...

subroutine	lapack_spptrf (UPLO, N, AP, ErrStat, ErrMsg)
	Compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. More...

subroutine	lapack_dgesvd (JOBU, JOBVT, M, N, A, S, U, VT, WORK, LWORK, ErrStat, ErrMsg)
	Compute singular value decomposition (SVD) for a general matrix, A. More...

subroutine	lapack_sgesvd (JOBU, JOBVT, M, N, A, S, U, VT, WORK, LWORK, ErrStat, ErrMsg)
	Compute singular value decomposition (SVD) for a general matrix, A. More...

subroutine	lapack_dtpttr (UPLO, N, AP, A, LDA, ErrStat, ErrMsg)
	Unpack a by-column-packed array into a 2D matrix format See documentation in DTPTTR/STPTTR source code. More...

subroutine	lapack_stpttr (UPLO, N, AP, A, LDA, ErrStat, ErrMsg)
	Unpack a by-column-packed array into a 2D matrix format. More...

Detailed Description

This code provides a wrapper for the LAPACK routines currently used at the NWTC (mainly codes in the FAST framework).

This enables us to call generic routines (not single- or double-precision specific ones) so that we don't have to change source code to compile in double vs. single precision.

Function/Subroutine Documentation

◆ lapack_dgbsv()

subroutine nwtc_lapack::lapack_dgbsv	(	integer, intent(in)	N,
		integer, intent(in)	KL,
		integer, intent(in)	KU,
		integer, intent(in)	NRHS,
		real(r8ki), dimension( :, : ), intent(inout)	AB,
		integer, dimension( : ), intent(out)	IPIV,
		real(r8ki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general banded solve: Computes the solution to system of linear equations A * X = B for GB (general, banded) matrices.

use LAPACK_GBSV (nwtc_lapack::lapack_gbsv) instead of this specific function.

Parameters

[in]	kl	The number of subdiagonals within the band of A. KL >= 0.
[in]	ku	The number of superdiagonals within the band of A. KU >= 0.
[in]	n	The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]	ab	On entry, the matrix A in band storage, in rows KL+1 to 2KL+KU+1; rows 1 to KL of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) On exit, details of the factorization: U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2KL+KU+1.
[in,out]	b	On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[out]	ipiv	The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dgemm()

subroutine nwtc_lapack::lapack_dgemm	(	character(1), intent(in)	TRANSA,
		character(1), intent(in)	TRANSB,
		real(r8ki), intent(in)	ALPHA,
		real(r8ki), dimension( :, : ), intent(in)	A,
		real(r8ki), dimension( :, : ), intent(in)	B,
		real(r8ki), intent(in)	BETA,
		real(r8ki), dimension( :, : ), intent(inout)	C,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general matrix multiply: computes C = alpha*op( A )*op( B ) + beta*C where op(x) = x or op(x) = x**T for matrices A, B, and C use LAPACK_GEMM (nwtc_lapack::lapack_gemm) instead of this specific function.

Parameters

[in]	transa	On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A. TRANSA = 'T' or 't', op( A ) = A**T.
[in]	transb	On entry, TRANSB specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = B**T.
[in]	alpha	On entry, ALPHA specifies the scalar alpha.
[in]	beta	On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.
[in]	a	Matrix A
[in]	b	Matrix B
[in,out]	c	Matrix C: Before entry, C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alphaop( A )op( B ) + beta*C ).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dgesv()

subroutine nwtc_lapack::lapack_dgesv	(	integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(inout)	A,
		integer, dimension( : ), intent(out)	IPIV,
		real(r8ki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general solve: Computes the solution to system of linear equations A * X = B for GE matrices.

use LAPACK_GESV (nwtc_lapack::lapack_gesv) instead of this specific function.

