stdlib_linalg_blas_s Module

SASUM takes the sum of the absolute values. uses unrolled loops for increment equal to one.

Arguments

Return Value real(kind=sp)

SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and returns a single precision result.

Arguments

Return Value real(kind=sp)

SCNRM2 returns the euclidean norm of a vector via the function name, so that SCNRM2 := sqrt( x*Hx )

Arguments

Return Value real(kind=sp)

SDOT forms the dot product of two vectors. uses unrolled loops for increments equal to one.

Arguments

Return Value real(kind=sp)

Compute the inner product of two vectors with extended precision accumulation. Returns S.P. result with dot product accumulated in D.P. SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+IINCX)SY(LY+IINCY), where LX = 1 if INCX >= 0, else LX = 1+(1-N)INCX, and LY is defined in a similar way using INCY.

Arguments

Return Value real(kind=sp)

SNRM2 returns the euclidean norm of a vector via the function name, so that SNRM2 := sqrt( x'*x ).

Arguments

Return Value real(kind=sp)

SAXPY constant times a vector plus a vector. uses unrolled loops for increments equal to one.

Arguments

SCOPY copies a vector, x, to a vector, y. uses unrolled loops for increments equal to 1.

Arguments

SGBMV performs one of the matrix-vector operations y := alphaAx + betay, or y := alphaATx + betay, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.

Arguments

SGEMM performs one of the matrix-matrix operations C := alphaop( A )op( B ) + betaC, where op( X ) is one of op( X ) = X or op( X ) = X*T, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Arguments

SGEMV performs one of the matrix-vector operations y := alphaAx + betay, or y := alphaATx + betay, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

Arguments

SGER performs the rank 1 operation A := alphaxy**T + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Arguments

applies a plane rotation.

Arguments

The computation uses the formulas sigma = sgn(a) if |a| > |b| = sgn(b) if |b| >= |a| r = sigmasqrt( a2 + b2 ) c = 1; s = 0 if r = 0 c = a/r; s = b/r if r != 0 The subroutine also computes z = s if |a| > |b|, = 1/c if |b| >= |a| and c != 0 = 1 if c = 0 This allows c and s to be reconstructed from z as follows: If z = 1, set c = 0, s = 1. If |z| < 1, set c = sqrt(1 - z2) and s = z. If |z| > 1, set c = 1/z and s = sqrt( 1 - c*2).

Arguments

SROTM applies the modified Givens transformation, $H$, to the 2-by-N matrix $$\left[ \begin{array}{c}SX^T\\SY^T\\ \end{array} \right],$$ where $^T$ indicates transpose. The elements of $SX$ are in SX(LX+IINCX), I = 0:N-1, where LX = 1 if INCX >= 0, else LX = (-INCX)N, and similarly for SY using LY and INCY. With SPARAM(1)=SFLAG, $H$ has one of the following forms: $$H=\underbrace{\begin{bmatrix}SH_{11} & SH_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1}, \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0}, \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1}, \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=-2}.$$
See SROTMG for a description of data storage in SPARAM.

Arguments

SROTMG Constructs the modified Givens transformation matrix $H$ which zeros the second component of the 2-vector $$\left[ {\sqrt{SD_1}\cdot SX_1,\sqrt{SD_2}\cdot SY_2} \right]^T.$$ With SPARAM(1)=SFLAG, $H$ has one of the following forms:
$$H=\underbrace{\begin{bmatrix}SH_{11} & SD_{12}\\SH_{21} & SH_{22}\end{bmatrix}}_{SFLAG=-1}, \underbrace{\begin{bmatrix}1 & SH_{12}\\SH_{21} & 1\end{bmatrix}}_{SFLAG=0}, \underbrace{\begin{bmatrix}SH_{11} & 1\\-1 & SH_{22}\end{bmatrix}}_{SFLAG=1}, \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{SFLAG=2}.$$ Locations 2-4 of SPARAM contain SH11, SH21, SH12 and SH22 respectively. (Values of 1.0, -1.0, or 0.0 implied by the value of SPARAM(1) are not stored in SPARAM.) The values of parameters GAMSQ and RGAMSQ may be inexact. This is OK as they are only used for testing the size of DD1 and DD2. All actual scaling of data is done using GAM.

Arguments

SSBMV performs the matrix-vector operation y := alphaAx + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric band matrix, with k super-diagonals.

Arguments

SSCAL scales a vector by a constant. uses unrolled loops for increment equal to 1.

Arguments

SSPMV performs the matrix-vector operation y := alphaAx + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.

Arguments

SSPR performs the symmetric rank 1 operation A := alphaxx**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form.

Arguments

SSPR2 performs the symmetric rank 2 operation A := alphaxyT + alphayxT + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form.

Arguments

SSWAP interchanges two vectors. uses unrolled loops for increments equal to 1.

Arguments

SSYMM performs one of the matrix-matrix operations C := alphaAB + betaC, or C := alphaBA + betaC, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

Arguments

SSYMV performs the matrix-vector operation y := alphaAx + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.

Arguments

SSYR performs the symmetric rank 1 operation A := alphaxx**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

Arguments

SSYR2 performs the symmetric rank 2 operation A := alphaxyT + alphayxT + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix.

Arguments

SSYR2K performs one of the symmetric rank 2k operations C := alphaABT + alphaBAT + betaC, or C := alphaATB + alphaBTA + betaC, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

Arguments

SSYRK performs one of the symmetric rank k operations C := alphaAAT + betaC, or C := alphaATA + betaC, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Arguments

STBMV performs one of the matrix-vector operations x := Ax, or x := ATx, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

Arguments

STBSV solves one of the systems of equations Ax = b, or ATx = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

Arguments

STPMV performs one of the matrix-vector operations x := Ax, or x := ATx, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form.

Arguments

STPSV solves one of the systems of equations Ax = b, or ATx = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

Arguments

STRMM performs one of the matrix-matrix operations B := alphaop( A )B, or B := alphaBop( A ), where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A**T.

Arguments

STRMV performs one of the matrix-vector operations x := Ax, or x := ATx, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Arguments

STRSM solves one of the matrix equations op( A )X = alphaB, or Xop( A ) = alphaB, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A**T. The matrix X is overwritten on B.

Arguments

STRSV solves one of the systems of equations Ax = b, or ATx = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.

Arguments