Procedures

Left-adjust the character sequence represented by the string. The length of the character sequence remains unchanged.

Right-adjust the character sequence represented by the string. The length of the character sequence remains unchanged.

Returns a boolean scalar where two arrays are element-wise equal within a tolerance. (Specification)

Sets the bits in set1 to the bitwise and of the original bits in set1 and set2. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Sets the bits in set1 to the bitwise and of the original bits in set1 with the bitwise negation of set2. The sets must have the same number of bits otherwise the result is undefined.

arange creates a one-dimensional array of the integer/real type with fixed-spaced values of given spacing, within a given interval. (Specification)

arg computes the phase angle in the interval (-π,π]. (Specification)

(Specification)

argd computes the phase angle of degree version in the interval (-180.0,180.0]. (Specification)

argpi computes the phase angle of circular version in the interval (-1.0,1.0]. (Specification)

Assign a character sequence to a string.

Used to define assignment for bitset_large. (Specification)

ASUM takes the sum of the absolute values.

AXPY constant times a vector plus a vector.

Returns an instance of type 'stringlist_index_type' representing backward index Specifications

Returns the number of bit positions in self.

Version experimental

Normal Distribution Cumulative Distribution Function (Specification)

Get uniform distribution cumulative distribution function (cdf) for integer, real and complex variables. (Specification)

Return the character sequence represented by the string.

Checks the value of a logical condition (Specification)

Computes the Cholesky factorization $A = L \cdot L^T$, or $A = U^T \cdot U$. (Specification)

Computes the Cholesky factorization $A = L \cdot L^T$, or $A = U^T \cdot U$. (Specification)

Remove trailing characters in set from string. If no character set is provided trailing whitespace is removed.

COPY copies a vector x to a vector y.

Copies the contents of the key, old_key, to the key, new_key (Specifications)

Copies the other data, other_in, to the variable, other_out (Specifications)

Pearson correlation of array elements (Specification)

Returns the number of times substring 'pattern' has appeared in the input string 'string' Specifications

Covariance of array elements (Specification)

Computes the cross product of two vectors, returning a rank-1 and size-3 array (Specification)

deg2rad converts phase angles from degrees to radians. (Specification)

Computes the determinant of a square matrix (Specification)

Creates a diagonal array or extract the diagonal elements of an array (Specification)

Computes differences between adjacent elements of an array. (Specification)

Version experimental

First derivative Legendre polynomial

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

DOTC forms the dot product of two complex vectors DOTC = X^H * Y

DOTU forms the dot product of two complex vectors DOTU = X^T * Y

Solves the eigendecomposition $A \cdot \bar{v} - \lambda \cdot \bar{v}$ for square matrix $A$. (Specification)

Solves the eigendecomposition $A \cdot \bar{v} - \lambda \cdot \bar{v}$ for a real symmetric $A = A^T$ or complex Hermitian $A = A^H$ square matrix. (Specification)

Returns the eigenvalues $lambda$, $A \cdot \bar{v} - \lambda \cdot \bar{v}$, for square matrix $A$. (Specification)

Returns the eigenvalues $lambda$, $A \cdot \bar{v} - \lambda \cdot \bar{v}$, for a real symmetric $A = A^T$ or complex Hermitian $A = A^H$ square matrix. (Specification)

Check whether a string ends with substring or not

Creates a new bitset, new, from a range, start_pos to stop_pos, in bitset old. If start_pos is greater than stop_pos the new bitset is empty. If start_pos is less than zero or stop_pos is greater than bits(old)-1 then if status is present it has the value index_invalid_error and new is undefined, otherwise processing stops with an informative message. (Specification)

Constructs the identity matrix. (Specification)

Return the positions of the false elements in array. Specification

Maps the 64 bit integer key to an unsigned integer value with only nbits bits where nbits is less than 64 (Specification)

Maps the 32 bit integer key to an unsigned integer value with only nbits bits where nbits is less than 32 (Specification)

Returns an instance of type 'stringlist_index_type' representing forward index Specifications

Finds the starting index of substring 'pattern' in the input 'string' Specifications

FNV_1 interfaces (Specification)

FNV_1 interfaces (Specification)

Hashes a key with the FNV_1 algorithm Arguments: key - the key to be hashed

FNV_1A interfaces (Specification)

FNV_1A interfaces (Specification)

Hashes a key with the FNV_1a algorithm (Specifications)

Frees the memory in a key (Specifications)

Frees the memory in the other data (Specifications)

Gamma function for integer and complex numbers

Computes Gauss-Legendre quadrature nodes and weights.