Parameters

[in]	n	The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in,out]	a	On entry, the N-by-N coefficient matrix A. On exit, the factors L and U from the factorization A = PLU; the unit diagonal elements of L are not stored.
[in,out]	b	On entry, the N-by-NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[out]	ipiv	The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dgesvd()

subroutine nwtc_lapack::lapack_dgesvd	(	character(1), intent(in)	JOBU,
		character(1), intent(in)	JOBVT,
		integer, intent(in)	M,
		integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(inout)	A,
		real(r8ki), dimension( : ), intent(out)	S,
		real(r8ki), dimension( :, : ), intent(out)	U,
		real(r8ki), dimension( :, : ), intent(out)	VT,
		real(r8ki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute singular value decomposition (SVD) for a general matrix, A.

use LAPACK_DGESVD (nwtc_lapack::lapack_dgesvd) instead of this specific function.

Parameters

[in]	jobu	'A': all M columns of U are returned in array U; 'S': the first min(m,n) columns of U (the left singular vectors) are returned in the array U; 'O': the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A; 'N': no columns of U (no left singular vectors) are computed.
[in]	jobvt	'A': all N rows of V^T are returned in the array VT; 'S': the first min(m,n) rows of V^T (the right singular vectors) are returned in the array VT; 'O': the first min(m,n) rows of V^T (the right singular vectors) are overwritten on the array A; 'N': no rows of V**T (no right singular vectors) are computed.
[in]	m	The number of rows of the input matrix A. M >= 0.
[in]	n	The number of columns of the input matrix A. N >= 0.
[in,out]	a	A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBU = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBVT = 'O', A is overwritten with the first min(m,n) rows of V**T (the right singular vectors, stored rowwise); if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A are destroyed.
[out]	s	S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).
[out]	u	U is DOUBLE PRECISION array, dimension (LDU,UCOL) (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU = 'A', U contains the M-by-M orthogonal matrix U; if JOBU = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBU = 'N' or 'O', U is not referenced.
[out]	vt	VT is DOUBLE PRECISION array, dimension (LDVT,N) If JOBVT = 'A', VT contains the N-by-N orthogonal matrix VT; if JOBVT = 'S', VT contains the first min(m,n) rows of VT (the right singular vectors, stored rowwise); if JOBVT = 'N' or 'O', VT is not referenced.
[in,out]	work	dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]	lwork	The dimension of the array WORK. LWORK >= MAX(1,5MIN(M,N)) for the paths (see comments inside code): PATH 1 (M much larger than N, JOBU='N') PATH 1t (N much larger than M, JOBVT='N') LWORK >= MAX(1,3MIN(M,N) + MAX(M,N),5*MIN(M,N)) for the other paths For good performance, LWORK should generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dgetrf()

subroutine nwtc_lapack::lapack_dgetrf	(	integer, intent(in)	M,
		integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(inout)	A,
		integer, dimension( : ), intent(out)	IPIV,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general matrix factorization: Factor matrix into A=PLU.

use LAPACK_GETRF (nwtc_lapack::lapack_getrf) instead of this specific function.

Parameters

[in]	m	The number of rows of the matrix A. M >= 0.
[in]	n	The number of columns of the matrix A. N >= 0.
[in,out]	a	On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = PLU; the unit diagonal elements of L are not stored.
[out]	ipiv	The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dgetri()

subroutine nwtc_lapack::lapack_dgetri	(	integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(inout)	A,
		integer, dimension( : ), intent(in)	IPIV,
		real(r8ki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute the inverse of a general matrix using the LU factorization.

use LAPACK_GETRI (nwtc_lapack::lapack_getri) instead of this specific function.

Parameters

[in]	n	The order of the matrix A. N >= 0.
[in]	lwork	The dimension of the array WORK. LWORK >= max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[in]	ipiv	dimension (N). The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
[in,out]	a	On entry, the factors L and U from the factorization A = PLU as computed by DGETRF. On exit, if INFO = 0, the inverse of the original matrix A.
[in,out]	work	On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dgetrs()

subroutine nwtc_lapack::lapack_dgetrs	(	character(1), intent(in)	TRANS,
		integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(in)	A,
		integer, dimension( : ), intent(in)	IPIV,
		real(r8ki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b.

use LAPACK_GETRS (nwtc_lapack::lapack_getrs) instead of this specific function.