Computes Gauss-Legendre-Lobatto quadrature nodes and weights.

GBMV performs one of the matrix-vector operations y := alphaAx + betay, or y := alphaATx + betay, or y := alpha*AHx + 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.

Returns the greatest common divisor of two integers (Specification)

GEMM 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 ) = XT or op( X ) = X*H, 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.

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

GER 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.

GERC performs the rank 1 operation A := alphaxy**H + 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.

GERU 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.

Vector norm: subroutine interface version: experimental

Getter function to retrieve standard library version

Read a whole line from a formatted unit into a string variable

HBMV 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 hermitian band matrix, with k super-diagonals.

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

HEMV 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 hermitian matrix.

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

HER2 performs the hermitian rank 2 operation A := alphaxyH + conjg( alpha )yxH + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

HER2K performs one of the hermitian rank 2k operations C := alphaABH + conjg( alpha )BAH + betaC, or C := alphaAHB + conjg( alpha )BHA + betaC, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

HERK performs one of the hermitian rank k operations C := alphaAAH + betaC, or C := alphaAHA + betaC, where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

HPMV 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 hermitian matrix, supplied in packed form.

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

HPR2 performs the hermitian rank 2 operation A := alphaxyH + conjg( alpha )yxH + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form.

Code in ASCII collating sequence.

Character-to-integer conversion function.

Position of a substring within a string.

Inverse of a square matrix (Specification)

Inversion of a square matrix (Specification)

Checks whether c is an ASCII letter (A .. Z, a .. z).

Checks whether c is a letter or a number (0 .. 9, a .. z, A .. Z).

Checks whether or not c is in the ASCII character set - i.e. in the range 0 .. 0x7F.

Checks whether or not c is a blank character. That includes the only the space and tab characters

Returns a boolean scalar/array where two scalar/arrays are element-wise equal within a tolerance. (Specification)

Checks whether c is a control character.

Checks if a matrix (rank-2 array) is diagonal (Specification)

Checks whether c is a digit (0 .. 9).

Checks whether or not c is a printable character other than the space character.

Checks if a matrix (rank-2 array) is Hermitian (Specification)

Checks if a matrix (rank-2 array) is Hessenberg (Specification)

Checks whether c is a digit in base 16 (0 .. 9, A .. F, a .. f).

Checks whether c is a lowercase ASCII letter (a .. z).

Checks whether c is a digit in base 8 (0 .. 7).

Checks whether or not c is a printable character - including the space character.

Checks whether or not c is a punctuation character. That includes all ASCII characters which are not control characters, letters, digits, or whitespace.

Checks if a matrix (rank-2 array) is skew-symmetric (Specification)

Checks if a matrix (rank-2 array) is square (Specification)

Checks if a matrix (rank-2 array) is symmetric (Specification)

Checks if a matrix (rank-2 array) is triangular (Specification)

Checks whether c is an uppercase ASCII letter (A .. Z).

Checks whether or not c is a whitespace character. That includes the space, tab, vertical tab, form feed, carriage return, and linefeed characters.

Computes the Kronecker product of two arrays of size M1xN1, and of M2xN2, returning an (M1M2)x(N1N2) array (Specification)

Legendre polynomial

Returns the length of the character sequence represented by the string.

Returns the length of the character sequence without trailing spaces represented by the string.

Lexically compare the order of two character sequences being greater equal, The left-hand side, the right-hand side or both character sequences can be represented by a string.

Lexically compare the order of two character sequences being greater, The left-hand side, the right-hand side or both character sequences can be represented by a string.

Flow control: on output flag present, return it; otherwise, halt on error

Create rank 1 array of linearly spaced elements If the number of elements is not specified, create an array with size 100. If n is a negative value, return an array with size 0. If n = 1, return an array whose only element is end (Specification)

Lexically compare the order of two character sequences being less equal, The left-hand side, the right-hand side or both character sequences can be represented by a string.

Lexically compare the order of two character sequences being less, The left-hand side, the right-hand side or both character sequences can be represented by a string.

Load multidimensional array in npy format (Specification)

Loads a 2D array from a text file (Specification)

Logarithm of factorial n!, integer variable

Logarithm of gamma function

Logarithm of lower incomplete gamma function

Logarithm of upper incomplete gamma function

Create rank 1 array of logarithmically spaced elements from basestart to baseend. If the number of elements is not specified, create an array with size 50. If n is a negative value, return an array with size 0. If n = 1, return an array whose only element is base**end. If no base is specified, logspace will default to using a base of 10

Lower incomplete gamma function

Computes the squares solution to system $A \cdot x = b$. (Specification)

Computes the integer, real [, complex] working space required by the least-squares solver (Specification)

Mean of array elements (Specification)

Median of array elements (Specification)

Computes a list of coordinate matrices from coordinate vectors. (Specification)

Central moment of array elements (Specification)

Moves the allocated character scalar from 'from' to 'to' Specifications

(Specification

(Specification)

(Specification)

NMHASH32 interfaces (Specification)

NMHASH32X interfaces (Specification)

Computes the vector norm of a generic-rank array $A$. (Specification)

NRM2 returns the euclidean norm of a vector via the function name, so that NRM2 := sqrt( x'*x )

Returns a 64 bit pseudo random integer, harvest, distributed uniformly over the odd integers of the 64 bit kind. (Specification)

Returns a 32 bit pseudo random integer, harvest, distributed uniformly over the odd integers of the int32 kind. (Specification)

Opens a file (Specification)

Determinant operator of a square matrix (Specification)

Inverse operator of a square matrix (Specification)

Concatenate two character sequences, the left-hand side, the right-hand side or both character sequences can be represented by a string.

Concatenates stringlist with the input entity Returns a new stringlist Specifications

Compare two character sequences for inequality, the left-hand side, the right-hand side or both character sequences can be represented by a string.

Compares stringlist for inequality with the input entity Returns a logical Specifications

Returns .true. if not all bits in set1 and set2 have the same value, .false. otherwise. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Compare two character sequences for being less, the left-hand side, the right-hand side or both character sequences can be represented by a string.

Returns .true. if the bits in set1 and set2 differ and the highest order different bit is set to 0 in set1 and to 1 in set2, .false. otherwise. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Compare two character sequences for being less than, the left-hand side, the right-hand side or both character sequences can be represented by a string.

Returns .true. if the bits in set1 and set2 are the same or the highest order different bit is set to 0 in set1 and to 1 in set2, .false. otherwise. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Compare two character sequences for equality, the left-hand side, the right-hand side or both character sequences can be represented by a string.

Compares stringlist for equality with the input entity Returns a logical Specifications

Comparison operators

Returns .true. if all bits in set1 and set2 have the same value, .false. otherwise. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Compare two character sequences for being greater, the left-hand side, the right-hand side or both character sequences can be represented by a string.

Returns .true. if the bits in set1 and set2 differ and the highest order different bit is set to 1 in set1 and to 0 in set2, .false. otherwise. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Compare two character sequences for being greater than, the left-hand side, the right-hand side or both character sequences can be represented by a string.