Parameters

[in]	trans	Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A*T X = B (Transpose) = 'C': A*T X = B (Conjugate transpose = Transpose)
[in]	n	The order of the matrix A. N >= 0.
[in]	ipiv	The pivot indices from DGETRF (nwtc_lapack::lapack_getrf); for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
[in]	a	The factors L and U from the factorization A = PLU as computed by DGETRF.
[in,out]	b	On entry, the right hand side matrix B. On exit, the solution matrix X.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dgetrs1()

subroutine nwtc_lapack::lapack_dgetrs1	(	character(1), intent(in)	TRANS,
		integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(in)	A,
		integer, dimension( : ), intent(in)	IPIV,
		real(r8ki), dimension( : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b.

use LAPACK_GETRS (nwtc_lapack::lapack_getrs) instead of this specific function.

Parameters

[in]	trans	Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A*T X = B (Transpose) = 'C': A*T X = B (Conjugate transpose = Transpose)
[in]	n	The order of the matrix A. N >= 0.
[in]	ipiv	The pivot indices from DGETRF (nwtc_lapack::lapack_getrf); for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
[in]	a	The factors L and U from the factorization A = PLU as computed by DGETRF.
[in,out]	b	On entry, the right hand side matrix B. On exit, the solution matrix X.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dggev()

subroutine nwtc_lapack::lapack_dggev	(	character(1), intent(in)	JOBVL,
		character(1), intent(in)	JOBVR,
		integer, intent(in)	N,
		real(r8ki), dimension( :, : ), intent(inout)	A,
		real(r8ki), dimension( :, : ), intent(inout)	B,
		real(r8ki), dimension( : ), intent(out)	ALPHAR,
		real(r8ki), dimension( : ), intent(out)	ALPHAI,
		real(r8ki), dimension( : ), intent(out)	BETA,
		real(r8ki), dimension( :, : ), intent(out)	VL,
		real(r8ki), dimension( :, : ), intent(out)	VR,
		real(r8ki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B).

use LAPACK_GGEV (nwtc_lapack::lapack_ggev) instead of this specific function.

Parameters

[in]	jobvl	= 'N': do not compute the left generalized eigenvectors; = 'V': compute the left generalized eigenvectors.
[in]	jobvr	= 'N': do not compute the right generalized eigenvectors; = 'V': compute the right generalized eigenvectors.
[in]	n	The order of the matrices A, B, VL, and VR. N >= 0.
[in]	lwork	The dimension of the array WORK. LWORK >= max(1,8*N). For good performance, LWORK must generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[in,out]	a	dimension (LDA, N). On entry, the matrix A in the pair (A,B). On exit, A has been overwritten.
[in,out]	b	dimension (LDB, N). On entry, the matrix B in the pair (A,B). On exit, B has been overwritten.
[out]	alphar	dimension (N). See comments for variable "Beta"
[out]	alphai	dimension (N). See comments for variable "Beta".
[out]	beta	On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the generalized eigenvalues. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) negative.

Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio alpha/beta. However, ALPHAR and ALPHAI will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).

Parameters

[out]	vl	dimension (LDVL,N). If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then u(j) = VL(:,j)+iVL(:,j+1) and u(j+1) = VL(:,j)-iVL(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVL = 'N'.
[out]	vr	dimension (LDVR,N). If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then v(j) = VR(:,j)+iVR(:,j+1) and v(j+1) = VR(:,j)-iVR(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVR = 'N'.
[in,out]	work	dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_dposv()

subroutine nwtc_lapack::lapack_dposv	(	character(1), intent(in)	UPLO,
		integer, intent(in)	N,
		integer, intent(in)	NRHS,
		real(r8ki), dimension( :, : ), intent(inout)	A,
		real(r8ki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute the solution to system of linear equations A * X = B for PO (positive-definite) matrices.

use LAPACK_POSV (nwtc_lapack::lapack_posv) instead of this specific function.