Returns .true. if the bits in set1 and set2 are the same or the highest order different bit is set to 1 in set1 and to 0 in set2, .false. otherwise. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Fallback value for optional arguments (Specification)

Sets the bits in set1 to the bitwise or of the original bits in set1 and set2. The sets must have the same number of bits otherwise the result is undefined. (Specification)

The generic subroutine interface implementing the ORD_SORT algorithm, a translation to Fortran 2008, of the "Rust" sort algorithm found in slice.rs https://github.com/rust-lang/rust/blob/90eb44a5897c39e3dff9c7e48e3973671dcd9496/src/liballoc/slice.rs#L2159 ORD_SORT is a hybrid stable comparison algorithm combining merge sort, and insertion sort. (Specification)

Computes the outer product of two vectors, returning a rank-2 array (Specification)

Left pad the input string Specifications

Right pad the input string Specifications

Version experimental

Normal Distribution Probability Density Function (Specification)

Get uniform distribution probability density (pdf) for integer, real and complex variables. (Specification)

PENGY_HASH interfaces (Specification)

Computes the QR factorization of matrix $A = Q R$. (Specification)

Computes the working array space required by the QR factorization solver (Specification)

rad2deg converts phase angles from radians to degrees. (Specification)

The generic subroutine interface implementing the LSD radix sort algorithm, see https://en.wikipedia.org/wiki/Radix_sort for more details. It is always O(N) in sorting random data, but need a O(N) buffer. (Specification)

Version experimental

Read a character sequence from a connected unformatted unit into the string.

Read a character sequence from a connected unformatted unit into the string.

Regularized (normalized) lower incomplete gamma function, P

Regularized (normalized) upper incomplete gamma function, Q

Repeats the character sequence hold by the string by the number of specified copies.

Replaces all the occurrences of substring 'pattern' in the input 'string' with the replacement 'replacement' Version: experimental

Reverses the character sequence hold by the input string

Reverse the character order in the input character variable (Specification)

ROT applies a plane rotation.

The computation uses the formulas |x| = sqrt( Re(x)2 + Im(x)2 ) sgn(x) = x / |x| if x /= 0 = 1 if x = 0 c = |a| / sqrt(|a|2 + |b|2) s = sgn(a) * conjg(b) / sqrt(|a|2 + |b|2) When a and b are real and r /= 0, the formulas simplify to r = sgn(a)sqrt(|a|2 + |b|*2) c = a / r s = b / r the same as in SROTG when |a| > |b|. When |b| >= |a|, the sign of c and s will be different from those computed by SROTG if the signs of a and b are not the same.

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

ROTMG Constructs the modified Givens transformation matrix $H$ which zeros the second component of the 2-vector $$\left[ {\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2} \right]^T.$$ With DPARAM(1)=DFLAG, $H$ has one of the following forms:
$$H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1}, \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0}, \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1}, \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}.$$ Locations 2-4 of DPARAM contain DH11, DH21, DH12 and DH22 respectively. (Values of 1.0, -1.0, or 0.0 implied by the value of DPARAM(1) are not stored in DPARAM.) 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.

Version experimental

Normal Distribution Random Variates (Specification)

Get uniformly distributed random variate for integer, real and complex variables. (Specification)

Save multidimensional array in npy format (Specification)

Saves a 2D array into a text file (Specification)

SBMV 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.

SCAL scales a vector by a constant.

Scan a string for the presence of a set of characters. Scans a string for any of the characters in a set of characters.

Compute the inner product of two vectors with extended precision accumulation and result. Returns D.P. dot product accumulated in D.P., for S.P. SX and SY SDOT = 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.

Hashes a key with the NMHASH32 hash algorithm (Specifications)

Hashes a key with the NMHASH32X hash algorithm (Specifications) Arguments: key - the key to be hashed seed - the seed (unused) for the hashing algorithm

Hashes a key with the waterhash algorithm (Specifications)

(Specification)

Fisher-Yates shuffle algorithm for a rank one array of integer, real and complex variables. (Specification)

Integrates sampled values using Simpson's rule (Specification)

Integrates sampled values using trapezoidal rule weights for given abscissas (Specification)

Extracts characters from the input string to return a new string

Solves the linear system $A \cdot x = b$ for the unknown vector $x$ from a square matrix $A$. (Specification)

Computes the squares solution to system $A \cdot x = b$. (Specification)

Solves the linear system $A \cdot x = b$ for the unknown vector $x$ from a square matrix $A$. (Specification)

The generic subroutine interface implementing the SORT algorithm, based on the introsort of David Musser. (Specification)

The generic subroutine interface implementing the SORT_INDEX algorithm, based on the "Rust" sort algorithm found in slice.rs https://github.com/rust-lang/rust/blob/90eb44a5897c39e3dff9c7e48e3973671dcd9496/src/liballoc/slice.rs#L2159 but modified to return an array of indices that would provide a stable sort of the rank one ARRAY input. (Specification)

SPMV 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.

SPOOKY_HASH interfaces (Specification)

SPR 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.

SPR2 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.

SROT applies a plane rotation, where the cos and sin (c and s) are real and the vectors cx and cy are complex. jack dongarra, linpack, 3/11/78.

SSCAL scales a complex vector by a real constant.

Check whether a string starts with substring or not

CAXPY constant times a vector plus a vector.

CCOPY copies a vector x to a vector y.

CDOTC forms the dot product of two complex vectors CDOTC = X^H * Y

CDOTU forms the dot product of two complex vectors CDOTU = X^T * Y

CGBMV performs one of the matrix-vector operations y := alphaAx + betay, or y := alphaATx + betay, or y := alpha*AHx + 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.

CGEMM 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 ) = XT or op( X ) = X*H, 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.

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

CGERC performs the rank 1 operation A := alphaxy**H + 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.

CGERU 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.

CHBMV 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 hermitian band matrix, with k super-diagonals.

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

CHEMV 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 hermitian matrix.

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

CHER2 performs the hermitian rank 2 operation A := alphaxyH + conjg( alpha )yxH + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

CHER2K performs one of the hermitian rank 2k operations C := alphaABH + conjg( alpha )BAH + betaC, or C := alphaAHB + conjg( alpha )BHA + betaC, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

CHERK performs one of the hermitian rank k operations C := alphaAAH + betaC, or C := alphaAHA + betaC, where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

CHPMV 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 hermitian matrix, supplied in packed form.

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

CHPR2 performs the hermitian rank 2 operation A := alphaxyH + conjg( alpha )yxH + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form.

The computation uses the formulas |x| = sqrt( Re(x)2 + Im(x)2 ) sgn(x) = x / |x| if x /= 0 = 1 if x = 0 c = |a| / sqrt(|a|2 + |b|2) s = sgn(a) * conjg(b) / sqrt(|a|2 + |b|2) When a and b are real and r /= 0, the formulas simplify to r = sgn(a)sqrt(|a|2 + |b|*2) c = a / r s = b / r the same as in SROTG when |a| > |b|. When |b| >= |a|, the sign of c and s will be different from those computed by SROTG if the signs of a and b are not the same.

CSCAL scales a vector by a constant.

CSROT applies a plane rotation, where the cos and sin (c and s) are real and the vectors cx and cy are complex. jack dongarra, linpack, 3/11/78.

CSSCAL scales a complex vector by a real constant.

CSWAP interchanges two vectors.

CSYMM 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.

CSYR2K 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.

CSYRK 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.

CTBMV performs one of the matrix-vector operations x := Ax, or x := ATx, or x := A*Hx, 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.

CTBSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

CTPMV performs one of the matrix-vector operations x := Ax, or x := ATx, or x := A*Hx, 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.

CTPSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

CTRMM 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 ) = AT or op( A ) = AH.

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

CTRSM 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 ) = AT or op( A ) = AH. The matrix X is overwritten on B.

CTRSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

DASUM takes the sum of the absolute values.

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

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

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

DGBMV 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.

DGEMM 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.

DGEMV 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.

DGER 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.

DNRM2 returns the euclidean norm of a vector via the function name, so that DNRM2 := sqrt( x'*x )

DROT applies a plane rotation.

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).