Parameters

[in]	n	The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]	a	On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U*TU or A = LL*T.
[in,out]	b	On entry, the N-by-NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[out]	errstat	Error level
[out]	errmsg	Message describing error
[in]	uplo	'U': Upper triangle of A is stored; 'L': Lower triangle of A is stored.

◆ lapack_dpptrf()

subroutine nwtc_lapack::lapack_dpptrf	(	character(1), intent(in)	UPLO,
		integer, intent(in)	N,
		real(r8ki), dimension( : ), intent(inout)	AP,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format.

use LAPACK_PPTRF (nwtc_lapack::lapack_pptrf) instead of this specific function.

Parameters

[in]	n	The order of the matrix A. N >= 0.
[in,out]	ap	AP is REAL array, dimension (N(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = UTU or A = LL*T, in the same storage format as A.

Further details: The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13 a14 a22 a23 a24 a33 a34 (aij = aji) a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Parameters

[out]	errstat	Error level
[out]	errmsg	Message describing error
[in]	uplo	'U': Upper triangle of A is stored; 'L': Lower triangle of A is stored.

◆ lapack_dtpttr()

subroutine nwtc_lapack::lapack_dtpttr	(	character(1), intent(in)	UPLO,
		integer, intent(in)	N,
		real(r8ki), dimension( : ), intent(in)	AP,
		real(r8ki), dimension( :,: ), intent(out)	A,
		integer, intent(in)	LDA,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Unpack a by-column-packed array into a 2D matrix format See documentation in DTPTTR/STPTTR source code.

Parameters

[in]	uplo	= 'U': A is an upper triangular matrix; 'L': A is a lower triangular matrix
[in]	n	The order of matrix A and AP.
[in]	lda	The leading dimension of the matrix A. LDA ? max(1,N)
[out]	errstat	Error level
[out]	errmsg	Message describing error
[in]	ap	Packed array
[out]	a	Unpacked array : Note AP(1)=A(1,1); AP(2)=A(1,2); AP(3)=A(2,2); AP(4)=A(1,3) etc. by column, upper triang

◆ lapack_sgbsv()

subroutine nwtc_lapack::lapack_sgbsv	(	integer, intent(in)	N,
		integer, intent(in)	KL,
		integer, intent(in)	KU,
		integer, intent(in)	NRHS,
		real(siki), dimension( :, : ), intent(inout)	AB,
		integer, dimension( : ), intent(out)	IPIV,
		real(siki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general banded solve: Computes the solution to system of linear equations A * X = B for GB (general, banded) matrices.

use LAPACK_GBSV (nwtc_lapack::lapack_gbsv) instead of this specific function.

Parameters

[in]	kl	The number of subdiagonals within the band of A. KL >= 0.
[in]	ku	The number of superdiagonals within the band of A. KU >= 0.
[in]	n	The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]	ab	On entry, the matrix A in band storage, in rows KL+1 to 2KL+KU+1; rows 1 to KL of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) On exit, details of the factorization: U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2KL+KU+1.
[in,out]	b	On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[out]	ipiv	The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sgemm()

subroutine nwtc_lapack::lapack_sgemm	(	character(1), intent(in)	TRANSA,
		character(1), intent(in)	TRANSB,
		real(siki), intent(in)	ALPHA,
		real(siki), dimension( :, : ), intent(in)	A,
		real(siki), dimension( :, : ), intent(in)	B,
		real(siki), intent(in)	BETA,
		real(siki), dimension( :, : ), intent(inout)	C,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general matrix multiply: computes C = alpha*op( A )*op( B ) + beta*C where op(x) = x or op(x) = x**T for matrices A, B, and C use LAPACK_GEMM (nwtc_lapack::lapack_gemm) instead of this specific function.

Parameters

[in]	transa	On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A. TRANSA = 'T' or 't', op( A ) = A**T.
[in]	transb	On entry, TRANSB specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = B**T.
[in]	alpha	On entry, ALPHA specifies the scalar alpha.
[in]	beta	On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.
[in]	a	Matrix A
[in]	b	Matrix B
[in,out]	c	Matrix C: Before entry, C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alphaop( A )op( B ) + beta*C ).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sgesv()

subroutine nwtc_lapack::lapack_sgesv	(	integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(inout)	A,
		integer, dimension( : ), intent(out)	IPIV,
		real(siki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general solve: Computes the solution to system of linear equations A * X = B for GE matrices.

use LAPACK_GESV (nwtc_lapack::lapack_gesv) instead of this specific function.

Parameters

[in]	n	The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in,out]	a	On entry, the N-by-N coefficient matrix A. On exit, the factors L and U from the factorization A = PLU; the unit diagonal elements of L are not stored.
[in,out]	b	On entry, the N-by-NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[out]	ipiv	The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sgesvd()

subroutine nwtc_lapack::lapack_sgesvd	(	character(1), intent(in)	JOBU,
		character(1), intent(in)	JOBVT,
		integer, intent(in)	M,
		integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(inout)	A,
		real(siki), dimension( : ), intent(out)	S,
		real(siki), dimension( :, : ), intent(out)	U,
		real(siki), dimension( :, : ), intent(out)	VT,
		real(siki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute singular value decomposition (SVD) for a general matrix, A.

use LAPACK_SGESVD (nwtc_lapack::lapack_sgesvd) instead of this specific function.

Parameters

[in]	jobu	'A': all M columns of U are returned in array U; 'S': the first min(m,n) columns of U (the left singular vectors) are returned in the array U; 'O': the first min(m,n) columns of U (the left singular vectors) are overwritten on the array A; 'N': no columns of U (no left singular vectors) are computed.
[in]	jobvt	'A': all N rows of V^T are returned in the array VT; 'S': the first min(m,n) rows of V^T (the right singular vectors) are returned in the array VT; 'O': the first min(m,n) rows of V^T (the right singular vectors) are overwritten on the array A; 'N': no rows of V**T (no right singular vectors) are computed.
[in]	m	The number of rows of the input matrix A. M >= 0.
[in]	n	The number of columns of the input matrix A. N >= 0.
[in,out]	a	A is SINGLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBU = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBVT = 'O', A is overwritten with the first min(m,n) rows of V**T (the right singular vectors, stored rowwise); if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A are destroyed.
[out]	s	S is SINGLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).
[out]	u	U is SINGLE PRECISION array, dimension (LDU,UCOL) (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU = 'A', U contains the M-by-M orthogonal matrix U; if JOBU = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBU = 'N' or 'O', U is not referenced.
[out]	vt	VT is SINGLE PRECISION array, dimension (LDVT,N) If JOBVT = 'A', VT contains the N-by-N orthogonal matrix VT; if JOBVT = 'S', VT contains the first min(m,n) rows of VT (the right singular vectors, stored rowwise); if JOBVT = 'N' or 'O', VT is not referenced.
[in,out]	work	dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]	lwork	The dimension of the array WORK. LWORK >= MAX(1,5MIN(M,N)) for the paths (see comments inside code): PATH 1 (M much larger than N, JOBU='N') PATH 1t (N much larger than M, JOBVT='N') LWORK >= MAX(1,3MIN(M,N) + MAX(M,N),5*MIN(M,N)) for the other paths For good performance, LWORK should generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sgetrf()

subroutine nwtc_lapack::lapack_sgetrf	(	integer, intent(in)	M,
		integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(inout)	A,
		integer, dimension( : ), intent(out)	IPIV,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general matrix factorization: Factor matrix into A=PLU.

use LAPACK_GETRF (nwtc_lapack::lapack_getrf) instead of this specific function.

Parameters

[in]	m	The number of rows of the matrix A. M >= 0.
[in]	n	The number of columns of the matrix A. N >= 0.
[in,out]	a	On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = PLU; the unit diagonal elements of L are not stored.
[out]	ipiv	The pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sgetri()

subroutine nwtc_lapack::lapack_sgetri	(	integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(inout)	A,
		integer, dimension( : ), intent(in)	IPIV,
		real(siki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute the inverse of a general matrix using the LU factorization.

use LAPACK_GETRI (nwtc_lapack::lapack_getri) instead of this specific function.