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

DROTMG Constructs the modified Givens transformation matrix $H$ which zeros the second component of the 2-vector $$\left[ {\sqrt{DD_1}\cdot DX_1,\sqrt{DD_2}\cdot DY_2} \right]^T.$$ With DPARAM(1)=DFLAG, $H$ has one of the following forms:
$$H=\underbrace{\begin{bmatrix}DH_{11} & DH_{12}\\DH_{21} & DH_{22}\end{bmatrix}}_{DFLAG=-1}, \underbrace{\begin{bmatrix}1 & DH_{12}\\DH_{21} & 1\end{bmatrix}}_{DFLAG=0}, \underbrace{\begin{bmatrix}DH_{11} & 1\\-1 & DH_{22}\end{bmatrix}}_{DFLAG=1}, \underbrace{\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}}_{DFLAG=-2}.$$ Locations 2-4 of DPARAM contain DH11, DH21, DH12 and DH22 respectively. (Values of 1.0, -1.0, or 0.0 implied by the value of DPARAM(1) are not stored in DPARAM.) 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.

DSBMV 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.

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

Compute the inner product of two vectors with extended precision accumulation and result. Returns D.P. dot product accumulated in D.P., for S.P. SX and SY DSDOT = 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.

DSPMV 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.

DSPR 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.

DSPR2 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.

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

DSYMM 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.

DSYMV 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.

DSYR 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.

DSYR2 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.

DSYR2K 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.

DSYRK 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.

DTBMV 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.

DTBSV 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.

DTPMV 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.

DTPSV 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.

DTRMM 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.

DTRMV 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.

DTRSM 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.

DTRSV 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.

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

DZNRM2 returns the euclidean norm of a vector via the function name, so that DZNRM2 := sqrt( x*Hx )

LSAME returns .TRUE. if CA is the same letter as CB regardless of case.

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

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

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

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

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

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

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.

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.

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.

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.

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.

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

applies a plane rotation.

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).

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.

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.

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.

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

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

XERBLA is an error handler for the LAPACK routines. It is called by an LAPACK routine if an input parameter has an invalid value. A message is printed and execution stops. Installers may consider modifying the STOP statement in order to call system-specific exception-handling facilities.

XERBLA_ARRAY assists other languages in calling XERBLA, the LAPACK and BLAS error handler. Rather than taking a Fortran string argument as the function's name, XERBLA_ARRAY takes an array of single characters along with the array's length. XERBLA_ARRAY then copies up to 32 characters of that array into a Fortran string and passes that to XERBLA. If called with a non-positive SRNAME_LEN, XERBLA_ARRAY will call XERBLA with a string of all blank characters. Say some macro or other device makes XERBLA_ARRAY available to C99 by a name lapack_xerbla and with a common Fortran calling convention. Then a C99 program could invoke XERBLA via: { int flen = strlen(func); lapack_xerbla(func, } Providing XERBLA_ARRAY is not necessary for intercepting LAPACK errors. XERBLA_ARRAY calls XERBLA.

ZAXPY constant times a vector plus a vector.

ZCOPY copies a vector, x, to a vector, y.

ZDOTC forms the dot product of two complex vectors ZDOTC = X^H * Y

ZDOTU forms the dot product of two complex vectors ZDOTU = X^T * Y

Applies a plane rotation, where the cos and sin (c and s) are real and the vectors cx and cy are complex. jack dongarra, linpack, 3/11/78.

ZDSCAL scales a vector by a constant.

ZGBMV performs one of the matrix-vector operations y := alphaAx + betay, or y := alphaATx + betay, or y := alpha*AHx + 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.

ZGEMM 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 ) = XT or op( X ) = X*H, 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.

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

ZGERC performs the rank 1 operation A := alphaxy**H + 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.

ZGERU 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.

ZHBMV 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 hermitian band matrix, with k super-diagonals.

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

ZHEMV 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 hermitian matrix.

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

ZHER2 performs the hermitian rank 2 operation A := alphaxyH + conjg( alpha )yxH + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

ZHER2K performs one of the hermitian rank 2k operations C := alphaABH + conjg( alpha )BAH + betaC, or C := alphaAHB + conjg( alpha )BHA + betaC, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

ZHERK performs one of the hermitian rank k operations C := alphaAAH + betaC, or C := alphaAHA + betaC, where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

ZHPMV 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 hermitian matrix, supplied in packed form.