Parameters

[in]	n	The order of the matrix A. N >= 0.
[in]	lwork	The dimension of the array WORK. LWORK >= max(1,N). For optimal performance LWORK >= N*NB, where NB is the optimal blocksize returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[in]	ipiv	dimension (N). The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
[in,out]	a	On entry, the factors L and U from the factorization A = PLU as computed by SGETRF. On exit, if INFO = 0, the inverse of the original matrix A.
[in,out]	work	On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sgetrs()

subroutine nwtc_lapack::lapack_sgetrs	(	character(1), intent(in)	TRANS,
		integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(in)	A,
		integer, dimension( : ), intent(in)	IPIV,
		real(siki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b.

use LAPACK_GETRS (nwtc_lapack::lapack_getrs) instead of this specific function.

Parameters

[in]	trans	Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A*T X = B (Transpose) = 'C': A*T X = B (Conjugate transpose = Transpose)
[in]	n	The order of the matrix A. N >= 0.
[in]	ipiv	The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
[in]	a	The factors L and U from the factorization A = PLU as computed by SGETRF.
[in,out]	b	On entry, the right hand side matrix B. On exit, the solution matrix X.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sgetrs1()

subroutine nwtc_lapack::lapack_sgetrs1	(	character(1), intent(in)	TRANS,
		integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(in)	A,
		integer, dimension( : ), intent(in)	IPIV,
		real(siki), dimension( : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

general solve of factorized matrix: Solve system of linear equations Ax=PLUx=b.

use LAPACK_GETRS (nwtc_lapack::lapack_getrs) instead of this specific function.

Parameters

[in]	trans	Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A*T X = B (Transpose) = 'C': A*T X = B (Conjugate transpose = Transpose)
[in]	n	The order of the matrix A. N >= 0.
[in]	ipiv	The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
[in]	a	The factors L and U from the factorization A = PLU as computed by SGETRF.
[in,out]	b	On entry, the right hand side matrix B. On exit, the solution matrix X.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sggev()

subroutine nwtc_lapack::lapack_sggev	(	character(1), intent(in)	JOBVL,
		character(1), intent(in)	JOBVR,
		integer, intent(in)	N,
		real(siki), dimension( :, : ), intent(inout)	A,
		real(siki), dimension( :, : ), intent(inout)	B,
		real(siki), dimension( : ), intent(out)	ALPHAR,
		real(siki), dimension( : ), intent(out)	ALPHAI,
		real(siki), dimension( : ), intent(out)	BETA,
		real(siki), dimension( :, : ), intent(out)	VL,
		real(siki), dimension( :, : ), intent(out)	VR,
		real(siki), dimension( : ), intent(inout)	WORK,
		integer, intent(in)	LWORK,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute generalized eigenvalues and/or eigenvectors for a pair of N-by-N real nonsymmetric matrices (A,B).

use LAPACK_GGEV (nwtc_lapack::lapack_ggev) instead of this specific function.

Parameters

[in]	jobvl	= 'N': do not compute the left generalized eigenvectors; = 'V': compute the left generalized eigenvectors.
[in]	jobvr	= 'N': do not compute the right generalized eigenvectors; = 'V': compute the right generalized eigenvectors.
[in]	n	The order of the matrices A, B, VL, and VR. N >= 0.
[in]	lwork	The dimension of the array WORK. LWORK >= max(1,8*N). For good performance, LWORK must generally be larger. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[in,out]	a	dimension (LDA, N). On entry, the matrix A in the pair (A,B). On exit, A has been overwritten.
[in,out]	b	dimension (LDB, N). On entry, the matrix B in the pair (A,B). On exit, B has been overwritten.
[out]	alphar	dimension (N). See comments for variable "Beta"
[out]	alphai	dimension (N). See comments for variable "Beta".
[out]	beta	On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the generalized eigenvalues. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) negative.

Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio alpha/beta. However, ALPHAR and ALPHAI will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).

Parameters

[out]	vl	dimension (LDVL,N). If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then u(j) = VL(:,j)+iVL(:,j+1) and u(j+1) = VL(:,j)-iVL(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVL = 'N'.
[out]	vr	dimension (LDVR,N). If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-th eigenvalues form a complex conjugate pair, then v(j) = VR(:,j)+iVR(:,j+1) and v(j+1) = VR(:,j)-iVR(:,j+1). Each eigenvector is scaled so the largest component has abs(real part)+abs(imag. part)=1. Not referenced if JOBVR = 'N'.
[in,out]	work	dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[out]	errstat	Error level
[out]	errmsg	Message describing error

◆ lapack_sposv()

subroutine nwtc_lapack::lapack_sposv	(	character(1), intent(in)	UPLO,
		integer, intent(in)	N,
		integer, intent(in)	NRHS,
		real(siki), dimension( :, : ), intent(inout)	A,
		real(siki), dimension( :, : ), intent(inout)	B,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute the solution to system of linear equations A * X = B for PO (positive-definite) matrices.

use LAPACK_POSV (nwtc_lapack::lapack_posv) instead of this specific function.

Parameters

[in]	n	The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	nrhs	The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]	a	On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U*TU or A = LL*T.
[in,out]	b	On entry, the N-by-NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
[out]	errstat	Error level
[out]	errmsg	Message describing error
[in]	uplo	'U': Upper triangle of A is stored; 'L': Lower triangle of A is stored.

◆ lapack_spptrf()

subroutine nwtc_lapack::lapack_spptrf	(	character(1), intent(in)	UPLO,
		integer, intent(in)	N,
		real(siki), dimension( : ), intent(inout)	AP,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format.

use LAPACK_PPTRF (nwtc_lapack::lapack_pptrf) instead of this specific function.

Parameters

[in]	n	The order of the matrix A. N >= 0.
[in,out]	ap	AP is REAL array, dimension (N(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)(2n-j)/2) = A(i,j) for j<=i<=n. See LAPACK_DPPTRF for further details. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = UTU or A = LL*T, in the same storage format as A.
[out]	errstat	Error level
[out]	errmsg	Message describing error
[in]	uplo	'U': Upper triangle of A is stored; 'L': Lower triangle of A is stored.

◆ lapack_stpttr()

subroutine nwtc_lapack::lapack_stpttr	(	character(1), intent(in)	UPLO,
		integer, intent(in)	N,
		real(siki), dimension( : ), intent(in)	AP,
		real(siki), dimension( :,: ), intent(out)	A,
		integer, intent(in)	LDA,
		integer(intki), intent(out)	ErrStat,
		character(*), intent(out)	ErrMsg
	)

Unpack a by-column-packed array into a 2D matrix format.

Parameters

[in]	uplo	= 'U': A is an upper triangular matrix; 'L': A is a lower triangular matrix
[in]	n	The order of matrix A and AP.
[in]	lda	The leading dimension of the matrix A. LDA ? max(1,N)
[out]	errstat	Error level
[out]	errmsg	Message describing error
[in]	ap	Packed array
[out]	a	Unpacked array : Note AP(1)=A(1,1); AP(2)=A(1,2); AP(3)=A(2,2); AP(4)=A(1,3) etc. by column, upper triang

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ lapack_dgbsv()

◆ lapack_dgemm()

◆ lapack_dgesv()

◆ lapack_dgesvd()

◆ lapack_dgetrf()

◆ lapack_dgetri()

◆ lapack_dgetrs()

◆ lapack_dgetrs1()

◆ lapack_dggev()

◆ lapack_dposv()

◆ lapack_dpptrf()

◆ lapack_dtpttr()

◆ lapack_sgbsv()

◆ lapack_sgemm()

◆ lapack_sgesv()

◆ lapack_sgesvd()

◆ lapack_sgetrf()

◆ lapack_sgetri()

◆ lapack_sgetrs()

◆ lapack_sgetrs1()

◆ lapack_sggev()

◆ lapack_sposv()

◆ lapack_spptrf()

◆ lapack_stpttr()