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

ZHPR2 performs the hermitian rank 2 operation A := alphaxyH + conjg( alpha )yxH + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form.

The computation uses the formulas |x| = sqrt( Re(x)2 + Im(x)2 ) sgn(x) = x / |x| if x /= 0 = 1 if x = 0 c = |a| / sqrt(|a|2 + |b|2) s = sgn(a) * conjg(b) / sqrt(|a|2 + |b|2) When a and b are real and r /= 0, the formulas simplify to r = sgn(a)sqrt(|a|2 + |b|*2) c = a / r s = b / r the same as in DROTG when |a| > |b|. When |b| >= |a|, the sign of c and s will be different from those computed by DROTG if the signs of a and b are not the same.

ZSCAL scales a vector by a constant.

ZSWAP interchanges two vectors.

ZSYMM 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.

ZSYR2K 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.

ZSYRK 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.

ZTBMV performs one of the matrix-vector operations x := Ax, or x := ATx, or x := A*Hx, 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.

ZTBSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

ZTPMV performs one of the matrix-vector operations x := Ax, or x := ATx, or x := A*Hx, 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.

ZTPSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

ZTRMM 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 ) = AT or op( A ) = AH.

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

ZTRSM 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 ) = AT or op( A ) = AH. The matrix X is overwritten on B.

ZTRSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

Constructor for new string instances

Constructor for stringlist Returns an instance of type stringlist_type Specifications

Remove leading and trailing whitespace characters.

Computes the singular value decomposition of a real or complex 2d matrix. (Specification)

Computes the singular values of a real or complex 2d matrix. (Specification)

Swap the values of the lhs and rhs arguments (Specification)

SWAP interchanges two vectors.

SYMM 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.

SYMV 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.

SYR 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.

SYR2 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.

SYR2K 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.

SYRK 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.

TBMV performs one of the matrix-vector operations x := Ax, or x := ATx, or x := A*Hx, 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.

TBSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

Returns the lowercase version of the character sequence hold by the input string

Convert character variable to lower case (Specification)

Conversion of strings to numbers (Specification)

Conversion of a stream of values in a string to numbers (Specification)

Get the constant value or uncertainty.

Returns the sentencecase version of the character sequence hold by the input string

Converts character sequence to sentence case (Specification)

Format or transfer other types as a string. (Specification)

Returns the titlecase version of the character sequence hold by the input string

Converts character sequence to title case (Specification)

Returns the uppercase version of the character sequence hold by the input string

Convert character variable to upper case (Specification)

TPMV performs one of the matrix-vector operations x := Ax, or x := ATx, or x := A*Hx, 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.

TPSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

Computes the trace of a matrix (Specification)

Integrates sampled values using trapezoidal rule (Specification)

Integrates sampled values using trapezoidal rule weights for given abscissas (Specification)

Returns the character sequence hold by the string without trailing spaces.

TRMM 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 ) = AT or op( A ) = AH.

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

TRSM 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 ) = AT or op( A ) = AH. The matrix X is overwritten on B.

TRSV solves one of the systems of equations Ax = b, or ATx = b, or A*Hx = 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.

Return the positions of the true elements in array. Specification

Uses the "random" odd 64 bit integer seed to map the 64 bit integer key to an unsigned integer value with only nbits bits where nbits is less than 64. (Specification)

Uses the "random" odd 32 bit integer seed to map the 32 bit integer key to an unsigned integer value with only nbits bits where nbits is less than 32 (Specification)

Upper incomplete gamma function

Variance of array elements (Specification)

Scan a string for the absence of a set of characters. Verifies that all the characters in string belong to the set of characters in set.

WATER_HASH interfaces (Specification)

Write the character sequence hold by the string to a connected formatted unit.

Write the character sequence hold by the string to a connected unformatted unit.

Sets the bits in set1 to the bitwise xor of the original bits in set1 and set2. The sets must have the same number of bits otherwise the result is undefined. (Specification)

Left pad the input string with zeros. Specifications